diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/7m2SPSzZXvs_postprocess.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/7m2SPSzZXvs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e5adb25a9a202586879ebe7a28627902fee3a847
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/7m2SPSzZXvs_postprocess.srt
@@ -0,0 +1,1008 @@
+1
+00:00:06,580 --> 00:00:11,700
+بالتعليقات السابقة، بدأنا مع نظرية الإيقوة وكذلك
+
+2
+00:00:11,700 --> 00:00:21,500
+نتكلم عن أساسية الإيقوة ومن ثم نتكلم عن تقارير
+
+3
+00:00:21,500 --> 00:00:25,280
+التجارب ونقول إن هناك أربع إختيارات، إما نفسك في
+
+4
+00:00:25,280 --> 00:00:29,920
+الداخل أو نفسك في الخارجبالإضافة إلى أشخاص في
+
+5
+00:00:29,920 --> 00:00:33,280
+الداخل و أشخاص في الخارج بمعنى آخر نستطيع أن نقارن
+
+6
+00:00:33,280 --> 00:00:39,940
+نفسنا مع أشخاص من داخل أو خارج المؤسسة أو نستطيع
+
+7
+00:00:39,940 --> 00:00:45,400
+أن نقارن أشخاص يعملون في نفس المؤسسة مع أشخاص من
+
+8
+00:00:45,400 --> 00:00:51,480
+الداخل أو خارج المؤسسة وبعد ذلك
+
+9
+00:00:54,140 --> 00:00:58,480
+قررنا تحديث حركة الإيقوطية وقررنا أن هناك اثنين
+
+10
+00:00:58,480 --> 00:01:05,340
+حالات هنا أولًا، إذا كان هناك إيقوطية، فالشخصين
+
+11
+00:01:05,340 --> 00:01:09,480
+يكونون أكثر مهتمين لتحافظ على حالة الوقت الآن،
+
+12
+00:01:09,480 --> 00:01:14,500
+حركة الإيقوطية، هنا قررنا أن إذا كان هناك إيقوطية،
+
+13
+00:01:14,500 --> 00:01:19,120
+فالعملاء يكونون أكثر مهتمين لتغيير الحالة لتقديم
+
+14
+00:01:19,120 --> 00:01:26,620
+الضغطوهنا يوجد ستة إستخدامات مختلفة، الأول هو إما
+
+15
+00:01:26,620 --> 00:01:30,460
+أننا سنغيّر المصادر، هنا نتحدث عن المعاملة نفسها
+
+16
+00:01:30,460 --> 00:01:35,620
+وكيف نتعامل مع أجزاء المعاملة، إما أننا سنغيّر
+
+17
+00:01:35,620 --> 00:01:41,500
+المصادر أو ربما نغيّر النتائج، هنا نتحدث عن
+
+18
+00:01:41,500 --> 00:01:48,880
+المصادر أو أجزاء المصادر ونتائجأو أننا سنغيّر
+
+19
+00:01:48,880 --> 00:01:55,160
+رؤيتنا لنفسنا أو ربما نغيّر رؤيتنا لشخص أخر. في كل
+
+20
+00:01:55,160 --> 00:02:00,400
+هذه الأربع حالات، نتحدث عن أشياء من المقارنة.
+
+21
+00:02:00,720 --> 00:02:06,780
+لذلك، سنفكر في تلك الأشياء وربما نفعل بعض
+
+22
+00:02:06,780 --> 00:02:14,660
+التغييرات، بالطبع إذا لم نكتفي بالوضع. هناك أشياء
+
+23
+00:02:14,660 --> 00:02:19,550
+أخرىالأشياء التي يمكن أن يفعلها الانسان هنا أو
+
+24
+00:02:19,550 --> 00:02:23,130
+الميكانيزمات التي يمكن أن يعتبرها الانسان واحدة
+
+25
+00:02:23,130 --> 00:02:31,110
+منها هو تغيير الشخص المصادر هنا نقول أننا سنقارن
+
+26
+00:02:31,110 --> 00:02:35,430
+نفسنا مع أشخاص داخل أو خارج المؤسسة أو مع أشخاص
+
+27
+00:02:35,430 --> 00:02:42,470
+داخل أو خارج هنا نتكلم عن تغييرإذا كنا نشعر أننا
+
+28
+00:02:42,470 --> 00:02:45,950
+لسنا مatisfied بالنتيجة أو بالنتيجة أو بالنتيجة أو
+
+29
+00:02:45,950 --> 00:02:47,370
+بالنتيجة أو بالنتيجة أو بالنتيجة أو بالنتيجة أو
+
+30
+00:02:47,370 --> 00:02:49,110
+بالنتيجة أو بالنتيجة أو بالنتيجة أو بالنتيجة أو
+
+31
+00:02:49,110 --> 00:02:51,510
+بالنتيجة أو بالنتيجة أو بالنتيجة أو بالنتيجة أو
+
+32
+00:02:51,510 --> 00:02:52,590
+بالنتيجة أو بالنتيجة أو بالنتيجة أو بالنتيجة أو
+
+33
+00:02:52,590 --> 00:02:54,590
+بالنتيجة أو بالنتيجة أو بالنتيجة أو بالنتيجة أو
+
+34
+00:02:54,590 --> 00:02:58,390
+بالنتيجة أو بالنتيجة أو بالنتيجة أو بالنتيجة أو
+
+35
+00:02:58,390 --> 00:03:00,010
+بالنتيجة أو بالنتيجة أو بالنتيجة أو بالنتيجة أو
+
+36
+00:03:00,010 --> 00:03:02,190
+بالنتيجة أو بالنتيجة أو بالنتيجة أو بالنتيجة
+
+37
+00:03:03,620 --> 00:03:10,360
+الشخصية ستفكر في التعافي من عمل واحد إلى عمل آخر
+
+38
+00:03:10,360 --> 00:03:16,460
+أو ربما حتى تفكر في ترك حالتها نفسها هنا نتحدث عن
+
+39
+00:03:16,460 --> 00:03:19,740
+اعتقاد نقلي الذي سينتهي في بعض المشاكل
+
+40
+00:03:19,740 --> 00:03:24,340
+للorganization بطريقة ما بالطبع سنكمن مع نظرة
+
+41
+00:03:24,340 --> 00:03:28,610
+الاستثمارأحد الأشياء المهمة المرتبطة بالمعرفة
+
+42
+00:03:28,610 --> 00:03:33,670
+الإيقوتي هي الوظيفة الوظيفة الوظيفة الوظيفة
+
+43
+00:03:33,670 --> 00:03:37,530
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+44
+00:03:37,530 --> 00:03:38,770
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+45
+00:03:38,770 --> 00:03:39,890
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+46
+00:03:39,890 --> 00:03:46,010
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+47
+00:03:46,010 --> 00:03:48,370
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+48
+00:03:48,370 --> 00:03:55,190
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيف
+
+49
+00:03:55,290 --> 00:04:02,650
+العامة العامة هي نوع من الواضحات العامة وما إذا
+
+50
+00:04:02,650 --> 00:04:05,350
+كانت الموظفين يتعاملون بشكل صحيح وما إذا كانت
+
+51
+00:04:05,350 --> 00:04:07,070
+الموظفين يتعاملون بشكل صحيح وما إذا كانت الموظفين
+
+52
+00:04:07,070 --> 00:04:08,510
+يتعاملون بشكل صحيح وما إذا كانت الموظفين يتعاملون
+
+53
+00:04:08,510 --> 00:04:10,270
+بشكل صحيح وما إذا كانت الموظفين يتعاملون بشكل صحيح
+
+54
+00:04:10,270 --> 00:04:13,430
+وما إذا كانت الموظفين يتعاملون بشكل صحيح وما إذا
+
+55
+00:04:13,430 --> 00:04:16,890
+كانت الموظفين يتعاملون بشكل صحيح وما إذا كانت
+
+56
+00:04:16,890 --> 00:04:23,010
+الموظفين يتعاملون بشكل
+
+57
+00:04:23,010 --> 00:04:26,720
+صحيح وما إذا كانت الموظفين يتالان نحن نتكلم عن
+
+58
+00:04:26,720 --> 00:04:32,960
+الواجبات المشاركة الواضحة الواضحة
+
+59
+00:04:32,960 --> 00:04:45,280
+الواضحة
+
+60
+00:04:45,280 --> 00:04:51,480
+الواضحة الواضحة الواضحة الواضحة الواضحة الواضحة
+
+61
+00:04:51,480 --> 00:04:56,230
+الواضحة الواضحوالتجارة التي نعطيها للمؤسسة وما
+
+62
+00:04:56,230 --> 00:05:00,770
+يعطيه الاخرين للمؤسسة وطبعا ما هي الميزانيات التي
+
+63
+00:05:00,770 --> 00:05:06,790
+نحصل عليها. فهنا نتكلم عن مجموعة الميزانيات.
+
+64
+00:05:07,070 --> 00:05:11,270
+الثاني هو القيادة التجارية. في القيادة التجارية،
+
+65
+00:05:11,270 --> 00:05:15,450
+هنا نتكلم عن التجارة أو التجارة التي يستخدمها
+
+66
+00:05:15,450 --> 00:05:20,230
+المؤسسة لتجارة الميزانيات.أولا، سنقوم بتحكم إذا
+
+67
+00:05:20,230 --> 00:05:23,910
+كنا مستحيلين أن نتعامل بشكل صحيح بشكل مناسب
+
+68
+00:05:23,910 --> 00:05:26,530
+للتعامل بشكل مناسب للتعامل بشكل صحيح بشكل مناسب
+
+69
+00:05:26,530 --> 00:05:28,770
+للتعامل بشكل مناسب للتعامل بشكل مناسب للتعامل بشكل
+
+70
+00:05:28,770 --> 00:05:31,370
+مناسب للتعامل بشكل مناسب للتعامل بشكل مناسب
+
+71
+00:05:31,370 --> 00:05:34,150
+للتعامل بشكل مناسب للتعامل بشكل مناسب للتعامل بشكل
+
+72
+00:05:34,150 --> 00:05:35,990
+مناسب للتعامل بشكل مناسب للتعامل بشكل مناسب
+
+73
+00:05:35,990 --> 00:05:43,370
+للتعامل بشكل مناسب للتعامل بشكل مناسب للتعامل بشكل
+
+74
+00:05:43,370 --> 00:05:50,350
+مناسب للتعامل بشكل مناسب للتأو إدارتهم مؤكدة في
+
+75
+00:05:50,350 --> 00:05:54,330
+المؤسسة أو إدارة الموظفات تتعامل مع الموظفين
+
+76
+00:05:54,330 --> 00:05:57,090
+بمعرفة إدارتهم بمعرفة إدارتهم بمعرفة إدارتهم
+
+77
+00:05:57,090 --> 00:05:59,350
+بمعرفة إدارتهم بمعرفة إدارتهم بمعرفة إدارتهم
+
+78
+00:05:59,350 --> 00:05:59,790
+بمعرفة إدارتهم بمعرفة إدارتهم بمعرفة إدارتهم
+
+79
+00:05:59,790 --> 00:06:08,270
+بمعرفة إدارتهم بمعرفة إدارتهم بمعرفة
+
+80
+00:06:08,270 --> 00:06:15,240
+إدارتهم بمعرفةلأ، أحيانًا، نحن نتكلم هنا عن
+
+81
+00:06:15,240 --> 00:06:21,380
+الواضحة العامة، ربما الأعمال ستجدوا أن هناك صحيحة
+
+82
+00:06:21,380 --> 00:06:24,700
+في أثنين من تلك المجالات، وربما في ثالث مجال، لا
+
+83
+00:06:24,700 --> 00:06:28,080
+يوجد صحيحة نستطيع أن نقولها هنا، لكن نحن نتكلم عن
+
+84
+00:06:28,080 --> 00:06:31,160
+الواضحة العامةوالتفكير هنا إذا كان هناك صحيحة
+
+85
+00:06:31,160 --> 00:06:35,480
+مؤسسية أو لا وهنا لسنا نتكلم عن الأسلحة والأسلحة
+
+86
+00:06:35,480 --> 00:06:38,400
+الأخيرة لسنا نتكلم عن إذا كان هناك صحيحة كاملة أو
+
+87
+00:06:38,400 --> 00:06:46,520
+لا لسنا نتكلم عن مستوى أو مستوى كامل أو مستوى كامل
+
+88
+00:06:46,520 --> 00:06:46,880
+أو مستوى كامل أو مستوى كامل أو مستوى كامل أو مستوى
+
+89
+00:06:46,880 --> 00:06:47,920
+مستوى كامل أو مستوى كامل أو مستوى كامل أو مستوى
+
+90
+00:06:47,920 --> 00:06:50,720
+كامل أو مستوى كامل أو مستوى كامل أو مستوى كامل أو
+
+91
+00:06:50,720 --> 00:06:56,210
+مستوى كامل أو مستالثورة الأخرى التي يجب أن نتكلم
+
+92
+00:06:56,210 --> 00:07:00,610
+عنها هنا وهي جزء من نظرية الهجوم التقليدية هي
+
+93
+00:07:00,610 --> 00:07:04,210
+نظرية الانتجار الان عندما نتكلم عن نظرية الانتجار
+
+94
+00:07:04,210 --> 00:07:08,850
+الان الموظفين أو المشغولين اللي يعملون داخل
+
+95
+00:07:08,850 --> 00:07:11,930
+المؤسسة هم اللي هم اللي هم اللي هم اللي هم اللي هم
+
+96
+00:07:11,930 --> 00:07:12,710
+اللي هم اللي هم اللي هم اللي هم اللي هم اللي هم
+
+97
+00:07:12,710 --> 00:07:13,590
+اللي هم اللي هم اللي هم اللي هم اللي هم اللي هم
+
+98
+00:07:13,590 --> 00:07:13,910
+اللي هم اللي هم اللي هم اللي هم اللي هم اللي هم
+
+99
+00:07:13,910 --> 00:07:15,830
+اللي هم اللي هم اللي هم اللي هم اللي هم اللي هم
+
+100
+00:07:15,830 --> 00:07:20,200
+اللي هم اللي هم اللي همالان، عندما يتجارب الوصول
+
+101
+00:07:20,200 --> 00:07:27,900
+إلى موظفين أو شخص يعمل في أي شركة عندما يتجارب
+
+102
+00:07:27,900 --> 00:07:28,060
+الوصول إلى موظفين أو شخص يعمل في أي شركة عندما
+
+103
+00:07:28,060 --> 00:07:29,880
+يتجارب الوصول إلى موظفين أو شخص يعمل في أي شركة
+
+104
+00:07:29,880 --> 00:07:32,220
+عندما يتجارب الوصول إلى موظفين أو شخص يعمل في أي
+
+105
+00:07:32,220 --> 00:07:32,620
+شركة عندما يتجارب الوصول إلى موظفين أو شخص يعمل في
+
+106
+00:07:32,620 --> 00:07:34,920
+أي شركة عندما يتجارب الوصول إلى موظفين أو شخص يعمل
+
+107
+00:07:34,920 --> 00:07:41,580
+في أي شركة عندما يتجارب الوصول إلى موظفين أو
+
+108
+00:07:41,580 --> 00:07:45,400
+شخص يعمل في أي شركة عندما يتجارب الوصول إلى موظفين
+
+109
+00:07:45,400 --> 00:07:47,420
+أو
+
+110
+00:07:49,310 --> 00:07:55,170
+ممكن إذا كانت النتيجة مناسبة للهدف الخاص، على سبيل
+
+111
+00:07:55,170 --> 00:07:58,810
+المثال حسنًا، وعندما نتحدث عن الهدف الخاص، فنحن
+
+112
+00:07:58,810 --> 00:08:05,090
+نتحدث عن ما هنا؟ نحن نتحدث عن احتاجات، مرة أخرى،
+
+113
+00:08:05,090 --> 00:08:08,530
+هنا نحن نتحدث عن إلى أي مستوى هؤلاء الهدفات مناسبة
+
+114
+00:08:08,530 --> 00:08:13,280
+عندما تساعد على احتياطاتناهذا هو الموضوع الرئيسي
+
+115
+00:08:13,280 --> 00:08:15,480
+عندما نتكلم عن تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة
+
+116
+00:08:15,480 --> 00:08:16,720
+تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة
+
+117
+00:08:16,720 --> 00:08:18,920
+تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة
+
+118
+00:08:18,920 --> 00:08:20,260
+تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة
+
+119
+00:08:20,260 --> 00:08:25,640
+تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة
+
+120
+00:08:25,640 --> 00:08:25,680
+تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة تخيلة
+
+121
+00:08:25,680 --> 00:08:34,740
+تخيلة تخيلة تخيلة تخيلة تخيلة
+
+122
+00:08:34,740 --> 00:08:41,030
+توهنا نتكلم عن التجارب التي يتم تجاربها الوظيفة،
+
+123
+00:08:41,030 --> 00:08:45,090
+نتكلم عن تجارب الوظيفة نفسها، ونتكلم عن تجارب
+
+124
+00:08:45,090 --> 00:08:47,430
+الوظيفة نفسها، ونتكلم عن تجارب الوظيفة نفسها،
+
+125
+00:08:47,430 --> 00:08:48,170
+ونتكلم عن تجارب الوظيفة نفسها، ونتكلم عن تجارب
+
+126
+00:08:48,170 --> 00:08:48,830
+الوظيفة نفسها، ونتكلم عن تجارب الوظيفة نفسها،
+
+127
+00:08:48,830 --> 00:08:50,570
+ونتكلم عن تجارب الوظيفة نفسها، ونتكلم عن تجارب
+
+128
+00:08:50,570 --> 00:08:52,650
+الوظيفة نفسها، ونتكلم عن تجارب الوظيفة نفسها،
+
+129
+00:08:52,650 --> 00:08:55,370
+ونتكلم عن تجارب الوظيفة نفسها، ونتكلم عن تجارالأن
+
+130
+00:08:55,370 --> 00:08:59,190
+هنا يوجد ثلاث مرحلات الرئيسية، إنها مثلًا إذا كان
+
+131
+00:08:59,190 --> 00:09:03,370
+الموظفين يسألوا نفسهم أسئلة، وإذا كانت الإجابة
+
+132
+00:09:03,370 --> 00:09:09,250
+نعم، فسيذهب الموظف إلى نفس المرحلة، وإذا كانت نقل،
+
+133
+00:09:09,250 --> 00:09:13,890
+فسيوقف الموظف، يعني في كلمة بسيطة، الموظفين لن
+
+134
+00:09:13,890 --> 00:09:22,440
+يقوموا بعمل إجارة إلا إذا كانوا يجدوا بإنجازاتهمأو
+
+135
+00:09:22,440 --> 00:09:25,400
+يساعدهم في تحقيق أهدافهم الخاصة أو في كلمة أخرى
+
+136
+00:09:25,400 --> 00:09:28,840
+يساعدهم في تحقيق أهدافهم الخاصة أو في كلمة أخرى
+
+137
+00:09:28,840 --> 00:09:29,420
+يساعدهم في تحقيق أهدافهم الخاصة أو في كلمة أخرى
+
+138
+00:09:29,420 --> 00:09:31,660
+يساعدهم في تحقيق أهدافهم الخاصة أو في كلمة أخرى
+
+139
+00:09:31,660 --> 00:09:33,140
+يساعدهم في تحقيق أهدافهم الخاصة أو في كلمة أخرى
+
+140
+00:09:33,140 --> 00:09:36,060
+يساعدهم في تحقيق أهدافهم الخاصة أو في كلمة أخرى
+
+141
+00:09:36,060 --> 00:09:39,420
+يساعدهم في تحقيق أهدافهم الخاصة أو في كلمة أخرى
+
+142
+00:09:39,420 --> 00:09:48,500
+يساعدهم في تحقيق أهداف
+
+143
+00:09:52,560 --> 00:09:56,880
+وإذا كانت علاقة هنا صحيحة فالشخص سيسأل نفسه أو
+
+144
+00:09:56,880 --> 00:10:01,640
+نفسه السؤال الثاني، وإذا لم يكن كذلك فالموظف سيغلق
+
+145
+00:10:01,640 --> 00:10:05,060
+الموضوع، لماذا؟ لأنه لا يوجد أمل لإيقاف أهداف
+
+146
+00:10:05,060 --> 00:10:22,540
+الشخصية أو لإيقاف الأشخاص
+
+147
+00:10:22,620 --> 00:10:28,240
+إذا لم نفعل ذلك، فسنفقد الموضوع. الآن، السؤال
+
+148
+00:10:28,240 --> 00:10:32,700
+الثاني هو أن نعرف علاقة الـ Performance Reward.
+
+149
+00:10:33,520 --> 00:10:36,560
+السؤال هنا هو، إذا وصلت إلى مستوى الـ Performance
+
+150
+00:10:38,480 --> 00:10:44,540
+أنا سأحصل عرض أو لا، فعلى مستوى التجارب التي
+
+151
+00:10:44,540 --> 00:10:48,780
+أستطيعها الوصول إليها، يجب أن أعرف إذا كانت
+
+152
+00:10:48,780 --> 00:10:53,200
+المجتمع مستمتع أو لا، إذا كانت المجتمع مستمتع أو
+
+153
+00:10:53,200 --> 00:11:00,320
+مطمئن،ثم هنا هناك توقع أن تحصل على حصة إذا لم يكن
+
+154
+00:11:00,320 --> 00:11:05,580
+ذلك فإن .. و ممكن إذا كانت السؤال الأولى مجرد نعم
+
+155
+00:11:05,580 --> 00:11:11,000
+و السؤال الثاني مجرد لا فإن الموظف أو الموظف سيغلق
+
+156
+00:11:11,000 --> 00:11:16,200
+الموضوع لماذا؟إذا كان الموظف قادر على التجارب،
+
+157
+00:11:16,200 --> 00:11:20,900
+فهذا سيساعد الموظف على الوصول إلى مستوى التجارب
+
+158
+00:11:20,900 --> 00:11:27,400
+المطلوب من المؤسسة، ولكن التجارب ليستإذا كانت
+
+159
+00:11:27,400 --> 00:11:32,940
+الموظفة ممتازة بالنسبة للموظف باعتبارها ثم الموظف
+
+160
+00:11:32,940 --> 00:11:39,540
+هنا سيغلق الموضوع الثالث مرحلة هو اكتشاف علاقات
+
+161
+00:11:39,540 --> 00:11:47,140
+الهدف والهدف الشخصي وهنا الموظف سيسأل نفسه أو نفسه
+
+162
+00:11:47,140 --> 00:11:54,640
+سؤال آخر هل هذا الهدف سيساعدني أو يساعدني
+
+163
+00:11:57,370 --> 00:12:02,610
+إذا كانت الإجابة صحيحة، فسنبدأ
+
+164
+00:12:02,610 --> 00:12:06,670
+بالتجارب لكي نحصل على مستوى التجارب لكي نحصل على
+
+165
+00:12:06,670 --> 00:12:08,070
+مستوى التجارب لكي نحصل على مستوى التجارب لكي نحصل
+
+166
+00:12:08,070 --> 00:12:09,370
+على مستوى التجارب لكي نحصل على مستوى التجارب لكي
+
+167
+00:12:09,370 --> 00:12:09,430
+لكي نحصل على مستوى التجارب لكي نحصل على مستوى
+
+168
+00:12:09,430 --> 00:12:10,150
+التجارب لكي نحصل على مستوى التجارب لكي نحصل على
+
+169
+00:12:10,150 --> 00:12:14,150
+مستوى التجارب لكي نحصل على مستوى التجارب لكي نحصل
+
+170
+00:12:14,150 --> 00:12:19,880
+على مستوى التجارب لكي نحفي حالة التجارب، يجب أن
+
+171
+00:12:19,880 --> 00:12:24,300
+يكون هناك ثلاثة إجابات، نعم، الأول، الثاني،
+
+172
+00:12:24,300 --> 00:12:27,820
+والثالث، والثالث، إذا كان أي واحد من هؤلاء أو في
+
+173
+00:12:27,820 --> 00:12:31,960
+أي من تلك المرات، إذا كانت الإجابة مفارقة، فالموظف
+
+174
+00:12:31,960 --> 00:12:39,270
+هنا سينقل الموضوع لأنهولا يتوقع أن يساعد المستخدم
+
+175
+00:12:39,270 --> 00:12:44,330
+في الوصول إلى أهداف أو في إيقاف أهدافه أو أهدافه.
+
+176
+00:12:44,830 --> 00:12:51,370
+حسنًا، هل هناك أسئلة حتى الآن؟ الآن، لكي نقوم
+
+177
+00:12:51,370 --> 00:12:58,230
+بتحويل نظرية المотивات التقليدية، هنا يجب أن نعتبر
+
+178
+00:12:59,620 --> 00:13:03,640
+هذه أربع مرات، أنا لا أتحدث فقط عن نظام التوقيع
+
+179
+00:13:03,640 --> 00:13:08,280
+هنا، أنا أتحدث عن جميع النظامات التي قد تحدثنا
+
+180
+00:13:08,280 --> 00:13:14,440
+عنها، لكن هنا نظام التوقيع يساعدنا في معرفة أن
+
+181
+00:13:14,440 --> 00:13:21,050
+هناك أربع أساسيات أساسية جدًا في أي حالةالعملاء
+
+182
+00:13:21,050 --> 00:13:26,190
+يجب أن يتعاملوا بالاستثمار، يجب أن يصلوا إلى مستوى
+
+183
+00:13:26,190 --> 00:13:30,510
+التجارب المطلوب من المؤسسة، ويجب أن يكون المعارفات
+
+184
+00:13:30,510 --> 00:13:36,070
+أعطوا من المؤسسات لإيقاف احتجازاتهم. عندما نتكلم
+
+185
+00:13:36,070 --> 00:13:40,070
+عن القدرات، الواضحة، وما إلى ذلك، إنه مهم عندما
+
+186
+00:13:40,070 --> 00:13:43,470
+نتكلم عن التجارب الوحيدة، عندما نتكلم عن تجارب
+
+187
+00:13:43,470 --> 00:13:48,230
+التجاربالأن عندما نتكلم عن الهجوم، هنا نتكلم عن ..
+
+188
+00:13:48,230 --> 00:13:51,610
+يعني على سبيل المثال، حتى علاقة بين الهجوم ومهارات
+
+189
+00:13:51,610 --> 00:13:55,800
+الشخصية، هي ليست محدودة فقط لجمهورية اليابانيةحتى
+
+190
+00:13:55,800 --> 00:14:01,100
+لو أردنا نتكلم عن مسلو أو كل الأسلحة التي يعتمد
+
+191
+00:14:01,100 --> 00:14:10,920
+عليها نحن نتكلم عن علاقة بين الهدف والمهارات
+
+192
+00:14:10,920 --> 00:14:15,900
+والمهارات الخاصة هنا نتكلم عن الهدفهو كيف نستطيع
+
+193
+00:14:15,900 --> 00:14:20,580
+تحقيق احتاجات مختلفة و كيف نستطيع تحقيق احتاجات
+
+194
+00:14:20,580 --> 00:14:20,960
+مختلفة و كيف نستطيع تحقيق احتاجات مختلفة و كيف
+
+195
+00:14:20,960 --> 00:14:23,240
+نستطيع تحقيق احتاجات مختلفة و كيف نستطيع تحقيق
+
+196
+00:14:23,240 --> 00:14:24,600
+احتاجات مختلفة و كيف نستطيع تحقيق احتاجات مختلفة و
+
+197
+00:14:24,600 --> 00:14:25,700
+كيف نستطيع تحقيق احتاجات مختلفة و كيف نستطيع تحقيق
+
+198
+00:14:25,700 --> 00:14:25,720
+احتاجات مختلفة و كيف نستطيع تحقيق احتاجات مختلفة و
+
+199
+00:14:25,720 --> 00:14:26,280
+كيف نستطيع تحقيق احتاجات مختلفة و كيف نستطيع تحقيق
+
+200
+00:14:26,280 --> 00:14:29,790
+احتاجات مختلفة و كيف نستطيع تحقيق احتاجليس فقط
+
+201
+00:14:29,790 --> 00:14:33,790
+تقرارات التجارة، ولكن أيضًا عندما نتكلم عن تقرارات
+
+202
+00:14:33,790 --> 00:14:36,910
+المотивة الأولى أو تقرارات المотивة على مطالبها،
+
+203
+00:14:36,910 --> 00:14:41,010
+يجب أن نتعامل مع كل تقراراتها كمجموعة، لماذا؟
+
+204
+00:14:41,010 --> 00:14:45,070
+لأننا قبل قليل قررنا أن لا احد من تقراراتها
+
+205
+00:14:45,070 --> 00:14:52,170
+سيعطينا تفسير مفهوم عن نفس المотивةسنقوم بالتحديث
+
+206
+00:14:52,170 --> 00:14:55,690
+عن كل هذه الحيوانات. بعض هذه الحيوانات ستقوم
+
+207
+00:14:55,690 --> 00:14:58,930
+بتغطية بعض المناطق والحيوانات الأخرى ستقوم بتغطية
+
+208
+00:14:58,930 --> 00:15:03,290
+المناطق المتبقية. لذلك، لكي نحصل على فهم مفهوم عن
+
+209
+00:15:03,290 --> 00:15:07,970
+المотивات، يجب أن نتعامل مع كل هذه الحيوانات ونعرف
+
+210
+00:15:07,970 --> 00:15:12,050
+ما هي علاقة ما وكيف هذه الحيوانات تساعد بعضها
+
+211
+00:15:12,050 --> 00:15:16,650
+البعض أو كيف تساعد بعضها البعض. حسنًا، الأخيرة
+
+212
+00:15:16,650 --> 00:15:21,620
+التي أريد أن أتحدث عنها هي المفاهيم العالمية.الان
+
+213
+00:15:21,620 --> 00:15:26,520
+عندما نتكلم عن نظرات مотивاتية، فهي عادةً مخصصة
+
+214
+00:15:26,520 --> 00:15:28,480
+بالثقافة الثقافية، مخصصة الثقافة الثقافية يعني هنا
+
+215
+00:15:28,480 --> 00:15:33,220
+أنها مؤثرة عاليًا من الثقافات، وهناك اختلافات من
+
+216
+00:15:33,220 --> 00:15:36,820
+واحدة ثقافة لواحدة أخرى، لهذا السبب عندما نتكلم عن
+
+217
+00:15:36,820 --> 00:15:43,080
+أكتر من هذه النظرات، لا نستطيعتعرف على تطبيق عالمي
+
+218
+00:15:43,080 --> 00:15:46,380
+لجميع هذه الحكومات وعندما نتحدث حتى عن مصطلح
+
+219
+00:15:46,380 --> 00:15:48,580
+الهيراركي للطريقات التي تحتاجها حكومة حكومة حكومة
+
+220
+00:15:48,580 --> 00:15:49,280
+حكومة حكومة حكومة حكومة حكومة حكومة حكومة حكومة
+
+221
+00:15:49,280 --> 00:15:53,000
+حكومة حكومة حكومة حكومة حكومة حكومة حكومة حكومة
+
+222
+00:15:53,000 --> 00:15:53,140
+حكومة حكومة حكومة حكومة حكومة حكومة حكومة حكومة
+
+223
+00:15:53,140 --> 00:15:53,700
+حكومة حكومة حكومة حكومة حكومة حكومة حكومة حكومة
+
+224
+00:15:53,700 --> 00:16:09,600
+حكومة حكومة حكومة حكومة حكومة حكومة حكومة حكومة
+
+225
+00:16:10,040 --> 00:16:19,000
+هو نفس الشكل عندما نتحدث عن مكللين ثيورينو نفس
+
+226
+00:16:19,000 --> 00:16:22,840
+الشيء عندما نتحدث عن نظرية الإيقوة، لا يوجد قواعد
+
+227
+00:16:22,840 --> 00:16:32,620
+عالمية لتلك النظرية، عادةً معنى الإيقوة مختلف عن
+
+228
+00:16:32,620 --> 00:16:39,540
+مجتمع أو مجتمع و نفس الشيء عندما نتحدث عن نظرية
+
+229
+00:16:39,540 --> 00:16:44,030
+أخرى، الوحيد المميز هناولا نستطيع .. يعني نحن ..
+
+230
+00:16:44,030 --> 00:16:49,610
+تقريبًا إختيارًا هو الـ Theory of Two Factors، The
+
+231
+00:16:49,610 --> 00:16:51,830
+Herzberg Theory عندما قلنا إن هناك عاملات
+
+232
+00:16:51,830 --> 00:16:57,670
+الهيجينية وعاملات المотивات، لماذا؟ لأن أكتر الناس
+
+233
+00:16:59,960 --> 00:17:05,200
+أو نحن نحب أن يكون العمل مثير للإهتمام، وهذا السبب
+
+234
+00:17:05,200 --> 00:17:11,320
+نعتبر أن هناك بعض الوثيقة، كما قلت، تقريبًا، هناك
+
+235
+00:17:11,320 --> 00:17:17,210
+نوع من الإقرار هناعندما نتكلم عن نظرية هيريسبورغ،
+
+236
+00:17:17,210 --> 00:17:20,590
+نظرية الـ two factors، نظرية الهيجينة ونظرية
+
+237
+00:17:20,590 --> 00:17:26,630
+المотивات، بطريقة ما يمكن
+
+238
+00:17:26,630 --> 00:17:30,890
+أن يكون مضمون باستخدام الكتورة، لكن حتى عندما
+
+239
+00:17:30,890 --> 00:17:36,340
+نتكلم عنماذا هي جزء من حاجات الهيجيم والحاجات
+
+240
+00:17:36,340 --> 00:17:43,180
+المدهشة؟ ربما يكون هناك اختلافات في مستوى هذه
+
+241
+00:17:43,180 --> 00:17:46,160
+الحاجات، ولكن ربما ليس في .. يعني عندما نتحدث عن
+
+242
+00:17:46,160 --> 00:17:49,340
+حاجات الهيجيم، نتحدث عن مدير السلريات وما إلى ذلك
+
+243
+00:17:49,620 --> 00:17:56,220
+ولكن ربما لا نتكلم عن العمول في المجموعات، نتكلم
+
+244
+00:17:56,220 --> 00:18:01,880
+عن العمول كعمول نحن لسنا نتكلم عن المديرات، إلى أي
+
+245
+00:18:01,880 --> 00:18:06,880
+مستوى هذا المديرات، على سبيل المثال، ممتاز أو نحن
+
+246
+00:18:06,880 --> 00:18:10,980
+نتكلم عن طريقة المديرات التعليميةهنا نتحدث عن شيء
+
+247
+00:18:10,980 --> 00:18:14,060
+مقارنة
+
+248
+00:18:14,060 --> 00:18:18,140
+من مجتمع واحد لمجتمع آخر ولكن المشكلة نفسها هي
+
+249
+00:18:18,140 --> 00:18:21,700
+تقريبًا نفسها ولكننا لا نتحدث عن كيف تكون هذه
+
+250
+00:18:21,700 --> 00:18:26,580
+المشكلة متوفرة أو كيف تستخدمها من مجتمع واحد
+
+251
+00:18:26,580 --> 00:18:33,760
+لمجتمع آخر أي أسئلة؟ طيب بيعطيك العافية شكرا،
+
+252
+00:18:33,760 --> 00:18:35,240
+بدكوا براك لامتحانات؟
+
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/96LTyAWtfko.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/96LTyAWtfko.srt
new file mode 100644
index 0000000000000000000000000000000000000000..724ebe91189e43773e09e4ed31a63d262201e5e2
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/96LTyAWtfko.srt
@@ -0,0 +1,707 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:10,170 --> 00:00:15,510
+طبعا سننتهي اليوم منطقة رقم 10 وأيضا سننتهي من المجلد
+
+3
+00:00:15,510 --> 00:00:21,370
+هناك بعض المواضيع التي يجب أن نتحدث عنها واحدة 
+
+4
+00:00:21,370 --> 00:00:25,590
+منها هي إذا كانت مجموعتنا دائما محتاجة أو لا وربما
+
+5
+00:00:25,590 --> 00:00:28,830
+إلى مدى ما تحدثنا عن هذه المواضيع
+
+6
+00:00:33,140 --> 00:00:39,080
+الأمر الوحيد الذي يمكننا أن نقوله بطريقة مختلفة أو 
+
+7
+00:00:39,080 --> 00:00:39,940
+يمكننا أن نقوله بطريقة مختلفة أو يمكننا أن نقوله
+
+8
+00:00:39,940 --> 00:00:40,760
+بطريقة مختلفة أو يمكننا أن نقوله بطريقة مختلفة أو
+
+9
+00:00:40,760 --> 00:00:41,560
+يمكننا أن نقوله بطريقة مختلفة أو يمكننا أن نقوله
+
+10
+00:00:41,560 --> 00:00:43,620
+بطريقة مختلفة أو يمكننا أن نقوله بطريقة مختلفة أو
+
+11
+00:00:43,620 --> 00:00:44,920
+يمكننا أن نقوله بطريقة مختلفة أو يمكننا أن نقوله
+
+12
+00:00:44,920 --> 00:00:47,780
+بطريقة مختلفة أو يمكننا أن نقوله بطريقة مختلفة أو
+
+13
+00:00:47,780 --> 00:00:50,500
+يمكننا أن نقوله بطريقة مختلفة أو يمكننا أن نقوله
+
+14
+00:00:50,500 --> 00:00:57,100
+بطريقة مختلفة أو يمكننا أن نقوله بطريقة مختلفة أو
+
+15
+00:00:57,100 --> 00:01:01,340
+يمكننا أن نقوله ب
+
+16
+00:01:02,130 --> 00:01:06,250
+الكثير من البرامج التي يحتاجها العمل الإنساني
+
+17
+00:01:06,250 --> 00:01:11,090
+لعمل مهمة معينة، أكثر من ذلك نحتاج إلى فريق، أقل 
+
+18
+00:01:11,090 --> 00:01:12,110
+من ذلك نحتاج إلى كثير من البرامج التي يحتاجها
+
+19
+00:01:12,110 --> 00:01:15,190
+العمل الإنساني لعمل مهمة معينة، أكثر من ذلك
+
+20
+00:01:15,190 --> 00:01:15,210
+البرامج التي يحتاج إلى كثير من البرامج التي يحتاج
+
+21
+00:01:15,210 --> 00:01:15,250
+إلى كثير من البرامج التي يحتاج إلى كثير من البرامج
+
+22
+00:01:15,250 --> 00:01:15,830
+التي يحتاج إلى كثير من البرامج التي يحتاج إلى كثير
+
+23
+00:01:15,830 --> 00:01:15,910
+من البرامج التي يحتاج إلى كثير من البرامج التي
+
+24
+00:01:15,910 --> 00:01:17,210
+يحتاج إلى كثير من البرامج التي يحتاج إلى كثير من
+
+25
+00:01:17,210 --> 00:01:22,490
+البرامج هذا ربما أحد المشكلات، المفهوم هنا هو أننا لا
+
+26
+00:01:22,490 --> 00:01:27,370
+نحتاج دوام دائما، أحيانا يمكننا أن نعمل عمل مع
+
+27
+00:01:27,370 --> 00:01:32,470
+مجموعة صغيرة أو حتى، وعلى أساس ما نقصد هنا، مع
+
+28
+00:01:32,470 --> 00:01:36,710
+مجموعات شخصية، فهذا يعتمد على بعض المشكلات هنا،
+
+29
+00:01:36,710 --> 00:01:40,950
+واحدة منها هي إلى مدى ما نحتاج للمعرفة المختلفة أو
+
+30
+00:01:40,950 --> 00:01:46,820
+تجارب مختلفة. الآن مشكلة أخرى هنا هي إلى مدى ما الـ
+
+31
+00:01:46,820 --> 00:01:51,200
+output needed is greater than individual effort
+
+32
+00:01:51,200 --> 00:01:55,880
+يعني sometimes there are simple tasks where the
+
+33
+00:01:55,880 --> 00:01:59,780
+output can be achieved depending on an individual
+
+34
+00:01:59,780 --> 00:02:03,720
+of course in such cases we do not need teams but
+
+35
+00:02:03,720 --> 00:02:07,860
+sometimes one individual cannot achieve the
+
+36
+00:02:07,860 --> 00:02:11,500
+desired results so in such cases we need more than
+
+37
+00:02:11,500 --> 00:02:17,760
+one individual and so on. العمل أو الموضوع نفسه أحد
+
+38
+00:02:17,760 --> 00:02:21,500
+المشكلات، ويمكننا أن نقول هنا أن كمية التجارب
+
+39
+00:02:21,500 --> 00:02:29,440
+أيضًا أحد المشكلات. ثالث نقطة هنا هي إلى مدى ما
+
+40
+00:02:29,440 --> 00:02:36,440
+نحتاج الناس لنقوم بعمل عمليات أو عمليات مختلفة
+
+41
+00:02:36,440 --> 00:02:39,300
+بطريقة مستقلة
+
+42
+00:02:41,230 --> 00:02:45,170
+وهذا يعني أننا بحاجة إلى مختلفة مهارات ومعارف
+
+43
+00:02:45,170 --> 00:02:46,670
+ومعروفات ومعروفات ومعروفات ومعروفات ومعروفات
+
+44
+00:02:46,670 --> 00:02:47,190
+ومعروفات ومعروفات ومعروفات ومعروفات ومعروفات
+
+45
+00:02:47,190 --> 00:02:47,210
+ومعروفات ومعروفات ومعروفات ومعروفات ومعروفات
+
+46
+00:02:47,210 --> 00:02:47,470
+ومعروفات ومعروفات ومعروفات ومعروفات ومعروفات
+
+47
+00:02:47,470 --> 00:02:49,730
+ومعروفات ومعروفات ومعروفات ومعروفات ومعروفات
+
+48
+00:02:49,730 --> 00:02:53,370
+ومعروفات ومعروفات ومعروفات ومعروفات ومعروفات
+
+49
+00:02:53,370 --> 00:03:00,030
+ومعروفات ومعروفات ومعروفات
+
+50
+00:03:03,780 --> 00:03:09,620
+نحتاج مجموعات مرة أخرى مجموعات مفيدة ومفيدة وكذلك
+
+51
+00:03:09,620 --> 00:03:14,300
+في أغلب الحالات ولكن هذا لا يعني بأي طريقة أننا
+
+52
+00:03:14,300 --> 00:03:19,860
+دائما نحتاج مجموعات. طبعا دائما نفكر في الموضوع إذا
+
+53
+00:03:19,860 --> 00:03:26,900
+الموضوع يرغب في تحقيق النتائج فنستخدم المجموعات
+
+54
+00:03:26,900 --> 00:03:31,980
+وإذا ليس ونحتاج مجموعة، ثم هنا يجب أن نبحث عن قطع
+
+55
+00:03:31,980 --> 00:03:33,940
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+56
+00:03:33,940 --> 00:03:34,160
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+57
+00:03:34,160 --> 00:03:37,780
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+58
+00:03:37,780 --> 00:03:39,580
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+59
+00:03:39,580 --> 00:03:39,660
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+60
+00:03:39,660 --> 00:03:56,680
+مختلفة مختلفة مختلفة مخت
+
+61
+00:03:57,240 --> 00:04:05,300
+أخرى، عادةً وهذا ربما غريب في مكان ما، يعني غريب
+
+62
+00:04:05,300 --> 00:04:12,820
+أن عمل فريق في البلدان الأخرى من USA أكثر توفرًا
+
+63
+00:04:13,710 --> 00:04:15,930
+though we can say when we talk about professional
+
+64
+00:04:15,930 --> 00:04:18,510
+success and so on, the private sector in the United
+
+65
+00:04:18,510 --> 00:04:20,690
+States of America are more successful in such
+
+66
+00:04:20,690 --> 00:04:24,970
+practices, but also the availability of the
+
+67
+00:04:24,970 --> 00:04:28,670
+practice itself in other countries, it is more okay.
+
+68
+00:04:28,670 --> 00:04:31,990
+of course when we talk about .. حد يسكر الباب لو 
+
+69
+00:04:31,990 --> 00:04:32,350
+سمحت
+
+70
+00:04:35,460 --> 00:04:39,080
+طبعا هنا قد يكون الكثير من الناس يتكلم عن كثير من
+
+71
+00:04:39,080 --> 00:04:41,500
+الناس يتكلم عن كثير من الناس يتكلم عن كثير من
+
+72
+00:04:41,500 --> 00:04:42,800
+الناس يتكلم عن كثير من الناس يتكلم عن كثير من
+
+73
+00:04:42,800 --> 00:04:43,820
+الناس يتكلم عن كثير من الناس يتكلم عن كثير من
+
+74
+00:04:43,820 --> 00:04:48,520
+الناس يتكلم عن كثير من الناس يتكلم عن كثير من
+
+75
+00:04:48,520 --> 00:04:53,140
+الناس يتكلم عن كثير من الناس يتكلم عن كثير من
+
+76
+00:04:53,140 --> 00:04:55,820
+الناس يتكلم عن كثير من الناس يتكلم عن كثير من
+
+77
+00:04:55,820 --> 00:04:59,980
+الناس يتكلم عن كثير من الناس يتكلم عن كثير من
+
+78
+00:04:59,980 --> 00:05:04,940
+الناس يتكلمون. أحد المشكلات أيضًا هي أن الناس الذين
+
+79
+00:05:04,940 --> 00:05:10,140
+يسيطرون على نفسهم ليسوا ناجحين عندما نتكلم عن
+
+80
+00:05:10,140 --> 00:05:16,200
+أمريكا أو مجتمعين فيها،  توجد تولرات عقلية للإنسانية وقد
+
+81
+00:05:16,200 --> 00:05:19,880
+تحدثنا عن هذا في الحلقة السابقة بأن هناك مجتمعين
+
+82
+00:05:19,880 --> 00:05:25,540
+مع تولرات عقلية عالية للإنسانية مثل أمريكا، وهناك
+
+83
+00:05:25,540 --> 00:05:27,600
+ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+84
+00:05:27,600 --> 00:05:28,940
+ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+85
+00:05:28,940 --> 00:05:33,260
+ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+86
+00:05:33,260 --> 00:05:41,900
+ثانوية ثانوية ثانوية ثانوية
+
+87
+00:05:42,070 --> 00:05:47,350
+و أيضا كلما كان هناك فرق قوية عالية بين مستوى
+
+88
+00:05:47,350 --> 00:05:51,510
+مختلف وكذلك وكذلك وكذا وكذا وكذا وكذا وكذا وكذا
+
+89
+00:05:51,510 --> 00:05:52,570
+وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+90
+00:05:52,570 --> 00:05:53,590
+وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+91
+00:05:53,590 --> 00:05:53,610
+وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+92
+00:05:53,610 --> 00:05:53,730
+وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+93
+00:05:53,730 --> 00:05:53,870
+وكذا وكذا وكذا وكذا وكذا وكذا وكذا
+
+94
+00:06:08,620 --> 00:06:13,240
+لماذا عندما نتحدث عن مقارنة قوة عالية ومقارنة قوة
+
+95
+00:06:13,240 --> 00:06:18,420
+عالية، لتذكر أنها كيف تشعر الحكومة على مستوى مختلف
+
+96
+00:06:18,420 --> 00:06:23,080
+ونحن نتحدث هنا عن علاقة بين مستوى أعلى وأسفل وكيف
+
+97
+00:06:23,080 --> 00:06:28,060
+تم تفكيرها، خاصة عندما نتحدث عن موظفين يعملون في
+
+98
+00:06:28,060 --> 00:06:33,360
+مؤسسات وما إلى ذلك. لماذا؟ عادةً عندما نتحدث عن
+
+99
+00:06:33,360 --> 00:06:36,820
+مقارنة طاقة عالية، فهناك أقل مواصلة للتواصل
+
+100
+00:06:36,820 --> 00:06:40,780
+والتواصل بين مجموعاتها. وعندما نتحدث عن شركات نحتاج
+
+101
+00:06:40,780 --> 00:06:44,820
+إلى أكثر مواصلة للتواصل والتواصل بين مجموعات أي شركة
+
+102
+00:06:44,820 --> 00:06:48,340
+وعندما نتحدث أيضًا عن تولرانس لشركات مختلفة، عادةً
+
+103
+00:06:48,340 --> 00:06:51,000
+يجب أن يتعاملوا مع بعضهم البعض، يتعاملوا مع
+
+104
+00:06:51,000 --> 00:06:53,000
+أهدافهم، يتعاملوا مع أهدافهم، يتعاملوا مع أهدافهم،
+
+105
+00:06:53,000 --> 00:06:56,600
+يتعاملوا مع أهدافهم، يتعاملوا مع أهدافهم، على قيمة
+
+106
+00:06:56,600 --> 00:07:01,880
+الناس، وعندما يكون هناك تلرانس قليل للإنسانية، فهنا
+
+107
+00:07:01,880 --> 00:07:06,520
+نتكلم عن قدرة الناس على التخطيط لأجهزة أكثر، وهذا
+
+108
+00:07:06,520 --> 00:07:11,180
+يؤثر عادةً على الناس بطريقة معينة، وهو موضوع آخر
+
+109
+00:07:11,180 --> 00:07:15,600
+يتعلق مع، ويمكننا أن نتكلم عنه بمعنى العمليات
+
+110
+00:07:15,600 --> 00:07:20,290
+العالمية. والثانوية هي مجموعة الانتجار العالمي
+
+111
+00:07:20,290 --> 00:07:26,010
+الانتجار العالمي الانتجار العالمي الانتجار العالمي
+
+112
+00:07:26,010 --> 00:07:27,850
+الانتجار العالمي الانتجار العالمي الانتجار العالمي
+
+113
+00:07:27,850 --> 00:07:27,890
+الانتجار العالمي الانتجار العالمي الانتجار العالمي
+
+114
+00:07:27,890 --> 00:07:27,950
+الانتجار العالمي الانتجار العالمي الانتجار العالمي
+
+115
+00:07:27,950 --> 00:07:28,230
+الانتجار العالمي الانتجار العالمي الانتجار العالمي
+
+116
+00:07:28,230 --> 00:07:30,190
+الانتجار العالمي الانتجار العالمي الانتجار العالمي
+
+117
+00:07:30,190 --> 00:07:33,210
+الانتجار
+
+118
+00:07:33,210 --> 00:07:37,970
+العالمي. عادةً عندما نتكلم عن الاختلافات
+
+119
+00:07:37,970 --> 00:07:41,470
+الوطنية، يعني الاختلافات التي حصلت من خلال
+
+120
+00:07:41,470 --> 00:07:44,490
+الاختلافات الوطنية، مثل الـ Ethnicity وأحيانًا 
+
+121
+00:07:44,490 --> 00:07:49,650
+حتى الدين أو المعاملات الثقافية وكذلك، عادةً، هذا
+
+122
+00:07:49,650 --> 00:07:54,990
+عادةً يقوم بتقليل فعالية الـ Team. ولكن أيضًا
+
+123
+00:07:54,990 --> 00:08:02,370
+المحققات تشير إلى أن الشركات التي تعمل معًا أكثر 
+
+124
+00:08:02,370 --> 00:08:07,850
+وقتًا، أكثر لديها أكثر قدرة على التعامل مع مشاكل
+
+125
+00:08:07,850 --> 00:08:12,070
+مثل هذه، عادةً لديهم فرصة أكثر لتفهم بعضهم البعض
+
+126
+00:08:12,730 --> 00:08:20,210
+عادةً تحل بعض المشاكل التي حصلت من غير فهم بعض
+
+127
+00:08:20,210 --> 00:08:25,190
+الأشياء وما إلى ذلك، لكن عادةً هذا يؤثر على فعالية
+
+128
+00:08:25,190 --> 00:08:28,480
+الوظيفة في الوظيفة الأساسية بطريقة مختلفة، لكن
+
+129
+00:08:28,480 --> 00:08:34,840
+عادةً فإن مجموعات بعد عدة أشهر كما ذكرت في نتائج
+
+130
+00:08:34,840 --> 00:08:38,360
+بعض المحققين، في أربع أشهر يتمكنوا من التعامل مع
+
+131
+00:08:38,360 --> 00:08:41,640
+مشكلتها بطريقة معينة. وعندما يتم التعامل مع
+
+132
+00:08:41,640 --> 00:08:47,020
+مشكلتها، فهنا نتحدث عن وهذا يجعل الوظيفة تتعامل مع
+
+133
+00:08:47,020 --> 00:08:50,500
+مشكلة الوظيفة ويعني هذا يجعل الوظيفة تتعامل مع
+
+134
+00:08:50,500 --> 00:08:58,620
+مشكلة الوظيفة ويعني هذا يجعل الوظيفة تتعامل مع
+
+135
+00:08:58,620 --> 00:09:03,080
+مشكلة الوظيفة
+
+136
+00:09:03,080 --> 00:09:07,380
+ويعني هذا يعني معرفة كيف يتعامل الوظيفة بشكل مختلف
+
+137
+00:09:07,380 --> 00:09:11,820
+وكيف يتعامل الوظيفة بشكل مختلف وكيف يتعامل الوظيفة
+
+138
+00:09:11,820 --> 00:09:21,100
+بشكل مختلف وكيف يتعامل الوظيفة بشكل مختلف
+
+139
+00:09:21,660 --> 00:09:26,900
+الخير الأخير لأتكلم عنه هو الـ effective teams
+
+140
+00:09:26,900 --> 00:09:30,000
+ربما في هذا الحلقه نحن نتكلم عن الكثير من النقطة و
+
+141
+00:09:30,000 --> 00:09:33,000
+أنا لن أتكلم عن هذه النقطة مرة أخرى، ما يتوفر هنا
+
+142
+00:09:33,000 --> 00:09:38,300
+ربما قصة عن ما قررنا أن نتكلم عنه في هذه الحلقة
+
+143
+00:09:38,300 --> 00:09:41,260
+عندما نتكلم عن الـ resource عندما نتكلم عن أربع 
+
+144
+00:09:41,260 --> 00:09:45,440
+المظاهر التي يجب أن تساعدنا في إصلاح قوات مفيدة
+
+145
+00:09:47,540 --> 00:09:53,940
+الوضع نفسه مهم جدًا، وخصوصًا تجارب الناس هي أيضًا 
+
+146
+00:09:53,940 --> 00:10:01,160
+مهمة بالإضافة إلى أشياء أخرى، في كل مجال هناك نقطة
+
+147
+00:10:01,160 --> 00:10:08,020
+مُختلفة، الأهم من هذه النقطة بالطبع بالإضافة أننا
+
+148
+00:10:08,020 --> 00:10:16,180
+نحتاج أن نذكر هنا نقطة أخرى مستقبلية، نقطة أو حالات
+
+149
+00:10:16,180 --> 00:10:21,460
+أو حالات يجب أن يساعد الجمهور أن يكون أكثر فائدة
+
+150
+00:10:21,460 --> 00:10:24,940
+، لذلك عندما نتحدث عن ما هي الشركتكترات للجمهور
+
+151
+00:10:24,940 --> 00:10:29,480
+جمهور، هنا نتحدث عن نفس الموضوع عندما نتحدث عن
+
+152
+00:10:29,480 --> 00:10:33,220
+كيفية إنشاء جمهور، جمهور، قلنا إن من أجل إنشاء فريق
+
+153
+00:10:33,220 --> 00:10:39,460
+مفيد يوجد بعض المشكلات التي يجب أن نتعامل معها في 
+
+154
+00:10:39,460 --> 00:10:44,520
+المؤسسة لكي نتأكد أننا لدينا فريق مفيد. على أيّة
+
+155
+00:10:44,520 --> 00:10:48,000
+حال، واحدة من الأشياء المهمة والتي كانت تتحدث عنها
+
+156
+00:10:48,000 --> 00:10:51,340
+أيضًا هو أن المجلدين المختارين لكي يكونوا شركاء 
+
+157
+00:10:52,500 --> 00:10:56,860
+الكثير من الناس الذين يكونوا مستعدين للعمل مع آخرين
+
+158
+00:10:56,860 --> 00:10:59,940
+أو يكونوا لديهم خاصيات ومميزات مثل هذه، الكثير من
+
+159
+00:10:59,940 --> 00:11:02,580
+الناس الذين يكونوا مستعدين للعمل مع آخرين أو يكونوا 
+
+160
+00:11:02,580 --> 00:11:02,840
+مستعدين للعمل مع آخرين أو يكونوا 
+
+161
+00:11:02,840 --> 00:11:04,140
+مستعدين للعمل مع آخرين أو يكونوا 
+
+162
+00:11:04,140 --> 00:11:07,100
+مستعدين للعمل مع آخرين أو يكونوا 
+
+163
+00:11:07,100 --> 00:11:09,220
+مستعدين للعمل مع آخرين أو يكونوا 
+
+164
+00:11:09,220 --> 00:11:12,400
+مستعدين للعمل مع آخرين أو يكونوا 
+
+165
+00:11:12,400 --> 00:11:15,560
+مستعدين للعمل مع آخرين أو يكونوا 
+
+166
+00:11:15,560 --> 00:11:19,200
+مستعدين للعمل مع آخرين أو يكونوا، ستالآن إذا لم يكن
+
+167
+00:11:19,200 --> 00:11:25,520
+الإنسان لديه أشكال أو أشكال أو شخصية أو شخصية أو
+
+168
+00:11:25,520 --> 00:11:26,440
+أو شخصية أو شخصية أو شخصية أو شخصية أو 
+
+169
+00:11:26,440 --> 00:11:29,600
+شخصية أو شخصية أو شخصية أو شخصية أو شخصية أو شخصية
+
+170
+00:11:29,600 --> 00:11:30,100
+أو شخصية أو شخصية أو شخصية أو شخصية أو شخصية أو
+
+171
+00:11:30,100 --> 00:11:34,860
+شخصية أو شخصية أو شخصية أو شخصية أو شخصية أو شخصية
+
+172
+00:11:34,860 --> 00:11:47,040
+أو شخصية أو شخصية أو شخصية أو شخص، نحن نتكلم هنا عن
+
+173
+00:11:47,040 --> 00:11:52,360
+تغيير بعض القدرات بطريقة إيجابية لتحسين قدرات 
+
+174
+00:11:52,360 --> 00:11:57,060
+المستخدمين للعمل في مجتمعين، بالطبع كل هذه الأشياء
+
+175
+00:11:57,060 --> 00:12:00,860
+مهمة لإيجاد
+
+176
+00:12:00,860 --> 00:12:09,800
+مجتمع مفيد يساعد في تفعيل عمليات ومهام مختلفة، أي
+
+177
+00:12:09,800 --> 00:12:12,880
+حاجة؟ طيب، يعطيكم العافية 
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/9xi9qAt9QBA.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/9xi9qAt9QBA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..63d93504cdbd29a0984b172cf84929a6075b02eb
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/9xi9qAt9QBA.srt
@@ -0,0 +1,1719 @@
+1
+00:00:09,450 --> 00:00:13,070
+Okay, we will continue with chapter number 
+
+2
+00:00:13,070 --> 00:00:16,510
+two. In the previous lecture, we had started with
+
+3
+00:00:16,510 --> 00:00:19,670
+discussing abilities and we said that there are
+
+4
+00:00:19,670 --> 00:00:22,670
+two types of abilities, intellectual abilities and
+
+5
+00:00:22,670 --> 00:00:27,250
+physical abilities. بالإضافة إلى ذلك، قررنا أننا
+
+6
+00:00:27,250 --> 00:00:33,150
+نتحدث عن مجالات مختلفة مرتبطة بكل مجال. قررنا أنه 
+
+7
+00:00:33,150 --> 00:00:37,330
+عندما نتحدث عن القدرات الإدراكية، يوجد مجالات 
+
+8
+00:00:37,330 --> 00:00:41,490
+مختلفة، ونفس الشيء عندما نتحدث عن المجالات بعد ذلك
+
+9
+00:00:41,490 --> 00:00:47,790
+قررنا ما هي دور الواقعات لـ OB و كيف هي مرتبطة 
+
+10
+00:00:47,790 --> 00:00:56,810
+بعد ذلك قررنا الشخصية البيولوجية و قررنا أنها
+
+11
+00:00:56,810 --> 00:01:02,550
+شخصية نفسية. قررنا شخصية مختلفة و في ذلك
+
+12
+00:01:02,550 --> 00:01:05,990
+الوقت قررنا أننا دائماً يجب أن نربط هذه الشخصية
+
+13
+00:01:05,990 --> 00:01:10,630
+بشخصية مختلفة أو مختلفة. نقول أننا دائماً نحتاج أن
+
+14
+00:01:10,630 --> 00:01:15,590
+نربط هذه الواضحات لـ Performance، Productivity،
+
+15
+00:01:15,590 --> 00:01:18,970
+Absentism، Turnover، Satisfaction، وما إلى ذلك،
+
+16
+00:01:18,970 --> 00:01:24,130
+حسنًا؟ لذلك، ليس مهماً فقط ما هو عمر أو جنس أو قيمة
+
+17
+00:01:24,130 --> 00:01:27,810
+أو دين أو لون، وما إلى ذلك، لا، الموضوع المهم هنا
+
+18
+00:01:27,810 --> 00:01:32,810
+هو ما هي التواصل أو ما هو تأثير العمر على
+
+19
+00:01:32,940 --> 00:01:37,260
+performance for example on productivity, turnover,
+
+20
+00:01:37,520 --> 00:01:40,840
+absenteeism, satisfaction and so on, experience
+
+21
+00:01:40,840 --> 00:01:44,800
+exactly. Okay, now we are going to start with a new
+
+22
+00:01:44,800 --> 00:01:49,340
+topic. Okay, we are going to talk about learning.
+
+23
+00:01:53,040 --> 00:01:55,960
+Learning, of course, when you talk about learning we
+
+24
+00:01:55,960 --> 00:01:58,980
+are not talking about education only. Education is
+
+25
+00:01:58,980 --> 00:02:02,080
+only one form of learning or one of the mechanisms.
+
+26
+00:02:02,080 --> 00:02:06,920
+There are other mechanisms. Okay, what is learning?
+
+27
+00:02:06,920 --> 00:02:11,340
+Yes, learning is a permanent change in an attitude 
+
+28
+00:02:11,340 --> 00:02:15,300
+or behavior towards as a result of experience. Okay.
+
+29
+00:02:15,300 --> 00:02:19,120
+It is a permanent change in behavior, okay, as a
+
+30
+00:02:19,120 --> 00:02:24,560
+result of experience. Okay, what form of change? Why
+
+31
+00:02:24,560 --> 00:02:29,580
+are we saying that it is a permanent change in
+
+32
+00:02:29,580 --> 00:02:34,660
+behavior? Why?
+
+33
+00:02:34,660 --> 00:02:37,320
+It is... why we... يعني we say always when we talk
+
+34
+00:02:37,320 --> 00:02:39,660
+about learning we describe it as a permanent
+
+35
+00:02:39,660 --> 00:02:43,120
+change in behavior. Yes.
+
+36
+00:02:48,170 --> 00:02:50,930
+When you talk about learning, it is a continuous
+
+37
+00:02:50,930 --> 00:02:54,130
+process. Okay, but I'm talking here about why it is
+
+38
+00:02:54,130 --> 00:02:56,590
+a permanent change in behavior. Learning process 
+
+39
+00:02:56,590 --> 00:02:59,790
+itself, it is a continuous process. It is ongoing
+
+40
+00:02:59,790 --> 00:03:03,230
+process. Okay, that's why I said that learning is
+
+41
+00:03:03,230 --> 00:03:05,590
+not limited only to education. Education is one
+
+42
+00:03:05,590 --> 00:03:08,350
+form of learning only. There are other forms which
+
+43
+00:03:08,350 --> 00:03:10,750
+we are going to discuss later on. Yes, because I
+
+44
+00:03:10,750 --> 00:03:13,410
+think learning is a two-stage process. Before 
+
+45
+00:03:13,410 --> 00:03:16,980
+learning and after learning. So after learning, some
+
+46
+00:03:16,980 --> 00:03:21,040
+changes will happen in attitudes and behavior that
+
+47
+00:03:21,040 --> 00:03:24,880
+will permanently change the attitudes of people.
+
+48
+00:03:25,100 --> 00:03:29,140
+الآن دعوني أعيد السؤال أو دعوني أتكلم عن الموضوع 
+
+49
+00:03:29,140 --> 00:03:33,540
+على أي حال، حسنًا؟ السؤال كان لماذا نسمي التعلم
+
+50
+00:03:33,540 --> 00:03:37,820
+كتغيير مستمر في السلوك، حسنًا؟ بالطبع ليس تمامًا
+
+51
+00:03:37,820 --> 00:03:41,420
+مستمرًا، إنه مستمر بشكل مرتبط، كما ذكرت هنا، حسنًا؟
+
+52
+00:03:41,420 --> 00:03:46,420
+هناك أشياء أخرى أستطيع أن أقولها هنا، تجارب
+
+53
+00:03:46,420 --> 00:03:51,480
+السلوك التي نسميها تجارب مقتصرة، حسنًا؟ لذلك الآن،
+
+54
+00:03:51,480 --> 00:03:55,450
+عندما نتحدث عن، على سبيل المثال، القصة، نستطيع أن
+
+55
+00:03:55,450 --> 00:03:58,690
+نغير اعتبارنا و نستطيع أن نغير نتائج الدراسة
+
+56
+00:03:58,690 --> 00:04:02,350
+ولكن عندما نتحدث عن الدراسة أو عن تغيير نتائج
+
+57
+00:04:02,350 --> 00:04:05,570
+الدراسة، سيأخذ المزيد من الوقت من التغيير، على
+
+58
+00:04:05,570 --> 00:04:10,030
+سبيل المثال، من رأينا نحو شيء، حسنًا؟ لذلك، هناك
+
+59
+00:04:10,030 --> 00:04:13,030
+بعض السلوكيات التي هي أسهل تغييرها و هناك
+
+60
+00:04:13,030 --> 00:04:15,970
+سلوكيات أخرى التي هي صعبة تغييرها. الآن عندما
+
+61
+00:04:15,970 --> 00:04:19,630
+نتحدث عن ذلك، لاحقًا، سنتحدث عن الخاصية، على سبيل
+
+62
+00:04:19,630 --> 00:04:23,130
+المثال. هو متغير ممكن تغييره دائمًا. كل هذه
+
+63
+00:04:23,130 --> 00:04:26,590
+السلوكيات ممكن تغييرها لكن هناك سلوكيات ممكن
+
+64
+00:04:26,590 --> 00:04:30,590
+تغييرها بسهولة و سلوكيات ممكن تغييرها بصعوبة. عندما
+
+65
+00:04:30,590 --> 00:04:32,970
+نتحدث عن طريقات شخصية على سبيل المثال عندما نتحدث
+
+66
+00:04:32,970 --> 00:04:36,930
+عن العلم عندما نتحدث عن قيم على سبيل المثال هذه
+
+67
+00:04:36,930 --> 00:04:40,110
+السلوكيات ممكن تغييرها بسهولة. ولكن في النهاية
+
+68
+00:04:40,110 --> 00:04:43,210
+ممكن تغييرها بسهولة وممكن تغييرها بصعوبة وممكن
+
+69
+00:04:43,210 --> 00:04:44,490
+تغييرها بسهولة وممكن تغييرها بصعوبة وممكن تغييرها
+
+70
+00:04:44,490 --> 00:04:46,310
+بسهولة وممكن تغييرها بصعوبة وممكن
+
+71
+00:04:49,230 --> 00:04:56,270
+مثلًا إذا كنا نقول إذا إذا إذا إذا إذا إذا إذا إذا
+
+72
+00:04:56,270 --> 00:04:56,590
+إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا
+
+73
+00:04:56,590 --> 00:04:57,190
+إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا
+
+74
+00:04:57,190 --> 00:04:57,250
+إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا
+
+75
+00:04:57,250 --> 00:04:57,490
+إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا
+
+76
+00:04:57,490 --> 00:04:57,550
+إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا إذا
+
+77
+00:04:57,550 --> 00:05:11,870
+إذا
+
+78
+00:05:11,870 --> 00:05:12,250
+إذا إ
+
+79
+00:05:19,440 --> 00:05:23,660
+عندما تتعلم الأشياء الجيدة، من الصعب أن تبقى لا
+
+80
+00:05:23,660 --> 00:05:29,960
+تتعلم الأشياء الجيدة. أحيانًا الناس تتعلم الأشياء
+
+81
+00:05:29,960 --> 00:05:34,380
+السيئة و هم يستمرون في فعل الأشياء السيئة. تفكير
+
+82
+00:05:34,380 --> 00:05:39,220
+الأشياء الصحيحة ماذا؟
+
+83
+00:05:39,220 --> 00:05:45,750
+أعتقد أن ...كل شخص متأكد من أفعاله أو أفعاله، لذلك
+
+84
+00:05:45,750 --> 00:05:50,610
+عندما يكون هناك تغيير، يأخذ المزيد من الوقت لتغيير
+
+85
+00:05:50,610 --> 00:05:57,510
+شخصيته أو حركة الشخص. فعندما يحدث هذا التغيير و
+
+86
+00:05:57,510 --> 00:06:03,670
+الإنسان متأكد أنه مناسب أو أحيانًا يكون ناجحًا يصبح
+
+87
+00:06:03,670 --> 00:06:05,870
+مرتبطًا بشكل مرتبط بشكل مرتبط بشكل مرتبط بشكل مرتبط
+
+88
+00:06:05,870 --> 00:06:08,110
+بشكل مرتبط بشكل مرتبط بشكل مرتبط بشكل مرتبط بشكل
+
+89
+00:06:08,110 --> 00:06:09,570
+مرتبط بشكل مرتبط بشكل مرتبط بشكل مرتبط بشكل مرتبط
+
+90
+00:06:09,570 --> 00:06:09,930
+بشكل مرتبط بشكل مرتبط بشكل مرتبط بشكل مرتبط بشكل
+
+91
+00:06:09,930 --> 00:06:12,150
+مرتبط بشكل مرتبط بشكل مرتبط بشكل مرتبط بشكل مرتبط
+
+92
+00:06:12,150 --> 00:06:17,350
+بشكل مرتبط ب
+
+93
+00:06:31,870 --> 00:06:37,230
+Okay، دعونا نتكلم عن الوقت الذي أخذه لإصلاح عبارة
+
+94
+00:06:37,230 --> 00:06:41,370
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+95
+00:06:41,370 --> 00:06:45,310
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+96
+00:06:45,310 --> 00:06:45,670
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+97
+00:06:45,670 --> 00:06:45,830
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+98
+00:06:45,830 --> 00:06:45,910
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+99
+00:06:45,910 --> 00:06:46,550
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+100
+00:06:46,550 --> 00:06:50,610
+عبارة. التعامل مع بعض السلوكيات التي طويلة. عندما 
+
+101
+00:06:50,610 --> 00:06:56,450
+نتكلم عن كم وقت تحتاجه، هناك سلوكيات أخرى أسهل 
+
+102
+00:06:56,450 --> 00:07:00,990
+وستأخذ أقل وقت. عندما نتكلم عن التعامل مع القيم مثلًا
+
+103
+00:07:00,990 --> 00:07:04,570
+التي سنتحدث عنها لاحقًا في قسم آخر. الشخصيات وما إلى
+
+104
+00:07:04,570 --> 00:07:09,410
+ذلك، عادة تأخذ هذه السلوكيات كثير من الوقت، لهذا
+
+105
+00:07:09,410 --> 00:07:15,640
+السبب، صعب التغيير. هناك سلوكيات أخرى. الخيارات التي
+
+106
+00:07:15,640 --> 00:07:21,280
+مرتبطة بالسلوك هي تأخذ أكثر من الوقت، فالأشياء
+
+107
+00:07:21,280 --> 00:07:25,100
+الأسهل تتغير أكثر من الوقت. إذا كان شخص ما عاد
+
+108
+00:07:25,100 --> 00:07:30,660
+يفعل شيء لعامين، فسيأخذ أكثر من الوقت لتغير
+
+109
+00:07:30,660 --> 00:07:35,500
+السلوك. إذا بدأنا نفعل شيء اليوم السابق، يكون سهل
+
+110
+00:07:35,500 --> 00:07:42,200
+تغييره اليوم، لكن تدرس نفس الدراسة لسنوات كثيرة،
+
+111
+00:07:42,200 --> 00:07:47,140
+فهذا يعني أنه سيأخذ المزيد من الوقت لتغيير الدراسة
+
+112
+00:07:47,140 --> 00:07:49,500
+أو السلوك وما إلى ذلك، لهذا السبب نقول أن التعلم
+
+113
+00:07:49,500 --> 00:07:54,470
+هو عامة مستمر مستمر مستمر مستمر مستمر مستمر
+
+114
+00:07:54,470 --> 00:07:55,370
+مستمر مستمر مستمر مستمر مستمر مستمر مستمر
+
+115
+00:07:55,370 --> 00:07:55,450
+مستمر مستمر مستمر مستمر مستمر مستمر مستمر
+
+116
+00:07:55,450 --> 00:07:58,290
+مستمر مستمر مستمر مستمر مستمر مستمر مستمر
+
+117
+00:07:58,290 --> 00:07:59,210
+مستمر مستمر مستمر مستمر مستمر مستمر مستمر
+
+118
+00:07:59,210 --> 00:07:59,910
+مستمر مستمر مستمر مستمر مستمر مستمر مستمر
+
+119
+00:07:59,910 --> 00:08:03,810
+مستمر مستمر مستمر مستمر مستمر مستمر مستمر
+
+120
+00:08:03,810 --> 00:08:14,190
+مستمر مستمر مستمر مستمر مستمر مستمر مستمر
+
+121
+00:08:14,220 --> 00:08:19,320
+آخر جزء من التعريف هو أن التعلم يتحول إلى نتيجة
+
+122
+00:08:19,320 --> 00:08:28,020
+تجارب تجارب تجارب تجارب تجارب
+
+123
+00:08:28,220 --> 00:08:32,600
+I think this experience becomes an experience when
+
+124
+00:08:32,600 --> 00:08:34,900
+you practice it for years and years, so it becomes
+
+125
+00:08:34,900 --> 00:08:39,160
+like you know this, you know this thing, so you
+
+126
+00:08:39,160 --> 00:08:42,100
+keep doing this, it becomes an experience because
+
+127
+00:08:42,100 --> 00:08:45,200
+it's a habit for you, up to nine years. Not
+
+128
+00:08:45,200 --> 00:08:48,500
+necessarily a habit, but it is an experience, يعني
+
+129
+00:08:48,500 --> 00:08:52,430
+it is something that we practice exactly or
+
+130
+00:08:52,430 --> 00:08:55,710
+something we have been through. Okay, that's why I
+
+131
+00:08:55,710 --> 00:08:58,210
+said education is a learning process but it is not
+
+132
+00:08:58,210 --> 00:09:01,590
+the only process. Okay, there are other processes
+
+133
+00:09:01,590 --> 00:09:05,930
+which will cause or make learning occur. 
+
+134
+00:09:22,750 --> 00:09:24,730
+Exactly, there are different classifications,
+
+135
+00:09:24,870 --> 00:09:28,540
+direct, indirect, programmed, unprogrammed، والكثير 
+
+136
+00:09:28,540 --> 00:09:35,300
+من الواضحات. أحيانًا الناس في عملية تجارب تجارب
+
+137
+00:09:35,300 --> 00:09:39,440
+تجارب تجارب
+
+138
+00:09:39,440 --> 00:09:42,540
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+139
+00:09:42,540 --> 00:09:45,680
+تجارب
+
+140
+00:09:45,750 --> 00:09:49,930
+بعض الأحيان نتكلم عن طريقة عامة مثل التعليم على 
+
+141
+00:09:49,930 --> 00:09:53,730
+سبيل المثال وكذلك مرة أخرى التعليم هو عملية
+
+142
+00:09:53,730 --> 00:10:00,370
+نعتبرها تغيير مستمر في التعامل يحدث بسبب تجارب
+
+143
+00:10:00,370 --> 00:10:04,750
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+144
+00:10:04,750 --> 00:10:04,830
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+145
+00:10:04,830 --> 00:10:11,530
+تجارب تجارب تجارب تجارب تجارب
+
+146
+00:10:11,530 --> 00:10:14,750
+تج
+
+147
+00:10:14,770 --> 00:10:17,830
+بالنسبة لهذا الموضوع، سنتحدث عن ثلاثة نظريات هنا.
+
+148
+00:10:17,970 --> 00:10:22,970
+الأول هو الوضع التجريبي والثاني هو الوضع التجريبي
+
+149
+00:10:22,970 --> 00:10:26,590
+والثالث هو الوضع التجريبي والتعلم الاجتماعي.
+
+150
+00:10:29,570 --> 00:10:32,470
+الوضع التجريبي الأول الذي يجب أن نتحدث عنه هو
+
+151
+00:10:32,470 --> 00:10:36,590
+الوضع التجريبي الوضع التجريبي كان هناك 
+
+152
+00:10:46,210 --> 00:10:55,470
+وكان هناك علماء روسيون أكثر من 110 سنة من قبل السنة
+
+153
+00:10:55,470 --> 00:11:01,370
+الماضية وكان يعمل تجارب على الحيوانات والحيوانات 
+
+154
+00:11:01,370 --> 00:11:07,890
+كان اسمه Pavlov وكان يحاول أن يشارك تجارب غير 
+
+155
+00:11:07,890 --> 00:11:16,530
+مطلوبة مع تجارب مطلوبة الآن عادةً .. أو في .. في ..
+
+156
+00:11:16,530 --> 00:11:20,830
+في التجارب الأولى، Pavlov بدأ يعطي الحيوانات
+
+157
+00:11:20,830 --> 00:11:24,690
+للحيوانات الطعام، والحيوانات وكذلك وعادة الحيوانات
+
+158
+00:11:24,690 --> 00:11:29,230
+تتردد عندما كان هناك طعام. كان هناك مدفع آخر هنا أو
+
+159
+00:11:29,230 --> 00:11:34,480
+مدفع الذي كان بالرنجلة، طبعا Pavlov بدأ يحرر الحرارة
+
+160
+00:11:34,480 --> 00:11:39,320
+ولكن لم يكن هناك إجابة. بعد ذلك، Pavlov بدأ يشارك
+
+161
+00:11:39,320 --> 00:11:46,960
+مدفع الهجوم الذي هو اللحم مع مدفع الهجوم الذي هو
+
+162
+00:11:46,960 --> 00:11:51,040
+الحرارة، طبعًا الحيوانات بدأت كل مرة تسمع الحرارة
+
+163
+00:11:51,040 --> 00:11:55,420
+يحررون الحرارة لأن كان هناك طعام. بعد ذلك، Pavlov
+
+164
+00:11:55,420 --> 00:12:00,040
+بدأ وكانوا يستخدمون فقط الـ bell ringing وكانوا
+
+165
+00:12:00,040 --> 00:12:06,160
+يأتون إلى نفس المكان حتى لو لم يكن هناك طعام.
+
+166
+00:12:06,480 --> 00:12:11,980
+لهذا السبب، عندما نتكلم عن تجارب كلاسيكية نقول إنها
+
+167
+00:12:11,980 --> 00:12:15,400
+تجارب تجارب في الواقع أن الشخص يتجرب
+
+168
+00:12:36,420 --> 00:12:40,300
+أو مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد
+
+169
+00:12:40,300 --> 00:12:40,900
+مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد
+
+170
+00:12:40,900 --> 00:12:43,860
+مجرد مجرد مجرد، وهذا السبب يسمونها تجارب غير مطلوبة
+
+171
+00:12:43,860 --> 00:12:49,840
+والتجارب المطلوبة كانت bell ringing التي نسميها تجارب 
+
+172
+00:12:49,840 --> 00:12:51,500
+غير مطلوبة تجارب غير مطلوبة تجارب غير مطلوبة تجارب
+
+173
+00:12:51,500 --> 00:12:52,380
+غير مطلوبة تجارب غير مطلوبة تجارب غير مطلوبة تجارب
+
+174
+00:12:52,380 --> 00:12:54,380
+غير مطلوبة تجارب غير مطلوبة تجارب غير مطلوبة تجارب
+
+175
+00:12:54,380 --> 00:12:54,400
+غير مطلوبة تجارب غير مطلوبة تجارب غير مطلوبة تجارب
+
+176
+00:12:54,400 --> 00:12:59,540
+غير مطلوبة تجارب غير مطلوبة تجارب غير مطلوبة تجارب
+
+177
+00:12:59,540 --> 00:13:02,960
+غير
+
+178
+00:13:02,960 --> 00:13:05,240
+مطلوبة ت
+
+179
+00:13:09,620 --> 00:13:14,840
+أو السلوكيات ممكن تكون مضمونة حتى لو لم يكن هناك 
+
+180
+00:13:14,840 --> 00:13:21,060
+علاقة بين السلوكيات والسلوكيات وهذه واحدة من
+
+181
+00:13:21,060 --> 00:13:23,840
+النظرية، طبعًا هذه النظرية
+
+182
+00:13:26,320 --> 00:13:31,020
+هناك فكرة جديدة مرتبطة بالمصطلح، ولكنها لا تتعامل
+
+183
+00:13:31,020 --> 00:13:32,960
+مع أي فكرة تتعامل مع أي فكرة تتعامل مع أي فكرة
+
+184
+00:13:32,960 --> 00:13:34,700
+تتعامل مع أي فكرة تتعامل مع أي فكرة تتعامل مع أي
+
+185
+00:13:34,700 --> 00:13:37,160
+فكرة تتعامل مع أي فكرة تتعامل مع أي فكرة تتعامل مع
+
+186
+00:13:37,160 --> 00:13:38,660
+أي فكرة تتعامل مع أي فكرة تتعامل مع أي فكرة تتعامل
+
+187
+00:13:38,660 --> 00:13:40,880
+مع أي فكرة تتعامل مع أي فكرة تتعامل مع أي فكرة
+
+188
+00:13:40,880 --> 00:13:44,180
+تتعامل مع أي فكرة تتعامل مع أي فكرة تتعامل مع أي
+
+189
+00:13:44,180 --> 00:13:48,340
+فكرة تتعامل مع أي فكرة تتعامل مع أي فكرة تتعامل مع
+
+190
+00:13:48,340 --> 00:13:54,340
+أي فكرة، ولا أحد من هذه الأفكار صحيح ولا أحد من هذه
+
+191
+00:13:54,340 --> 00:13:58,140
+الأفكار غير صحيح، هذه طريقة كيف يجب أن نتعامل مع 
+
+192
+00:13:58,140 --> 00:14:02,860
+هذه الأفكار، إنها ستعطينا الكثير من الانتصافات
+
+193
+00:14:02,860 --> 00:14:09,060
+والمفاهيم التي مرتبطة بالتعلم وكيف يحدث ذلك، لكن 
+
+194
+00:14:09,060 --> 00:14:11,740
+لا أحد من هذه الأفكار صحيح ولا أحد من هذه الأفكار
+
+195
+00:14:12,660 --> 00:14:17,260
+عندما نتكلم عن تجارب Pavlov والوضع العسكري، فهو
+
+196
+00:14:17,260 --> 00:14:23,540
+سيشرح جزء من الواقع، لكن بالطبع ليس سيشرح كل
+
+197
+00:14:23,540 --> 00:14:31,500
+الواقع، هناك نظرية أخرى هي الواضحة الواضحة الواضحة
+
+198
+00:14:31,500 --> 00:14:34,000
+الواضحة الواضحة الواضحة الواضحة الواضحة الواضحة
+
+199
+00:14:34,000 --> 00:14:34,680
+الواضحة الواضحة الواضحة الواضحة الواضحة الواضحة
+
+200
+00:14:34,680 --> 00:14:35,400
+الواضحة الواضحة الواضحة الواضحة الواضحة الواضحة
+
+201
+00:14:35,400 --> 00:14:41,500
+الواضحة الواضحة الواضحة الواضحة الواضحة الواضحة
+
+202
+00:14:41,500 --> 00:14:45,580
+الواضحة، إذا كانت الناس جيدة أو أفضل بعد التصرف، هم
+
+203
+00:14:45,580 --> 00:14:51,280
+سيفعلون شيء إذا كانوا يتوقعون أن هناك نتيجة أو
+
+204
+00:14:51,280 --> 00:14:53,980
+نتيجة أو نتيجة أو نتيجة أو نتيجة أو نتيجة أو نتيجة
+
+205
+00:14:53,980 --> 00:14:54,560
+أو نتيجة أو نتيجة أو نتيجة أو نتيجة أو نتيجة أو
+
+206
+00:14:54,560 --> 00:14:54,620
+نتيجة أو نتيجة أو نتيجة أو نتيجة أو نتيجة أو نتيجة
+
+207
+00:14:54,620 --> 00:14:57,400
+أو نتيجة أو نتيجة أو نتيجة أو نتيجة أو نتيجة أو
+
+208
+00:14:57,400 --> 00:14:57,900
+نتيجة أو نتيجة أو نتيجة أو نتيجة أو نتيجة أو نتيجة
+
+209
+00:14:57,900 --> 00:15:01,560
+أو نتيجة أو نتيجة أو نتيجة أو نتيجة أو نتيجة أو
+
+210
+00:15:01,560 --> 00:15:11,170
+نتيجة أو نتيجة أو نتيجة،  عن اتفاقات المتوقعات، إذا 
+
+211
+00:15:11,170 --> 00:15:14,970
+كانوا يتوقعون أنها جيدة، سيفعلون شيء، إذا كانوا
+
+212
+00:15:14,970 --> 00:15:22,170
+يتوقعون أنها خاطئة، لن يفعلوا الشيء. الآن العلماء
+
+213
+00:15:22,170 --> 00:15:27,150
+الذين صنعوا هذه النظرية اسمه Skinner، طبعًا Skinner كان 
+
+214
+00:15:27,150 --> 00:15:32,690
+واحدًا من المهندسين، هو من خلال محاولات مرتبطة
+
+215
+00:15:32,690 --> 00:15:34,850
+ بالعبارة عن العبارة عن العبارة عن العبارة عن
+
+216
+00:15:34,850 --> 00:15:37,410
+العبارة عن العبارة عن العبارة عن العبارة عن
+
+217
+00:15:37,410 --> 00:15:38,790
+العبارة عن العبارة عن العبارة عن العبارة عن
+
+218
+00:15:38,790 --> 00:15:39,710
+العبارة عن العبارة عن العبارة عن العبارة عن
+
+219
+00:15:39,710 --> 00:15:39,730
+العبارة عن العبارة عن العبارة عن العبارة عن
+
+220
+00:15:39,730 --> 00:15:40,850
+العبارة عن العبارة عن العبارة عن العبارة عن
+
+221
+00:15:40,850 --> 00:15:43,190
+العبارة عن العبارة عن العبارة عن العبارة عن
+
+222
+00:15:43,190 --> 00:15:50,010
+العبارة
+
+223
+00:15:50,010 --> 00:15:53,150
+عن العب
+
+224
+00:16:04,510 --> 00:16:10,510
+وهذا صحيح لأن عندما نفعل شيء، الكثير منا يفكر
+
+225
+00:16:10,510 --> 00:16:14,430
+قبل أن يفعله، لكن هناك الناس الذين لا يفكرون فيما
+
+226
+00:16:14,430 --> 00:16:22,470
+يفعلونه، وأحيانًا عندما نفعل شيء، يصبح مثل عادة
+
+227
+00:16:22,470 --> 00:16:28,350
+أو شيء يعتمد على عقلك، وتفكر قبل أن تفعله، هناك
+
+228
+00:16:28,350 --> 00:16:33,670
+قيادات، في بعض الأحيان تصبح مثلًا تريد أن تفعل هذا
+
+229
+00:16:33,670 --> 00:16:39,230
+الشيء، ولكنك فقط تفكر، لذلك ليس .. ليس بالطبع أنك لا 
+
+230
+00:16:39,230 --> 00:16:44,520
+تفكر في حركتك، أنت تفكر، أنت تفكر، لكن ..ليس
+
+231
+00:16:44,520 --> 00:16:48,700
+دائمًا، ليس دائمًا، Okay يعني we can say sometimes
+
+232
+00:16:48,700 --> 00:16:52,380
+people their actions are totally reflects for a
+
+233
+00:16:52,380 --> 00:16:55,180
+situation but this we cannot generalize anyway
+
+234
+00:16:55,180 --> 00:16:58,560
+okay and even in most cases we cannot consider
+
+235
+00:16:58,560 --> 00:17:01,600
+okay usually people think about what are the
+
+236
+00:17:01,600 --> 00:17:04,460
+consequences يعني we have we think we have
+
+237
+00:17:04,460 --> 00:17:07,240
+feelings and so on yes I think this is a little
+
+238
+00:17:07,240 --> 00:17:10,220
+bit strange because I believe it contradicts with
+
+239
+00:17:10,220 --> 00:17:12,200
+the operant conditioning we are saying in the
+
+240
+00:17:12,200 --> 00:17:16,340
+operant conditioning that لدينا أعمال معينة لأننا
+
+241
+00:17:16,340 --> 00:17:19,580
+نتوقع أن شيء يحدث، فهذا يعني أننا نفكر في
+
+242
+00:17:19,580 --> 00:17:26,830
+النتائج، فهناك حالات كما قالت إيمان، نحن نتعامل
+
+243
+00:17:26,830 --> 00:17:32,430
+بطريقة محدودة بدون أن نفكر في التأثيرات، لكن أكثر
+
+244
+00:17:32,430 --> 00:17:36,250
+من الوقت عندما يتعلق التعامل والعمل، أعتقد أن الناس
+
+245
+00:17:36,250 --> 00:17:42,410
+تفكر فيما سيحدث من الخارج، لذلك أنا لا أتفق بذلك
+
+246
+00:17:42,410 --> 00:17:44,630
+تمامًا، وهذا هو السبب لما تقولين أن التعامل ليس 
+
+247
+00:17:44,630 --> 00:17:48,730
+مرتبطًا تمامًا، في بعض الأحيان يمكن أن يكون، ولكننا لا 
+
+248
+00:17:48,730 --> 00:17:51,410
+نستطيع أن نجزم هذا المصطلح على أي حال، عندما نتحدث
+
+249
+00:17:51,410 --> 00:17:57,050
+عن الوضع الواضح، أنه مرتبط بكيف الناس، هو يجب أن يكون
+
+250
+00:17:57,050 --> 00:17:59,810
+لديه تجارب مع التجارب، يعني in other words, if
+
+251
+00:17:59,810 --> 00:18:01,710
+they have positive experience, they are going to
+
+252
+00:18:01,710 --> 00:18:03,350
+repeat the behavior, if they have negative
+
+253
+00:18:03,350 --> 00:18:06,630
+experience, they are going to avoid the behavior
+
+254
+00:18:10,040 --> 00:18:13,900
+طبعًا في النظريات الأخرى، سنتحدث عن كيف يمكن الناس أن 
+
+255
+00:18:13,900 --> 00:18:19,100
+يتعلموا من الآخرين، لأننا لا نحتاج دائمًا .. لا نحتاج 
+
+256
+00:18:19,100 --> 00:18:22,360
+دائمًا أن نتعلم من حالتنا لكي نتعلم من حالتنا لكي 
+
+257
+00:18:22,360 --> 00:18:23,720
+نتعلم من حالتنا لكي نتعلم من حالتنا لكي نتعرف
+
+258
+00:18:23,720 --> 00:18:26,700
+على حالتنا لكي نتعلم من حالتنا لكي نتعرف على
+
+259
+00:18:26,700 --> 00:18:28,660
+حالتنا لكي نتعلم من حالتنا لكي نتعرف على حالتنا
+
+260
+00:18:28,660 --> 00:18:30,560
+لكي نتعلم من حالتنا لكي نتعرف على حالتنا لكي
+
+261
+00:18:30,560 --> 00:18:31,080
+نتعلم من حالتنا لكي نتعرف على حالتنا لكي نتعرف
+
+262
+00:18:31,080 --> 00:18:34,030
+على حالتنا لكي نتهذا السبب، عندما نتكلم عن
+
+263
+00:18:34,030 --> 00:18:38,390
+النتائج الاصطناعية، هي أكثر أنها مرتبطة بمشاعر 
+
+264
+00:18:38,390 --> 00:18:40,750
+قبلية مرتبطة بالوضع
+
+265
+00:18:43,920 --> 00:18:50,540
+مع نظرية Skinner، لماذا؟ لأن هنا الموضوع هو تطبيق
+
+266
+00:18:50,540 --> 00:18:54,540
+التجارب التجارب بدون التفكير، لهذا السبب قلت إن هذا
+
+267
+00:18:54,540 --> 00:19:00,020
+مصطلح لتحسين الواضح، لكن بعض الأشخاص قد يكون لديهم
+
+268
+00:19:00,020 --> 00:19:04,500
+تجارب خاطئة أو شيء ما، ولكن بعد بعض الوقت، تفكر في 
+
+269
+00:19:04,500 --> 00:19:09,080
+تكرار السلوك، ولكن بإصلاح الوضع على سبيل المثال، أو
+
+270
+00:19:09,080 --> 00:19:11,960
+تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ
+
+271
+00:19:11,960 --> 00:19:12,560
+تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ
+
+272
+00:19:12,560 --> 00:19:16,400
+تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ
+
+273
+00:19:16,400 --> 00:19:17,100
+تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ
+
+274
+00:19:17,100 --> 00:19:22,320
+تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ تأخذ
+
+275
+00:19:22,320 --> 00:19:27,380
+تأخذ تأ
+
+276
+00:19:27,410 --> 00:19:31,690
+Okay, usually when we talk .. when we are through
+
+277
+00:19:31,690 --> 00:19:34,030
+.. when we are through a certain experience, we
+
+278
+00:19:34,030 --> 00:19:37,070
+learn from that experience, and in most cases the
+
+279
+00:19:37,070 --> 00:19:41,310
+human behavior is going to develop some sort of ..
+
+280
+00:19:41,310 --> 00:19:48,830
+we can say تطور فيها، تجارب تجارب تجارب تجارب تجارب 
+
+281
+00:19:48,830 --> 00:19:49,250
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+282
+00:19:49,250 --> 00:19:51,410
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+283
+00:19:51,410 --> 00:19:52,070
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+284
+00:19:52,070 --> 00:19:52,250
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+285
+00:19:52,250 --> 00:20:00,610
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+286
+00:20:00,610 --> 00:20:06,430
+تجارب تجار
+
+287
+00:20:06,480 --> 00:20:10,140
+Okay, and direct experience, okay. Now, in previous
+
+288
+00:20:10,140 --> 00:20:12,740
+theories, the direct experience was taken into 
+
+289
+00:20:12,740 --> 00:20:15,280
+consideration. Now, when you talk about the
+
+290
+00:20:15,280 --> 00:20:17,820
+social learning theory here, we are talking about
+
+291
+00:20:17,820 --> 00:20:20,800
+direct experience in addition to other mechanisms
+
+292
+00:20:20,800 --> 00:20:24,500
+here, such as the observation. That's why I said
+
+293
+00:20:24,500 --> 00:20:29,080
+that not always we must go through a certain
+
+294
+00:20:29,080 --> 00:20:31,980
+situation in order to learn from the situation. We 
+
+295
+00:20:31,980 --> 00:20:36,110
+can learn from الآخرين تجربة ونستطيع أن نحصل على
+
+296
+00:20:36,110 --> 00:20:41,150
+تجربة من هذه الطريقة عندما نتكلم عن نظرية التدرس
+
+297
+00:20:41,150 --> 00:20:45,390
+الاجتماعي، هناك أربع أنواع من التجارب الدراسية الاجتماعية
+
+298
+00:20:45,390 --> 00:20:51,310
+الأولى هي التجارب التهيئية، مشروع التجارب ومشروع
+
+299
+00:20:51,310 --> 00:20:56,150
+المصادر، والمشروع التجارب، والمشروع التجارب، والمشروع
+
+300
+00:20:56,150 --> 00:21:03,010
+التجارب، والمشروع التجارب، والمشروع التجارب، والمشروع
+
+301
+00:21:03,010 --> 00:21:08,090
+التجارب، والمشروع التجارب، والمشروع التجارب، والمشروع
+
+302
+00:21:08,090 --> 00:21:08,590
+التجارب، والمشروع التجارب، والمشروع التجارب، والمشروع
+
+303
+00:21:08,590 --> 00:21:10,130
+التجارب، والمشروع التجارب، والمشروع التجارب، والمشروع
+
+304
+00:21:10,130 --> 00:21:14,530
+التجارب، والمشروع التجارب، والمشروع التجارب 
+
+305
+00:21:19,320 --> 00:21:24,400
+نحن نتذكر الحاجات وبالتالي نقوم بتعلم حاجات جديدة
+
+306
+00:21:24,400 --> 00:21:30,360
+عندما نتحدث عن التجارب التجارية، هنا نتحدث أكثر عن
+
+307
+00:21:30,360 --> 00:21:35,200
+التجارب التجارية. تشاهد أشخاص أو أشخاص تجارب تجارب
+
+308
+00:21:35,200 --> 00:21:35,500
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+309
+00:21:35,500 --> 00:21:36,840
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+310
+00:21:36,840 --> 00:21:37,160
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+311
+00:21:37,160 --> 00:21:37,440
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+312
+00:21:37,440 --> 00:21:54,580
+تجارب تجارب تجارب تج
+
+313
+00:21:54,800 --> 00:22:02,500
+والتحديات المختلفة هي تحديات تركز على علاقة ما هي
+
+314
+00:22:02,500 --> 00:22:07,400
+علاقة بين الاستثمار غير المضمون والاستثمار 
+
+315
+00:22:07,400 --> 00:22:11,300
+المضمون، وكيف يمكن أن يتعامل الناس بسبب استثمار غير
+
+316
+00:22:11,300 --> 00:22:19,210
+مضمون وهو غير مرتبط بالوضع في الوضع الواقعي نتعلم
+
+317
+00:22:19,210 --> 00:22:24,290
+هنا من خلال القرار، ما هي التأثيرات وإذا كانت 
+
+318
+00:22:24,290 --> 00:22:29,890
+التأثيرات أفضل أو أقل، سنقرر كيف نتعامل بحيث الوضع
+
+319
+00:22:29,890 --> 00:22:34,190
+الواقعي التجريبية نتعلم من خلال تجاربنا، ولكن
+
+320
+00:22:34,190 --> 00:22:38,650
+أيضًا نستطيع أن نتعلم من خلال ملاحظات تستخدم في 
+
+321
+00:22:38,650 --> 00:22:40,870
+ميكانيزمات مختلفة أو برامج مختلفة أو برامج
+
+322
+00:22:40,870 --> 00:22:42,150
+مختلفة أو برامج مختلفة أو برامج مختلفة أو
+
+323
+00:22:42,150 --> 00:22:42,650
+برامج مختلفة أو برامج مختلفة أو برامج
+
+324
+00:22:42,650 --> 00:22:43,630
+مختلفة أو برامج مختلفة أو برامج مختلفة أو
+
+325
+00:22:43,630 --> 00:22:44,550
+برامج مختلفة أو برامج مختلفة أو برامج
+
+326
+00:22:44,550 --> 00:22:46,630
+مختلفة أو برامج مختلفة أو برامج مختلفة أو
+
+327
+00:22:46,630 --> 00:22:53,200
+برامج مختلفة أو برامج مختلفة يعني it is not
+
+328
+00:22:53,200 --> 00:22:56,060
+considered here. Okay, that's why I have said that
+
+329
+00:22:56,060 --> 00:22:59,100
+behavior, some people consider behavior as totally
+
+330
+00:22:59,100 --> 00:23:03,460
+reflects to a certain situation, which is not true.
+
+331
+00:23:03,460 --> 00:23:07,700
+It is true in some cases, but we cannot generalize 
+
+332
+00:23:07,700 --> 00:23:11,480
+those concepts or mechanisms. Okay, any questions 
+
+333
+00:23:11,480 --> 00:23:17,500
+till now? أحد أهم اتفاقيات اتفاقيات اتفاقيات اتفاقات
+
+334
+00:23:17,500 --> 00:23:20,420
+اتفاقيات اتفاقيات اتفاقيات اتفاقيات اتفاقيات اتفاقيات
+
+335
+00:23:20,420 --> 00:23:24,580
+اتفاقيات اتفاقيات اتفاقيات اتفاقيات اتفاقيات اتفاقيات
+
+336
+00:23:25,130 --> 00:23:30,070
+وهذه الأفكار التي تحدثنا عنها يجب أن تساعدنا أو
+
+337
+00:23:30,070 --> 00:23:34,690
+تساعد الوظيفة في تصميم أفكار الموظفين، عندما نتحدث 
+
+338
+00:23:34,690 --> 00:23:37,830
+عن تصميم الأفكار، هنا نتحدث عن تصميم أفكار مختلفة 
+
+339
+00:23:37,830 --> 00:23:42,970
+بطريقة مستمرة باستخدام ميكانيزمات مختلفة التي 
+
+340
+00:23:42,970 --> 00:23:47,730
+تحدثنا عنها وأخرى التي سنتحدث عنها، فنحن نتحدث هنا
+
+341
+00:23:47,730 --> 00:23:54,510
+عن تغيير الأفكار بعمل تجارب للإنسان في شكل مناسب
+
+342
+00:23:54,510 --> 00:24:03,170
+ لأهدافنا أو لما نريده كمدير أو كمؤسسة، فهو تغيير
+
+343
+00:24:03,170 --> 00:24:07,510
+السلوك، تغيير السلوك، تدرس السلوك بطريقة معينة،
+
+344
+00:24:07,510 --> 00:24:14,420
+حسنًا؟ الآن، لكي نفعل ذلك، يجب أن ندخل أو ما يسمى
+
+345
+00:24:14,420 --> 00:24:18,920
+كمثال، تصميم الحياة. هناك أمثلة مختلفة يمكن 
+
+346
+00:24:18,920 --> 00:24:25,120
+تأخذها المنظمة لتصميم الحياة لأعمال المؤسسات. هذه
+
+347
+00:24:25,120 --> 00:24:30,580
+الأمثلة لدينا أربع أمثلة هنا: تصميم الحياة 
+
+348
+00:24:30,580 --> 00:24:35,760
+المناسبة، تصميم الحياة المفاجئة، والتعزيز، والتعزيز
+
+349
+00:24:35,760 --> 00:24:36,820
+والتعزيز، والتعزيز، والتعزيز، والتعزيز، والتعزيز
+
+350
+00:24:36,820 --> 00:24:36,920
+والتعزيز، والتعزيز، والتعزيز، والتعزيز، والتعزيز
+
+351
+00:24:36,920 --> 00:24:40,440
+والتعزيز، والتعزيز، والتعزيز، والتعزيز
+
+352
+00:24:43,260 --> 00:24:50,280
+والآخرين. عادةً نتعامل مع احتياط سلبي،
+
+353
+00:24:50,280 --> 00:24:57,800
+إذا ماذا يجب أن نفعل مع احتياط سلبي؟ يجب أن
+
+354
+00:24:57,800 --> 00:25:02,840
+نحرره ونعيده ويجب أن نتأكد من أنه مستمر وكذلك،
+
+355
+00:25:02,840 --> 00:25:07,400
+الاحتياط السلبي يجب أن نخلصه، نتخلص منه، نتحرك منه،
+
+356
+00:25:07,400 --> 00:25:09,460
+نتحرك منه، نتحرك منه، نتحرك منه، نتحرك منه، نتحرك
+
+357
+00:25:09,460 --> 00:25:10,280
+منه، نتحرك منه، نتحرك منه، نتحرك منه، نتحرك منه،
+
+358
+00:25:10,280 --> 00:25:10,680
+نتحرك منه، نتحرك منه، نتحرك منه، نتحرك منه، نتحرك
+
+359
+00:25:10,680 --> 00:25:14,940
+منه، نتحرك منه، نتعن طريق تحسين الواقع المناسب،
+
+360
+00:25:14,940 --> 00:25:18,800
+لدينا اتصالين هنا التي نستخدمها، الأول هو تحسين
+
+361
+00:25:18,800 --> 00:25:23,680
+الواقع المناسب، والثاني هو تحسين الواقع المناسب،
+
+362
+00:25:23,680 --> 00:25:26,040
+وفي تحسين الواقع المناسب، عندما يكون هناك واقع 
+
+363
+00:25:26,040 --> 00:25:30,260
+مناسب، نستطيع تحسين الواقع، ببساطة، وهذا نسميه
+
+364
+00:25:30,260 --> 00:25:34,640
+تحسين الواقع المناسب. وهنا نعطي الوضع اللي نريده
+
+365
+00:25:34,640 --> 00:25:39,240
+بهذا الوضع. الآن في تدعيم نقل، انتظر، إنه تدعيم 
+
+366
+00:25:39,240 --> 00:25:42,940
+ولكنه نقل، بعض الناس يعتقدون أن تدعيم نقل هو 
+
+367
+00:25:42,940 --> 00:25:48,520
+إعجاب، لكنه ليس إعجاب، إنه فقط أحيانًا الوظيفة 
+
+368
+00:25:48,520 --> 00:25:54,950
+تقرر تدعيم عملية لأنهم متأخرين، ولكن تلك الموظفين
+
+369
+00:25:54,950 --> 00:25:57,530
+الذين لم يلعبوا ليسوا سيكونون مجرد مجرد مجرد مجرد
+
+370
+00:25:57,530 --> 00:25:57,690
+مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد
+
+371
+00:25:57,690 --> 00:26:01,370
+مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد
+
+372
+00:26:01,370 --> 00:26:01,910
+مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد مجرد
+
+373
+00:26:01,910 --> 00:26:13,930
+مجرد مجرد مجرد مجرد مجرد
+
+374
+00:26:13,930 --> 00:26:16,430
+مجرد
+
+375
+00:26:18,300 --> 00:26:23,200
+ولكن مرة أخرى، إنه استخدام لإعادة إلى حركة أفضل، حركة
+
+376
+00:26:23,200 --> 00:26:28,180
+أفضل. لماذا؟ لأن الناس اللي يتعاملون بشكل خاطئ، هم
+
+377
+00:26:28,180 --> 00:26:31,520
+سيكونون محققين، على سبيل المثال. الآن، الإنهاء
+
+378
+00:26:31,520 --> 00:26:40,070
+والمحقق يستخدمون لإيقاف حركة أفضل.  الانقراض هو مثل ..
+
+379
+00:26:40,070 --> 00:26:43,930
+دعوني أتكلم في كلمات بسيطة، هو مثل إيقاف الكلام، و
+
+380
+00:26:43,930 --> 00:26:47,990
+دعوني أعطي مثال بسيطة، مثلما يكون في مدرسة، مدرس
+
+381
+00:26:47,990 --> 00:26:53,070
+يتعامل مع طفل أو طلاب، وهناك طلاب يحاول أن يتعامل
+
+382
+00:26:53,070 --> 00:26:56,650
+بطريقة ذكية وما إلى ذلك، وأكثر من ذلك، المدرس
+
+383
+00:26:56,650 --> 00:27:01,890
+يعطي اهتمام للطلاب، ولا تفعل ذلك، بـ التعامل نفسك
+
+384
+00:27:01,890 --> 00:27:05,890
+وكذلك، أكثر التعامل سيزداد في بعض الأحيان، لذلك في 
+
+385
+00:27:05,890 --> 00:27:09,530
+حالة كهذه أحيانًا يكون أفضل أن تستخدم الإنهاء
+
+386
+00:27:09,530 --> 00:27:15,960
+لتنقل هذا الطفل أو طلابك، ولا تدفع الاهتمام. هذه 
+
+387
+00:27:15,960 --> 00:27:18,800
+الاختصارات تسمى كـ Extinction. وفي بعض الأحيان هذا 
+
+388
+00:27:18,800 --> 00:27:22,800
+سيساعد في إزالة السلوك أكثر من التعزيز.
+
+389
+00:27:46,150 --> 00:27:52,730
+أقول أن الأولين يتعاملون بشكل إيجابي، والثالث 
+
+390
+00:27:52,730 --> 00:27:57,410
+والرابع يتعاملون بشكل إيجابي. الأولين يتعاملون بشكل
+
+391
+00:27:57,410 --> 00:27:57,650
+إيجابي. الأولين يتعاملون بشكل إيجابي. الأولين
+
+392
+00:27:57,650 --> 00:27:58,370
+يتعاملون بشكل إيجابي. الأولين يتعاملون بشكل إيجابي
+
+393
+00:27:58,370 --> 00:28:03,110
+الأولين يتعاملون بشكل إيجابي. الأولين يتعاملون
+
+394
+00:28:03,110 --> 00:28:08,910
+بشكل إيجابي. الأولين يتعاملون
+
+395
+00:28:08,910 --> 00:28:10,370
+بشكل إيجابي. الأولين يتعاملون بشكل إيجابي. الأولين 
+
+396
+00:28:10,370 --> 00:28:11,630
+يتعاملون بشكل إيجابي. الأولين يتعاملون بشكل إيجابي
+
+397
+00:28:11,630 --> 00:28:15,190
+الأولين يتعاملون بشكل الشيء اللي يحتاجه هو إما أننا 
+
+398
+00:28:15,190 --> 00:28:21,430
+سنستخدم إدارة جيدة أو إدارة خاطئة أو إدارة خاطئة 
+
+399
+00:28:21,430 --> 00:28:22,450
+خاطئة أو إدارة خاطئة أو إدارة خاطئة أو إدارة خاطئة
+
+400
+00:28:22,450 --> 00:28:22,790
+أو إدارة خاطئة أو إدارة خاطئة أو إدارة خاطئة أو
+
+401
+00:28:22,790 --> 00:28:25,770
+إدارة خاطئة أو إدارة خاطئة أو إدارة خاطئة أو إدارة
+
+402
+00:28:25,770 --> 00:28:30,290
+خاطئة أو إدارة خاطئة أو إدارة خاطئة أو إدارة خاطئ
+
+403
+00:28:31,090 --> 00:28:35,730
+هي استخدامها مع حركة أفضل التي ليست محتاجة بعد الآن
+
+404
+00:28:35,730 --> 00:28:39,710
+وحركة أفضل التي ليست محتاجة بعد الآن هي غير مفيدة 
+
+405
+00:28:39,710 --> 00:28:44,130
+للقـ شركة، ربما ليس مؤلمة، ولكن على أي حال، لماذا لا 
+
+406
+00:28:44,130 --> 00:28:48,930
+نقوم بإضافة هذه الحركة أفضل ولا نقوم بإضافة هذا
+
+407
+00:28:48,930 --> 00:28:49,770
+الحركة، نقوم بإضافة هذه الحركة، نقوم بإضافة هذا
+
+408
+00:28:49,770 --> 00:28:54,970
+الحركة. عادةً الشركات عندما لا تحتاج حركة أفضل ليس
+
+409
+00:28:54,970 --> 00:28:59,660
+مهمة. هي ليست مهمة للشركة، التحقيق ليس مهمة للتعامل
+
+410
+00:28:59,660 --> 00:29:05,420
+لإعادة التعامل، لذلك يستخدمون الإنهاء، الإنهاء في
+
+411
+00:29:05,420 --> 00:29:09,480
+أشخاص أخرى يستخدمونه لإيقاف التعامل الأساسي 
+
+412
+00:29:09,480 --> 00:29:14,400
+بالطريقة التي ذكرناها، عندما نتحدث عن التعامل هنا
+
+413
+00:29:14,400 --> 00:29:21,130
+نحن نتحدث عن تطبيق التعامل بشكل مباشر ومباشر ومباشر
+
+414
+00:29:21,130 --> 00:29:22,890
+ومباشر ومباشر ومباشر ومباشر ومباشر ومباشر ومباشر
+
+415
+00:29:22,890 --> 00:29:25,430
+ومباشر ومباشر ومباشر ومباشر ومباشر ومباشر ومباشر
+
+416
+00:29:25,430 --> 00:29:27,990
+ومباشر ومباشر ومباشر ومباشر ومباشر ومباشر ومباشر
+
+417
+00:29:27,990 --> 00:29:28,190
+ومباشر ومباشر ومباشر ومباشر ومباشر ومباشر ومباشر
+
+418
+00:29:28,190 --> 00:29:28,450
+ومباشر ومباشر ومباشر ومباشر ومباشر ومباشر ومباشر
+
+419
+00:29:28,450 --> 00:29:34,500
+ومباشر ومباشر ومباشر ومباشر ومباشر ومIt is purely
+
+420
+00:29:34,500 --> 00:29:38,080
+psychological theories. Okay, most of those
+
+421
+00:29:38,080 --> 00:29:40,500
+scientists that we have mentioned are not
+
+422
+00:29:40,500 --> 00:29:42,980
+specialized in organizational behavior, they are
+
+423
+00:29:42,980 --> 00:29:45,940
+specialized in psychology, okay, but again we said
+
+424
+00:29:45,940 --> 00:29:48,060
+that one of the most important disciplines which
+
+425
+00:29:48,060 --> 00:29:50,500
+contributed to organizational behavior is
+
+426
+00:29:50,500 --> 00:29:53,620
+psychology, that's why we use those theories to
+
+427
+00:29:53,620 --> 00:29:56,700
+explain human behavior even within the
+
+428
+00:29:56,700 --> 00:29:58,400
+organization, okay 
+
+429
+00:30:05,030 --> 00:30:09,770
+مخيل بكفي ده دخلنا أكتر من هيك مش راحين نلحق نخلص
+
+430
+00:30:09,770 --> 00:30:16,630
+كل شيء طيب .. في الكتاب صار شيء فيه .. 
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/9xi9qAt9QBA_raw.json b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/9xi9qAt9QBA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f587f433002ac651aa036c997dcfeb5aa52b4de8
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/9xi9qAt9QBA_raw.json
@@ -0,0 +1 @@
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تجارب على الحيوانات والحيوانات كان اسمه Pavlov وكان يحاول أن يشارك تجارب غير مطلوبة مع تجارب مطلوبة", "tokens": [2407, 41361, 34105, 4117, 11203, 2304, 16606, 12602, 41779, 1829, 5551, 4117, 2655, 2288, 9154, 20154, 8608, 1863, 3660, 9154, 12174, 36150, 21136, 1863, 3660, 9673, 46958, 10632, 4032, 41361, 7251, 25957, 1211, 6055, 7435, 9640, 3555, 15844, 21542, 1829, 2407, 7649, 9307, 16070, 5016, 1829, 2407, 7649, 9307, 25961, 24525, 2304, 3224, 39062, 28257, 4032, 41361, 7251, 5016, 995, 12610, 14739, 7251, 8592, 9640, 4117, 6055, 7435, 9640, 3555, 32771, 13546, 3714, 9566, 1211, 37746, 3660, 20449, 6055, 7435, 9640, 3555, 3714, 9566, 1211, 37746, 3660], "avg_logprob": -0.5365767302838239, "compression_ratio": 1.7771084337349397, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 646.21, "end": 646.65, "word": "وكان", "probability": 0.5048828125}, {"start": 646.65, "end": 647.09, "word": " هناك", "probability": 0.7386474609375}, {"start": 647.09, "end": 647.73, "word": " 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"end": 1429.05, "text": "وهذه الأفكار التي تحدثنا عنها يجب أن تساعدنا أو تساعد الوظيفة في تصميم أفكار الموظفين عندما نتحدث عن تصميم الأفكار، هنا نتحدث عن تصميم أفكار مختلفة بطريقة مستمرة باستخدام ميكانيزمات مختلفة التي تحدثنا عنها وأخرى التي سنتحدث عنها، فنحن نتحدث هنا عن تغيير الأفكار", "tokens": [2407, 3224, 24192, 16247, 5172, 4117, 9640, 38392, 6055, 24401, 12984, 8315, 18871, 11296, 7251, 7435, 3555, 14739, 6055, 3794, 995, 22488, 8315, 34051, 6055, 3794, 995, 22488, 2423, 2407, 19913, 33911, 3660, 8978, 6055, 9381, 2304, 32640, 5551, 5172, 4117, 9640, 9673, 2407, 19913, 5172, 9957, 43242, 15042, 8717, 2655, 24401, 12984, 18871, 6055, 9381, 2304, 32640, 16247, 5172, 4117, 9640, 12399, 34105, 8717, 2655, 24401, 12984, 18871, 6055, 9381, 2304, 32640, 5551, 5172, 4117, 9640, 3714, 46456, 46538, 3660, 4724, 9566, 16572, 28671, 3714, 14851, 29973, 3660, 4724, 995, 14851, 9778, 3215, 10943, 3714, 1829, 41361, 1829, 11622, 2304, 9307, 3714, 46456, 46538, 3660, 38392, 6055, 24401, 12984, 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"probability": 0.91650390625}, {"start": 1796.7, "end": 1797.62, "word": " organization", "probability": 0.9248046875}, {"start": 1797.62, "end": 1798.4, "word": " okay", "probability": 0.86767578125}], "temperature": 1.0}, {"id": 82, "seek": 181663, "start": 1805.03, "end": 1816.63, "text": "مخيل بكفي ده دخلنا أكتر من هيك مش راحين نلحق نخلص كل إشي طيب .. في الكتاب صار إشي فيه ..", "tokens": [2304, 9778, 26895, 4724, 4117, 41185, 11778, 3224, 11778, 9778, 1211, 8315, 5551, 4117, 2655, 2288, 9154, 39896, 4117, 37893, 12602, 39319, 9957, 8717, 1211, 5016, 4587, 8717, 9778, 1211, 9381, 28242, 11933, 8592, 1829, 23032, 1829, 3555, 4386, 8978, 33251, 2655, 16758, 20328, 9640, 11933, 8592, 1829, 8978, 3224, 4386], "avg_logprob": -0.20943510102537963, "compression_ratio": 1.3693693693693694, "no_speech_prob": 0.0, "words": [{"start": 1805.03, "end": 1805.35, "word": "مخيل", "probability": 0.7220865885416666}, {"start": 1805.35, "end": 1805.71, "word": " بكفي", "probability": 0.6983235677083334}, {"start": 1805.71, "end": 1805.85, "word": " ده", "probability": 0.7890625}, {"start": 1805.85, "end": 1806.19, "word": " دخلنا", "probability": 0.9749755859375}, {"start": 1806.19, "end": 1806.47, "word": " أكتر", "probability": 0.87188720703125}, {"start": 1806.47, "end": 1806.63, "word": " من", "probability": 0.99072265625}, {"start": 1806.63, "end": 1806.83, "word": " هيك", "probability": 0.924072265625}, {"start": 1806.83, "end": 1806.99, "word": " مش", "probability": 0.64697265625}, {"start": 1806.99, "end": 1807.27, "word": " راحين", "probability": 0.8640950520833334}, {"start": 1807.27, "end": 1807.75, "word": " نلحق", "probability": 0.914306640625}, {"start": 1807.75, "end": 1809.77, "word": " نخلص", "probability": 0.8443603515625}, {"start": 1809.77, "end": 1809.95, "word": " كل", "probability": 0.97998046875}, {"start": 1809.95, "end": 1810.65, "word": " إشي", "probability": 0.9305013020833334}, {"start": 1810.65, "end": 1811.49, "word": " طيب", "probability": 0.8712565104166666}, {"start": 1811.49, "end": 1811.75, "word": " ..", "probability": 0.345458984375}, {"start": 1811.75, "end": 1812.49, "word": " في", "probability": 0.52294921875}, {"start": 1812.49, "end": 1812.81, "word": " الكتاب", "probability": 0.98681640625}, {"start": 1812.81, "end": 1813.07, "word": " صار", "probability": 0.9892578125}, {"start": 1813.07, "end": 1813.33, "word": " إشي", "probability": 0.8927408854166666}, {"start": 1813.33, "end": 1814.15, "word": " فيه", "probability": 0.80224609375}, {"start": 1814.15, "end": 1816.63, "word": " ..", "probability": 0.900390625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1818.42425, "duration_after_vad": 1754.8606249999968}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/Ikc8ylP24Kg_postprocess.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/Ikc8ylP24Kg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b81ad748d6bca9b6313d706664b2e7c87d3e5e68
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/Ikc8ylP24Kg_postprocess.srt
@@ -0,0 +1,1468 @@
+1
+00:00:13,130 --> 00:00:18,230
+في هذا الحلقة، سنتحدث عن مهمة مهارات التعامل
+
+2
+00:00:18,230 --> 00:00:22,890
+الإجتماعي وهذا هو النقطة الأولى التي سنبدأ بها
+
+3
+00:00:22,890 --> 00:00:27,170
+بإضافة إلى بعض النقطة الأخرى، ماذا يفعل الرئيس؟ ما
+
+4
+00:00:27,170 --> 00:00:29,710
+هي مهارتهم؟ ما هي رقمهم؟ ما هي مهارتهم؟ ما هي
+
+5
+00:00:29,710 --> 00:00:34,730
+المهارات التي يجب أن تكون لها لتسيير مؤسسات
+
+6
+00:00:34,730 --> 00:00:39,240
+مختلفة؟ بالإضافة إلى ذلك، يجب أنتفهم مصطلح الهجوم
+
+7
+00:00:39,240 --> 00:00:44,820
+وما هو مصطلح الهجوم، ونحتاج أن نفهم كيف هو مصطلح
+
+8
+00:00:44,820 --> 00:00:48,560
+الهجوم أو ما هي قيمة مصطلح الهجوم في الدراسات
+
+9
+00:00:48,560 --> 00:00:53,860
+السياسية وكيف يستخدمه في محققات مختلفة وكيف يتم
+
+10
+00:00:53,860 --> 00:00:58,840
+تطبيقه من مؤسسات مختلفةبالإضافة إلى ذلك، هناك
+
+11
+00:00:58,840 --> 00:01:02,620
+مواضيع أخرى بالطبع، في أكتر منها نحن نتكلم عن
+
+12
+00:01:02,620 --> 00:01:05,760
+المصطلحات الأساسية المرتبطة بالمعاملات التجاربية
+
+13
+00:01:05,760 --> 00:01:12,280
+لأبدأ هذه القصة، دعوني أبدأ بسؤال، ما هي مهارات
+
+14
+00:01:12,280 --> 00:01:15,820
+المعاملات التجاربية؟
+
+15
+00:01:15,820 --> 00:01:19,700
+ماذا نعني بمهارات المعاملات التجاربية؟
+
+16
+00:01:24,510 --> 00:01:30,450
+ممكن هم المهارات اللي مرتبطة بالشخصية أو بالمدير
+
+17
+00:01:30,450 --> 00:01:35,070
+نفسه يعني، لديه مهارات تتعلق بالتعامل مع أخرين
+
+18
+00:01:35,070 --> 00:01:41,450
+ومشاركة المعلومات وكيف تتعامل مع المؤسسة ومشاركة
+
+19
+00:01:41,450 --> 00:01:42,570
+المؤسسة ومشاركة المؤسسة ومشاركة المؤسسة ومشاركة
+
+20
+00:01:42,570 --> 00:01:42,830
+المؤسسة ومشاركة المؤسسة ومشاركة المؤسسة ومشاركة
+
+21
+00:01:42,830 --> 00:01:42,890
+المؤسسة ومشاركة المؤسسة ومشاركة المؤسسة ومشاركة
+
+22
+00:01:42,890 --> 00:01:45,350
+المؤسسة ومشاركة المؤسسة ومشاركة المؤسسة ومشاركة
+
+23
+00:01:45,350 --> 00:01:48,050
+المؤسسة ومشاركة
+
+24
+00:01:49,160 --> 00:01:52,100
+Now for each manager or any manager should have
+
+25
+00:01:52,100 --> 00:01:55,600
+some packages of skills okay يعني for example
+
+26
+00:01:55,600 --> 00:01:58,420
+there are technical skills which is important okay
+
+27
+00:01:58,420 --> 00:02:01,860
+but in addition to technical skills there is
+
+28
+00:02:01,860 --> 00:02:06,410
+interpersonal skillsالتي نعتبرها مهمة بالنسبة
+
+29
+00:02:06,410 --> 00:02:11,730
+للشركات أو الهجوم اللذي سنقوم بمعرفته لذلك عندما
+
+30
+00:02:11,730 --> 00:02:16,410
+نتكلم عن مهارات شخصية نتكلم عن المهارات التي يجب
+
+31
+00:02:16,410 --> 00:02:20,070
+أن تساعد الناس أو الرئيسين في المؤسسات لتتعامل مع
+
+32
+00:02:20,070 --> 00:02:23,350
+أخرين بعض هذه المهارات أو المهمة أكتر هي مهارات
+
+33
+00:02:23,350 --> 00:02:26,250
+الرئيسية بإضافة إلى مهارات التcommunication وما
+
+34
+00:02:26,250 --> 00:02:30,250
+إلى ذلك حسنًا الآن هذه المهارات نعتبرها مهمة لماذا
+
+35
+00:02:30,250 --> 00:02:34,710
+هي مهمة؟why interpersonal skills is critical يعني
+
+36
+00:02:34,710 --> 00:02:37,150
+when we talk about technical skills we say that it
+
+37
+00:02:37,150 --> 00:02:39,870
+is very important but when we talk about
+
+38
+00:02:39,870 --> 00:02:43,490
+interpersonal skills we say that it is critical or
+
+39
+00:02:43,490 --> 00:02:45,670
+in a different way we are giving it more
+
+40
+00:02:45,670 --> 00:02:50,860
+importance here why? yesأعتقد أن فهم الإبداع
+
+41
+00:02:50,860 --> 00:02:55,440
+الإبداعي لديه رولة كبيرة ورولة مهمة لإبقاء
+
+42
+00:02:55,440 --> 00:03:02,180
+الموظفين ممتازين، وهو موضوع لأي رئيس أو ممتاز من
+
+43
+00:03:02,180 --> 00:03:09,750
+شركة أو شركة لإبقاء الأموات عالية،وهي السبب في
+
+44
+00:03:09,750 --> 00:03:12,670
+أنها محتاجة، يعني عندما نتحدث عن مهارات متشاركة،
+
+45
+00:03:12,670 --> 00:03:18,670
+هنا نتحدث عن واحد من أهم أو بعض أهم مهارات لتحقيق
+
+46
+00:03:18,670 --> 00:03:21,990
+النتائج، حسنا؟ عندما نتحدث عن مؤسسات، نحتاج مهارات
+
+47
+00:03:21,990 --> 00:03:29,350
+متشاركة لتحسين نفع المؤسسة، بالطبع، لتحسين نفع
+
+48
+00:03:29,350 --> 00:03:33,090
+المؤسسة، نحتاج أولًا لتحسين نفع الشخص الذي يعمل
+
+49
+00:03:33,090 --> 00:03:38,250
+داخل المؤسسةتقل، على سبيل المثال، قيمة الابسنطيز
+
+50
+00:03:38,250 --> 00:03:45,270
+في المجلد، تقل المخاطر، تحل المشاكل، وهذا يجب أن
+
+51
+00:03:45,270 --> 00:03:50,270
+يتم عمله من خلال التعامل مع أخرين، مجلد، نحن نتكلم
+
+52
+00:03:50,270 --> 00:03:54,090
+عن جسد أورجاني، جسد أورجاني، هناك فرقات مختلفة
+
+53
+00:03:54,090 --> 00:03:58,850
+تتعامل مع بعضها البعض، حسنًا؟ لذلك، ليس مسألة ..
+
+54
+00:03:58,850 --> 00:04:06,100
+ليس مثل أسلحة، هنا نتكلم عن الناستتعامل مع مهارات
+
+55
+00:04:06,100 --> 00:04:09,640
+مختلفة ومن هؤلاء الناس بالطبع نفكر ونفهم ونشعر
+
+56
+00:04:09,640 --> 00:04:15,440
+وكذلك وهو السبب ان مهارات مختلفة مهمة هنا مرة أخرى
+
+57
+00:04:15,440 --> 00:04:18,700
+عندما نتكلم عن مهارات تقنيات هي مهمة جدًا هي
+
+58
+00:04:18,700 --> 00:04:23,380
+محتاجة لكي نتعامل مع مجالات مختلفة من العمل لكن في
+
+59
+00:04:23,380 --> 00:04:29,080
+نفس الوقت مهارات مختلفة هي ايضاوهو مهم جدًا، ونقول
+
+60
+00:04:29,080 --> 00:04:34,460
+إنه مهم جدًا، لماذا؟ لأنه مهم أن نتعامل مع أشخاص
+
+61
+00:04:34,460 --> 00:04:38,040
+مختلفة، أشخاص يعملون داخل المؤسسة، وهذا يجب أن
+
+62
+00:04:38,040 --> 00:04:42,560
+يتحسن قوة المؤسسة لتحقيق أفضل نتائج عندما يتعلق
+
+63
+00:04:42,560 --> 00:04:48,230
+بالإدارة والأشياء المرتبطة معالعمل، الآن لماذا هو
+
+64
+00:04:48,230 --> 00:04:52,730
+مهم مرة أخرى؟ وانه مهم ان تحسن مستمرًا هؤلاء
+
+65
+00:04:52,730 --> 00:04:55,930
+القدرات وعندما نتكلم عن القدرات التجارية، انه
+
+66
+00:04:55,930 --> 00:05:03,070
+أيضًا مهم ان تعمل مستمرًا لتحسن أو تحسن هؤلاء
+
+67
+00:05:03,070 --> 00:05:04,370
+القدرات
+
+68
+00:05:06,890 --> 00:05:10,870
+ربما تخلق مجال عمل مدينة مدينة مدينة مدينة مدينة
+
+69
+00:05:10,870 --> 00:05:11,450
+مدينة مدينة مدينة مدينة مدينة مدينة مدينة مدينة
+
+70
+00:05:11,450 --> 00:05:15,010
+مدينة مدينة مدينة مدينة مدينة مدينة مدينة مدينة
+
+71
+00:05:15,010 --> 00:05:23,690
+مدينة مدينة مدينة مدينة مدينة مدينة مدينة مدينة
+
+72
+00:05:23,690 --> 00:05:27,210
+مدينة مدينة
+
+73
+00:05:27,590 --> 00:05:31,070
+لأن بعد كل شيء الرومانية هي إسراء، يعني كل واحد
+
+74
+00:05:31,070 --> 00:05:36,210
+يجب أن يعمل و يتواصل مع بعضهما لإعطاء أشياء جودة
+
+75
+00:05:36,210 --> 00:05:42,250
+جيدة أو أي شيء أو .. هذا صحيح، لكن دعنا نفكر بشكل
+
+76
+00:05:42,250 --> 00:05:46,330
+خارجي، يعني الأشياء التي تتحدث عنها حتى الآن هي
+
+77
+00:05:46,330 --> 00:05:49,750
+مرتبطة بالorganization نفسها، وهي المهمة، لكن دعنا
+
+78
+00:05:49,750 --> 00:05:54,490
+نفكر خارج الorganization أعتقد أنه لا .. لا يوجد
+
+79
+00:05:54,490 --> 00:05:58,970
+..هياركيز كما كانت قبلها، لذلك عندما يتعلق
+
+80
+00:05:58,970 --> 00:06:02,250
+بالorganization هي أكتر مفتوحة و تتعامل مع الاخرين
+
+81
+00:06:02,250 --> 00:06:06,290
+بشكل عام أو بشكل عام أو بشكل عام أو بشكل عام أو
+
+82
+00:06:06,290 --> 00:06:07,550
+بشكل عام او بشكل عام او بشكل عام او بشكل عام او
+
+83
+00:06:07,550 --> 00:06:11,030
+بشكل عام او بشكل عام او بشكل عام او بشكل عام او
+
+84
+00:06:11,030 --> 00:06:13,750
+بشكل عام او بشكل عام او بشكل عام او بشكل عام او
+
+85
+00:06:13,750 --> 00:06:15,130
+بشكل عام او بشكل عام او بشكل عام او بشكل عام او
+
+86
+00:06:15,130 --> 00:06:17,130
+بشكل عام او بشكل عام او بشكل عام او بشكل عام او
+
+87
+00:06:17,130 --> 00:06:22,110
+بشكل عام او بشكل
+
+88
+00:06:22,110 --> 00:06:24,870
+عامand at the same time we are talking about an
+
+89
+00:06:24,870 --> 00:06:26,910
+environment which is not static, we are talking
+
+90
+00:06:26,910 --> 00:06:30,070
+about dynamic and very dynamic environment usually
+
+91
+00:06:30,070 --> 00:06:34,290
+okay so it is important to always enhance or
+
+92
+00:06:34,290 --> 00:06:38,550
+improve the competences or interpersonal skills
+
+93
+00:06:38,550 --> 00:06:42,310
+again when you talk about skills, when you talk
+
+94
+00:06:42,310 --> 00:06:45,610
+about abilities it is important to have skills, to
+
+95
+00:06:45,610 --> 00:06:47,950
+have competences, to have abilities but what is
+
+96
+00:06:47,950 --> 00:06:50,630
+more important always is to develop those
+
+97
+00:06:50,630 --> 00:06:54,020
+competences, skills, abilitiesلماذا؟ لأنه دائما
+
+98
+00:06:54,020 --> 00:06:59,560
+يوجد أشخاص أخرون يقاتلون معنا، ونحتاج لإيجاب أفضل
+
+99
+00:06:59,560 --> 00:07:03,340
+نتيجة، وهذا يعني أننا نحتاج أن نحفظ قدراتنا
+
+100
+00:07:03,340 --> 00:07:09,050
+ومقداراتنا على مبادئ مستمر، حسنا؟سلسلة التعامل
+
+101
+00:07:09,050 --> 00:07:13,450
+الإجتماعي، هنا يجب أن نتحدث عن المدير وما يفعله
+
+102
+00:07:13,450 --> 00:07:16,970
+المدير في المؤسسات، طبعا، السلسلة التعامل
+
+103
+00:07:16,970 --> 00:07:20,890
+الإجتماعي ليست فقط .. ليست فقط سلسلة التي يجب أن
+
+104
+00:07:20,890 --> 00:07:23,110
+تكون للمدير بها، نحن نتحدث عن السلسلة التي يجب أن
+
+105
+00:07:23,110 --> 00:07:27,350
+تكون لكل موظف في المؤسسات، لكن عندما نتحدث عن
+
+106
+00:07:27,350 --> 00:07:31,850
+المدير، ربما نتحدث هنا عن المهمة المرتبطية في تلك
+
+107
+00:07:31,850 --> 00:07:35,270
+السلسلة، يعني المدير يجب أن يدرس الآخرين، يجب
+
+108
+00:07:37,290 --> 00:07:41,310
+Manage other people, they are the people who must
+
+109
+00:07:41,310 --> 00:07:45,590
+take decisions in order to give space for others
+
+110
+00:07:45,590 --> 00:07:48,130
+to accomplish different duties and
+
+111
+00:07:48,130 --> 00:07:53,490
+responsibilities Who's manager? Who is the
+
+112
+00:07:53,490 --> 00:07:58,790
+manager? The person who is responsible for
+
+113
+00:07:58,790 --> 00:08:04,530
+managing the organizationمن خلال التنظيف و التنظيف
+
+114
+00:08:04,530 --> 00:08:08,750
+و التنظيف و التنظيف و التنظيف و التنظيف و التنظيف
+
+115
+00:08:08,750 --> 00:08:09,930
+و التنظيف و التنظيف و التنظيف و التنظيف و التنظيف
+
+116
+00:08:09,930 --> 00:08:11,810
+و التنظيف و التنظيف و التنظيف و التنظيف و التنظيف
+
+117
+00:08:11,810 --> 00:08:11,870
+و التنظيف و التنظيف و التنظيف و التنظيف و التنظيف
+
+118
+00:08:11,870 --> 00:08:12,090
+و التنظيف و التنظيف و التنظيف و التنظيف و التنظيف
+
+119
+00:08:12,090 --> 00:08:12,210
+و التنظيف و التنظيف و التنظيف و التنظيف و التنظيف
+
+120
+00:08:12,210 --> 00:08:12,330
+و التنظيف و التنظيف و التنظيف و التنظيف و التنظيف
+
+121
+00:08:12,330 --> 00:08:12,890
+و التنظيف و التنظيف و التنظيف و التنظيف و التنظيف
+
+122
+00:08:12,890 --> 00:08:25,230
+و التنظيف و التنظيف و
+
+123
+00:08:25,350 --> 00:08:32,130
+all the organization stuff planning projects all
+
+124
+00:08:32,130 --> 00:08:36,350
+the organization how may I say it what is about
+
+125
+00:08:36,350 --> 00:08:40,010
+the employees okay but يعني okay when we talk
+
+126
+00:08:40,010 --> 00:08:43,130
+about management we say that management in
+
+127
+00:08:43,130 --> 00:08:46,290
+management we deal with four basic functions
+
+128
+00:08:46,290 --> 00:08:49,150
+planning organizing leading and controlling okay
+
+129
+00:08:49,150 --> 00:08:53,580
+why we need those functions?yes to accomplish the
+
+130
+00:08:53,580 --> 00:08:55,740
+organizational goals and objectives okay it is
+
+131
+00:08:55,740 --> 00:08:57,720
+important to achieve organizational goals and
+
+132
+00:08:57,720 --> 00:09:00,400
+objectives so when we talk about managers the main
+
+133
+00:09:00,400 --> 00:09:03,300
+important role of managers is to get things done
+
+134
+00:09:03,300 --> 00:09:06,680
+or to achieve goals and objectives this is the
+
+135
+00:09:06,680 --> 00:09:10,460
+most important rule when we talk about managers
+
+136
+00:09:10,460 --> 00:09:14,200
+okay in order to get things done or achieve goals
+
+137
+00:09:14,200 --> 00:09:16,660
+and objectives of course through others using
+
+138
+00:09:16,660 --> 00:09:20,790
+different resources and so onهم يحتاجون للعمل داخل
+
+139
+00:09:20,790 --> 00:09:26,810
+المؤسفة وداخل المؤسفة يحتاجون للإستخدام منظومات
+
+140
+00:09:26,810 --> 00:09:30,530
+رئيسية التي سنتحدث عنها لاحقا، لكن ماذا يعني
+
+141
+00:09:30,530 --> 00:09:36,350
+مؤسفة؟هم مثلًا مجتمع من الناس اللي يعمل و يتعامل
+
+142
+00:09:36,350 --> 00:09:39,370
+مع بعضهم البعض لتحقيق القواعد الانتجارية و هذا ما
+
+143
+00:09:39,370 --> 00:09:43,050
+قلت قبل قليل من الوقت عندما نتحدث عن انتجارات نحن
+
+144
+00:09:43,050 --> 00:09:47,410
+نتحدث عن جسدان انتجاري يتعامل مع بعضهم البعض عندما
+
+145
+00:09:47,410 --> 00:09:52,270
+نتحدث عن انتجار نحن نتحدث هنا عن جسد يحتوي على
+
+146
+00:09:52,270 --> 00:09:55,850
+اكثر من اثنين اشخاص يعملوا مع بعضهم البعض بالطبع
+
+147
+00:09:55,850 --> 00:10:00,170
+في مؤسسات كبيرة يوجد عشر آلاف أشخاص و أحيانًا ألف
+
+148
+00:10:00,170 --> 00:10:04,970
+آلاف أشخاص يعملوا مع بعضهم البعضوشركة طبعا كل هذه
+
+149
+00:10:04,970 --> 00:10:08,570
+الناس في طريقة معينة يجب أن تتعامل مع بعضها البعض
+
+150
+00:10:08,570 --> 00:10:12,730
+لذلك عندما نتكلم عن الشركات هنا نتكلم عن مجلس
+
+151
+00:10:12,730 --> 00:10:19,170
+مجتمع متعامل مع بعض الناس يعملوا مع بعضهم البعض و
+
+152
+00:10:19,170 --> 00:10:22,890
+يتعاملوا مع بعضهم البعض بالطبع لإنهاء مهارات
+
+153
+00:10:22,890 --> 00:10:24,490
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+154
+00:10:24,490 --> 00:10:26,950
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+155
+00:10:26,950 --> 00:10:28,350
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+156
+00:10:28,350 --> 00:10:33,040
+ومهارات ومهارات ومهارات ومهارات ومماذا هو
+
+157
+00:10:33,040 --> 00:10:42,560
+الانتجام؟ ماذا هو الانتجام؟ نعم؟ إنه البرنامج
+
+158
+00:10:42,560 --> 00:10:46,320
+لتنظيم وإنشاء ومحكمة وإدارة وإدارة وإدارة وإدارة
+
+159
+00:10:46,320 --> 00:10:48,900
+وإدارة وإدارة وإدارة وإدارة وإدارة وإدارة وإدارة
+
+160
+00:10:48,900 --> 00:10:50,200
+وإدارة وإدارة وإدارة وإدارة وإدارة وإدارة وإدارة
+
+161
+00:10:50,200 --> 00:10:51,280
+وإدارة وإدارة وإدارة وإدارة وإدارة وإدارة وإدارة
+
+162
+00:10:51,280 --> 00:10:52,320
+وإدارة وإدارة وإدارة وإدارة وإدارة وإدارة وإدارة
+
+163
+00:10:52,320 --> 00:10:56,540
+وإدارة
+
+164
+00:10:56,540 --> 00:11:03,810
+وإدارة وإدارة وإدارما هي المصادر المهمة اللي
+
+165
+00:11:03,810 --> 00:11:10,750
+نحتاجها لتحقيق مهارات ومهارات ومهارات؟ مصادر،
+
+166
+00:11:10,750 --> 00:11:13,130
+مصادر، مصادر، مصادر، مصادر، مصادر، مصادر، مصادر،
+
+167
+00:11:13,130 --> 00:11:13,210
+مصادر، مصادر، مصادر، مصادر، مصادر، مصادر، مصادر،
+
+168
+00:11:13,210 --> 00:11:14,950
+مصادر، مصادر، مصادر، مصادر، مصادر، مصادر، مصادر،
+
+169
+00:11:14,950 --> 00:11:15,010
+مصادر، مصادر، مصادر، مصادر، مصادر، مصادر، مصادر،
+
+170
+00:11:15,010 --> 00:11:19,610
+مصادر، مصادر، مصادر، مصادر، مصادر، مصادر، مصادر،
+
+171
+00:11:19,610 --> 00:11:24,160
+مصادر، مصادرHuman resources, money, machinery,
+
+172
+00:11:24,520 --> 00:11:27,880
+equipment and so on and raw material okay So when
+
+173
+00:11:27,880 --> 00:11:30,080
+we talk about resources one of the most important
+
+174
+00:11:30,080 --> 00:11:33,100
+resources is a human resource okay And here again
+
+175
+00:11:33,100 --> 00:11:35,540
+we need to go back to discuss the basic concepts
+
+176
+00:11:35,540 --> 00:11:38,920
+related to organization behavior Now in your
+
+177
+00:11:38,920 --> 00:11:41,860
+studying while you are studying management okay
+
+178
+00:11:41,860 --> 00:11:46,690
+business administrationتدرس فقط اتجارات مرتبطة
+
+179
+00:11:46,690 --> 00:11:48,930
+بشكل مباشر مع مصادر الإنسان، وهو عملية عملية مصادر
+
+180
+00:11:48,930 --> 00:11:52,310
+الإنسان ومعالجة العملية العملية العملية العملية
+
+181
+00:11:52,310 --> 00:11:54,030
+العملية العملية العملية العملية العملية العملية
+
+182
+00:11:54,030 --> 00:11:55,410
+العملية العملية العملية العملية العملية العملية
+
+183
+00:11:55,410 --> 00:11:58,610
+العملية العملية العملية العملية العملية العملية
+
+184
+00:11:58,610 --> 00:12:02,770
+العملية العملية العملية العملية العملية العملية
+
+185
+00:12:02,770 --> 00:12:03,450
+العملية العملية العملية العملية العملية العملية
+
+186
+00:12:03,450 --> 00:12:08,390
+العملية العملية العملية العملية
+
+187
+00:12:08,390 --> 00:12:14,210
+العتعامل مع بعض المدرسات، حيث أنها مدرسات مختلفة.
+
+188
+00:12:14,730 --> 00:12:20,390
+لكي نطور بشكل إيجابي مهارات الإنسان، علينا أن نفهم
+
+189
+00:12:20,390 --> 00:12:25,950
+الهجوم. لذلك، يحتاج أيضًا، لكي نطور بشكل إيجابي
+
+190
+00:12:25,950 --> 00:12:30,430
+مهارات الإنسان، يحتاج أيضًا، لكي نفهم الهجوم.
+
+191
+00:12:32,650 --> 00:12:36,350
+لذلك، مرة أخرى، عندما نتحدث عن الوظيفة، نتحدث عن
+
+192
+00:12:36,350 --> 00:12:43,250
+استخدامأفضل استخدام مصادر متوفرة باستخدام مهارات
+
+193
+00:12:43,250 --> 00:12:46,310
+مختلفة لتحقيق مهارات مؤسسة ومهارات مؤسسة ومهارات
+
+194
+00:12:46,310 --> 00:12:48,210
+مؤسسة ومهارات مؤسسة لتحقيق مهارات مؤسسة ومهارات
+
+195
+00:12:48,210 --> 00:12:48,430
+مؤسسة ومهارات مؤسسة ومهارات مؤسسة ومهارات مؤسسة
+
+196
+00:12:48,430 --> 00:12:48,870
+ومهارات مؤسسة ومهارات مؤسسة ومهارات مؤسسة ومهارات
+
+197
+00:12:48,870 --> 00:12:56,000
+ومهارات مؤسسة ومهارات مؤسسة ومهارات مؤOrganizing,
+
+198
+00:12:56,440 --> 00:13:00,240
+leading and controlling. Okay؟ Those functions it
+
+199
+00:13:00,240 --> 00:13:03,220
+is important to utilize resources in order to
+
+200
+00:13:03,220 --> 00:13:06,240
+achieve organizational goals and objectives. Still
+
+201
+00:13:06,240 --> 00:13:09,880
+we need to discuss more what managers do. Okay؟
+
+202
+00:13:09,880 --> 00:13:13,460
+When you talk about managers, managers play
+
+203
+00:13:13,460 --> 00:13:17,980
+different roles in the organization. Okay؟و في نفس
+
+204
+00:13:17,980 --> 00:13:23,100
+الوقت سنتحدث لاحقا بأن الرئيسين يحتاجون قدرات
+
+205
+00:13:23,100 --> 00:13:28,420
+معينة وكذلك أولا دعنا نتحدث عن القوانين هناك ثلاث
+
+206
+00:13:28,420 --> 00:13:34,520
+قوانين أساسية يجب أن تلعبها الرئيس في المؤسسة
+
+207
+00:13:34,520 --> 00:13:38,880
+القوانين التجاربية القوانين المعلومات
+
+208
+00:13:42,070 --> 00:13:45,250
+القواعد التقليدية، حسنا؟ لذلك عندما نتكلم عن
+
+209
+00:13:45,250 --> 00:13:51,450
+القواعد التقليدية، هنا نتكلم أكتر عن القواعد أو
+
+210
+00:13:51,450 --> 00:13:57,570
+هذه القواعد التي مرتبطة بالتعامل مع الآخرين وما
+
+211
+00:13:57,570 --> 00:14:01,280
+إلى ذلك عندما نتكلم عن القواعد المعلوميةهنا نحن
+
+212
+00:14:01,280 --> 00:14:05,220
+نتكلم عن الهجوم أو الحصول على المعلومات ومن ثم
+
+213
+00:14:05,220 --> 00:14:08,040
+المشاركة من هذه المعلومات لشركات أو شركات مختلفة
+
+214
+00:14:08,040 --> 00:14:09,200
+أو شركات أو شركات مختلفة أو شركات مختلفة أو شركات
+
+215
+00:14:09,200 --> 00:14:09,480
+مختلفة أو شركات مختلفة أو شركات مختلفة أو شركات
+
+216
+00:14:09,480 --> 00:14:11,740
+مختلفة أو شركات مختلفة أو شركات مختلفة أو شركات
+
+217
+00:14:11,740 --> 00:14:13,920
+مختلفة أو شركات مختلفة أو شركات مختلفة أو شركات
+
+218
+00:14:13,920 --> 00:14:13,980
+مختلفة أو شركات مختلفة أو شركات مختلفة أو شركات
+
+219
+00:14:13,980 --> 00:14:14,140
+مختلفة أو شركات مختلفة أو شركات مختلفة أو شركات
+
+220
+00:14:14,140 --> 00:14:19,380
+مختلفة أو شركات مختلفة أو شركات مختلفة أو شركات
+
+221
+00:14:19,380 --> 00:14:28,100
+مختلفة أو
+
+222
+00:14:28,100 --> 00:14:36,510
+شLeader and Liaison who can give me an example for
+
+223
+00:14:36,510 --> 00:14:39,250
+the rule or figurehead rule
+
+224
+00:14:46,920 --> 00:14:51,740
+الرئيس الرئيس هو المدير اللي يمثل مؤسسة أو يعتبر
+
+225
+00:14:51,740 --> 00:14:55,860
+نفسه .. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة
+
+226
+00:14:55,860 --> 00:14:56,000
+.. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة ..
+
+227
+00:14:56,000 --> 00:14:58,960
+مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة
+
+228
+00:14:58,960 --> 00:14:59,280
+.. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة ..
+
+229
+00:14:59,280 --> 00:15:04,000
+مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة
+
+230
+00:15:04,000 --> 00:15:12,780
+.. مؤسسة .. مؤسسة .. مؤسسة .. مؤسسة
+
+231
+00:15:12,780 --> 00:15:18,350
+.. مؤسسة ..is more responsible for the motivation
+
+232
+00:15:18,350 --> 00:15:21,970
+and supporting them okay the managers should
+
+233
+00:15:21,970 --> 00:15:25,490
+support other people working within a organization
+
+234
+00:15:25,490 --> 00:15:28,310
+motivating those employees who are working within
+
+235
+00:15:28,310 --> 00:15:31,270
+the organization this is one of the most important
+
+236
+00:15:31,270 --> 00:15:37,170
+rules of leaders okay to motivate others to guide
+
+237
+00:15:37,170 --> 00:15:42,400
+others and so on okay liaisonhe's the manager who
+
+238
+00:15:42,400 --> 00:15:44,780
+facilitates communication within the organization
+
+239
+00:15:44,780 --> 00:15:47,460
+within the organization between different units,
+
+240
+00:15:47,560 --> 00:15:50,700
+different departments and so on so here we are
+
+241
+00:15:50,700 --> 00:15:53,500
+talking about rules that is related to
+
+242
+00:15:53,500 --> 00:15:57,860
+interacting, communicating with others and so on
+
+243
+00:15:57,860 --> 00:16:00,140
+okay when you talk about interpersonal rules we
+
+244
+00:16:00,140 --> 00:16:02,320
+must not understand that it is only a matter of
+
+245
+00:16:02,320 --> 00:16:05,600
+communication leadership skills is part of
+
+246
+00:16:05,600 --> 00:16:08,860
+interpersonal rules okay communication is another
+
+247
+00:16:08,860 --> 00:16:13,500
+part of interpersonalولكنها ليست فقط التعامل مع
+
+248
+00:16:13,500 --> 00:16:17,420
+الآخرين، بل في أضافة إلى ذلك، الوصول للآخرين وما
+
+249
+00:16:17,420 --> 00:16:22,840
+إلى ذلك، لكنه مهم أن نتعامل مع الآخرين، لكي نتعامل
+
+250
+00:16:22,840 --> 00:16:25,300
+مع الآخرين، يجب أن نكون لدينا مهارات الرئيسية،
+
+251
+00:16:25,300 --> 00:16:28,800
+مهارات التعامل، وما إلى ذلك، حسنًا؟ مجموعة أخرى من
+
+252
+00:16:28,800 --> 00:16:33,260
+القواعد هي القواعد المعلومية، حسنًا؟ هنا نتحدث عن
+
+253
+00:16:33,260 --> 00:16:40,310
+monitorDisseminator in addition to box space okay
+
+254
+00:16:40,310 --> 00:16:45,390
+monitor .. managers must monitor all activities
+
+255
+00:16:45,390 --> 00:16:49,550
+working .. done within the organization Monitoring
+
+256
+00:16:49,550 --> 00:16:52,790
+different activities means that managers are going
+
+257
+00:16:52,790 --> 00:16:59,170
+to collect huge bulk of data okayالتي ستحصل علىها
+
+258
+00:16:59,170 --> 00:17:03,870
+من خلال مقالات مختلفة ومقالات ومقالات ومقالات
+
+259
+00:17:03,870 --> 00:17:04,010
+ومقالات ومقالات ومقالات ومقالات ومقالات ومقالات
+
+260
+00:17:04,010 --> 00:17:04,130
+ومقالات ومقالات ومقالات ومقالات ومقالات ومقالات
+
+261
+00:17:04,130 --> 00:17:04,470
+ومقالات ومقالات ومقالات ومقالات ومقالات ومقالات
+
+262
+00:17:04,470 --> 00:17:06,230
+ومقالات ومقالات ومقالات ومقالات ومقالات ومقالات
+
+263
+00:17:06,230 --> 00:17:06,550
+ومقالات ومقالات ومقالات ومقالات ومقالات ومقالات
+
+264
+00:17:06,550 --> 00:17:12,370
+ومقالات ومقالات ومقالات ومقالات ومقالات ومقالات
+
+265
+00:17:12,370 --> 00:17:23,010
+ومقالات ومقال
+
+266
+00:17:23,110 --> 00:17:26,670
+analyse this data and after that they are going to
+
+267
+00:17:26,670 --> 00:17:30,970
+know which is good for us and which is bad again
+
+268
+00:17:30,970 --> 00:17:33,570
+it's going to be used taking different decisions
+
+269
+00:17:33,570 --> 00:17:36,730
+but also this data yes maybe to apply the problems
+
+270
+00:17:37,440 --> 00:17:40,660
+المهم أيضًا أن لا يكون هناك مشكلة، ولكن مهم أيضًا
+
+271
+00:17:40,660 --> 00:17:45,440
+أيضًا لجميع الشركات والمجتمعات التي تعمل داخل
+
+272
+00:17:45,440 --> 00:17:50,060
+المؤسسة، وهو السبب في القوانين التعليمية الموجودة
+
+273
+00:17:50,060 --> 00:17:55,040
+في هذه القوانين التعليمية الموجودة
+
+274
+00:17:55,040 --> 00:17:59,740
+في هذه القوانين
+
+275
+00:18:07,820 --> 00:18:11,980
+rule here is to provide B with the needed data
+
+276
+00:18:11,980 --> 00:18:17,630
+which was received from A spokespersonsomeone who
+
+277
+00:18:17,630 --> 00:18:20,050
+talks on behalf of the organization okay it is
+
+278
+00:18:20,050 --> 00:18:23,950
+يعني when you talk about there are some activities
+
+279
+00:18:23,950 --> 00:18:27,610
+or rules here which is related to facilitation
+
+280
+00:18:27,610 --> 00:18:31,230
+okay facilitating communication between different
+
+281
+00:18:31,230 --> 00:18:34,110
+units for example like liaison it is like
+
+282
+00:18:34,110 --> 00:18:37,510
+coordinating between different units when you talk
+
+283
+00:18:37,510 --> 00:18:39,650
+about spokesperson here we are talking about the
+
+284
+00:18:39,650 --> 00:18:43,340
+manager representing the organizationExplaining
+
+285
+00:18:43,340 --> 00:18:45,980
+what is the rule, what are the main policies, what
+
+286
+00:18:45,980 --> 00:18:50,680
+are the strategies, directions and so on The third
+
+287
+00:18:50,680 --> 00:18:53,720
+package here is decisional rules When you talk
+
+288
+00:18:53,720 --> 00:18:56,140
+about decisional rules, we are talking about a
+
+289
+00:18:56,140 --> 00:18:58,360
+package of rules which is related to taking
+
+290
+00:18:58,360 --> 00:19:02,200
+decisions Now here there are again different
+
+291
+00:19:02,200 --> 00:19:05,560
+examples Entrepreneur, disturbance handler,
+
+292
+00:19:05,820 --> 00:19:09,640
+resource allocator and negotiator Entrepreneur
+
+293
+00:19:14,810 --> 00:19:20,130
+بس ان maybe creativity creativity is important
+
+294
+00:19:20,130 --> 00:19:27,590
+why؟ one of the most important role of a manager
+
+295
+00:19:27,590 --> 00:19:35,160
+is to decide what is the futureإدارات المؤسسة وإذا
+
+296
+00:19:35,160 --> 00:19:39,300
+كان هناك فرصة معينة التي يجب أن تكون أخذها من
+
+297
+00:19:39,300 --> 00:19:44,960
+المؤسسة المؤسسات يحتاجون الناس لإيجاب ما هي المهام
+
+298
+00:19:44,960 --> 00:19:47,340
+المستقبلية حتى وإذا كنا نتكلم عن اختيارات
+
+299
+00:19:47,340 --> 00:19:51,180
+استراتيجية المؤسسة وما إلى ذلك أشخاص مثهم يجب أن
+
+300
+00:19:51,180 --> 00:19:56,360
+يكونوا مخلصين، حسنًا؟ ولكن هنا نسمّقهم كـPioneers،
+
+301
+00:19:56,360 --> 00:20:02,200
+حسنًا؟ أو كمشروع هنا أو كمشروع، نقول أنأو مؤسسة
+
+302
+00:20:02,200 --> 00:20:05,620
+مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة
+
+303
+00:20:05,620 --> 00:20:08,740
+مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة
+
+304
+00:20:08,740 --> 00:20:11,900
+مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة
+
+305
+00:20:11,900 --> 00:20:14,660
+مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة
+
+306
+00:20:14,660 --> 00:20:17,560
+مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة مؤسسة
+
+307
+00:20:17,560 --> 00:20:28,100
+مؤسسة مؤسسة مؤسسة مؤ
+
+308
+00:20:32,240 --> 00:20:39,600
+yes it is
+
+309
+00:20:39,600 --> 00:20:43,560
+normal that problems happen and someone must deal
+
+310
+00:20:43,560 --> 00:20:45,940
+with the problems okay now the manager role is to
+
+311
+00:20:45,940 --> 00:20:47,940
+deal with different problems happen within the
+
+312
+00:20:47,940 --> 00:20:50,820
+organization whether it is internal or it is
+
+313
+00:20:50,820 --> 00:20:53,660
+external and so on so if there is any internal
+
+314
+00:20:53,660 --> 00:20:56,740
+problem the management should work in order to
+
+315
+00:20:56,740 --> 00:21:00,180
+resolve those problemsوفي نفس الوقت، إذا كان هناك
+
+316
+00:21:00,180 --> 00:21:03,320
+مشاكل خارجية، يجب أيضًا أن يكون هناك قوانين تلقيها
+
+317
+00:21:03,320 --> 00:21:07,280
+المدير هنا لتلقي المشاكل. لذلك، عندما نتكلم عن الـ
+
+318
+00:21:07,280 --> 00:21:12,580
+Disturbance Handling، أي مشكلة تلقيها المدير أو
+
+319
+00:21:12,580 --> 00:21:16,860
+المديرة من المؤسسة، يجب أن يأخذ قرارات لتلقي هذه
+
+320
+00:21:16,860 --> 00:21:20,240
+المشاكل. Resource AllocatorWe said that when we
+
+321
+00:21:20,240 --> 00:21:21,940
+talk about management, we are talking about
+
+322
+00:21:21,940 --> 00:21:24,900
+utilizing resources, using functions in order to
+
+323
+00:21:24,900 --> 00:21:28,320
+achieve goals Yes? Allocate the resources to
+
+324
+00:21:28,320 --> 00:21:33,720
+perform it and take the businesses Okay, so always
+
+325
+00:21:33,720 --> 00:21:36,720
+when you talk about resources, we say that
+
+326
+00:21:36,720 --> 00:21:41,440
+resources is limited Even if it is huge, but at
+
+327
+00:21:41,440 --> 00:21:44,960
+the end it is always limited That's why always it
+
+328
+00:21:44,960 --> 00:21:48,320
+is important to allocate the resources, okay?
+
+329
+00:21:48,860 --> 00:21:54,960
+بالنسبة إلى ماذا سوف نستخدم المصادر؟ المحتاجات
+
+330
+00:21:54,960 --> 00:21:58,700
+الرئيسية من المؤسسات حسنا، و لدينا استراتيجيات،
+
+331
+00:21:58,700 --> 00:22:03,260
+لدينا مخططات عملية، كل مجلس لديه عمليات لتوفيرها،
+
+332
+00:22:03,260 --> 00:22:06,920
+و لتوفير هذه العمليات، هناك احتاجات لها، لذلك يجب
+
+333
+00:22:06,920 --> 00:22:12,640
+أن نطور مجموعة من القرارات لكي نستخدم المصادر، لا
+
+334
+00:22:12,640 --> 00:22:17,730
+احد من المجلسين يجب أن يأخذ أكتر منأو أقل من
+
+335
+00:22:17,730 --> 00:22:23,230
+الحاجة الحقيقية، باعتبار المصادر ومهاراتنا، سنعطي
+
+336
+00:22:23,230 --> 00:22:26,730
+المصادر إلى مجموعات مختلفة في المؤسسة
+
+337
+00:22:32,020 --> 00:22:36,520
+وهو أيضًا مشكلة مهمة أيضًا أن المصادر يجب أن تكون
+
+338
+00:22:36,520 --> 00:22:41,660
+مراقبة لكي نأكد أنها تستخدم بطريقة مفيدة ومفيدة
+
+339
+00:22:41,660 --> 00:22:44,920
+وليس من أجل مفروض الوظيفة وما إلى ذلك، ولكن من أجل
+
+340
+00:22:44,920 --> 00:22:48,060
+مفروض العمل فقط، لذلك حتى لو كانت استخدامة لمفروض
+
+341
+00:22:48,060 --> 00:22:51,780
+العمل، يجب أن نتأكد أنها استخدامة مفيدة وما إلى
+
+342
+00:22:51,780 --> 00:22:53,340
+ذلك، وليس من أجل مفروض العمل، وليس من أجل مفروض
+
+343
+00:22:53,340 --> 00:22:53,700
+العمل، وليس من أجل مفروض العمل، وليس من أجل مفروض
+
+344
+00:22:53,700 --> 00:22:56,040
+العمل، وليس من أجل مفروض العمل، وليس من أجل مفروض
+
+345
+00:22:56,040 --> 00:22:56,240
+الع
+
+346
+00:23:01,420 --> 00:23:04,160
+person or the manager who negotiates and talks
+
+347
+00:23:04,160 --> 00:23:07,720
+with external parties to make like compromises
+
+348
+00:23:07,720 --> 00:23:11,940
+sometimes or agreements and so on okay it is like
+
+349
+00:23:11,940 --> 00:23:16,260
+spokesperson but in a different aspect okay so
+
+350
+00:23:16,260 --> 00:23:19,300
+here we are talking negotiations usually done when
+
+351
+00:23:19,300 --> 00:23:24,280
+there is some sort ofمعاقبات بين الشركات المختلفة
+
+352
+00:23:24,280 --> 00:23:30,240
+ويجب أن نصل إلى اتفاق، حسنًا مؤسسة مونتز اتفاق،
+
+353
+00:23:30,240 --> 00:23:35,580
+ولكن مجدًا التعامل محتاج هنا، ولكن مجدًا عندما
+
+354
+00:23:35,580 --> 00:23:40,620
+نتحدث عن اتفاق هنا، نتحدث عن اتفاق مع شركات أخرى
+
+355
+00:23:40,620 --> 00:23:45,190
+عندما يكون هناك اتفاق لكي نصلإذا كنت تشارك
+
+356
+00:23:45,190 --> 00:23:48,810
+اتفاقات، حسنا؟ الأن هؤلاء هم بعض القوانين التي
+
+357
+00:23:48,810 --> 00:23:52,430
+تلعبها الوظيفة، ويمكنك تخيل هنا كيف هو أهمية عملية
+
+358
+00:23:52,430 --> 00:23:54,650
+العملية العملية العملية العملية العملية عملية
+
+359
+00:23:54,650 --> 00:23:56,110
+العملية عملية العملية عملية العملية عملية العملية
+
+360
+00:23:56,110 --> 00:23:56,190
+عملية العملية عملية العملية عملية العملية عملية
+
+361
+00:23:56,190 --> 00:23:56,510
+العملية عملية العملية عملية العملية عملية العملية
+
+362
+00:23:56,510 --> 00:23:57,030
+عملية العملية عملية العملية عملية العملية عملية
+
+363
+00:23:57,030 --> 00:23:57,110
+العملية عملية العملية عملية العملية عملية العملية
+
+364
+00:23:57,110 --> 00:24:00,770
+عملية العملية عملية العملية عملية العملية عملية
+
+365
+00:24:00,770 --> 00:24:10,280
+العملية عملية العملية عملية العملية عمليةلسنا
+
+366
+00:24:10,280 --> 00:24:15,100
+نتكلم عن السيكولوجيا بشكل عام، نحن نتكلم عن عملاء
+
+367
+00:24:15,100 --> 00:24:19,560
+العمل، وهذا مرتبط بجهة مؤسسة
+
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/Ikc8ylP24Kg_raw.json b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/Ikc8ylP24Kg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..77243d7788f89c086e7a2b06da5e3adbe8cbd903
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/Ikc8ylP24Kg_raw.json
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3794, 3794, 3660], "avg_logprob": -0.6437500143051147, "compression_ratio": 1.4757281553398058, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1449.9, "end": 1450.28, "word": "لسنا", "probability": 0.4717203776041667}, {"start": 1450.28, "end": 1450.6, "word": " نتكلم", "probability": 0.890869140625}, {"start": 1450.6, "end": 1450.82, "word": " عن", "probability": 0.8310546875}, {"start": 1450.82, "end": 1451.42, "word": " السيكولوجيا", "probability": 0.68505859375}, {"start": 1451.42, "end": 1451.6, "word": " بشكل", "probability": 0.6005859375}, {"start": 1451.6, "end": 1451.94, "word": " عام،", "probability": 0.6908365885416666}, {"start": 1451.94, "end": 1453.54, "word": " نحن", "probability": 0.5652669270833334}, {"start": 1453.54, "end": 1454.2, "word": " نتكلم", "probability": 0.75848388671875}, {"start": 1454.2, "end": 1454.4, "word": " عن", "probability": 0.96484375}, {"start": 1454.4, "end": 1455.1, "word": " عملاء", "probability": 0.45135498046875}, {"start": 1455.1, "end": 1456.34, "word": " العمل،", "probability": 0.3428955078125}, {"start": 1456.34, "end": 1457.0, "word": " وهذا", "probability": 0.55615234375}, {"start": 1457.0, "end": 1458.24, "word": " مرتبط", "probability": 0.7203369140625}, {"start": 1458.24, "end": 1458.56, "word": " بجهة", "probability": 0.39996337890625}, {"start": 1458.56, "end": 1459.56, "word": " مؤسسة", "probability": 0.7012939453125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1462.741, "duration_after_vad": 1415.6231249999992}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/KR41VoNPZvs.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/KR41VoNPZvs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..357aca20166a2d9c4b86a3e1b99535680df095ed
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/KR41VoNPZvs.srt
@@ -0,0 +1,1547 @@
+1
+00:00:06,230 --> 00:00:14,450
+لدينا أيضًا نتكلم عن نظرية الدافع و X & Y اليوم
+
+2
+00:00:14,450 --> 00:00:21,390
+سوف نكمل مع بعض هذه النظريات، أولًا سوف نبدأ مع
+
+3
+00:00:21,390 --> 00:00:29,500
+نظرية هيرزبرغ، هذا الفيوري يتكلم 
+
+4
+00:00:29,500 --> 00:00:35,980
+عن مشكلة الدافع، يعني نعرف أن الناس في مواقع 
+
+5
+00:00:35,980 --> 00:00:40,260
+مختلفة يتعاملون مع الإنسان إما بالدافع أو بالإنسان 
+
+6
+00:00:40,260 --> 00:00:45,700
+غير دافع، هنا سنتحدث عن اتصالين مختلفين، الأول هو 
+
+7
+00:00:46,460 --> 00:00:52,980
+التجارب التقليدية التي اقتنعت بها هو أن الناس أو 
+
+8
+00:00:52,980 --> 00:00:54,160
+تفاجئوا أو تفاجئوا أو تفاجئوا أو تفاجئوا أو
+
+9
+00:00:54,160 --> 00:00:55,940
+تفاجئوا أو تفاجئوا أو تفاجئوا أو تفاجئوا أو
+
+10
+00:00:55,940 --> 00:00:57,040
+تفاجئوا أو تفاجئوا أو تفاجئوا أو تفاجئوا أو
+
+11
+00:00:57,040 --> 00:00:57,580
+تفاجئوا أو تفاجئوا أو تفاجئوا أو تفاجئوا أو
+
+12
+00:00:57,580 --> 00:00:58,740
+تفاجئوا أو تفاجئوا أو تفاجئوا أو تفاجئوا أو
+
+13
+00:00:58,740 --> 00:01:03,700
+تفاجئوا أو تفاجئوا أو تفاجئوا أو تفاجئوا أو
+
+14
+00:01:03,700 --> 00:01:07,060
+تفاجئوا
+
+15
+00:01:07,060 --> 00:01:09,540
+أو
+
+16
+00:01:11,780 --> 00:01:17,460
+هيرزبرغ قال أن بين الدافع والدافع لا يوجد مجال
+
+17
+00:01:17,460 --> 00:01:21,100
+آخر، لا يوجد دافع ولا دافع 
+
+18
+00:01:28,420 --> 00:01:32,280
+هو مستوى الدافع، وفي نفس الوقت لا يصلحوا مستوى
+
+19
+00:01:32,280 --> 00:01:38,120
+الدافع، كمان كمان كمان كمان كمان كمان كمان كمان 
+
+20
+00:01:38,120 --> 00:01:38,400
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+21
+00:01:38,400 --> 00:01:40,900
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+22
+00:01:40,900 --> 00:01:41,920
+كمان
+
+23
+00:01:55,960 --> 00:02:02,000
+أيضًا، اقترح أن هناك عوامل مختلفة، أولًا، يسمى
+
+24
+00:02:02,000 --> 00:02:06,320
+العوامل النظافة،  والثاني يسمى العوامل 
+
+25
+00:02:06,320 --> 00:02:10,000
+المحفزة، العوامل 
+
+26
+00:02:10,000 --> 00:02:14,160
+النظافة النظافة النظافة النظافة النظافة
+
+27
+00:02:14,160 --> 00:02:14,540
+النظافة النظافة النظافة النظافة النظافة
+
+28
+00:02:14,540 --> 00:02:16,420
+النظافة النظافة النظافة النظافة النظافة
+
+29
+00:02:16,420 --> 00:02:19,400
+النظافة النظافة النظافة النظافة النظافة
+
+30
+00:02:19,400 --> 00:02:20,580
+النظافة النظافة النظافة النظافة النظافة
+
+31
+00:02:20,580 --> 00:02:24,220
+النظافة
+
+32
+00:02:24,240 --> 00:02:26,840
+لذلك إذا لم يكن هناك عوامل النظافة ممنوعة من 
+
+33
+00:02:26,840 --> 00:02:31,740
+المؤسسة، فهنا نستطيع أن نتحدث عن الدافع من
+
+34
+00:02:31,740 --> 00:02:34,780
+الموظفين، ولكن إذا كانت الموظفين ممنوعة من
+
+35
+00:02:34,780 --> 00:02:38,480
+المؤسسة، فهذا لا يعني أن هناك دافع، فهذا يعني
+
+36
+00:02:38,480 --> 00:02:40,980
+أنه لا يوجد دافع
+
+37
+00:02:43,030 --> 00:02:47,010
+الثاني هو العوامل المحفزة، عندما تتكلم عن
+
+38
+00:02:47,010 --> 00:02:50,650
+العوامل المحفزة، ولا تقدر تقدر تقدر تقدر تقدر
+
+39
+00:02:50,650 --> 00:02:51,710
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+40
+00:02:51,710 --> 00:02:53,390
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+41
+00:02:53,390 --> 00:02:55,030
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+42
+00:02:55,030 --> 00:02:55,250
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+43
+00:02:55,250 --> 00:02:56,610
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+44
+00:02:56,610 --> 00:02:59,740
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر الآن إذا
+
+45
+00:02:59,740 --> 00:03:03,700
+كانت هذه المصادر موفقة من المؤسسة، فهنا يمكننا 
+
+46
+00:03:03,700 --> 00:03:10,140
+نتكلم عن الدافع، هذه كانت نظرية Herzberg، دعونا 
+
+47
+00:03:10,140 --> 00:03:14,840
+نأخذ بعض الأمثلة عن العوامل النظافة والمحفوظة،
+
+48
+00:03:14,840 --> 00:03:21,180
+بالطبع العوامل النظافة هي عوامل أساسية، يعني
+
+49
+00:03:21,180 --> 00:03:27,320
+مثلما نتكلم عن الراتب، المساعدة، وشركات، مؤسسات
+
+50
+00:03:27,320 --> 00:03:31,100
+ومؤسسات ومؤسسات ومؤسسات ومؤسسات
+
+51
+00:03:35,930 --> 00:03:39,550
+العوامل المحفوظة، عندما نتكلم عن العوامل المحفوظة
+
+52
+00:03:39,550 --> 00:03:43,930
+هنا نتكلم عن العوامل المحفوظة، يعني in level it is 
+
+53
+00:03:43,930 --> 00:03:47,190
+like we can say that it is more important for
+
+54
+00:03:47,190 --> 00:03:51,850
+individuals، okay like achievement، recognition، the
+
+55
+00:03:51,850 --> 00:03:54,530
+work design itself، how it is designed and up to
+
+56
+00:03:54,530 --> 00:03:57,790
+what extent it is fulfilling needs of employees
+
+57
+00:03:58,200 --> 00:04:02,460
+وهكذا، وطبعًا المسؤولية في إضافة إلى أشياء أخرى، 
+
+58
+00:04:02,460 --> 00:04:06,100
+فهذه الأشياء هي جزء من النظافة وهي جزء من
+
+59
+00:04:06,100 --> 00:04:06,860
+النظافة وهي جزء من النظافة وهي جزء من 
+
+60
+00:04:06,860 --> 00:04:10,380
+النظافة وهي جزء من النظافة وهي جزء من 
+
+61
+00:04:10,380 --> 00:04:12,300
+النظافة وهي جزء من الطبيعة
+
+62
+00:04:14,830 --> 00:04:20,830
+عن طريق ملاحظة هيرزبرغ، كان ينصح بأن هناك جزء 
+
+63
+00:04:20,830 --> 00:04:25,470
+أساسي بين الدافع والدافع، وفي هذه المنطقة لا 
+
+64
+00:04:25,470 --> 00:04:29,550
+يوجد دافع، وفي نفس الوقت لا يوجد دافع، مثلًا إذا 
+
+65
+00:04:29,550 --> 00:04:35,980
+كان الناس لا يشعرون بأي شيء تجاه عمله، طبعًا، كيف
+
+66
+00:04:35,980 --> 00:04:39,500
+تتأكد أن الموظفين ليسوا غاضبين، يجب أن تتأكد أن 
+
+67
+00:04:39,500 --> 00:04:42,720
+المؤسسة تقدر تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+68
+00:04:42,720 --> 00:04:46,140
+تقدر
+
+69
+00:04:46,140 --> 00:04:48,180
+تقدر
+
+70
+00:04:58,300 --> 00:05:10,380
+المهم هو المشكلة المهمة
+
+71
+00:05:10,380 --> 00:05:16,520
+المهمة المهمة
+
+72
+00:05:16,520 --> 00:05:21,720
+المهمة المهمة المهمة المهمة المهمة المهمة المهمة
+
+73
+00:05:32,030 --> 00:05:35,870
+ماذا يعني ذلك؟ إذا كان هناك مقاطع أساسية بين
+
+74
+00:05:35,870 --> 00:05:41,610
+الدافع والدافع الخاطئ؟ لقد تحدثنا عن الدافع 
+
+75
+00:05:41,610 --> 00:05:45,770
+السابق، قلنا إن هناك طرقًا مختلفة لتحسين الدافع،
+
+76
+00:05:45,770 --> 00:05:50,150
+قلنا إننا نستطيع استخدام سؤال واحد بسيط لنسأل 
+
+77
+00:05:50,150 --> 00:05:52,690
+المستخدم إذا كانوا مستمتعين أو لا، أو نستطيع
+
+78
+00:05:52,690 --> 00:05:58,310
+استخدام الأسئلة والتحديدات لكي نعرف في ما هي
+
+79
+00:05:58,310 --> 00:06:03,650
+المناطق التي تشجعها أو لا تشجعها في ذلك الوقت، إذا
+
+80
+00:06:03,650 --> 00:06:07,790
+تذكر، قلنا إننا نسأل أسئلة واحدة بسيطة، وهذه ستجلب
+
+81
+00:06:07,790 --> 00:06:12,290
+لنا معلومات مرتبطة بالتشجيع بشكل عام، إذا كانت 
+
+82
+00:06:12,290 --> 00:06:16,070
+عميلنا تشجع أو لا، لكن إذا كنت تريد أن تعرف لماذا
+
+83
+00:06:16,070 --> 00:06:21,150
+يشجعونه أو من ماذا يشجعونه، فيجب أن نستخدم أدوات 
+
+84
+00:06:21,150 --> 00:06:28,190
+أكثر لتحقيق هذه المشكلة، أعني هنا لكي نعرف ماذا هي
+
+85
+00:06:28,190 --> 00:06:35,710
+السبب في انخفاض الدافع؟ هذا يعني أنه لا يوجد علاقة
+
+86
+00:06:35,710 --> 00:06:40,230
+مباشرة بين الانخفاض والدافع، بعض الناس يعتقدون أن 
+
+87
+00:06:40,230 --> 00:06:47,110
+الانخفاض والدافع هو مثل طريقة التي يتحرك الناس من
+
+88
+00:06:47,110 --> 00:06:52,870
+الانخفاض إلى الدافع أو عكس من الدافع إلى انخفاض
+
+89
+00:06:52,870 --> 00:06:58,680
+لكنه ليس بهذه الطريقة، ليس بهذه الطريقة، عادةً نحن
+
+90
+00:06:58,680 --> 00:07:02,680
+مستمتعين من أشياء معينة وفي نفس الوقت نكون غير
+
+91
+00:07:02,680 --> 00:07:07,040
+مستمتعين من أشياء أخرى، لذلك هنا لسنا نتكلم عن 
+
+92
+00:07:07,040 --> 00:07:12,480
+شعورين مختلفين، عندما نتكلم عن مستمتع وغير مستمتع، 
+
+93
+00:07:12,480 --> 00:07:18,180
+لا، نحن نتكلم عن أشخاص مختلفين، ممكن يشعروا بأنهم
+
+94
+00:07:18,180 --> 00:07:22,200
+مستمتعون من شيء وفي نفس الوقت ممكن يشعروا بأنهم
+
+95
+00:07:22,200 --> 00:07:27,620
+مستمتعون من شيء آخر، لماذا؟ لأننا لا نتحدث عن نفس
+
+96
+00:07:27,620 --> 00:07:31,720
+البرنامج هنا أو لا نتحدث عن مشاكل مختلفة، نحن نتحدث
+
+97
+00:07:31,720 --> 00:07:35,120
+هنا مرة أخرى عن تصميمات مختلفة، تصميمات مختلفة يعني 
+
+98
+00:07:35,120 --> 00:07:42,590
+أن كل واحد، عندما نتكلم عن شعور أو شعور، نتكلم عن
+
+99
+00:07:42,590 --> 00:07:46,830
+حالات مختلفة، نتكلم عن حالات مختلفة، نتكلم عن 
+
+100
+00:07:46,830 --> 00:07:53,190
+شعور مختلف، وممكن أن الموظفين يشعروا بشعور من 
+
+101
+00:07:53,190 --> 00:07:57,570
+شيء آخر، ولكن في نفس الوقت يشعروا بشعور من شيء 
+
+102
+00:07:57,570 --> 00:07:58,190
+آخر
+
+103
+00:08:01,540 --> 00:08:06,320
+هنا، يعني، أحد الأشياء المهمة هي أن المؤسسات يجب 
+
+104
+00:08:06,320 --> 00:08:10,500
+أن تفكر في كيفية تقليل هذا الانخفاض، وفي نفس 
+
+105
+00:08:10,500 --> 00:08:15,820
+الوقت يجب أن تفكر في كيفية إزالة الانخفاض، بدلًا 
+
+106
+00:08:15,820 --> 00:08:20,340
+من أن تلك المشكلة تكون مفاجئة، كما تسمى بـ
+
+107
+00:08:20,340 --> 00:08:24,830
+Herzberg، ولكن هنا نهتم أكثر بالاتصالات أن هناك بعض
+
+108
+00:08:24,830 --> 00:08:28,450
+العوامل، إذا كانت تأخذ من المؤسسة على الأقل
+
+109
+00:08:28,450 --> 00:08:34,150
+المؤسسة ستؤكد أنه لا يوجد مفاجأة، إذا لم يكن هناك
+
+110
+00:08:34,150 --> 00:08:38,670
+مفاجأة، فهناك تحكم جيد على عدد الانتقال، عدد
+
+111
+00:08:38,670 --> 00:08:41,290
+الانتقال، عدد العمل المساعد، عدد العمل المساعد،
+
+112
+00:08:41,290 --> 00:08:41,830
+المساعد، عدد العمل المساعد، عدد العمل المساعد،
+
+113
+00:08:41,830 --> 00:08:44,290
+العمل المساعد، عدد العمل المساعد، عدد العمل
+
+114
+00:08:44,290 --> 00:08:50,450
+المساعد، عدد العمل المساعد، عدد العمل المساعد، إذا
+
+115
+00:08:50,450 --> 00:08:55,010
+ازدادنا بشكل مستمر، فنستطيع أن نتكلم عن نتيجة أفضل
+
+116
+00:08:55,010 --> 00:09:00,310
+التي تم إجرائها في المؤسسة، هنا دعونا نقوم بالتحديث عن 
+
+117
+00:09:00,310 --> 00:09:04,020
+هيرزبرغ، تفاصيل تفاصيل تفاصيل تفاصيل تفاصيل تفاصيل
+
+118
+00:09:04,020 --> 00:09:06,060
+تفاصيل تفاصيل تفاصيل تفاصيل تفاصيل تفاصيل تفاصيل
+
+119
+00:09:06,060 --> 00:09:16,340
+تفاصيل تفاصيل تفاصيل تفاصيل تفاصيل تفاصيل
+
+120
+00:09:16,340 --> 00:09:20,800
+تفاصيل تفاصيل تفاصيل تفاصيل تفاصيل تفاصيل تفاصيل
+
+121
+00:09:21,970 --> 00:09:26,430
+نقول أن الناس عادةً إذا فعلوا شيء صحيح سيسمون هذا
+
+122
+00:09:26,430 --> 00:09:31,830
+ لأنفسهم، وإذا واجهوا أو فعلوا شيء غير صحيح سيسمون
+
+123
+00:09:31,830 --> 00:09:37,430
+هذا للأشخاص الآخرين أو سيُعَذِّبون أشخاصًا آخرين، وهذا يعني 
+
+124
+00:09:37,430 --> 00:09:44,110
+أن الناس عادةً سيُعَذِّبون المؤسسة أو المدير، خاصة
+
+125
+00:09:44,110 --> 00:09:47,450
+عندما نتحدث عن هذا الشعور، وإذا كان هناك شيء متعلق
+
+126
+00:09:47,450 --> 00:09:54,980
+بالشعور، فربما يقوموا بإعادة هذا إلى عملهم وإعادة 
+
+127
+00:09:54,980 --> 00:09:58,840
+عملهم وإعادة عملهم وإعادة عملهم وإعادة عملهم
+
+128
+00:09:58,840 --> 00:09:58,860
+وإعادة عملهم وإعادة عملهم وإعادة عملهم وإعادة
+
+129
+00:09:58,860 --> 00:09:59,340
+عملهم وإعادة عملهم وإعادة عملهم وإعادة عملهم
+
+130
+00:09:59,340 --> 00:10:00,900
+وإعادة عملهم وإعادة عملهم وإعادة عملهم وإعادة
+
+131
+00:10:00,900 --> 00:10:08,560
+عملهم وإعادة عملهم وإعادة عملهم وإعادة
+
+132
+00:10:08,560 --> 00:10:13,300
+عملهم وإعادة العمل، بالإضافة إلى النقطة الأولى التي 
+
+133
+00:10:13,300 --> 00:10:19,220
+تشير إلى أن الناس عادةً يتعاني من أو يكون لديه نوع
+
+134
+00:10:19,220 --> 00:10:22,720
+من الاضطرابات الخاصة، نستطيع أيضًا أن نقول هنا أن 
+
+135
+00:10:22,720 --> 00:10:28,860
+هناك اضطرابات أخرى وأخطاء مرتبطة بالوضع نفسه وكيف 
+
+136
+00:10:28,860 --> 00:10:32,080
+سيقوم الموظفين بالتحقق من جميع هذه المشكلة التي 
+
+137
+00:10:32,080 --> 00:10:38,940
+يجب أن تكون مواصلة من مؤسسة، هيرزبرغ عندما اقترح أو 
+
+138
+00:10:38,940 --> 00:10:44,450
+طور هذه النظرية، لأنه لم يستخدم مصادر محددة لتقوم
+
+139
+00:10:44,450 --> 00:10:51,550
+بمجارة الدافع، كانت نوع من نظرية حيبوتية التي
+
+140
+00:10:51,550 --> 00:10:56,670
+كانت مقترحة من هيرزبرغ، لكنه لم يكن هناك مقارنة من 
+
+141
+00:10:56,670 --> 00:11:01,030
+الانتصار، بمعنى أنه لم يحاول أن يكتشف لماذا
+
+142
+00:11:01,030 --> 00:11:05,190
+الموظفون مستمتعون ولماذا في حالات أخرى مستمتعون،
+
+143
+00:11:05,190 --> 00:11:07,270
+فهو فقط رسم المدالة
+
+144
+00:11:14,250 --> 00:11:21,610
+ولا يستخدم أي من الأدوات التي يمكن استخدامها لتقوم 
+
+145
+00:11:21,610 --> 00:11:24,110
+بتقديم الإنتاج وقبل قليل من الوقت قبل قليل من
+
+146
+00:11:24,110 --> 00:11:24,990
+الوقت قبل قليل من الوقت قبل قليل من الوقت قبل قليل
+
+147
+00:11:24,990 --> 00:11:26,410
+من الوقت قبل قليل من الوقت قبل قليل من الوقت قبل
+
+148
+00:11:26,410 --> 00:11:28,090
+قليل من الوقت قبل قليل من الوقت قبل قليل من الوقت
+
+149
+00:11:28,090 --> 00:11:29,670
+قبل قليل من الوقت
+
+150
+00:11:39,010 --> 00:11:43,690
+هو استخدام تحقيقات أو محاولات أكثر لتحقيق في أي
+
+151
+00:11:43,690 --> 00:11:53,210
+مكان أن موظفون مفاجئون بسبب العمل وهكذا مرة أخرى
+
+152
+00:11:53,210 --> 00:11:56,070
+هنا نحن نتحدث عن نظرية نفسية أخرى
+
+153
+00:11:58,590 --> 00:12:03,450
+هو يقوم بتجارب أكثر من المشاكل و أيضا هيرزبرغ
+
+154
+00:12:03,450 --> 00:12:07,070
+أعتقد أن هناك علاقة ما بين الانتصاف والنشاط 
+
+155
+00:12:07,070 --> 00:12:07,910
+والنشاط والنشاط والنشاط والنشاط والنشاط والنشاط
+
+156
+00:12:07,910 --> 00:12:08,290
+والنشاط والنشاط والنشاط والنشاط والنشاط والنشاط
+
+157
+00:12:08,290 --> 00:12:09,250
+والنشاط والنشاط والنشاط والنشاط والنشاط والنشاط
+
+158
+00:12:09,250 --> 00:12:09,770
+والنشاط والنشاط والنشاط والنشاط والنشاط والنشاط
+
+159
+00:12:09,770 --> 00:12:10,210
+والنشاط والنشاط والنشاط والنشاط والنشاط والنشاط
+
+160
+00:12:10,210 --> 00:12:10,710
+والنشاط والنشاط والنشاط والنشاط والنشاط والنشاط
+
+161
+00:12:10,710 --> 00:12:10,830
+والنشاط والنشاط والنشاط والنشاط والنشاط والنشاط
+
+162
+00:12:10,830 --> 00:12:16,650
+والنشاط والنشاط والـيعني in other words he assumed
+
+163
+00:12:16,650 --> 00:12:20,730
+that without supporting this assumption by a
+
+164
+00:12:20,730 --> 00:12:24,850
+research unlike other issues or other topics we
+
+165
+00:12:24,850 --> 00:12:27,750
+have discussed earlier where we said that there is
+
+166
+00:12:27,750 --> 00:12:30,390
+a relation between productivity and satisfaction
+
+167
+00:12:30,720 --> 00:12:35,160
+ولكن كانت مؤسسة على نوع من المحققين وهنا هيرزبرغ
+
+168
+00:12:35,160 --> 00:12:40,560
+لم يدعم فكرة أن هناك علاقة بين الانتصاف والنشاط
+
+169
+00:12:40,560 --> 00:12:49,700
+بالنوع من المحققين مرة أخرى قبل مرة قبل مرة قبل
+
+170
+00:12:49,700 --> 00:12:51,820
+مرة قبل مرة قبل مرة قبل مرة قبل مرة قبل مرة قبل
+
+171
+00:12:51,820 --> 00:12:53,340
+مرة قبل مرة قبل مرة قبل مرة قبل مرة قبل
+
+172
+00:13:00,790 --> 00:13:08,150
+هنا نستطيع أن نأخذ نقطة مفيدة لنفهم كيف يتعامل
+
+173
+00:13:08,150 --> 00:13:12,170
+الناس عندما يتعلق بالحركة من كل هذه النظريات
+
+174
+00:13:12,170 --> 00:13:15,510
+ولكننا لا يجب أن نأخذ أي نظرية من هذه النظريات
+
+175
+00:13:15,510 --> 00:13:22,290
+كمقياس ولا ننقل أي نوع من تلك النظرات، هناك شيء
+
+176
+00:13:22,290 --> 00:13:27,410
+مفيد في كل نوع من تلك النظرات، وهو النقطة التي يجب
+
+177
+00:13:27,410 --> 00:13:31,470
+أن نركز عليها أكثر عندما نتكلم عن الانتقال الذي
+
+178
+00:13:31,470 --> 00:13:39,330
+نسميه هنا، هنا نتكلم عن الانتقال إلى فتح
+
+179
+00:13:40,850 --> 00:13:44,790
+والتفكير في تقنيات تقنيات تقنيات تقنيات تقنيات
+
+180
+00:13:44,790 --> 00:13:47,570
+تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات
+
+181
+00:13:47,570 --> 00:13:49,670
+تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات
+
+182
+00:13:49,670 --> 00:13:50,290
+تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات
+
+183
+00:13:50,290 --> 00:13:50,350
+تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات
+
+184
+00:13:50,350 --> 00:13:53,010
+تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات
+
+185
+00:13:53,010 --> 00:13:54,110
+تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات
+
+186
+00:13:54,110 --> 00:13:59,110
+تقنيات تقنيات تقنيات تقنيات تقنيات تقنيات
+
+187
+00:13:59,110 --> 00:14:07,550
+تقنيات مكليلاند أيضا هنا نتكلم عن نظرات أساسية
+
+188
+00:14:07,550 --> 00:14:12,730
+الدوافع ونحن نتكلم عن نظرات مصطلحات ونحن نتكلم
+
+189
+00:14:12,730 --> 00:14:18,650
+عن نظرات مصطلحات ونحن نتكلم عن نظرات مصطلحات ونحن
+
+190
+00:14:18,650 --> 00:14:22,510
+نتكلم عن نظرات مصطلحات ونحن نتكلم عن نظرات مصطلحات
+
+191
+00:14:23,000 --> 00:14:26,180
+واحد من هذه النظرات هي نظرات مكليلاند الـ three
+
+192
+00:14:26,180 --> 00:14:28,680
+needs نظرات مكليلاند الـ three needs نظرات مكليلاند
+
+193
+00:14:28,680 --> 00:14:29,100
+نظرات مكليلاند الـ three needs نظرات مكليلاند الـ
+
+194
+00:14:29,100 --> 00:14:29,880
+three needs نظرات مكليلاند الـ three needs نظرات
+
+195
+00:14:29,880 --> 00:14:30,900
+مكليلاند الـ three needs نظرات مكليلاند الـ three
+
+196
+00:14:30,900 --> 00:14:34,540
+needs نظرات مكليلاند الـ three needs نظرات مكليلاند
+
+197
+00:14:34,540 --> 00:14:35,260
+الـ three needs نظرات مكليلاند الـ three needs
+
+198
+00:14:35,260 --> 00:14:37,600
+نظرات مكليلاند الـ three needs نظرات مكليلاند الـ
+
+199
+00:14:37,600 --> 00:14:41,440
+three needs نظرات مكليلاند الـ three needs نظرات
+
+200
+00:14:41,440 --> 00:14:44,480
+مكليلاند الـ three needs نظرات مكليلاند الـ three
+
+201
+00:14:44,480 --> 00:14:50,160
+needs نظرات مكليلاند الـ three عندما نتكلم عن حاجة
+
+202
+00:14:50,160 --> 00:14:56,700
+لإنجاز نحن نتكلم عن حاجة لإنجاز أو لإنجاز أو
+
+203
+00:14:56,700 --> 00:15:00,960
+لإنجاز نحن نتكلم عن حاجة لإنجاز أو لإنجاز نحن
+
+204
+00:15:00,960 --> 00:15:01,180
+نتكلم عن حاجة لإنجاز أو لإنجاز نحن نتكلم عن حاجة
+
+205
+00:15:01,180 --> 00:15:02,340
+لإنجاز نحن نتكلم عن حاجة لإنجاز أو لإنجاز نحن
+
+206
+00:15:02,340 --> 00:15:02,400
+نتكلم عن حاجة لإنجاز نحن نتكلم عن حاجة لإنجاز نحن
+
+207
+00:15:02,400 --> 00:15:02,600
+نتكلم عن حاجة لإنجاز نحن نتكلم عن حاجة لإنجاز نحن
+
+208
+00:15:02,600 --> 00:15:06,300
+نتكلم بهذا المعنى عندما نتحدث عن حاجة للقوة هنا
+
+209
+00:15:06,300 --> 00:15:11,440
+نتحدث عن حاجة للتحكم بالآخرين كيف يقوموا أو يتعاملوا
+
+210
+00:15:11,440 --> 00:15:16,320
+مع عملهم وعندما نتحدث عن حاجة للتواصل هنا نتحدث عن
+
+211
+00:15:16,320 --> 00:15:20,000
+حاجة للتواصل الاجتماعي مع الآخرين نتحدث عن التواصل
+
+212
+00:15:20,000 --> 00:15:23,140
+الاجتماعي أو التواصل الاجتماعي الاجتماعي الاجتماعي
+
+213
+00:15:23,140 --> 00:15:25,180
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماعي
+
+214
+00:15:25,180 --> 00:15:32,460
+الاجتماعي الاجتماعي الاجتماعي الاجتماعي الاجتماع
+
+215
+00:15:32,510 --> 00:15:35,930
+هناك مشكلة يجب أن نتحدث عنها وهي مرتبطة بهذه
+
+216
+00:15:35,930 --> 00:15:41,270
+النظرية بالطبع مثلما تحدثنا عن نظرية مسلوس نقول أن
+
+217
+00:15:41,270 --> 00:15:44,610
+هذه الاحتياجات ليست كلها احتياجات ونفس الشيء عندما
+
+218
+00:15:44,610 --> 00:15:48,910
+تحدثنا عن نظرية ألدرفر للاحتياجات أيضا نظرية
+
+219
+00:15:48,910 --> 00:15:56,480
+الاحتياجات وهو نفس المصطلح وهنا نتحدث عن نفس الأساس
+
+220
+00:15:56,480 --> 00:15:59,900
+أيضا ولكن هناك بعض الأشياء التي يجب أن نتحدث عنها
+
+221
+00:15:59,900 --> 00:16:03,920
+هنا واحدة من هذه الأشياء هي أن الواجهين غالبا لا
+
+222
+00:16:03,920 --> 00:16:10,000
+يتجهون إلى عمليات صعبة وفي نفس الوقت لا يتجهون إلى
+
+223
+00:16:10,000 --> 00:16:11,960
+عمليات بسيطة
+
+224
+00:16:14,870 --> 00:16:21,630
+ما نسميه في حالة الصعوبة 50 50 فرصة للنجاح يعني هم
+
+225
+00:16:21,630 --> 00:16:26,570
+يذهبون للعمل أو العمل الذي ليس بسهولة لكن في نفس
+
+226
+00:16:26,570 --> 00:16:32,330
+الوقت لا يوجد حرص عالي أو ليس صعب كثير لماذا؟
+
+227
+00:16:32,330 --> 00:16:35,550
+لماذا يحصل الوصول للوصول للوصول للوصول للوصول
+
+228
+00:16:35,550 --> 00:16:41,330
+للوصول للوصول للوصول للوصول للوصول للوصول
+
+229
+00:16:41,850 --> 00:16:45,010
+لا يوجد صعوبة عالية ولكن في نفس الوقت لا يوجد
+
+230
+00:16:45,010 --> 00:16:51,010
+صعوبة عالية، إنها تحدي ولكنها ليست ممكنة أو ليست
+
+231
+00:16:51,010 --> 00:17:00,450
+صعبة جدا لماذا؟ لماذا يركزوا على تلك المهارات؟
+
+232
+00:17:00,450 --> 00:17:04,830
+أنا أسمع من اسمهم، إنهم لا يريدون إنجاز، إنهم
+
+233
+00:17:04,830 --> 00:17:07,730
+يريدون إنجاز شيء، إنهم لا يريدون أن يضيعوا وقتهم
+
+234
+00:17:09,140 --> 00:17:13,140
+إذا كانت المهمة صعبة جدًا، فسيكون مضغوط وقت وما
+
+235
+00:17:13,140 --> 00:17:17,880
+إلى ذلك وليس هناك أجهزة وإذا كانت بسيطة، نحن نتحدث
+
+236
+00:17:17,880 --> 00:17:23,200
+هنا عن عدم محاولة، وعادةً يذهبون للوصول للمحاولة
+
+237
+00:17:24,530 --> 00:17:27,690
+وهو ما نسميه عملية صعبة أو عملية صعبة أو عملية
+
+238
+00:17:27,690 --> 00:17:29,830
+صعبة أو عملية صعبة أو عملية صعبة أو عملية صعبة أو
+
+239
+00:17:29,830 --> 00:17:30,410
+عملية صعبة أو عملية صعبة أو عملية صعبة أو عملية
+
+240
+00:17:30,410 --> 00:17:32,730
+صعبة أو عملية صعبة أو عملية صعبة أو عملية صعبة أو
+
+241
+00:17:32,730 --> 00:17:33,390
+عملية صعبة أو عملية صعبة أو عملية صعبة أو عملية
+
+242
+00:17:33,390 --> 00:17:38,310
+صعبة أو عملية صعبة أو عملية صعبة أو عملية صعبة أو
+
+243
+00:17:38,310 --> 00:17:43,570
+صعبة أو عملية صعبة أو عملية صعبة أو عملية صعبة أو
+
+244
+00:17:43,570 --> 00:17:50,560
+عمل هؤلاء الناس يذهبون بعد مهارات أو مهارات مدرسية
+
+245
+00:17:50,560 --> 00:17:52,220
+مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية
+
+246
+00:17:52,220 --> 00:17:53,200
+مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية
+
+247
+00:17:53,200 --> 00:17:55,260
+مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية
+
+248
+00:17:55,260 --> 00:17:56,440
+مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية
+
+249
+00:17:56,440 --> 00:18:07,100
+مدرسية مدرسية مدرسية مدرسية مدرسية مدرسية
+
+250
+00:18:07,100 --> 00:18:11,680
+مدرسية
+
+251
+00:18:11,680 --> 00:18:13,500
+مدر
+
+252
+00:18:16,200 --> 00:18:21,320
+لماذا يقومون بإظهار مستوى أعظم من المسؤولية الخاصة
+
+253
+00:18:21,320 --> 00:18:29,620
+أو المسؤولية الشخصية؟ كيف
+
+254
+00:18:29,620 --> 00:18:32,400
+يستطيعون أن يأخذوا المساعدة للإنجاز إذا لم يقوموا
+
+255
+00:18:32,400 --> 00:18:35,060
+بإقرار المسؤولية الشخصية؟
+
+256
+00:18:39,570 --> 00:18:46,990
+ونحن نتحدث أيضا عن امتحانات أخرى مرتبطة بشخصية
+
+257
+00:18:46,990 --> 00:18:53,230
+نفسها هذا سبب لأن الناس يختارون أو يظهرون عدد
+
+258
+00:18:53,230 --> 00:18:56,630
+كبير من المسؤولية الشخصية، لقد تحدثنا عن ذلك
+
+259
+00:18:56,630 --> 00:19:00,990
+سابقًا، هناك نقطة أخرى مرتبطة بخطر مدرسي لأنها
+
+260
+00:19:00,990 --> 00:19:05,850
+محتاجة للإيقاف، لكن الناس يختارون أيضا إنجاز،
+
+261
+00:19:05,850 --> 00:19:09,950
+فهنا يمكننا أن نقول إن هناك ثلاثة أشكال أساسية
+
+262
+00:19:09,950 --> 00:19:17,110
+مرتبطة بشخصية الناس أو اعتقادهم بطريقة معينة تظهر
+
+263
+00:19:17,110 --> 00:19:21,550
+عدد عالي من مسؤولية الشخصية، لماذا؟ لأنهم يحتاجون
+
+264
+00:19:21,550 --> 00:19:26,610
+أن يعتمدوا على مسؤولية الشخصية، لأن هذا طريقهم  لأخذ
+
+265
+00:19:26,610 --> 00:19:32,350
+المساعدة لتحقيق الإنجاز مرة أخرى هو أنهم يتبعون
+
+266
+00:19:32,350 --> 00:19:32,810
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+267
+00:19:32,810 --> 00:19:33,710
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+268
+00:19:33,710 --> 00:19:35,370
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+269
+00:19:35,370 --> 00:19:42,410
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+270
+00:19:42,410 --> 00:19:43,510
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+271
+00:19:43,510 --> 00:19:43,550
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+272
+00:19:43,550 --> 00:19:45,650
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+273
+00:19:45,650 --> 00:19:55,350
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+274
+00:19:55,350 --> 00:20:03,750
+إذا كان هناك إنجاز يجب أن يكون هناك إنجاز لعملهم
+
+275
+00:20:03,750 --> 00:20:07,550
+إذا كانوا يفعلون شيء خاطئ يريدون أن يقولوا لهم لا
+
+276
+00:20:07,550 --> 00:20:11,640
+تفعلوا بهذه الطريقة فتفعلوا بطريقة أخرى سيكون
+
+277
+00:20:11,640 --> 00:20:15,540
+أسوأ على سبيل المثال هنا نحن نتحدث عن إنجاز من
+
+278
+00:20:15,540 --> 00:20:19,760
+أشياء مختلفة من هنا الأول هو المعرفة من مديرية
+
+279
+00:20:19,760 --> 00:20:23,940
+أعلى مستوى والثاني
+
+280
+00:20:23,940 --> 00:20:30,700
+هو الحصول على إنجاز في حال كان هناك حاجة لتحسين 
+
+281
+00:20:30,700 --> 00:20:34,960
+بعض المهارات وما إلى ذلك مجموعة أخرى مرتبطة مع تلك
+
+282
+00:20:34,960 --> 00:20:43,130
+المواصلين هي أنهم ليسوا مديرين جيدين Usually, high
+
+283
+00:20:43,130 --> 00:20:48,090
+need for achievement does not produce managers،
+
+284
+00:20:48,090 --> 00:20:53,470
+usually it produces more professional people، why؟
+
+285
+00:20:56,490 --> 00:21:01,930
+لماذا أشخاص مثلها ليسوا رئيسين جيدين؟ دعوني أعيد
+
+286
+00:21:01,930 --> 00:21:05,510
+هنا كلماتي، أنا لا أعني أنهم ليسوا رئيسين جيدين، 
+
+287
+00:21:05,510 --> 00:21:09,490
+على الأقل، إنهم لا يوجدوا فرصة جيدة لكي يكونوا
+
+288
+00:21:09,490 --> 00:21:14,890
+رئيسين جيدين
+
+289
+00:21:18,250 --> 00:21:24,290
+هم جيدين في فعالية تجارب مثل هذه، ليس تجارب مثل
+
+290
+00:21:24,290 --> 00:21:30,090
+هذه، إنهم يركزون على شخص واحد فقط
+
+291
+00:21:33,130 --> 00:21:38,530
+الآن دعوني أعود إلى الموضوع 50-50، عندما نقول إنهم
+
+292
+00:21:38,530 --> 00:21:43,030
+يتبعون عمليات عندما يكون هناك فرصة 50-50، المعنى
+
+293
+00:21:43,030 --> 00:21:48,650
+هنا كان إنهم لا يتبعون عمليات بسيطة جدا ولا عمليات
+
+294
+00:21:48,650 --> 00:21:52,490
+صعبة جدا لماذا؟ لأن عندما نتكلم عن عمومات بسيطة، لا
+
+295
+00:21:52,490 --> 00:21:55,890
+يوجد محاولة و عندما نتكلم عن عمومات صعبة جدا، هنا
+
+296
+00:21:55,890 --> 00:22:01,290
+نتكلم عن أنه لا يوجد محاولة، فهذا
+
+297
+00:22:01,290 --> 00:22:05,330
+يعني أنه لا يوجد اتفاق لحاجة الوصول للمحاولة، لأنه
+
+298
+00:22:05,330 --> 00:22:09,790
+شيء عادي، يمكن أن يفعله أحد وإذا كان صعبًا أيضًا
+
+299
+00:22:09,790 --> 00:22:15,810
+هنا نحن نتحدث عن أننا لسنا نستجيب للنتائج وهذا
+
+300
+00:22:15,810 --> 00:22:19,990
+يعني أيضًا أننا لا نستطيع أن نفعل ما نحتاجه للوصول
+
+301
+00:22:19,990 --> 00:22:21,010
+إلى الوصول إلى الوصول إلى الوصول إلى الوصول إلى
+
+302
+00:22:21,010 --> 00:22:21,450
+إلى الوصول إلى الوصول إلى الوصول إلى الوصول إلى
+
+303
+00:22:21,450 --> 00:22:22,410
+الوصول إلى الوصول إلى الوصول إلى الوصول إلى الوصول
+
+304
+00:22:22,410 --> 00:22:22,430
+إلى الوصول إلى الوصول إلى الوصول إلى الوصول إلى
+
+305
+00:22:22,430 --> 00:22:24,930
+الوصول إلى الوصول إلى الوصول إلى الوصول إلى الوصول
+
+306
+00:22:24,930 --> 00:22:28,590
+إلى الوصول إلى الوصول إلى الوصول إلى الوصول إلى
+
+307
+00:22:28,590 --> 00:22:32,430
+الوصول
+
+308
+00:22:32,460 --> 00:22:37,240
+بمعنى أنهم لا يجعلونهم رئيسين جيدين بالطبع هناك
+
+309
+00:22:37,240 --> 00:22:42,920
+مشكلة أخرى هناك نظر آخر يجب أن ندخله عادة أشخاص
+
+310
+00:22:42,920 --> 00:22:46,140
+مثلهم يفعلون أشياء بأنفسهم يعني عادة أشخاص مثلهم
+
+311
+00:22:46,140 --> 00:22:52,460
+هم أكثر عاملين في فعل أعمال معينة في أماكن معينة
+
+312
+00:22:55,700 --> 00:23:00,000
+وهم يحبون أن يفعلوا أشياء بأنفسهم، يحبون أن يفعلوا
+
+313
+00:23:00,000 --> 00:23:03,580
+العمل، هذا السبب أنهم ليسوا مديرين جيدين، هنا
+
+314
+00:23:03,580 --> 00:23:09,320
+المركز هو المركز الشخصي، نحن نتكلم عن مركز شخصي
+
+315
+00:23:09,320 --> 00:23:15,040
+أكثر من مركز مجتمعي أو مركز مؤسسي، هذا السبب أن
+
+316
+00:23:15,040 --> 00:23:21,400
+الناس غالبا لا يملكون فرصة جيدة لكي يكونوا مديرين هذا
+
+317
+00:23:21,400 --> 00:23:24,960
+السبب لما قلت أنه يجب أن أعيد كلماتي، السؤال
+
+318
+00:23:24,960 --> 00:23:29,840
+الصحيح لماذا لا يكونوا رئيسين جيدين، لا يملكون فرصة
+
+319
+00:23:29,840 --> 00:23:35,700
+جيدة لكي يكونوا رئيسين جيدين، لكن على أية حال يمكن
+
+320
+00:23:35,700 --> 00:23:37,940
+أن يكون لديهم فرصة، هنا لسنا نتكلم عن نتيجة
+
+321
+00:23:37,940 --> 00:23:42,600
+أفضل، لكن الناس مثل هذه، عادةً تحب أن تستخدم
+
+322
+00:23:42,600 --> 00:23:47,180
+قدراتهم في التعامل مع عمليات معينة أكثر من التعامل
+
+323
+00:23:47,180 --> 00:23:53,580
+مع مشكلة متعلقة هذا السبب أن المركز هنا هو شخصي و
+
+324
+00:23:53,580 --> 00:23:56,780
+هذا السبب أن أشخاص كهذه غالبا لا يوجد فرصة أن
+
+325
+00:23:56,780 --> 00:24:00,980
+يكونوا رئيسين جيدين أيضًا بعض الدراسات تظهر أن أكثر
+
+326
+00:24:00,980 --> 00:24:07,330
+رئيسين جيدين لا يوجد حاجة عالية للإنجاز عندما نتكلم
+
+327
+00:24:07,330 --> 00:24:11,410
+عن احتياجات قليلة للإنجاز ليس بالطبع أننا نتكلم عن
+
+328
+00:24:11,410 --> 00:24:17,570
+خطأ هنا، ربما نتكلم عن إنجاز بطريقة مختلفة أو من
+
+329
+00:24:17,570 --> 00:24:20,510
+ناحية مختلفة، لكن عندما نتكلم عن احتياجات للإنجاز،
+
+330
+00:24:20,510 --> 00:24:24,290
+نتكلم عن مشكلة شخصية هنا، أنني أحتاج أن أثبت أنني
+
+331
+00:24:24,290 --> 00:24:28,490
+أنجزت، لكن هنا المشكلة هي أن تلك الباحثات يجدون
+
+332
+00:24:28,490 --> 00:24:33,110
+أن الرئيسين، وأنا أتحدث هنا عن مدراء مستخدمين، لا
+
+333
+00:24:33,110 --> 00:24:40,750
+يحتاجون لإنجاز كبير. ماذا هو مركزهم إذا لم يكن
+
+334
+00:24:40,750 --> 00:24:46,390
+لديهم حاجة عالية للإنجاز؟
+
+335
+00:24:46,390 --> 00:24:55,490
+ماذا هو مركزهم هنا؟ هم مركزون
+
+336
+00:24:55,490 --> 00:24:58,270
+أكثر على ماذا؟ 
+
+337
+00:25:02,990 --> 00:25:06,750
+في معظم الحالات، في طريقة كيف مكليلان تتكلم عن
+
+338
+00:25:06,750 --> 00:25:15,870
+الموضوع على سبيل المثال، هنا هناك نظرية أكثر من
+
+339
+00:25:15,870 --> 00:25:23,870
+نظرية شخصية، ما هي المواضيع الأخرى؟ هل هناك
+
+340
+00:25:23,870 --> 00:25:27,750
+أفكار أكثر عن لماذا المديرين العاملين لا يكونوا
+
+341
+00:25:27,750 --> 00:25:33,600
+بحاجة كبيرة للإنجاز؟ هنا نتحدث أكثر عن اتجاهات مؤسسة
+
+342
+00:25:33,600 --> 00:25:39,980
+أكثر من اتجاهات مؤسسة واحدة مثلما قلت في الموضوع
+
+343
+00:25:39,980 --> 00:25:45,380
+الأول أنهم يفكرون
+
+344
+00:25:45,380 --> 00:25:50,700
+أكثر في إيجارات مؤسسة أو إيجارات مؤسسة أو إيجارات
+
+345
+00:25:50,700 --> 00:25:52,700
+مؤسسة أو إيجارات مؤسسة أو إيجارات مؤسسة أو إيجارات
+
+346
+00:25:52,700 --> 00:25:54,460
+مؤسسة أو إيجارات مؤسسة أو إيجارات مؤسسة أو إيجارات
+
+347
+00:25:54,460 --> 00:25:54,820
+مؤسسة أو إيجارات مؤسسة أو إيجارات مؤسسة أو إيجارات
+
+348
+00:25:54,820 --> 00:25:57,500
+مؤسسة أو إيجارات مؤسسة أو إيجارات مؤسسة أو إيجارات
+
+349
+00:25:57,500 --> 00:26:02,180
+مؤسسات بشكل عام، هذا يعني أنهم لديهم .. ربما 
+
+350
+00:26:02,180 --> 00:26:05,000
+يمكننا أن نسمعها في العالم الآخر أنهم لديهم حاجة
+
+351
+00:26:05,000 --> 00:26:09,020
+عالية للإنجاز ولكن ليس بالطبع حاجة عالية لإنجاز
+
+352
+00:26:09,020 --> 00:26:12,960
+عندما نتحدث عن حاجة عالية للإنجاز، هنا نتحدث عن
+
+353
+00:26:12,960 --> 00:26:16,340
+إدارة الداخلية لإنجاز نتائج أو مهارات وما إلى
+
+354
+00:26:16,340 --> 00:26:20,280
+ذلك، لكن عندما نتحدث عن مديرين، هنا نتحدث عن أكثر
+
+355
+00:26:20,280 --> 00:26:25,680
+حاجة للنجاح وهو السبب في أنهم أكثر مجتمعي أو يانتز
+
+356
+00:26:25,680 --> 00:26:30,220
+وليس مجتمعي أو يانتز على الأقل في أغلب الحالات نحن
+
+357
+00:26:30,220 --> 00:26:32,700
+قد تحدثنا عن هذه المشاكل من قبل أننا لا نستطيع أن
+
+358
+00:26:32,700 --> 00:26:36,680
+نأخذ أي شيء كأبسلوت كل المشاكل اللي نتحدث عنها
+
+359
+00:26:36,680 --> 00:26:42,840
+بطريقة مرتبطة أخرى، آخرين نقطعين لنتحدث عن مكللنز
+
+360
+00:26:42,840 --> 00:26:51,050
+بحاجة إلى نظرية عادةً مديرين يحتاجون
+
+361
+00:26:51,050 --> 00:26:58,910
+للقوة وليس للمشاركة فإذا كنا نحتاج أن نسمح لمديرين
+
+362
+00:26:58,910 --> 00:27:02,230
+بالنسبة لهذه الاثنين الاحتياطات نستطيع أن نقول هنا
+
+363
+00:27:02,230 --> 00:27:07,050
+أن المديرين العالي ليسوا محتاجين للمشاركة وليسوا
+
+364
+00:27:07,050 --> 00:27:14,010
+محتاجين للقوة وليسوا محتاجين للمشاركة
+
+365
+00:27:16,270 --> 00:27:18,950
+الآن نحن نتكلم عن مشكلة الوصول للإيجار من نقطة
+
+366
+00:27:18,950 --> 00:27:22,150
+مختلفة، ونقول أن المديرين يحتاجون لإيجار كبير
+
+367
+00:27:22,150 --> 00:27:23,270
+للإنجاز
+
+368
+00:27:26,120 --> 00:27:33,720
+إذا كنا نتكلم عن تهوية مكللنز ثلاث حاجات ونشارك
+
+369
+00:27:33,720 --> 00:27:37,200
+تهوية مكللنز ثلاث حاجات لهؤلاء المديرين، نقول مرة
+
+370
+00:27:37,200 --> 00:27:41,160
+أخرى بأن المديرين لا يحتاجون لإنجاز كبير، ولا
+
+371
+00:27:41,160 --> 00:27:45,620
+يحتاجون لإيقاف كبير، ولكن بالتأكيد يحتاجون إلى
+
+372
+00:27:47,790 --> 00:27:53,310
+ونستطيع أن نفهم لماذا يحتاجون للقوة كبيرة لأنهم
+
+373
+00:27:53,310 --> 00:27:58,650
+يحتاجون للتحكم في المشكلة وإنشاء مخططين ويحتاجون
+
+374
+00:27:58,650 --> 00:28:03,150
+للتتبع كيف يتم الأشياء بشركات مختلفة تعمل في
+
+375
+00:28:03,150 --> 00:28:07,310
+المؤسسة آخر نقطة أريد أن أتكلم عنها هنا
+
+376
+00:28:10,960 --> 00:28:14,900
+كانت مدعومة بعمل جيد حتى لو كان بعض الناس
+
+377
+00:28:14,900 --> 00:28:20,660
+يسمونها ليست نظرية عملية جدا نفهم لماذا كل النظرية
+
+378
+00:28:20,660 --> 00:28:26,040
+ليست عملية جدا لأن بعد كل شيء نحن نتكلم عن هذه
+
+379
+00:28:26,040 --> 00:28:26,640
+الأشياء
+
+380
+00:28:29,350 --> 00:28:34,030
+وليس هناك نظر مفهوم لأي نظر من هذه النظرات ولكن
+
+381
+00:28:34,030 --> 00:28:37,290
+هذا واحد من النظرات التي كانت مدعومة من عمل جيد 
+
+382
+00:28:37,290 --> 00:28:38,130
+عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+383
+00:28:38,130 --> 00:28:39,110
+عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+384
+00:28:39,110 --> 00:28:42,970
+عمل عمل عمل
+
+385
+00:28:42,970 --> 00:28:43,770
+عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+386
+00:28:43,770 --> 00:28:47,910
+عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+387
+00:28:47,910 --> 00:28:50,370
+عمل 
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/ObsphEXNFRI_postprocess.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/ObsphEXNFRI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f93b41d86583e1f6800905ae657cd14160476086
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/ObsphEXNFRI_postprocess.srt
@@ -0,0 +1,1828 @@
+1
+00:00:08,230 --> 00:00:12,970
+اليوم سنكمل مع نظرية الهجوم، وفي دراسات قبلها نحنا
+
+2
+00:00:12,970 --> 00:00:22,570
+نتكلم عن ما نسميه نظرية الهجوم المصطلحة في هذه
+
+3
+00:00:22,570 --> 00:00:27,290
+الدراسة سوف نتكلم عن نظرية الهجوم التقليدية، وفي
+
+4
+00:00:27,290 --> 00:00:33,550
+هذه النظرية سوف نتكلم عن نظرية نظرية الهجومالفكرة
+
+5
+00:00:33,550 --> 00:00:38,450
+السابقة التي كنا ندرسها تتكلم عن المشكلة المشغولة
+
+6
+00:00:38,450 --> 00:00:43,150
+من خلال تشرح المحتاجات وما هي علاقة بين المحتاجات
+
+7
+00:00:43,150 --> 00:00:48,550
+والمشغولة، ولكن من الآن، سندرس كيف حدث الprocess
+
+8
+00:00:48,550 --> 00:00:54,750
+نفسههذه السبب .. يعني .. او هنا نحن نتحدث عن مصادر
+
+9
+00:00:54,750 --> 00:00:58,390
+مختلفة بشكل عامة وهي نظريات محيطية محيطية محيطية
+
+10
+00:00:58,390 --> 00:01:00,390
+محيطية محيطية محيطية محيطية محيطية محيطية محيطية
+
+11
+00:01:00,390 --> 00:01:00,710
+محيطية محيطية محيطية محيطية محيطية محيطية محيطية
+
+12
+00:01:00,710 --> 00:01:05,550
+محيطية محيطية محيطية محيطية محيطية محيطية محيطية
+
+13
+00:01:05,550 --> 00:01:09,330
+محيطية محيطية محيطية محيطية محيطية محيطية محيطية
+
+14
+00:01:09,330 --> 00:01:19,590
+محيطية محيطية محيطية محيطية محيطية محيط
+
+15
+00:01:19,610 --> 00:01:23,270
+لذلك، إذا أدرك الإنسان أن المدافعات التي يتم
+
+16
+00:01:23,270 --> 00:01:26,870
+إعطائها جديدة ليست أقل من المدافعات السابقة،
+
+17
+00:01:26,870 --> 00:01:33,690
+فبالعكس أن الإنسان لن يكون محررًا كافيًا لعمل. هنا
+
+18
+00:01:33,690 --> 00:01:36,730
+يمكننا
+
+19
+00:01:36,730 --> 00:01:43,110
+أن نشرح ذلك باعتبار أن إعطاء تجارب تجارب تجارب
+
+20
+00:01:43,110 --> 00:01:48,510
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+21
+00:01:48,510 --> 00:01:51,920
+تجارب تجارب تجارب تجارب تجارب تبالطبع في الثورات
+
+22
+00:01:51,920 --> 00:01:54,940
+الأخرى، عندما نتحدث عن أمر مستمر ومستمر، هناك
+
+23
+00:01:54,940 --> 00:01:58,900
+تفسيرات مختلفة، ولكن هنا بالنسبة لثورة كوجينية،
+
+24
+00:01:58,900 --> 00:02:04,090
+هنا نتحدث أكتر عن مотивات كلمةأو إدارة غير مستحيلة
+
+25
+00:02:04,090 --> 00:02:07,290
+إذا
+
+26
+00:02:07,290 --> 00:02:12,950
+كانت تجارب مثل هذه مستحيلة تجارب مثل هذه مستحيلة
+
+27
+00:02:12,950 --> 00:02:16,270
+تجارب مثل هذه مستحيلة تجارب مثل هذه مستحيلة تجارب
+
+28
+00:02:16,270 --> 00:02:21,750
+مثل هذه مستحيلة تجارب مثل هذه مستحيلة تجارب مثل
+
+29
+00:02:21,750 --> 00:02:21,830
+هذه مستحيلة تجارب مثل هذه مستحيلة تجارب مثل هذه
+
+30
+00:02:21,830 --> 00:02:22,070
+مستحيلة تجارب مثل هذه مستحيلة تجارب مثل هذه
+
+31
+00:02:22,070 --> 00:02:22,870
+مستحيلة تجارب مثل هذه مستحيلة تجارب مثل هذه
+
+32
+00:02:22,870 --> 00:02:23,870
+مستحيلة تجارب مثل هذه مستحيلة تجارب مثل هذه
+
+33
+00:02:23,870 --> 00:02:29,810
+مستحيلة تجارب مثل هذه مستحيلة تجارب مثل هذه
+
+34
+00:02:29,810 --> 00:02:37,640
+مستحيلة تجاروهي علاقة ما بين إجراء وإجراء إجراء
+
+35
+00:02:37,640 --> 00:02:42,540
+إجراء
+
+36
+00:02:42,540 --> 00:02:55,040
+إجراء إجراء
+
+37
+00:02:55,040 --> 00:03:00,880
+إجراء إجراء إجراء
+
+38
+00:03:00,880 --> 00:03:04,610
+إجراء إجراءعندما نتكلم عن الهجوم الاستراني، فهنا
+
+39
+00:03:04,610 --> 00:03:07,030
+نتكلم عن الهجوم الاستراني أو الهجوم الانتجابي أو
+
+40
+00:03:07,030 --> 00:03:09,130
+الهجوم الانتجابي أو الهجوم الانتجابي أو الهجوم
+
+41
+00:03:09,130 --> 00:03:11,210
+الانتجابي أو الهجوم الانتجابي أو الهجوم الانتجابي
+
+42
+00:03:11,210 --> 00:03:13,290
+أو الهجوم الانتجابي أو الهجوم الانتجابي أو الهجوم
+
+43
+00:03:13,290 --> 00:03:14,330
+الانتجابي أو الهجوم الانتجابي أو الهجوم الانتجابي
+
+44
+00:03:14,330 --> 00:03:14,430
+أو الهجوم الانتجابي أو الهجوم الانتجابي أو الهجوم
+
+45
+00:03:14,430 --> 00:03:17,630
+الانتجابي أو الهجوم الانتجابي أو الهجوم الانتجابي
+
+46
+00:03:17,630 --> 00:03:22,250
+أو الهجوم
+
+47
+00:03:22,250 --> 00:03:31,560
+الانتجابي أو اللماذا تتعلق تلك الارتفاع؟ ماذا أخر؟
+
+48
+00:03:42,560 --> 00:03:45,740
+في المقالات السابقة عندما تحدثنا عن نظرية
+
+49
+00:03:45,740 --> 00:03:49,400
+المотивات الأولى، قلنا إن الناس لديها نوعين مختلفة
+
+50
+00:03:49,400 --> 00:03:54,600
+من المحتاجات و بعض هذه المحتاجات، حتى في الطبيعة،
+
+51
+00:03:54,600 --> 00:03:58,560
+مختلفة، حسنًا، إذا تتذكر، على سبيل المثال، ماسلو
+
+52
+00:03:58,560 --> 00:04:04,800
+لم يدخل داخل المحتاجات المستخدمة و المستخدمات
+
+53
+00:04:04,800 --> 00:04:11,340
+المستخدمة أو المحتاجات تم تصميمها بطريقة مختلفةإذا
+
+54
+00:04:11,340 --> 00:04:14,280
+تذكر، على سبيل المثال، تقنية الـTwo Factors لـ
+
+55
+00:04:14,280 --> 00:04:18,180
+Herzberg، كان يقوم بتصميم .. أكثر منكم لم تقضي هذه
+
+56
+00:04:18,180 --> 00:04:23,160
+الدراسة، أعتقد، يعني، حسنًا، هنا الـ Reward نفسها
+
+57
+00:04:23,160 --> 00:04:28,500
+كانت تقوم بتصميم الـ Two .. هنا نحن نتحدث عن
+
+58
+00:04:28,500 --> 00:04:32,360
+الواجهات الهيجيوية والواجهات المدهشة، الواجهات
+
+59
+00:04:32,360 --> 00:04:35,860
+الهيجيوية هي مستخدمة في الطبيعة، لكن هنا لسنا
+
+60
+00:04:35,860 --> 00:04:41,060
+نتحدث عن كلمة كلمة، حسنًا، نحن نتحدث عن مختلفةأو
+
+61
+00:04:41,060 --> 00:04:45,280
+المفروضات الممنوعة من المؤسسة والمفروضات المدعومة
+
+62
+00:04:45,280 --> 00:04:48,380
+المدعومة المدعومة المدعومة المدعومة المدعومة
+
+63
+00:04:48,380 --> 00:04:48,440
+المدعومة المدعومة المدعومة المدعومة المدعومة
+
+64
+00:04:48,440 --> 00:04:48,520
+المدعومة المدعومة المدعومة المداعومة المداعومة
+
+65
+00:04:48,520 --> 00:04:48,820
+المداعومة المداعومة المداعومة المداعومة المداعومة
+
+66
+00:04:48,820 --> 00:04:49,220
+المداعومة المداعومة المداعومة المداعومة المداعومة
+
+67
+00:04:49,220 --> 00:04:51,600
+المداعومة المداعومة المداعومة المداعومة المداعومة
+
+68
+00:04:51,600 --> 00:04:55,180
+المداعومة المداعومة المداعومة المداعومة المداعومة
+
+69
+00:04:55,180 --> 00:05:02,760
+المداعومة المداعومة المداعومة المداعومة الم
+
+70
+00:05:07,480 --> 00:05:11,260
+يعني anyway there is a relation between intrinsic
+
+71
+00:05:11,260 --> 00:05:16,740
+and extrinsic but يعني I do not agree with what
+
+72
+00:05:16,740 --> 00:05:20,960
+was said just right now that maybe people some
+
+73
+00:05:20,960 --> 00:05:24,220
+people they prefer like if all the time they
+
+74
+00:05:24,220 --> 00:05:27,020
+prefer intrinsic or financial and others they
+
+75
+00:05:27,020 --> 00:05:29,880
+prefer extrinsic because this is related to the
+
+76
+00:05:29,880 --> 00:05:34,470
+needsإذا كنا نريد أن نعرف أهمية تلك الهجومات،
+
+77
+00:05:34,470 --> 00:05:38,150
+نستطيع أن نعرفها باعتبار محتاجات الشخصية. بعض
+
+78
+00:05:38,150 --> 00:05:42,770
+الناس في حالات معينة، يفضلون الهجومات التجارية،
+
+79
+00:05:42,770 --> 00:05:47,310
+وفي حالات أخرى، يفضلون الهجومات التجارية. لكننا لا
+
+80
+00:05:47,310 --> 00:05:50,750
+نستطيع أن نقل، لا نستطيع أن نقول أن بعض الناس
+
+81
+00:05:50,750 --> 00:05:54,050
+دائما يفضلون الهجومات التجارية، وبعض الناس دائما
+
+82
+00:05:54,050 --> 00:05:55,690
+يفضلون الهجومات التجارية.
+
+83
+00:05:59,810 --> 00:06:03,930
+وهو مختلف قليل أيضا، لأننا لا نتكلم فقط عن
+
+84
+00:06:03,930 --> 00:06:10,490
+التصميم، بل نتكلم عن أن الناس إذا حصلت على تجارب
+
+85
+00:06:10,490 --> 00:06:15,030
+محددة، بعد ذلك ستبحث دائما عن تجارب أعلى مستوى
+
+86
+00:06:16,180 --> 00:06:21,960
+لذلك، إذا أحصلوا على إيجار مستخدم، فلن يبحثوا عن
+
+87
+00:06:21,960 --> 00:06:27,860
+إيجار مستخدم، بل سوف يبحثوا عن إيجار أسوأ أو أكثر
+
+88
+00:06:27,860 --> 00:06:32,980
+مهمة، وما إلى ذلك، وهذا ليس دائمًا صحيح. حسنًا،
+
+89
+00:06:32,980 --> 00:06:38,310
+قبل أن أكمل مع هذه النظراتهنا نحتاج أيضًا أن نعتمد
+
+90
+00:06:38,310 --> 00:06:41,250
+على أن في المقالات السابقة قبلها قررنا نتناقض
+
+91
+00:06:41,250 --> 00:06:47,510
+نظرية الهجوم الأولى أو ما نسميه نظرية
+
+92
+00:06:47,510 --> 00:06:52,190
+الهجوم المصطلح والمصطلح والمصطلح والمصطلح والمصطلح
+
+93
+00:06:52,190 --> 00:06:53,190
+والمصطلح والمصطلح والمصطلح والمصطلح والمصطلح
+
+94
+00:06:53,190 --> 00:06:54,870
+والمصطلح والمصطلح والمصطلح والمصطلح والمصطلح
+
+95
+00:06:54,870 --> 00:07:02,030
+والمصطلح والمصطلح والم
+
+96
+00:07:02,140 --> 00:07:06,260
+لأن الـ Needs-Based Theories يظهر لنا لماذا الناس
+
+97
+00:07:06,260 --> 00:07:11,200
+محررين لأنهم لديهم احتاجات مختلفة وما إلى ذلك ولكن
+
+98
+00:07:11,200 --> 00:07:16,300
+كيف سوف يقبلوا احتجازاتهم، هذا ما نتحدث عنه هنا
+
+99
+00:07:16,300 --> 00:07:18,720
+عندما نتحدث عن الـ Contemporary Theories، نحن هنا
+
+100
+00:07:18,720 --> 00:07:22,360
+نتحدث عن الميكانيزمات، ماذا يفعل الناس في حالة ..
+
+101
+00:07:22,360 --> 00:07:25,780
+ماذا يفعل الانسان والموظفين في حالة لإيقاف
+
+102
+00:07:25,780 --> 00:07:28,400
+احتجازاتهم؟ على أية حال، عندما نتحدث عن The
+
+103
+00:07:28,400 --> 00:07:34,010
+Cognitive Evaluation Theory،يعني basic theories we
+
+104
+00:07:34,010 --> 00:07:37,580
+can sayالتي تتحدث عن نظراء التحليل التقديمي
+
+105
+00:07:37,580 --> 00:07:38,940
+المشروعي المشروعي المشروعي المشروعي المشروعي
+
+106
+00:07:38,940 --> 00:07:40,260
+المشروعي المشروعي المشروعي المشروعي المشروعي
+
+107
+00:07:40,260 --> 00:07:41,720
+المشروعي المشروعي المشروعي المشروعي المشروعي
+
+108
+00:07:41,720 --> 00:07:42,100
+المشروعي المشروعي المشروعي المشروعي المشروعي
+
+109
+00:07:42,100 --> 00:07:44,600
+المشروعي المشروعي المشروعي المشروعي المشروعي
+
+110
+00:07:44,600 --> 00:07:45,160
+المشروعي المشروعي المشروعي المشروعي المشروعي
+
+111
+00:07:45,160 --> 00:07:45,740
+المشروعي المشروعي المشروعي المشروعي المشروعي
+
+112
+00:07:45,740 --> 00:07:55,500
+المشروعي المشروعي المشروعي المشروعي المشروعي
+
+113
+00:07:55,500 --> 00:08:01,780
+المشروع
+
+114
+00:08:03,300 --> 00:08:10,380
+يعني اكتشاف علاقة بين لماذا موظفين يبحثون عن هدف
+
+115
+00:08:10,380 --> 00:08:17,900
+معين وإن الوصول لهذا الهدف يتجاوز مع قيمهم
+
+116
+00:08:17,900 --> 00:08:22,580
+وعلاقاتهم وما إلى ذلك، فعندما يكون هناك علاقة، فإن
+
+117
+00:08:22,580 --> 00:08:26,180
+الموظفين هنا سيكونون أكتشاف ومعينة وما إلى ذلك،
+
+118
+00:08:26,180 --> 00:08:30,500
+وهذا يجب أن يتجاوز على تجارب في طريقة إيجابية،
+
+119
+00:08:30,500 --> 00:08:38,860
+فهنا نتحدث عنوالعلاقات بين السببات الخاصة وإذا
+
+120
+00:08:38,860 --> 00:08:42,060
+كانت هذه السببات منافسة معاملة معاملة معاملة
+
+121
+00:08:42,060 --> 00:08:45,120
+معاملة معاملة معاملة معاملة معاملة معاملة معاملة
+
+122
+00:08:45,120 --> 00:08:45,440
+معاملة معاملة معاملة معاملة معاملة معاملة معاملة
+
+123
+00:08:45,440 --> 00:08:45,460
+معاملة معاملة معاملة معاملة معاملة معاملة معاملة
+
+124
+00:08:45,460 --> 00:08:45,560
+معاملة معاملة معاملة معاملة معاملة معاملة معاملة
+
+125
+00:08:45,560 --> 00:08:47,890
+معاملة معاملة معاملة معاملة معاملة معاملة معهذا
+
+126
+00:08:47,890 --> 00:08:52,530
+سيكون حالة صحيحة حيث يكون هناك اتفاق نفسي متوفر
+
+127
+00:08:52,530 --> 00:08:58,310
+إذا كان هناك نوع من الانتصاف هنا أو اتفاق بين هذين
+
+128
+00:08:58,310 --> 00:09:02,610
+الانتصافين فالموظفين هنا سيكونون أقل مناسبين وهذا
+
+129
+00:09:02,610 --> 00:09:08,810
+يجب أن يتفاعل على نفسه بطريقة ناجحةهذا السبب في
+
+130
+00:09:08,810 --> 00:09:15,770
+نهاية الفيديو أن الناس المفضلة أكثر سعادة ومفهومة
+
+131
+00:09:15,770 --> 00:09:20,230
+لأن تجاربها ستكون
+
+132
+00:09:20,230 --> 00:09:26,310
+أفضل بكثير.الثورة الأخرى التي هي جزء من الثورات
+
+133
+00:09:26,310 --> 00:09:30,290
+التقليدية للمотивات هي الـ Goal Setting Theory
+
+134
+00:09:30,470 --> 00:09:34,250
+النظر الى الـ goal setting theory هنا نتحدث عن
+
+135
+00:09:34,250 --> 00:09:41,430
+علاقة بين الهدف و الواجهة، يعني هنا الفكرة
+
+136
+00:09:41,430 --> 00:09:45,870
+الأساسية عندما نتحدث عن نظر الهدف و الواجهة هي كيف
+
+137
+00:09:45,870 --> 00:09:48,430
+يمكن أن يكون الواجهة تعمل بشكل أفضل، ما هي علاقة
+
+138
+00:09:48,430 --> 00:09:52,810
+بين الهدف و الواجهة؟ كيف يمكن الهدف أن يحرر الناس
+
+139
+00:09:52,810 --> 00:09:54,510
+لتعمل بشكل أفضل؟
+
+140
+00:09:58,170 --> 00:10:04,130
+الناس دائما يحاولون أن تحقيق مهارتها، إذا
+
+141
+00:10:04,130 --> 00:10:09,650
+كانت المجتمع لم يقوم بتحقيق هذا مهارة، أنا سأقوم
+
+142
+00:10:09,650 --> 00:10:14,730
+بتحقيق هذا مهارة، وسأحرز نفسي في تحقيق هذا مهارة،
+
+143
+00:10:14,730 --> 00:10:19,910
+وهذا بالطبع سيأثر على تحقيقتيوهذا السبب في اقتراح
+
+144
+00:10:19,910 --> 00:10:23,210
+هذه النظرية أن أكثر مهاراتها محددة، أكثر مهاراتها
+
+145
+00:10:23,210 --> 00:10:26,470
+ماضية، أكثر مهاراتها مهاجمة، على سبيل المثال، أكثر
+
+146
+00:10:26,470 --> 00:10:32,180
+الناس يقومون بإدارة الـBetaولكن هنا هناك شيء يجب
+
+147
+00:10:32,180 --> 00:10:36,220
+أن نعتمد عليه أن بعد الوصول للهجوم يجب أن يكون
+
+148
+00:10:36,220 --> 00:10:40,700
+هناك شيء موفر من المؤسسة لأن بعد كل ما كنا نتكلم
+
+149
+00:10:40,700 --> 00:10:44,960
+هنا عن كيف نحرر موظفين موظفين موظفين هنا نتكلم عن
+
+150
+00:10:44,960 --> 00:10:49,780
+اتصالين من موظفين موظفين موظفين موظفين موظفين
+
+151
+00:10:49,780 --> 00:10:49,940
+موظفين موظفين موظفين موظفين موظفين موظفين موظفين
+
+152
+00:10:49,940 --> 00:10:50,240
+موظفين موظفين موظفين موظفين موظفين موظفين موظفين
+
+153
+00:10:50,240 --> 00:10:54,140
+موظفين موظفين موظفين موظفين موظفين موظفين موظفين
+
+154
+00:10:54,140 --> 00:10:58,200
+موظ
+
+155
+00:10:59,380 --> 00:11:07,360
+هذا سيكون صعب جدًا لنا لإنشاء موظفين ممتازين
+
+156
+00:11:07,360 --> 00:11:12,720
+ممتازين
+
+157
+00:11:12,720 --> 00:11:12,920
+ممتازين ممتازين ممتازين ممتازين ممتازين ممتازين
+
+158
+00:11:12,920 --> 00:11:13,380
+ممتازين ممتازين ممتازين ممتازين ممتازين ممتازين
+
+159
+00:11:13,380 --> 00:11:13,400
+ممتازين ممتازين ممتازين ممتازين ممتازين ممتازين
+
+160
+00:11:13,400 --> 00:11:13,540
+ممتازين ممتازين ممتازين ممتازين ممتازين ممتازين
+
+161
+00:11:13,540 --> 00:11:16,060
+ممتازين ممتازين
+
+162
+00:11:26,340 --> 00:11:28,120
+مهارات مهارات مهارات مهارات مهارات مهارات مهارات
+
+163
+00:11:28,120 --> 00:11:30,980
+مهارات مهارات مهارات مهارات مهارات مهارات مهارات
+
+164
+00:11:30,980 --> 00:11:32,760
+مهارات مهارات مهارات مهارات مهارات مهارات مهارات
+
+165
+00:11:32,760 --> 00:11:33,760
+مهارات مهارات مهارات مهارات مهارات مهارات مهارات
+
+166
+00:11:33,760 --> 00:11:34,360
+مهارات مهارات مهارات مهارات مهارات مهارات مهارات
+
+167
+00:11:34,360 --> 00:11:34,760
+مهارات مهارات مهارات مهارات مهارات مهارات مهارات
+
+168
+00:11:34,760 --> 00:11:55,660
+مهارات مهارات مهارات مهارات مهارات مهارات مهارات
+
+169
+00:11:55,700 --> 00:11:58,120
+يعني here we are talking about the needs of
+
+170
+00:11:58,120 --> 00:12:02,740
+employees and the rewards provided by after those
+
+171
+00:12:02,740 --> 00:12:05,720
+goals and achieve results if they achieve those
+
+172
+00:12:05,720 --> 00:12:09,380
+results then they are going to have rewards why
+
+173
+00:12:09,380 --> 00:12:11,000
+they are going to have rewards because they
+
+174
+00:12:11,000 --> 00:12:12,920
+achieve the results which mean that the
+
+175
+00:12:12,920 --> 00:12:15,660
+organization is more successful it is achieving
+
+176
+00:12:15,660 --> 00:12:17,260
+its goals more profit
+
+177
+00:12:23,020 --> 00:12:28,720
+في نفس الوقت، هذا يعني أن الموظفين يتوفروا
+
+178
+00:12:28,720 --> 00:12:34,080
+بحاجتهم، لذلك هذا الهجوم هو الهجوم المدعوم لإنجاز
+
+179
+00:12:34,080 --> 00:12:38,860
+الهجوم لأن أفضل النتائج تم إجراءها للorganization
+
+180
+00:12:38,860 --> 00:12:45,140
+في نفس الوقت، هذا هو المعنى المستخدم لإنجاز حاجات
+
+181
+00:12:45,140 --> 00:12:47,980
+الموظفين، نعم
+
+182
+00:12:52,280 --> 00:12:57,260
+بالطبع، سوف نتكلم بعد ذلك عن الـMBR، الـManagement
+
+183
+00:12:57,260 --> 00:13:00,360
+By Objectives، إنه واحد من خمس مهمات على شأنهم،
+
+184
+00:13:00,360 --> 00:13:03,520
+يعني يجب أن يكون هناك نوع من خطط استراتيجية
+
+185
+00:13:03,520 --> 00:13:07,440
+للorganization أو الوظيفة، وفقًا لذلك يمكنهم أن
+
+186
+00:13:07,440 --> 00:13:11,560
+يقرروا ما هي المهمات، مع التحكم في الوظيفة، سوف
+
+187
+00:13:11,560 --> 00:13:16,300
+نتكلم عن الميكانيزم في الصفحة التالية، ولكن أولًا،
+
+188
+00:13:16,300 --> 00:13:21,680
+لماذا المهمات الصعبة مهمة هنا؟لماذا الهدف الصعب
+
+189
+00:13:21,680 --> 00:13:25,080
+مهم؟
+
+190
+00:13:25,080 --> 00:13:30,980
+لأن
+
+191
+00:13:30,980 --> 00:13:35,760
+الهدف الصعب يجعل المستخدمين يقوموا بعمل أكثر إجراء
+
+192
+00:13:35,760 --> 00:13:37,720
+لإعطاء أفعال أفضل للمستخدمين
+
+193
+00:13:49,840 --> 00:13:52,880
+الأمر ليس بسهولة للوصول إليه أو الوصول إليه، إنه
+
+194
+00:13:52,880 --> 00:13:57,340
+ليس عمل بسهولة فقط لإنهاء هذا الهدف، فإذا أردت
+
+195
+00:13:57,340 --> 00:14:00,520
+إنهاءه، يجب أن أكون محررًا، إنه ليس شيء بسهولة.
+
+196
+00:14:00,820 --> 00:14:05,680
+حسنًا، هنا لا يجب أن نخلص ما قد تحدثنا في المقال
+
+197
+00:14:05,680 --> 00:14:13,860
+السابق، في المقال السابق، قد تحدثنا عن حاجة للوصول
+
+198
+00:14:13,860 --> 00:14:20,110
+إلى الهدف، وفي مجال مختلف،أشياء فقط هنا نحن نتكلم
+
+199
+00:14:20,110 --> 00:14:22,490
+عن مشاكل الداخلية التي مرتبطة أيضًا
+
+200
+00:14:22,490 --> 00:14:27,910
+بالorganization وكيف هي التخطيط للوضع عامًا في
+
+201
+00:14:27,910 --> 00:14:30,530
+الواقع
+
+202
+00:14:38,060 --> 00:14:42,540
+نحن نقول إنهم يتبعون
+
+203
+00:14:42,540 --> 00:14:49,480
+مهارات صعبة أو مهارات
+
+204
+00:14:49,480 --> 00:14:53,080
+صعبة بشكل تقليدي يفضلون حاجات مهارات صعبة لأنها
+
+205
+00:14:53,080 --> 00:14:56,140
+ليست
+
+206
+00:14:56,140 --> 00:15:01,880
+ممكنة تحقيقها وفي نفس الوقت لا يتبعون مهارات بسيطة
+
+207
+00:15:02,020 --> 00:15:06,580
+والسيئات الأسهل لأن أي شخص يستطيع فعل ذلك ولكن
+
+208
+00:15:06,580 --> 00:15:10,760
+عندما نتكلم عن نظر الهجوم نحن لسنا نتكلم عن
+
+209
+00:15:10,760 --> 00:15:17,760
+الموضوع من نفس المنصة نحن نستخدم من ناحية مختلفة
+
+210
+00:15:17,760 --> 00:15:24,860
+عادة الهجوم الصعب يجب أن يجعل الانسان يركز أكتر
+
+211
+00:15:24,860 --> 00:15:28,520
+على الهجوم الهجوم هنا نتكلم عن المؤسسة وكيف
+
+212
+00:15:28,520 --> 00:15:30,960
+المؤسسة ستجعل
+
+213
+00:15:32,450 --> 00:15:37,190
+أحد الأشياء المحتاجة هنا هي أن الموظفين يركزوا على
+
+214
+00:15:37,190 --> 00:15:42,420
+الوصول للهجوم ويحصلوا على هجوم صعبيعني enhance we
+
+215
+00:15:42,420 --> 00:15:45,020
+can say here or motivate employees to focus more
+
+216
+00:15:45,020 --> 00:15:48,760
+on the achievement of goals another issue here is
+
+217
+00:15:48,760 --> 00:15:52,140
+difficult goals especially when it is linked to
+
+218
+00:15:52,140 --> 00:15:54,360
+rewards in a previous lecture when we have
+
+219
+00:15:54,360 --> 00:15:57,200
+discussed achievement and need for achievement we
+
+220
+00:15:57,200 --> 00:16:00,800
+discussed the need itself here we are discussing
+
+221
+00:16:00,800 --> 00:16:03,700
+the mechanism and that's what I said at the
+
+222
+00:16:03,700 --> 00:16:05,140
+beginning that in the early theory
+
+223
+00:16:08,210 --> 00:16:14,230
+أو الـ needs-based theories والتحقيق التقليدي هنا
+
+224
+00:16:14,230 --> 00:16:18,770
+أكتر نحن نتكلم عن التجارب نفسها كيف تحدث المотивات
+
+225
+00:16:18,770 --> 00:16:24,950
+حسنا فالان هذه بعض الأشياء لماذا يجب أن تكون
+
+226
+00:16:24,950 --> 00:16:28,430
+مهارات صعبة أيضًا يجب أن تزيد المقاومة على سبيل
+
+227
+00:16:28,430 --> 00:16:33,330
+المثال يجب أن يحفظ أفعالية وإفعالية هذه الأشياء
+
+228
+00:16:33,330 --> 00:16:38,280
+حسناعندما نستخدم نظرات مواجهة أهداف نحن لا
+
+229
+00:16:38,280 --> 00:16:43,580
+نستخدمها فقط مع مواجهين أعلى، لهذا السبب قلت أننا
+
+230
+00:16:43,580 --> 00:16:48,640
+لا يجب أن نفقد مشكلة الاحتياطات والمواجهة
+
+231
+00:16:48,640 --> 00:16:54,640
+الاحتياطية ومواجهة أهداف نهائية
+
+232
+00:16:54,640 --> 00:16:57,920
+ومواجهة أهداف نهائيةومن المتوقع أن يكونوا أكثر
+
+233
+00:16:57,920 --> 00:17:03,080
+مهتمين في هذه الحالة، لكننا لا نصنع تلك التطبيقات
+
+234
+00:17:03,080 --> 00:17:07,340
+فقط لأولئك الذين يحتاجون إيجار كبير
+
+235
+00:17:11,970 --> 00:17:17,950
+وإدارة أو تأثير العلاقات بين أهداف وأهداف، فهناك
+
+236
+00:17:17,950 --> 00:17:22,290
+مشكلة مختلفة، دعنا نتكلم عن بعض هذه المشكلة، واحدة
+
+237
+00:17:22,290 --> 00:17:24,910
+من هذه المشكلة هي مقرارات أهداف، أكتر الوظيفة
+
+238
+00:17:24,910 --> 00:17:31,410
+مقرارات أهداف، أكتر، بالطبع، هذا مجتمع جيد، نستطيع
+
+239
+00:17:31,410 --> 00:17:34,590
+القول، أو مجتمع أهداف كذلك
+
+240
+00:17:36,510 --> 00:17:40,390
+أيضًا، يتوقع أن أكثر مجتمعًا، أكتر مجتمعًا، أكتر
+
+241
+00:17:40,390 --> 00:17:44,310
+مجتمعًا، أكتر مجتمعًا، أكتر مجتمعًا، أكتر مجتمعًا،
+
+242
+00:17:44,310 --> 00:17:45,010
+أكتر مجتمعًا، أكتر مجتمعًا، أكتر مجتمعًا، أكتر
+
+243
+00:17:45,010 --> 00:17:45,250
+مجتمعًا، أكتر مجتمعًا، أكتر مجتمعًا، أكتر مجتمعًا،
+
+244
+00:17:45,250 --> 00:17:46,670
+أكتر مجتمعًا، أكتر مجتمعًا، أكتر مجتمعًا، أكتر
+
+245
+00:17:46,670 --> 00:17:54,970
+مجتمعًا، أكتر مجتمعًا،
+
+246
+00:17:54,970 --> 00:17:59,110
+أكتر مجتمعًا،
+
+247
+00:17:59,110 --> 00:18:04,500
+أكتر ملماذا في حالتنا مثلها نتوقع انهيار أكتر
+
+248
+00:18:04,500 --> 00:18:13,220
+لإنجاز الهدف؟ أعتقد أنه في مجتمع مجتمع مجتمع مجتمع
+
+249
+00:18:13,220 --> 00:18:13,940
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+250
+00:18:13,940 --> 00:18:14,000
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+251
+00:18:14,000 --> 00:18:16,980
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+252
+00:18:16,980 --> 00:18:17,320
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+253
+00:18:17,320 --> 00:18:17,940
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+254
+00:18:17,940 --> 00:18:27,740
+مجتمع مجتمع م
+
+255
+00:18:29,570 --> 00:18:32,430
+بعد كل شيء، الهدف المحدد هو الهدف المحدد، والناس
+
+256
+00:18:32,430 --> 00:18:35,250
+يستطيعون فهمه بسهولة، ويعرفون ما يجب عليهم فعله،
+
+257
+00:18:35,250 --> 00:18:37,230
+وما هي المقاومات التي يجب عليهم الوصول إليها، وما
+
+258
+00:18:37,230 --> 00:18:40,310
+إلى ذلك، لهذا السبب .. يعني، واحدة من الأشياء التي
+
+259
+00:18:40,310 --> 00:18:44,610
+سوف تأثر على علاقة الهدف المحدد هنا هي
+
+260
+00:18:47,680 --> 00:18:54,060
+طبعا هنا نتحدث عن حالات أسوأ التي نحبها هنا أكتر
+
+261
+00:18:54,060 --> 00:19:00,280
+أسوأ هي أسوأ لأنها ستكون متعرفة جيدا يعني الناس
+
+262
+00:19:00,280 --> 00:19:04,180
+مرتبطة أكتر بأشياء أسوأ الآن عندما نتحدث عن أشياء
+
+263
+00:19:04,180 --> 00:19:09,880
+أسوأ هنا نحن لا ن .. يعني فقط قبل عدة دقائق قبل
+
+264
+00:19:09,880 --> 00:19:10,100
+عدة دقائق قبل عدة دقائق قبل عدة دقائق قبل عدة
+
+265
+00:19:10,100 --> 00:19:10,340
+دقائق قبل عدة دقائق قبل عدة دقائق قبل عدة دقائق
+
+266
+00:19:10,340 --> 00:19:14,420
+قبل عدة دقائق قبل عدة دقائقولكن عندما نقول عمل
+
+267
+00:19:14,420 --> 00:19:19,360
+بسيط هنا، نتكلم عن عمل نفسه. عمل نفسه ببساطة إذا
+
+268
+00:19:19,360 --> 00:19:22,940
+كان مرتبط بالمهارات الشخصية، على سبيل المثال، أكثر
+
+269
+00:19:22,940 --> 00:19:27,100
+مقاومة هنا بين الشخص والوظيفة، أكثر عملها سيكون
+
+270
+00:19:27,100 --> 00:19:31,600
+ببساطة. بمعنى صعب، لسنا نتكلم عن إنشاء حاجز لكي
+
+271
+00:19:33,310 --> 00:19:38,690
+هندر ممكنة الوصول للهجوم، هنا نحن نتكلم عن شيء صعب
+
+272
+00:19:38,690 --> 00:19:46,150
+في تلك التعاملات، عادةً تجارب التعاملات هي أسهل
+
+273
+00:19:46,150 --> 00:19:52,110
+للإنسان لديه القدرة على الوصول لهذه التعاملات
+
+274
+00:19:52,110 --> 00:19:58,130
+الثالث فاكتر هنا هو التجارب التجاربية، الآن يتوقع
+
+275
+00:19:58,130 --> 00:20:04,880
+أكتر أن تجارب كهذه في أمريكاأو دعوني أقول أنه في
+
+276
+00:20:04,880 --> 00:20:09,200
+العالم الكيبطالي يكون أكثر مستخدمًا، حسنًا؟ في
+
+277
+00:20:09,200 --> 00:20:14,220
+حالة أخرى، في كل مكان يوجد مجتمع خاص، ليس حتى في
+
+278
+00:20:14,220 --> 00:20:18,980
+أمريكا والأوروبا، حتى إذا كنا نتحدث عن أسطسيا على
+
+279
+00:20:18,980 --> 00:20:22,500
+سبيل المثال، يتوقع أن يعمل، حسنًا؟ حتى هنا في غزة،
+
+280
+00:20:22,500 --> 00:20:25,580
+إذا كنا نتحدث عن مجتمع خاص، يتوقع أن يعمل، لكن هنا
+
+281
+00:20:25,580 --> 00:20:29,510
+يجب أن نصنع المجتمع بطريقة عمليةنحن نتكلم عن
+
+282
+00:20:29,510 --> 00:20:32,990
+الاحتياطات مرة أخرى ونتكلم عن الهجوم وإيجاد وإيجاد
+
+283
+00:20:32,990 --> 00:20:38,960
+علاقة بين الاحتياطات والهجومإذا المجتمع لم يتطور
+
+284
+00:20:38,960 --> 00:20:43,700
+بطريقة مشروعية، فلا يمكننا أن نتوقع هنا نتيجة جيدة
+
+285
+00:20:43,700 --> 00:20:48,640
+من هذه التطبيقات ولكن لماذا قالت هنا إنها أكثر
+
+286
+00:20:48,640 --> 00:20:52,000
+ممكن تطبيقية في أمريكا الأقل؟ لأننا نتكلم عن هذا
+
+287
+00:20:52,000 --> 00:20:55,400
+الموضوع عن طريق العلم، حسنًا، هناك مشكلة تتعلق
+
+288
+00:20:55,400 --> 00:21:01,480
+بالكبيتاليزم وكيف يفكر الناس، وانتصار الشخصية في
+
+289
+00:21:01,480 --> 00:21:05,940
+التفكير وما إلى ذلك، ولكن دعنا نتكلم من نظر مختلفة
+
+290
+00:21:05,940 --> 00:21:12,550
+هناالجزء الخاص في كل البلدين يمتلك فرصة جيدة
+
+291
+00:21:12,550 --> 00:21:17,210
+لإستخدام هذه النظرات ويحصل على نتيجة إيجابية إذا
+
+292
+00:21:17,210 --> 00:21:20,810
+كان هناك أسئلة حتى الآن عن نظرة الـ goal setting
+
+293
+00:21:20,810 --> 00:21:27,850
+دعنا نكمل واحد من تطبيقات نظرة ال goal setting هي
+
+294
+00:21:29,770 --> 00:21:32,270
+وهو الـ Management by Objectives وعندما نتكلم عن
+
+295
+00:21:32,270 --> 00:21:36,790
+الـ Management by Objectives هو موديل تم تطويره
+
+296
+00:21:36,790 --> 00:21:42,170
+بيتر دركر وهو واحد من الناس المعروفين عندما نتكلم
+
+297
+00:21:42,170 --> 00:21:45,150
+عن الهدف من الهدف من الهدف من الهدف من الهدف من
+
+298
+00:21:45,150 --> 00:21:45,950
+الهدف من الهدف من الهدف من الهدف من الهدف من الهدف
+
+299
+00:21:45,950 --> 00:21:48,230
+من الهدف من الهدف من الهدف من الهدف من الهدف من
+
+300
+00:21:48,230 --> 00:21:49,970
+الهدف من الهدف من الهدف من الهدف من الهدف من الهدف
+
+301
+00:21:49,970 --> 00:21:55,030
+من الهدف من الهدف
+
+302
+00:21:55,030 --> 00:22:00,990
+منولكن هذه الحقيقة استخدمت حتى اليوم وليس فقط
+
+303
+00:22:00,990 --> 00:22:05,650
+بطريقة ما سنتحدث عنها، إنها استخدمت لإعجاب تجارب
+
+304
+00:22:05,650 --> 00:22:10,580
+الأعمالهو مجرد
+
+305
+00:22:10,580 --> 00:22:14,340
+عملية تخطيط عندما نتكلم عن عملية تخطيط بمهارات
+
+306
+00:22:14,340 --> 00:22:17,320
+تخطيط بمهارات تخطيط بمهارات تخطيط بمهارات تخطيط
+
+307
+00:22:17,320 --> 00:22:17,360
+بمهارات تخطيط بمهارات تخطيط بمهارات تخطيط بمهارات
+
+308
+00:22:17,360 --> 00:22:17,840
+تخطيط بمهارات تخطيط بمهارات تخطيط بمهارات تخطيط
+
+309
+00:22:17,840 --> 00:22:19,980
+بمهارات تخطيط بمهارات تخطيط بمهارات تخطيط بمهارات
+
+310
+00:22:19,980 --> 00:22:24,000
+تخطيط بمهارات تخطيط بمهارات تخطيط بمهارات تخطيط
+
+311
+00:22:24,000 --> 00:22:31,450
+بمهارات تخطيط بمهاراتوميكانيزمات لتحقيق المهتمين
+
+312
+00:22:31,450 --> 00:22:35,430
+تم تطبيقها وهذا ببساطة الهدف من الهدف من الهدف من
+
+313
+00:22:35,430 --> 00:22:51,510
+الهدف من الهدف من الهدف من الهدف من الهدف
+
+314
+00:22:51,750 --> 00:22:58,370
+الشخصين الذين يشاركون في تصميم الخطوط لتحقيق الهدف
+
+315
+00:22:58,370 --> 00:23:06,030
+و بعد ذلك يقومون بتحقيق الخطوط و بعد ذلك يقومون
+
+316
+00:23:06,030 --> 00:23:11,250
+بتحقيق الخطوط و بعد ذلك يقومون بتحقيق الخطوط و بعد
+
+317
+00:23:11,250 --> 00:23:15,410
+ذلك يقومون بتحقيق الخطوط و بعد ذلك يقومون بتحقيق
+
+318
+00:23:15,410 --> 00:23:16,450
+الخطوط و بعد ذلك يقومون بتحقيق الخطوط و بعد ذلك
+
+319
+00:23:16,450 --> 00:23:20,940
+يقومون بتحقيق الخطوط و بعد ذلك يقومون بتحقيقهنا
+
+320
+00:23:20,940 --> 00:23:24,900
+نتكلم عن أشياء مختلفة، واحد من المشكلة هنا هو أننا
+
+321
+00:23:24,900 --> 00:23:28,720
+نتكلم عن خطوات مؤسسة جيدة بين الشخصيات ومؤسسة
+
+322
+00:23:28,720 --> 00:23:34,360
+نفسها، نتكلم هنا عن أهمية التجارب بين مديرات
+
+323
+00:23:34,360 --> 00:23:43,400
+ومستخدمين أقل، نتكلم هنا عن أهمية التخطيط ك文化 أو
+
+324
+00:23:43,400 --> 00:23:50,860
+ميكانيزمفي المؤسسة التي تستخدمها على مبادرة مستمرة
+
+325
+00:23:50,860 --> 00:23:55,520
+حسنا، فنحن نتكلم هنا عن أشياء مختلفة مرتبطة بهذه
+
+326
+00:23:55,520 --> 00:23:58,080
+النظرية الآن، ما يجب أن نفعله في الوظيفة الوظيفة
+
+327
+00:23:58,080 --> 00:24:02,440
+يجب أن يشجع الموظفين كيف يمكن الوظيفة الوظيفة
+
+328
+00:24:02,440 --> 00:24:09,820
+الوظيفة يشجع الموظفين؟ بالطبع كما ذكرت سابقًا،
+
+329
+00:24:09,820 --> 00:24:11,460
+إنها واحدة من تطبيقات الوظيفة
+
+330
+00:24:33,550 --> 00:24:39,610
+أو الـ MBO يمكن أن يشجع الموظفين
+
+331
+00:24:42,130 --> 00:24:46,410
+ماذا قلت قبل ثلاث أو أربع دقائق، هو أن الموظفين
+
+332
+00:24:46,410 --> 00:24:50,370
+لديهم إحتاجات، والمؤسسات يجب أن تقدروا إيجارها،
+
+333
+00:24:50,370 --> 00:24:54,640
+ويجب أن نعرف الاتصال بين الإحتاجات وإيجارهاعندما
+
+334
+00:24:54,640 --> 00:24:58,960
+نتكلم عن تلك الانتجارات، لسنا نتكلم عن أن شيء
+
+335
+00:24:58,960 --> 00:25:03,640
+سيحدث مجرد الوقت نفسه، لسنا نتكلم عن كيف يقوم
+
+336
+00:25:03,640 --> 00:25:08,840
+الموظفين بإيجاب أو فهم النتائج وما هي إتجاراتهم،
+
+337
+00:25:08,840 --> 00:25:11,740
+لذلك إذا كانوا الموظفين يجدوا أنهم يستطيعون تحقيق
+
+338
+00:25:11,740 --> 00:25:16,380
+مهارات معينة وإن المؤسسة ستعطيهم بعض المعادلات
+
+339
+00:25:16,380 --> 00:25:23,180
+ويحتاجون إلى ما سيكون المعادلات تتفاجئوهنا نستطيع
+
+340
+00:25:23,180 --> 00:25:29,100
+أن نعرف الاتصال بين الوظيفة الوظيفة الوظيفة
+
+341
+00:25:29,100 --> 00:25:32,160
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+342
+00:25:32,160 --> 00:25:35,960
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+343
+00:25:35,960 --> 00:25:36,760
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+344
+00:25:36,760 --> 00:25:39,660
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+345
+00:25:39,660 --> 00:25:42,240
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+346
+00:25:42,240 --> 00:25:43,200
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+347
+00:25:43,200 --> 00:25:46,740
+الوظيفة
+
+348
+00:25:46,740 --> 00:25:53,410
+الوظيفة الوظالعملاء الأولى هم مهتمين ومثبتين
+
+349
+00:25:53,410 --> 00:25:58,030
+ومجرمين نفهم لماذا مهتمين ومثبتين ومثبتين ومثبتين
+
+350
+00:25:58,030 --> 00:26:01,410
+ومثبتين ومثبتين ومثبتين ومثبتين ومثبتين ومثبتين
+
+351
+00:26:01,410 --> 00:26:05,670
+ومثبتين ومثبتين
+
+352
+00:26:16,560 --> 00:26:25,480
+ماذا يعني بالضبط؟ هل نقدر
+
+353
+00:26:25,480 --> 00:26:30,800
+نقوم بتقديم مهارات غير مفهومة؟ مهارات غير مفهومة
+
+354
+00:26:30,800 --> 00:26:36,640
+يجب أن تكونTangible، حسنًا، عندما نتحدث عن مهارات
+
+355
+00:26:36,640 --> 00:26:40,660
+تكون تانجيبال، هنا نتحدث عن شيء في النهاية يمكننا
+
+356
+00:26:40,660 --> 00:26:43,700
+أن نحصل عليه، حسنًا؟ لسنا نتحدث عن شيء تانجيبال
+
+357
+00:26:43,700 --> 00:26:47,260
+بمعنى أنه شيء يمكننا أن نحصل عليه، شيء يمكننا أن
+
+358
+00:26:47,260 --> 00:26:52,120
+نقوم به، شيء يمكننا أن نتعامل به، شيء يمكننا أن
+
+359
+00:26:52,120 --> 00:26:55,990
+نسمح به، على سبيل المثال، وكذلك، حسنًا؟هنا نحن
+
+360
+00:26:55,990 --> 00:26:59,110
+نتكلم عن هدفين مستقلين، إذا لم يكن هؤلاء الهدفين
+
+361
+00:26:59,110 --> 00:27:03,610
+مستقلين، فسيكون صعب التسجيل من الهدفين، لهذا السبب
+
+362
+00:27:03,610 --> 00:27:06,690
+يجب أن يكون كل الهدفين مستقلين، وعندما نتكلم عن
+
+363
+00:27:06,690 --> 00:27:10,910
+هدفين مستقلين، هناك مشكلة أخرى التي يجب أن نتكلم
+
+364
+00:27:10,910 --> 00:27:15,570
+عنها أيضًا، وهي أن الهدفين المستقلينبإمكاننا أن
+
+365
+00:27:15,570 --> 00:27:21,470
+نقول هنا بشكل محدد، الموظفين يستطيعون فهم يستطيعون
+
+366
+00:27:21,470 --> 00:27:24,290
+أن يذهبون بعدهم، يستطيعون .. وما إلى ذلك، لذلك هنا
+
+367
+00:27:24,290 --> 00:27:28,250
+نتحدث عن شيء يمكن الموظفين أن يتعامل معه بسهولة،
+
+368
+00:27:28,250 --> 00:27:31,150
+أنا لا أتحدث عن صعوبة المهمة نفسها، أنا أتحدث عن
+
+369
+00:27:31,150 --> 00:27:39,740
+فهم الموضوع نفسه، الأن Verifiableلأن في عملية
+
+370
+00:27:39,740 --> 00:27:40,340
+الوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+371
+00:27:40,340 --> 00:27:42,700
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+372
+00:27:42,700 --> 00:27:46,440
+للوصول للوصول للوصول للوصول للوصول للوصول للوصول
+
+373
+00:27:46,440 --> 00:27:58,820
+للوصول للوصول للوصول للوصولوإذا كان هناك حاجات أو
+
+374
+00:27:58,820 --> 00:28:05,400
+مشكلة تظهر أو شيء ثم يجب أن نفعل شيء لأن في
+
+375
+00:28:05,400 --> 00:28:10,800
+النهاية يجب أن نحصل على نتيجة ليست فقط إيجاب مهمة
+
+376
+00:28:10,800 --> 00:28:16,560
+ومن ثم تحصل على هذا المهمةوالتفكير في كل حالات
+
+377
+00:28:16,560 --> 00:28:23,680
+أخرى، كل حالات هنا يجب أن يتم تفكيرها. كيف يعمل
+
+378
+00:28:23,680 --> 00:28:27,780
+هذا الموضوع؟ وكانت السؤال هل الموظفين سيحصلون على
+
+379
+00:28:27,780 --> 00:28:35,560
+تحقيق مهارتهم؟ بالطبع لاعندما أقول بالطبع ليس كما
+
+380
+00:28:35,560 --> 00:28:40,420
+يبدو ولكن علينا التطور لحالة صحيحة، علينا أن نكون
+
+381
+00:28:40,420 --> 00:28:44,540
+مؤسسة، علينا أن نكون مؤسسة، علينا أن نكون مؤسسة،
+
+382
+00:28:44,540 --> 00:28:44,600
+نكون مؤسسة، علينا أن نكون مؤسسة، علينا أن نكون
+
+383
+00:28:44,600 --> 00:28:46,080
+مؤسسة، علينا أن نكون مؤسسة، علينا أن نكون مؤسسة،
+
+384
+00:28:46,080 --> 00:28:48,140
+علينا أن نكون مؤسسة، علينا أن نكون مؤسسة، علينا أن
+
+385
+00:28:48,140 --> 00:28:49,220
+نكون مؤسسة، علينا أن نكون مؤسسة، علينا أن نكون
+
+386
+00:28:49,220 --> 00:28:55,460
+مؤسسة، علينا أن نكون مؤسسة، عأو مجلد أو مجلد وما
+
+387
+00:28:55,460 --> 00:29:01,260
+إلى ذلك وعندما يطلب الموظفين المشاركة في MBO أو
+
+388
+00:29:01,260 --> 00:29:03,400
+عملية الوصول للأموال ومشاركة الوصول للأموال هنا
+
+389
+00:29:03,400 --> 00:29:05,640
+يطلبون أن يطلبوا أن يطلبوا ان يطلبوا ان يطلبوا ان
+
+390
+00:29:05,640 --> 00:29:07,380
+يطلبوا ان يطلبوا ان يطلبوا ان يطلبوا ان يطلبوا ان
+
+391
+00:29:07,380 --> 00:29:08,020
+يطلبوا ان يطلبوا ان يطلبوا ان يطلبوا ان يطلبوا ان
+
+392
+00:29:08,020 --> 00:29:09,360
+يطلبوا ان يطلبوا ان يطلبوا ان يطلبوا ان يطلبوا ان
+
+393
+00:29:09,360 --> 00:29:10,660
+يطلبوا ان يطلبوا ان يطلبوا ان يطلبوا ان يطلبوا ان
+
+394
+00:29:10,660 --> 00:29:15,020
+يطلبوا ان
+
+395
+00:29:15,020 --> 00:29:20,710
+يطلبالهدف السياسي يتم تحريره في مستوى مختلف لهدف
+
+396
+00:29:20,710 --> 00:29:28,050
+صغير ليس فقط في مرة واحدة نحن نتكلم ربما عن ..
+
+397
+00:29:28,050 --> 00:29:35,750
+يتعامل مع مؤسسة نفسها كم مرة نحتاج تحرر هذه الهدف.
+
+398
+00:29:35,930 --> 00:29:40,870
+بعد ذلك،
+
+399
+00:29:40,870 --> 00:29:42,390
+الموظفين يُسألون
+
+400
+00:29:45,200 --> 00:29:49,260
+السيباريجية للسيباريجيين أو رئيسهم، السيباريجيين
+
+401
+00:29:49,260 --> 00:29:55,020
+السيباريجيين للسيباريجيين لتطوير الخطة لأول عام،
+
+402
+00:29:55,020 --> 00:29:59,100
+على سبيل المثال، 3 أشهر، 6 أشهر، 1 عام، مهما كان،
+
+403
+00:29:59,100 --> 00:30:04,420
+سيكون هناك قرار من الوقت وهو أحد الأشياء المهمة
+
+404
+00:30:04,420 --> 00:30:08,080
+عندما نتكلم عن الواجهة من أهداف نحن لا نعرف أهداف
+
+405
+00:30:08,080 --> 00:30:10,340
+بدون أن نصلحها إلى الوقت
+
+406
+00:30:16,150 --> 00:30:22,390
+وهنا نتحدث عن تحريك مهاراتهم إلى مهارات أصغر بعد
+
+407
+00:30:22,390 --> 00:30:26,750
+ذلك مهارات الموظفين بمساعدة مهارات المديرين هم هم
+
+408
+00:30:26,750 --> 00:30:29,740
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هملتحقيق
+
+409
+00:30:29,740 --> 00:30:33,840
+مع وقت محدد من الوقت وعند تصميم هذا البرنامج،
+
+410
+00:30:33,840 --> 00:30:38,980
+اكتشفوا مراتب الوقت، اكتشفوا رولة المؤسسة، رولة
+
+411
+00:30:38,980 --> 00:30:42,820
+الموظف، انه أو نفسها، وأيضًا هنا نتحدث عن
+
+412
+00:30:42,820 --> 00:30:47,290
+المطالبات التي يجب أن تكونأو مؤسسة، ومعرفة
+
+413
+00:30:47,290 --> 00:30:49,910
+إيجابها، ومعرفة إيجابها، ومعرفة إيجابها، ومعرفة
+
+414
+00:30:49,910 --> 00:30:52,390
+إيجابها، ومعرفة إيجابها، ومعرفة إيجابها، ومعرفة
+
+415
+00:30:52,390 --> 00:30:54,970
+إيجابها، ومعرفة إيجابها، ومعرفة إيجابها، ومعرفة
+
+416
+00:30:54,970 --> 00:30:56,150
+إيجابها، ومعرفة إيجابها، ومعرفة إيجابها، ومعرفة
+
+417
+00:30:56,150 --> 00:30:57,270
+إيجابها، ومعرفة إيجابها، ومعرفة إيجابها، ومعرفة
+
+418
+00:30:57,270 --> 00:31:03,270
+إيجابها، ومعرفة إيجابها، ومعرفة إيجابها، ومعرفة
+
+419
+00:31:03,270 --> 00:31:09,420
+إيجابها، ومعرفة إيميكانيزم لأن بعد تحقيق الهدف هنا
+
+420
+00:31:09,420 --> 00:31:14,820
+يوجد بعض الميزانيات التي تم إعطائها المؤسسة عندما
+
+421
+00:31:14,820 --> 00:31:22,180
+نتكلم عن مهاجمات ومهاجمات المهم هو الهدف المهم هو
+
+422
+00:31:22,180 --> 00:31:30,280
+الهدف المهم هو الهدف المهم هو الهدف المهم هو الهدف
+
+423
+00:31:30,280 --> 00:31:32,260
+المهم هو الهدف المهم هو الهدف المهم هو الهدف المهم
+
+424
+00:31:32,260 --> 00:31:33,280
+هو الهدف المهم هو الهدف المهم هو الهدف المهم هو
+
+425
+00:31:33,280 --> 00:31:34,680
+الهدف المهم هو الهدف المهم هو الهدف المهم هو الهدف
+
+426
+00:31:34,680 --> 00:31:37,270
+المهم هو الهدف المهم هو الهدف المهم هوأو
+
+427
+00:31:37,270 --> 00:31:41,130
+الاختيارات المشاركة، وقد قلت في البداية بأننا
+
+428
+00:31:41,130 --> 00:31:46,570
+نستخدم هنا تجارب مشاركة، التخطيط يتم بين الموظف
+
+429
+00:31:46,570 --> 00:31:52,970
+والمشارك، الموظف يستخدم تجارب مشاركة، الموظف لا
+
+430
+00:31:52,970 --> 00:31:56,130
+يصنعوا
+
+431
+00:31:56,130 --> 00:31:59,980
+خطواتهم الخاصةوهي تصميم خططها الخاصة بمساعدة
+
+432
+00:31:59,980 --> 00:32:05,280
+محافظاتها ومن الواضح أنها تتجارب مع إقرار المؤسسة
+
+433
+00:32:05,280 --> 00:32:08,600
+يجب أن يكون هنا في النهاية .. نحن نتحدث هنا عن
+
+434
+00:32:08,600 --> 00:32:13,500
+عملية مفهوم أو مفهوم، عملية مفهوم، عملية مفهوم،
+
+435
+00:32:13,500 --> 00:32:13,700
+عملية مفهوم، عملية مفهوم، عملية مفهوم، عملية
+
+436
+00:32:13,700 --> 00:32:14,040
+عملية مفهوم، عملية مفهوم، عملية مفهوم، عملية
+
+437
+00:32:14,040 --> 00:32:16,220
+مفهوم، عملية مفهوم، عملية مفهوم، عملية مفهوم،
+
+438
+00:32:16,220 --> 00:32:24,520
+عملية مفهوم، عملية مفوأيضًا نتحدث عن وقت محدد
+
+439
+00:32:24,520 --> 00:32:29,960
+للتبديل ومعرفة المهمة أو المهمة على سبيل المثال
+
+440
+00:32:29,960 --> 00:32:34,060
+وكذلك ومعرفة الهجوم ومعرفة الهجوم ومعرفة الهجوم
+
+441
+00:32:34,060 --> 00:32:41,620
+ومعرفة الهجوم ومعرفة الهجوم ومعرفة الهجوم ومعرفة
+
+442
+00:32:41,620 --> 00:32:43,480
+الهجوم ومعرفة الهجوم ومعرفة الهجوم ومعرفة الهجوم
+
+443
+00:32:43,480 --> 00:32:48,390
+ومعرفة الهجوم ومعرفة الهجوم ومعرفة الهجومأو على
+
+444
+00:32:48,390 --> 00:32:53,930
+أقل على طرق أو ميلادات، يجب أن يكون هناك نوع من
+
+445
+00:32:53,930 --> 00:33:03,370
+إعادة إعادة إعادة، لماذا؟ وما
+
+446
+00:33:03,370 --> 00:33:06,870
+هو أهم هنا هو الوصول للهجوم في النهاية وفي بعض
+
+447
+00:33:06,870 --> 00:33:11,250
+الأحيان يوجد مشكلة مهمة موجودة وما إلى ذلك، لذلك
+
+448
+00:33:11,250 --> 00:33:14,770
+يجب أن نقوم بعض الأحيان بتحقيق أو تغيير الخطة وما
+
+449
+00:33:14,770 --> 00:33:21,390
+إلى ذلكوهنا باستمرار أحيانًا يكون هناك مشكلة تم
+
+450
+00:33:21,390 --> 00:33:29,440
+تخيلها بشكل غير صحيح ويجب أن نفكر فيها مرة أخرىهنا
+
+451
+00:33:29,440 --> 00:33:32,300
+يجب أن يكون هناك إعجاب تجارية دائما، واحد من
+
+452
+00:33:32,300 --> 00:33:36,980
+الأشياء المهمة أيضًا هي أن الإعجاب تجارية نفسها هي
+
+453
+00:33:36,980 --> 00:33:45,200
+شيء سيحرر عملياتها، يعني إنها إشارة لإدارة
+
+454
+00:33:45,200 --> 00:33:50,300
+مديراتها أنها مهتمة بالإنجاز للهواتف والهواتف وما
+
+455
+00:33:50,300 --> 00:33:54,640
+إلى ذلك، لذلك نفسها هي شيء يميزه عنصرية عندما
+
+456
+00:33:54,640 --> 00:34:00,160
+نتكلم عن علاقة بين المديراتemployees okay any
+
+457
+00:34:00,160 --> 00:34:03,020
+questions؟ أبطئي كله عافية
+
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/PoiZWTA-FRI_raw.json b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/PoiZWTA-FRI_raw.json
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@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3007, "start": 7.25, "end": 30.07, "text": "سنتحدث عن ديناميكا الوحيدة وخاصة سنتحدث عن مشاكل مرتبطة بمفهوم الوظيفة في هذا الفيديو سنتحدث عن بعض النظريات التي تشرح كيف يصبح الناس محفوظين بالطبع هناك نظرات مختلفة", "tokens": [3794, 1863, 2655, 24401, 12984, 18871, 11778, 1829, 8315, 2304, 1829, 4117, 995, 2423, 2407, 5016, 25708, 3660, 4032, 9778, 33546, 3660, 8608, 1863, 2655, 24401, 12984, 18871, 37893, 995, 28820, 3714, 43500, 3555, 9566, 3660, 4724, 2304, 5172, 3224, 20498, 2423, 2407, 19913, 33911, 3660, 8978, 23758, 27188, 1829, 16254, 2407, 8608, 1863, 2655, 24401, 12984, 18871, 45030, 11242, 28239, 19913, 16572, 9307, 38392, 6055, 46309, 5016, 9122, 33911, 7251, 9381, 49628, 2423, 8315, 3794, 3714, 5016, 5172, 2407, 19913, 9957, 20666, 9566, 3555, 3615, 34105, 4117, 8717, 19913, 2288, 9307, 3714, 46456, 46538, 3660], "avg_logprob": -0.6356314629623571, "compression_ratio": 1.8484848484848484, "no_speech_prob": 1.6093254089355469e-06, "words": 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"probability": 0.704833984375}, {"start": 97.98, "end": 98.36, "word": " بالطبع", "probability": 0.83740234375}, {"start": 98.36, "end": 100.18, "word": " نحن", "probability": 0.617431640625}, {"start": 100.18, "end": 101.02, "word": " أيضًا", "probability": 0.8560791015625}, {"start": 101.02, "end": 101.72, "word": " سنقوم", "probability": 0.5565185546875}, {"start": 101.72, "end": 102.12, "word": " بمراجعة", "probability": 0.5535888671875}, {"start": 102.12, "end": 102.68, "word": " بعض", "probability": 0.625244140625}, {"start": 102.68, "end": 103.32, "word": " الثورات", "probability": 0.79852294921875}, {"start": 103.32, "end": 103.44, "word": " المتطورة", "probability": 0.49296875}, {"start": 103.44, "end": 103.76, "word": " أو", "probability": 0.95703125}, {"start": 103.76, "end": 104.36, "word": " التقليدية", "probability": 0.53427734375}, {"start": 104.36, "end": 105.26, "word": " التي", "probability": 0.37060546875}, {"start": 105.26, "end": 106.36, "word": " تشرح", 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{"start": 1199.8, "end": 1200.1, "word": " عملية", "probability": 0.97998046875}, {"start": 1200.1, "end": 1200.36, "word": " عملية", "probability": 0.97998046875}, {"start": 1200.36, "end": 1200.36, "word": " عملية", "probability": 0.978515625}, {"start": 1200.36, "end": 1200.36, "word": " عملية", "probability": 0.9775390625}, {"start": 1200.36, "end": 1200.36, "word": " عملية", "probability": 0.9767252604166666}, {"start": 1200.36, "end": 1200.36, "word": " عملية", "probability": 0.9739583333333334}, {"start": 1200.36, "end": 1202.16, "word": " عملية", "probability": 0.966796875}, {"start": 1202.16, "end": 1203.08, "word": " ع", "probability": 0.98681640625}], "temperature": 1.0}, {"id": 54, "seek": 123171, "start": 1203.47, "end": 1231.71, "text": "لسنا نتكلم عن إيجابية مليئة، لا يوجد أي شيء مثل إيجابية مليئة بالكامل، مهمتين المحتاجين للإنسان مختلفين من مرة إلى مرة أخرى، للإنسان نفسه، نحن نتكلم عن حركة مختلفة من مرة إلى مرة أخرى، أحيانًا الناس يشعرون أن هناك فرصة لإيجاب محتاج محدد، 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"probability": 0.9091796875}, {"start": 2310.33, "end": 2311.31, "word": " نتائج،", "probability": 0.528271484375}, {"start": 2311.31, "end": 2311.53, "word": " لذلك", "probability": 0.64599609375}, {"start": 2311.53, "end": 2311.93, "word": " بدلا", "probability": 0.4708251953125}, {"start": 2311.93, "end": 2313.57, "word": " من", "probability": 0.8603515625}, {"start": 2313.57, "end": 2313.65, "word": " طريقة", "probability": 0.6250813802083334}, {"start": 2313.65, "end": 2313.65, "word": " رئيسية", "probability": 0.6922119140625}, {"start": 2313.65, "end": 2313.83, "word": " أكتر", "probability": 0.610504150390625}, {"start": 2313.83, "end": 2314.47, "word": " عامة", "probability": 0.5760498046875}, {"start": 2314.47, "end": 2315.63, "word": " أو", "probability": 0.892578125}, {"start": 2315.63, "end": 2315.93, "word": " طريقة", "probability": 0.7128092447916666}, {"start": 2315.93, "end": 2316.59, "word": " رئيسية", "probability": 0.8386962890625}, {"start": 2316.59, "end": 2316.99, "word": " قديمة،", "probability": 0.5212631225585938}, {"start": 2316.99, "end": 2317.49, "word": " سيكون", "probability": 0.74072265625}, {"start": 2317.49, "end": 2317.49, "word": " هناك", "probability": 0.945068359375}, {"start": 2317.49, "end": 2318.31, "word": " طريقة", "probability": 0.8953450520833334}, {"start": 2318.31, "end": 2318.31, "word": " رئيسية", "probability": 0.8640625}, {"start": 2318.31, "end": 2318.41, "word": " أكتر", "probability": 0.9046630859375}, {"start": 2318.41, "end": 2319.09, "word": " عامة", "probability": 0.6504720052083334}, {"start": 2319.09, "end": 2319.23, "word": " أو", "probability": 0.82421875}, {"start": 2319.23, "end": 2319.83, "word": " أكتر", "probability": 0.767578125}, {"start": 2319.83, "end": 2319.83, "word": " عامة", "probability": 0.686767578125}, {"start": 2319.83, "end": 2321.21, "word": " لكي", "probability": 0.8134765625}, {"start": 2321.21, "end": 2321.75, "word": " نتحكم", "probability": 0.80340576171875}, {"start": 2321.75, "end": 2321.95, "word": " في", "probability": 0.85302734375}, {"start": 2321.95, "end": 2323.33, "word": " الموضوع،", "probability": 0.6821044921875}, {"start": 2323.33, "end": 2323.63, "word": " هل", "probability": 0.53179931640625}, {"start": 2323.63, "end": 2323.97, "word": " لديك", "probability": 0.665283203125}, {"start": 2323.97, "end": 2324.89, "word": " أسئلة؟", "probability": 0.7806396484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2333.16425, "duration_after_vad": 2276.8731249999955}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/bAD6BZD0FmM_postprocess.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/bAD6BZD0FmM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..75f5ad918689cae401a47499b79e06ab648a7f7e
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/bAD6BZD0FmM_postprocess.srt
@@ -0,0 +1,1864 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:09,570 --> 00:00:14,030
+طيب، اليوم سنكمل مع مصطلحات الجماعة، في دراسة
+
+3
+00:00:14,030 --> 00:00:21,070
+قبلها، نحن نتكلم عن اتفاقين، اولا كانت .. اتفاقين،
+
+4
+00:00:21,070 --> 00:00:24,870
+اولا كانت .. اتفاقين، اتفاقين، اتفاقين، اتفاقين،
+
+5
+00:00:24,870 --> 00:00:25,010
+اتفاقين، اتفاقين، اتفاقين، اتفاقين، اتفاقين،
+
+6
+00:00:25,010 --> 00:00:26,550
+اتفاقين، اتفاقين، اتفاقين، اتفاقين، اتفاقين،
+
+7
+00:00:26,550 --> 00:00:31,730
+اتفاقين، اتفاقين، اتفاقين، اتفاق
+
+8
+00:00:34,050 --> 00:00:38,490
+سنكمل مع هذه المصطلحات، وسنتكلم عن مصطلح الوضع
+
+9
+00:00:38,490 --> 00:00:40,490
+ومصطلح المصطلح ومصطلح المصطلح ومصطلح المصطلح
+
+10
+00:00:40,490 --> 00:00:41,130
+ومصطلح المصطلح ومصطلح المصطلح ومصطلح المصطلح
+
+11
+00:00:41,130 --> 00:00:41,550
+ومصطلح المصطلح ومصطلح المصطلح ومصطلح المصطلح
+
+12
+00:00:41,550 --> 00:00:42,590
+ومصطلح المصطلح ومصطلح المصطلح ومصطلح المصطلح
+
+13
+00:00:42,590 --> 00:00:43,150
+ومصطلح المصطلح ومصطلح المصطلح ومصطلح المصطلح
+
+14
+00:00:43,150 --> 00:00:49,670
+ومصطلح المصطلح ومصطلح المصطلح ومصطلح المصطلعندما
+
+15
+00:00:49,670 --> 00:00:55,310
+نتحدث عن موقع، هنا نتحدث عن موقع مخصص في المجتمع
+
+16
+00:00:55,310 --> 00:01:05,080
+أو مجموعة أخرى أو مجموعة أخرىعندما نتكلم عن
+
+17
+00:01:05,080 --> 00:01:10,560
+الوظيفة، نتكلم عن موقع مخصص للمجتمع، يمكن أن يكون
+
+18
+00:01:10,560 --> 00:01:15,720
+مجموعة من مجموعات أخرى أو مجموعة من مجموعة من
+
+19
+00:01:15,720 --> 00:01:22,960
+مجموعات أخرى. عندما نتكلم عن الوظيفة وموقع مخصص
+
+20
+00:01:22,960 --> 00:01:28,060
+للمجتمع، نتكلم عن مجموعة أو مجموعة مختلفة من
+
+21
+00:01:28,060 --> 00:01:32,870
+مجموعات مختلفةيعني there are people in higher
+
+22
+00:01:32,870 --> 00:01:38,710
+ranks than others and vice versa of course of
+
+23
+00:01:38,710 --> 00:01:45,290
+course here we must not confuse status with the
+
+24
+00:01:45,290 --> 00:01:51,450
+ruleتكون هناك علاقة لكنها ليست نفس الشيء، نحن
+
+25
+00:01:51,450 --> 00:01:55,390
+نتكلم عن أشياء مختلفة في القواعد، كنا نتكلم عن
+
+26
+00:01:55,390 --> 00:02:00,450
+شخصية ثم مجموعة، ما هي العمليات التي يتطلب أن
+
+27
+00:02:00,450 --> 00:02:05,790
+تتميأ بشخص محدد؟ عندما نتكلم عن الوظيفة، نتكلم
+
+28
+00:02:05,790 --> 00:02:09,900
+أكتر عن الموقع، وهذا يتعلق أكتر على القوةفي
+
+29
+00:02:09,900 --> 00:02:15,360
+مجموعات مختلفة، وما هي القوية التي لديها لتدخل
+
+30
+00:02:15,360 --> 00:02:22,160
+مجموعات مختلفة في نفس المجموعة. هناك ما يسمى كـ
+
+31
+00:02:22,160 --> 00:02:26,440
+Status Characteristics Theory، وفقًا لـ Status
+
+32
+00:02:26,440 --> 00:02:29,900
+Characteristics Theory، هناك ثلاث أشياء أساسية
+
+33
+00:02:29,900 --> 00:02:38,020
+أساسية هنا، التي تساعد الشخصيات في اكتشاف شخصيتهم.
+
+34
+00:02:39,980 --> 00:02:45,020
+الأول هو القوة التي لديها الشخص عن أشخاص أخرين
+
+35
+00:02:45,020 --> 00:02:48,720
+وعندما نتكلم عن القوة يعني على سبيل المثال عادةً
+
+36
+00:02:48,720 --> 00:02:53,040
+القادة لديها أكتر قوة من المساعدين على سبيل
+
+37
+00:02:53,040 --> 00:02:55,860
+المثال، الناس في المقالات الأعلى لديهم أكتر قوة
+
+38
+00:02:55,860 --> 00:02:59,980
+لأنهم لديهم أكتر قوة من أشخاص أخرين وما إلى ذلك،
+
+39
+00:02:59,980 --> 00:03:06,310
+لذلك أحد الأشياء المهمة التي ستكونالساعدة أو التي
+
+40
+00:03:06,310 --> 00:03:11,950
+ستحصل على اكتشاف مصطلح الانسان داخل أي فريق، القوة
+
+41
+00:03:11,950 --> 00:03:15,250
+التي يحصل عليها عندما نتحدث عن القوة، عامة ما
+
+42
+00:03:15,250 --> 00:03:22,370
+نتحدث عن مشاكل عامة هنا، التي ستعطي
+
+43
+00:03:22,370 --> 00:03:27,430
+الانسان بعض الشركة قوة.النقطة الثانيةالمهم هو
+
+44
+00:03:27,430 --> 00:03:31,930
+القدرة على المشاركة في أهداف المجتمع وهنا نتكلم
+
+45
+00:03:31,930 --> 00:03:34,930
+أكتر عن مهارات ومهارات ومهارات ومهارات ومهارات
+
+46
+00:03:34,930 --> 00:03:35,690
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+47
+00:03:35,690 --> 00:03:37,430
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+48
+00:03:37,430 --> 00:03:37,590
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+49
+00:03:37,590 --> 00:03:38,630
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+50
+00:03:38,630 --> 00:03:38,650
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+51
+00:03:38,650 --> 00:03:54,410
+ومهارات ومهارات ومهارات وم
+
+52
+00:03:54,920 --> 00:03:59,660
+الثاني هو الواقع الروحاني أو ما يسمى كاريزما بعض
+
+53
+00:03:59,660 --> 00:04:07,380
+الشخصين لديهم كاريزما مفيد لهم أو سيساعدهم
+
+54
+00:04:09,530 --> 00:04:12,910
+أو كيف يمكن أن يتعاملوا مع أخرين أو كيف يمكن أن
+
+55
+00:04:12,910 --> 00:04:15,550
+يتواصلوا مع أخرين أو يتعاملوا مع أخرين أو يتعاملوا
+
+56
+00:04:15,550 --> 00:04:16,330
+مع أخرين أو يتعاملوا مع أخرين أو يتعاملوا مع أخرين
+
+57
+00:04:16,330 --> 00:04:17,330
+أو يتعاملوا مع أخرين أو يتعاملوا مع أخرين أو
+
+58
+00:04:17,330 --> 00:04:17,870
+يتعاملوا مع أخرين أو يتعاملوا مع أخرين أو يتعاملوا
+
+59
+00:04:17,870 --> 00:04:19,150
+مع أخرين أو يتعاملوا مع أخرين أو يتعاملوا مع أخرين
+
+60
+00:04:19,150 --> 00:04:19,170
+أو يتعاملوا مع أخرين أو يتعاملوا مع أخرين أو
+
+61
+00:04:19,170 --> 00:04:20,350
+يتعاملوا مع أخرين أو يتعاملوا مع أخرين أو يتعاملوا
+
+62
+00:04:20,350 --> 00:04:27,050
+مع أخرين أو يتعاملوا مع أخرين أو
+
+63
+00:04:27,050 --> 00:04:36,420
+يتعوالثالث هو شخصيته نفسها أو كاريزما الشخصية. هذه
+
+64
+00:04:36,420 --> 00:04:43,020
+الأشياء ستساعد كل شخص في مجتمعه أو مجتمعه أو
+
+65
+00:04:43,020 --> 00:04:44,440
+مجتمعه أو مجتمعه أو مجتمعه أو مجتمعه أو مجتمعه أو
+
+66
+00:04:44,440 --> 00:04:45,240
+مجتمعه أو مجتمعه أو مجتمعه أو مجتمعه أو مجتمعه أو
+
+67
+00:04:45,240 --> 00:04:45,940
+مجتمعه أو مجتمعه أو مجتمعه أو مجتمعه أو مجتمعه أو
+
+68
+00:04:45,940 --> 00:04:51,640
+مجتمعه أو مجتمعه أو مجتمعههو سيكون ملاحظًا بشخص
+
+69
+00:04:51,640 --> 00:04:56,620
+آخر في نفس المجتمع كما نستطيع أن نلاحظ هنا، ليس
+
+70
+00:04:56,620 --> 00:05:01,200
+كلها مشكلة أساسية هنا هناك مشكلة مرتبطة بالمؤسسة
+
+71
+00:05:01,200 --> 00:05:05,680
+نفسها حيث أن المؤسسة ستعطي نوع من القوة ولكن أيضًا
+
+72
+00:05:05,680 --> 00:05:10,340
+هناك مشكلة متعلقة بالشخص مثلًاعندما نتكلم عن
+
+73
+00:05:10,340 --> 00:05:13,480
+القدرات والقدرات وما إلى ذلك وعندما نتكلم عن
+
+74
+00:05:13,480 --> 00:05:20,420
+الكاريزما. كل هذه الأشياء يمكن أن تشكل مجموعة أي
+
+75
+00:05:20,420 --> 00:05:26,500
+شخص في مجموعة معينة. لماذا نتكلم عن مجموعة؟ لأن
+
+76
+00:05:26,500 --> 00:05:32,940
+هناك تأثير على مجموعات مختلفة. سوف نتكلم عن بعض
+
+77
+00:05:32,940 --> 00:05:38,640
+الأشياء المهمة. في الحلقة السابقة، كنا نتكلم عن
+
+78
+00:05:39,390 --> 00:05:45,830
+الان عندما نتكلم عن قواعد و تأكيد هنا نتوقع أن
+
+79
+00:05:45,830 --> 00:05:54,470
+هناك تأكيد على قواعد و تأكيد يعني مثلا
+
+80
+00:05:57,710 --> 00:06:06,190
+على سبيل المثال، يتوقع أن الشخصين بقيمة عالية لا
+
+81
+00:06:06,190 --> 00:06:12,870
+يظهروا .. أو لا يكونوا متواضعين في نفس المستوى
+
+82
+00:06:12,870 --> 00:06:20,900
+للقانون، على سبيل المثال، كشخص آخر بقيمة أقلأيضًا،
+
+83
+00:06:20,900 --> 00:06:25,040
+كان ملاحظًا بشكل مختلف من المحققين أن المستخدمين
+
+84
+00:06:25,040 --> 00:06:28,660
+الذين لديهم مستوى عالي أحيانًا يظهروا بعض الشيء من
+
+85
+00:06:28,660 --> 00:06:30,540
+الوظائف الوظائف العملية الوظائف العملية الوظائف
+
+86
+00:06:30,540 --> 00:06:31,240
+الوظائف الوظائف الوظائف الوظائف الوظائف الوظائف
+
+87
+00:06:31,240 --> 00:06:32,220
+الوظائف الوظائف الوظائف الوظائف الوظائف الوظائف
+
+88
+00:06:32,220 --> 00:06:33,620
+الوظائف الوظائف الوظائف الوظائف الوظائف الوظائف
+
+89
+00:06:33,620 --> 00:06:35,800
+الوظائف الوظائف الوظائف الوظائف الوظائف الوظائف
+
+90
+00:06:35,800 --> 00:06:38,770
+الوظائف الوظائف الوظائف الوظيعني as we can
+
+91
+00:06:38,770 --> 00:06:43,070
+understand here that there is some sort of we can
+
+92
+00:06:43,070 --> 00:06:47,170
+say a space for people with high status okay but
+
+93
+00:06:47,170 --> 00:06:52,250
+this space is not open all the way it is to an
+
+94
+00:06:52,250 --> 00:06:57,160
+extent or to a certain limitالتي لا يجب أن تخلق
+
+95
+00:06:57,160 --> 00:07:05,760
+قوتها لتحقيق مهارتها ومهاراتها بالطبع أيضًا عندما
+
+96
+00:07:05,760 --> 00:07:09,420
+نتحدث عن التعامل كانوا يلاحظوا أن الناس اللي كانوا
+
+97
+00:07:09,420 --> 00:07:15,030
+في مستوى عالي كانوا أكثر مقررينأكثر مقررًا، يعني
+
+98
+00:07:15,030 --> 00:07:20,450
+أنهم مقررين عندما يحتاجوا لإختيار قرار و ليس
+
+99
+00:07:20,450 --> 00:07:26,290
+بالطبع قرار عندما يحكموا أو يسيطروا على أخرين،
+
+100
+00:07:26,290 --> 00:07:31,410
+كانوا مقررين ومقررين بشكل كثير بدون أن يتحدثوا أو
+
+101
+00:07:31,410 --> 00:07:37,350
+يتحدثوا عن الكثير من المشكلتين، حسنًا؟ و بالطبع،
+
+102
+00:07:37,350 --> 00:07:42,820
+هؤلاء يتوقعون أن يكونوا في بعض الحالات نقاطالمشكلة
+
+103
+00:07:42,820 --> 00:07:49,240
+هنا مرتبطة بـ Status وكيفية تأثير تلك المشكلة مثل
+
+104
+00:07:49,240 --> 00:07:53,520
+الـ Norm, Confirmity, Group, Interaction أيضًا،
+
+105
+00:07:53,520 --> 00:07:58,580
+كانوا ملاحظين باعتبار المحققين أنه عندما يكون هناك
+
+106
+00:07:58,580 --> 00:08:01,580
+اختلافات عالية أو اختلافات كبيرة بين الـ Status و
+
+107
+00:08:01,580 --> 00:08:04,940
+Status، يعني عندما يكون هناك فرقكان هناك فرق كبير
+
+108
+00:08:04,940 --> 00:08:09,680
+بين مستوى السلسل والمستوى السلسل الأسفل، وكان أقل
+
+109
+00:08:09,680 --> 00:08:17,420
+مجتمع في الأفكار متوفر، يعني كان هناك أقل محادثات،
+
+110
+00:08:17,420 --> 00:08:21,320
+والناس في مستوى السلسل الأسفل، كانوا أقل مستعدين
+
+111
+00:08:21,320 --> 00:08:28,440
+لإيجاب أفكارهم عن حالة أو حلول وما إلى ذلك، وهو
+
+112
+00:08:28,440 --> 00:08:33,080
+السبب في أننا قلنا ذلككان هناك عدد محدود للأفكار
+
+113
+00:08:33,080 --> 00:08:40,300
+المشاركة بشخص بقيمة أقل، وهذا أيضًا يعني أن
+
+114
+00:08:40,300 --> 00:08:46,460
+الإبداع محدود هنا على الجهة الأخرى. الآن مشكلة
+
+115
+00:08:46,460 --> 00:08:51,110
+أخرى هي الميزانيةأيضًا، كان ملاحظًا أنه في كل
+
+116
+00:08:51,110 --> 00:08:52,730
+مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة
+
+117
+00:08:52,730 --> 00:08:54,850
+مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة
+
+118
+00:08:54,850 --> 00:08:56,230
+مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة
+
+119
+00:08:56,230 --> 00:08:56,490
+مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة
+
+120
+00:08:56,490 --> 00:08:59,030
+مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة
+
+121
+00:08:59,030 --> 00:09:13,030
+مقارنة مقارنة مقارنة مقارنة مقارنة مقارنة مق
+
+122
+00:09:13,060 --> 00:09:19,160
+في حالة تقليل الضغط، فالشخصية ستأخذ أدوات مختلفة
+
+123
+00:09:19,160 --> 00:09:24,580
+التي نعتبرها أدوات تقليل الضغط، وعلى مدى تقليل
+
+124
+00:09:24,580 --> 00:09:28,420
+الأدوات التي تقليل الضغط، وعلى مدى تقليل الأدوات
+
+125
+00:09:28,420 --> 00:09:32,160
+التي تقليل الضغط، وعلى مدى تقليل الأدوات التي
+
+126
+00:09:32,160 --> 00:09:33,760
+تقليل الضغط، وعلى مدى تقليل الأدوات التي تقليل
+
+127
+00:09:33,760 --> 00:09:36,480
+الضغط، وعلى مدى تقليل الأدوات التي تقليل الضغط،
+
+128
+00:09:36,480 --> 00:09:37,340
+وعلى مدى تقليل الأدوات التي تقليل الضغط، وعلى مدى
+
+129
+00:09:37,340 --> 00:09:41,500
+تقليل الأدوات التي تقليل الضغط،
+
+130
+00:09:41,500 --> 00:09:46,040
+وعلى مدىللقوة عن مشكلة مرتبطة بالرعاية التي تتعلق
+
+131
+00:09:46,040 --> 00:09:49,500
+بالرعاية التي تتعلق بالرعاية التي تتعلق بالرعاية
+
+132
+00:09:49,500 --> 00:09:49,780
+التي تتعلق بالرعاية التي تتعلق بالرعاية التي تتعلق
+
+133
+00:09:49,780 --> 00:09:51,080
+بالرعاية التي تتعلق بالرعاية التي تتعلق بالرعاية
+
+134
+00:09:51,080 --> 00:09:54,020
+التي تتعلق بالرعاية التي تتعلق بالرعاية التي تتعلق
+
+135
+00:09:54,020 --> 00:09:54,300
+بالرعاية التي تتعلق بالرعاية التي تتعلق بالرعاية
+
+136
+00:09:54,300 --> 00:09:55,260
+بالرعاية التي تتعلق بالرعاية التي تتعلق بالرعاية
+
+137
+00:09:55,260 --> 00:10:01,380
+التي تتعلق بالرعاية التي تتعلق بالرعاية التي تتعلق
+
+138
+00:10:01,840 --> 00:10:06,120
+وهو تنسيق
+
+139
+00:10:06,120 --> 00:10:13,000
+الأشخاص الموجودين في أي مؤسسة أخر مصالح هنا هي الـ
+
+140
+00:10:13,000 --> 00:10:18,480
+Size بالطبع عندما نتحدث عن الـ Size في كلمات بسيطة
+
+141
+00:10:18,480 --> 00:10:23,860
+نحن نتحدث عن عدد مجموعات مجتمع مجتمعات عادة تكون
+
+142
+00:10:23,860 --> 00:10:28,160
+مصممة أو مصممة إلى اتنين مجموعات واحدة من المصممات
+
+143
+00:10:28,160 --> 00:10:32,800
+باعتبار الـ Sizeمجموعات صغيرة ومجموعات كبيرة. الان
+
+144
+00:10:32,800 --> 00:10:37,280
+لا يوجد مقال يمكننا أن نقوله لكن باعتقاد على
+
+145
+00:10:37,280 --> 00:10:42,900
+الأقصى في الكتابة التي نتعامل معها هنا نستطيع أن
+
+146
+00:10:42,900 --> 00:10:46,540
+نقول أنه عندما يكون هناك أكثر من 12 شخص نعتبر
+
+147
+00:10:46,540 --> 00:10:50,080
+المجموعة كمجموعة كبيرة عندما يكون المقابل أكثر من
+
+148
+00:10:50,080 --> 00:10:56,500
+7 او أقل هنا نتحدث عن مجموعة صغيرة وإذا كانت بين 7
+
+149
+00:10:56,500 --> 00:11:03,480
+و12 نتحدث عن مجموعة كبيرةوللحديث عن هذا الموضوع،
+
+150
+00:11:03,480 --> 00:11:10,100
+ليس هناك عمليات عامة، لا عمليات عامة للمجموعات،
+
+151
+00:11:10,100 --> 00:11:14,120
+ولكن بالطبع سوف نجد في هذه القصة وفي القصة القادمة
+
+152
+00:11:14,120 --> 00:11:21,050
+أن المجموعات الصغيرة أكثر إيجابيةهذا موضوع مهم،
+
+153
+00:11:21,050 --> 00:11:24,730
+ولكن في بعض الأحيان، لكي نكمل مهمة معينة، نحتاج
+
+154
+00:11:24,730 --> 00:11:28,010
+لجمهور كبير من الناس. يعتمد على المهمة نفسها، وما
+
+155
+00:11:28,010 --> 00:11:32,810
+هي الميزانيات المحتاجة للإنسان لإنقاذ المهمة أو
+
+156
+00:11:32,810 --> 00:11:36,510
+لإنقاذ المهمة. لكن مرة أخرى، عندما نتحدث عن صمم،
+
+157
+00:11:36,510 --> 00:11:44,500
+نتحدث عن عدد من الانسانبعض المجموعات، بالطبع ما هو
+
+158
+00:11:44,500 --> 00:11:49,220
+أفضل استخدام من المجموعات عندما نتحدث عن صغير أو
+
+159
+00:11:49,220 --> 00:11:54,840
+كبير، هذه الطاولة ستعطينا نوع من التقارير مثلما
+
+160
+00:11:54,840 --> 00:12:00,160
+نتحدث عن السرعة، يتوقع أن المجموعات الصغيرة أسرع،
+
+161
+00:12:00,160 --> 00:12:05,260
+لماذا؟ لماذا المجموعات الصغيرة أسرع؟
+
+162
+00:12:16,250 --> 00:12:22,390
+Okay but usually the potential for conflicts among
+
+163
+00:12:22,390 --> 00:12:28,430
+smaller groups is higherلأن الاتصال هو أكتر عندما
+
+164
+00:12:28,430 --> 00:12:34,110
+نتحدث عن .. يعني إذا كنا خمس أصدقاء معًا، فالممكنة
+
+165
+00:12:34,110 --> 00:12:38,510
+للمشكلة بين واحد واخد هو من واحد لخمس، لكن إذا كنا
+
+166
+00:12:38,510 --> 00:12:41,630
+اتصالين كثير من الوقت، فالممكنة هنا هي من واحد
+
+167
+00:12:41,630 --> 00:12:46,270
+لاثنين، فنحن نتحدث عن أكترالمفروض .. ليس بالطبع
+
+168
+00:12:46,270 --> 00:12:50,510
+ولكن المفروض أن المشكلة بين المجموعات الصغيرة هي
+
+169
+00:12:50,510 --> 00:12:55,850
+عادة أعلى لأن مستوى التفاعل عادة أعلى، أكثر هناك
+
+170
+00:12:55,850 --> 00:12:59,830
+أشخاص، أقل .. هناك مشكلة أخرى، ولكن إذا كنا نتحدث
+
+171
+00:12:59,830 --> 00:13:06,050
+عن هذا الموضوع بشكل محدد، حسنًا؟ ولكن المعدد
+
+172
+00:13:06,050 --> 00:13:11,890
+الصغير يعني أن التcommunication أسهلوالترحيز في
+
+173
+00:13:11,890 --> 00:13:18,550
+المعلومات على سبيل المثال أسهل والتحكم أيضًا أسهل
+
+174
+00:13:18,550 --> 00:13:22,210
+وما إلى ذلك، فنحن نتحدث عن بعض الواضحين هنا التي
+
+175
+00:13:22,210 --> 00:13:27,800
+ستساعد في إكمال العمل في مرات أقل من الوقتالقيم
+
+176
+00:13:27,800 --> 00:13:33,640
+الانسانية تتوقع أيضًا أن تكون أفضل في مجموعات
+
+177
+00:13:33,640 --> 00:13:38,600
+أصغر، لماذا؟ لأن في مجموعات أصغر، القواعد ماضية
+
+178
+00:13:38,600 --> 00:13:45,140
+واضحة جدًا بالضبط، الوزيارات والعملات أيضًا مخصصة
+
+179
+00:13:45,140 --> 00:13:50,300
+جدًا هنا، وقيم المتعامل بين المجموعات الأصغر أيضًا
+
+180
+00:13:53,560 --> 00:13:59,600
+ولكن عندما نتكلم عن مجموعات أكتر، يتوقع أن المشكلة
+
+181
+00:13:59,600 --> 00:14:05,120
+تكون أفضل من المجموعات الصغيرة، لماذا؟ لماذا في
+
+182
+00:14:05,120 --> 00:14:10,360
+المجموعات الأكتر، يتوقع
+
+183
+00:14:10,360 --> 00:14:13,300
+أن المشكلة تكون أفضل من المجموعات الصغيرة؟
+
+184
+00:14:15,490 --> 00:14:19,690
+لأن في المجموعات الصغيرة، كما قلنا، لدينا اتفاق
+
+185
+00:14:19,690 --> 00:14:23,770
+كبير بين مجموعاتنا، لذلك أعتقد أنهم يريدون أن
+
+186
+00:14:23,770 --> 00:14:26,490
+يتعاملوا مع بعضهم البعض لتحديد المشكلة، وكل من
+
+187
+00:14:26,490 --> 00:14:33,710
+لديه فكرة وفكرة يريد أن يتحكم في هذه الفكرة ويريد
+
+188
+00:14:33,710 --> 00:14:38,650
+ذلكحسنًا، لكننا قلنا إن مستوى التجارب الصغيرة
+
+189
+00:14:38,650 --> 00:14:44,170
+عندما نتحدث عن تجارب واحدة وعندما نتحدث عن تجارب
+
+190
+00:14:44,170 --> 00:14:47,010
+عامة في النهاية، فسنجد أيضًا أن المجموعات الصغيرة
+
+191
+00:14:47,010 --> 00:14:51,550
+لديها تجارب عامة أعلى في كل مجموعة، نعم؟ في الكثير
+
+192
+00:14:51,550 --> 00:14:56,150
+من المجموعات العامة، يمكنك استخدام الكثير من
+
+193
+00:14:56,150 --> 00:15:03,110
+الأفكاربالضبط، هنا نحن نتحدث عن مشاركة أكتر فكرة،
+
+194
+00:15:03,110 --> 00:15:06,430
+نحن لدينا أكتر شخصيات، طريقات مختلفة للتفكير،
+
+195
+00:15:06,430 --> 00:15:10,090
+مراتب مختلفة، تجارب مختلفة وما إلى ذلك، وهو السبب
+
+196
+00:15:10,090 --> 00:15:15,810
+من المتوقع أن قدرتهم في حل المشكلة هي أكتر من
+
+197
+00:15:15,810 --> 00:15:21,390
+واحدة فكرة أو أكتر من .. نحن نتحدث هنا عن مجموعة
+
+198
+00:15:21,390 --> 00:15:27,660
+من الفكرةو أيضًا هنا عندما نتكلم عن .. إنه مرتبط
+
+199
+00:15:27,660 --> 00:15:32,740
+هنا، الانتجار، الانتجار، لأن كما ذكرت قبل، هنا
+
+200
+00:15:32,740 --> 00:15:36,860
+نتكلم عن تجارب مختلفة، نتكلم عن مهارات مختلفة
+
+201
+00:15:36,860 --> 00:15:41,670
+أيضًا، طريقات التفكير وما إلى ذلكوكل هذا سيضيف بعض
+
+202
+00:15:41,670 --> 00:15:47,070
+الانتجار لجمهور المجتمع بالطبع وهذا سيحفز نقطة
+
+203
+00:15:47,070 --> 00:15:50,790
+ثلاثها بطريقة مرتبطة بطريقة مرتبطة نحن نتكلم عن
+
+204
+00:15:50,790 --> 00:15:54,450
+الوصول للهدف وهو سيكون أفضل جدًا عندما نتكلم عن
+
+205
+00:15:54,450 --> 00:15:59,850
+مجموعات أكتر واحدة من أشياء أهم من مجموعات أكتر
+
+206
+00:15:59,850 --> 00:16:05,030
+نحن نتكلم عن مجالات مختلفة، تجارب، فكافة، فكافة،
+
+207
+00:16:05,030 --> 00:16:05,270
+فكافة، فكافة، فكافة، فكافة، فكافة، فكافة، فكافة،
+
+208
+00:16:05,270 --> 00:16:09,090
+فكافة، فكافة، فكافة، فكافة، فكافة، فكافة،على قيمة
+
+209
+00:16:09,090 --> 00:16:11,390
+المجموعات، ولكن مرة أخرى عندما نتكلم عن مجموعات
+
+210
+00:16:11,390 --> 00:16:17,130
+أصغر، يوجد أشياء أخرى مرتبطة بالتعامل، مثلًا،
+
+211
+00:16:17,130 --> 00:16:21,870
+مستخدام المعلومات، التعامل، أيضًا عندما نتكلم عن
+
+212
+00:16:21,870 --> 00:16:27,050
+التعامل بين مجموعات أصغر، فهو أسهل وأفضل في
+
+213
+00:16:27,050 --> 00:16:32,520
+تقاريره إلى مجموعات أكبريوجد .. يعني .. نستطيع أن
+
+214
+00:16:32,520 --> 00:16:35,800
+نقول بروز وكونز لكل نقطة عندما نتكلم عن مجموعات
+
+215
+00:16:35,800 --> 00:16:42,220
+صغيرة أو كبيرة. الآن، لازم نتكلم عن الصمم، واحد من
+
+216
+00:16:42,220 --> 00:16:47,220
+المشكلات التي مرتبطة بعمل مجموعات هي ما نسميه الـ
+
+217
+00:16:47,220 --> 00:16:49,820
+social looping. الآن عندما نتكلم عن ال social
+
+218
+00:16:49,820 --> 00:16:51,820
+looping هنا، نستخدم
+
+219
+00:16:54,920 --> 00:17:03,200
+الأول هو تجارب الشخصيات التي تقوم بتجاربها أو تقوم
+
+220
+00:17:03,200 --> 00:17:04,900
+بتجاربها أو تقوم بتجاربها أو تقوم بتجاربها أو تقوم
+
+221
+00:17:04,900 --> 00:17:05,140
+بتجاربها أو تقوم بتجاربها أو تقوم بتجاربها أو تقوم
+
+222
+00:17:05,140 --> 00:17:07,060
+بتجاربها أو تقوم بتجاربها أو تقوم بتجاربها أو تقوم
+
+223
+00:17:07,060 --> 00:17:09,180
+بتجاربها أو تقوم بتجاربها أو تقوم بتجاربها أو تقوم
+
+224
+00:17:09,180 --> 00:17:09,580
+بتجاربها أو تقوم بتجاربها أو تقوم بتجاربها أو تقوم
+
+225
+00:17:09,580 --> 00:17:09,680
+بتجاربها أو تقوم بتجاربها أو تقوم بتجاربها أو تقوم
+
+226
+00:17:09,680 --> 00:17:13,200
+بتجاربها أو تقوم بتجاربها أو تقوم بتجاربها أو تقوم
+
+227
+00:17:13,200 --> 00:17:21,740
+بتجاربها أو
+
+228
+00:17:21,740 --> 00:17:26,500
+تقومو بالطبع هذا مؤلم لجميع المجموعات لأن عادة بين
+
+229
+00:17:26,500 --> 00:17:32,700
+المجموعات نتوقع أن يكون هناك مجموعات
+
+230
+00:17:32,700 --> 00:17:36,600
+تتعامل مع بعضها البعض لأن كل شخص يتعامل مع حركة
+
+231
+00:17:36,600 --> 00:17:42,520
+معينة وهنا نتحدث عن التعامل مع هذه الحركات لكي
+
+232
+00:17:42,520 --> 00:17:48,040
+نتعامل مع المهمة الأخيرةالان عندما نتكلم عن
+
+233
+00:17:48,040 --> 00:17:52,360
+الانقلاب الاجتماعي،
+
+234
+00:17:52,360 --> 00:17:56,940
+نجد هناك اثنين أسباب يسببون انقلاب الاجتماع
+
+235
+00:17:56,940 --> 00:17:59,840
+الاجتماعي واحدة من هذه الأسباب هي المشكلة
+
+236
+00:17:59,840 --> 00:18:02,720
+الاختلاف. في بعض الأحيان عندما يشعر الناس أنهم
+
+237
+00:18:02,720 --> 00:18:06,600
+يتعاملون بشكل غير صحيح، هم سيقومون بعمل أعمال أقل.
+
+238
+00:18:07,170 --> 00:18:12,630
+وهذا واحد من السبب. الآن السبب الثاني هو ما نسميه
+
+239
+00:18:12,630 --> 00:18:16,250
+الـ free riders أو الانفجار من المسؤلية، في
+
+240
+00:18:16,250 --> 00:18:21,470
+مجموعات كبيرة عادة بعض الناس تعتمد على أكتر من ما
+
+241
+00:18:21,470 --> 00:18:29,380
+يجب على الآخرينهذا السبب ان المجتمع يجب ان يتجاوز
+
+242
+00:18:29,380 --> 00:18:31,660
+الانتجارات من الانتجارات الاجتماعية الاجتماعية
+
+243
+00:18:31,660 --> 00:18:35,400
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+244
+00:18:35,400 --> 00:18:38,160
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+245
+00:18:38,160 --> 00:18:38,420
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+246
+00:18:38,420 --> 00:18:41,080
+الاجتماعية الاجتماعية الاجتماعية الاجتماعية
+
+247
+00:18:41,080 --> 00:18:47,380
+الاجتماعية الاجتماع
+
+248
+00:18:47,420 --> 00:18:51,760
+أو كيف؟ يعني شيء متشابه لهذا الموضوع. لذلك هنا نحن
+
+249
+00:18:51,760 --> 00:18:55,020
+لدينا أثنين أسباب مرة أخرى. واحدة منها هو شعور
+
+250
+00:18:55,020 --> 00:19:01,760
+بالفوضى وهذا سيجعل بعض الناس تقضي أفعال أقل في بعض
+
+251
+00:19:01,760 --> 00:19:06,140
+الحالات وفي بعض الوقت نحن نتحدث عن مجموعة المسؤلية
+
+252
+00:19:06,140 --> 00:19:11,980
+أو ما هو يعني هنا ما نسميه أو ما نسميه مرحلين
+
+253
+00:19:11,980 --> 00:19:15,640
+خفافي هؤلاء الناس الذين سيعتمدوا على الآخرين
+
+254
+00:19:15,640 --> 00:19:21,710
+لإنهاءassignments okay how to reduce social
+
+255
+00:19:21,710 --> 00:19:27,310
+loafing how to reduce social loafing among groups
+
+256
+00:19:27,310 --> 00:19:30,650
+yes
+
+257
+00:19:30,650 --> 00:19:35,570
+maybe by giving this specific example specific
+
+258
+00:19:35,570 --> 00:19:39,490
+description so this will help everyone to know
+
+259
+00:19:39,490 --> 00:19:44,010
+what he or she is supposed to doOkay، this is one
+
+260
+00:19:44,010 --> 00:19:45,870
+of the points when you talk about authority and
+
+261
+00:19:45,870 --> 00:19:52,590
+how authority is allocated for each individual or
+
+262
+00:19:52,590 --> 00:19:54,950
+how each individual is assigned for some
+
+263
+00:19:54,950 --> 00:19:57,930
+authorities، this is one of the reasons، what
+
+264
+00:19:57,930 --> 00:19:59,170
+else؟
+
+265
+00:20:01,160 --> 00:20:05,720
+هذا ايضا واحد من الأسلحة التي نستطيع استخدامها
+
+266
+00:20:05,720 --> 00:20:09,400
+ولكن دعوني أسأل سؤال سوشيال لوفينج سيظهر أكتر في
+
+267
+00:20:09,400 --> 00:20:13,700
+مجموعات أكتر أو أكتر؟ في مجموعات أكتر، لذا أكتر
+
+268
+00:20:13,700 --> 00:20:18,240
+المجموعات هي فرصة، لكن كما قلت قبل أننا أحيانًا
+
+269
+00:20:18,240 --> 00:20:23,890
+نحتاج مجموعات أكتر، حتى ننجح في مجموعات معينةهنا
+
+270
+00:20:23,890 --> 00:20:29,270
+نأتي إلى المصطلح الأساسي يمكنني أن أقول هنا أنه لا
+
+271
+00:20:29,270 --> 00:20:33,090
+يوجد حاجة لجمهور مجتمع حتى وإن هناك أفضل فرص
+
+272
+00:20:33,090 --> 00:20:39,550
+لجمهور أصغر لكن مرة أخرى نحتاج لجمهور مجتمع بحسب
+
+273
+00:20:39,550 --> 00:20:45,050
+صميم المهمة، حسنًا؟ لذلك لا يمكننا أن نقل الرقم
+
+274
+00:20:45,050 --> 00:20:50,690
+لأن هناك فرص لجمهور أصغر لأن أحيانًا نحتاج لرقم
+
+275
+00:20:50,690 --> 00:20:56,280
+أكبرأو قيمة معينة. مرة أخرى، دعنا نتكلم عن بعض
+
+276
+00:20:56,280 --> 00:20:59,360
+الانتجارات المنجرية لتقليل الانتجارات الاجتماعية
+
+277
+00:20:59,360 --> 00:21:04,160
+بين مجموعات مختلفة. أحد المشكلة هنا هي المساعدة
+
+278
+00:21:04,160 --> 00:21:06,100
+الشخصية. وعندما نتكلم عن المساعدة الشخصية، هنا
+
+279
+00:21:06,100 --> 00:21:11,500
+نتكلم عن إيجابة الحكومة بطريقة واضحة جدًا، لديها
+
+280
+00:21:11,500 --> 00:21:17,820
+مثلًا مصطلحات عمل حيث يتم إيجابة الموظفين بطريقة
+
+281
+00:21:17,860 --> 00:21:22,520
+يوجد أيضًا إشارات التجارب التي يتم إيجابها
+
+282
+00:21:22,520 --> 00:21:27,120
+المؤسسة، على سبيل المثال، للإشارات الإشارة للإشارة
+
+283
+00:21:27,120 --> 00:21:27,200
+للإشارة للإشارة للإشارة للإشارة للإشارة للإشارة
+
+284
+00:21:27,200 --> 00:21:29,880
+للإشارة للإشارة للإشارة للإشارة للإشارة للإشارة
+
+285
+00:21:29,880 --> 00:21:33,040
+للإشارة
+
+286
+00:21:33,160 --> 00:21:40,240
+وهي مهمة تحسين المساعدة الانسانية لأنه عندما نتكلم
+
+287
+00:21:40,240 --> 00:21:43,280
+عن الانسانية الاجتماعية نحن لا نتكلم عن مجموعة
+
+288
+00:21:43,280 --> 00:21:46,280
+انسانية اجتماعية نحن نتكلم عن بعض الانسانين الذين
+
+289
+00:21:46,280 --> 00:21:49,380
+يحاولون أن يقوموا بإنقاذ أفعالهم أو أن يقوموا بعمل
+
+290
+00:21:49,380 --> 00:21:55,720
+أقلهنا نحتاج لإزالة المساعدة الانسانية لتقليل
+
+291
+00:21:55,720 --> 00:21:59,480
+الانتجار الاجتماعي واحد من الأشياء أو بعض الأشياء
+
+292
+00:21:59,480 --> 00:22:01,600
+التي نستطيعها أن نفعلها لتقليل الانتجار الاجتماعي
+
+293
+00:22:01,600 --> 00:22:06,200
+هي إجراء مهارات مجتمع بطريقة واضحة لأن هذا سيساعد
+
+294
+00:22:06,200 --> 00:22:06,640
+المجتمع
+
+295
+00:22:09,440 --> 00:22:14,040
+تطبيقات تتطور في هذه التطبيقات يوجد عمومات موظفة
+
+296
+00:22:14,040 --> 00:22:20,340
+لشخص مختلف عمومات موظفة تتطور في هذه التطبيقات
+
+297
+00:22:20,340 --> 00:22:24,260
+التطبيقات تتطور في هذه التطبيقات تتطور في هذه
+
+298
+00:22:24,260 --> 00:22:24,620
+التطبيقات تتطور في هذه التطبيقات تتطور في هذه
+
+299
+00:22:24,620 --> 00:22:27,440
+التطبيقات تتطور في هذه التطبيقات تتطور في هذه
+
+300
+00:22:27,440 --> 00:22:32,860
+التطبيقات تتطور في هذه التطبيقات تتطور في هذه
+
+301
+00:22:32,860 --> 00:22:38,170
+التطبيقاتوإعطاء فرصة لجمهور المجتمع أن يتعاملوا مع
+
+302
+00:22:38,170 --> 00:22:41,690
+بعضهم البعض، وإعطاء وقت للتعامل مع بعضهم البعض،
+
+303
+00:22:41,690 --> 00:22:45,190
+وهذا سيساعد أيضًا في تقليل الانتجار الاجتماعي،
+
+304
+00:22:45,190 --> 00:22:50,710
+وأحد الأشياء المهمة هي أن تشجع جمهور المجتمع مع
+
+305
+00:22:50,710 --> 00:22:53,850
+بعضهم البعض، وإعطاء فرصة لجمهور المجتمعيعني okay
+
+306
+00:22:53,850 --> 00:22:56,790
+if the assignment finally is fulfilled not
+
+307
+00:22:56,790 --> 00:22:59,930
+necessarily that all group members are going to be
+
+308
+00:22:59,930 --> 00:23:03,990
+rewarded some of the group members might be
+
+309
+00:23:03,990 --> 00:23:07,350
+rewarded less or they might not be rewarded
+
+310
+00:23:07,350 --> 00:23:10,830
+because their contribution was limited or it was
+
+311
+00:23:10,830 --> 00:23:15,310
+or there was no contributionعادةً عندما نتكلم عن
+
+312
+00:23:15,310 --> 00:23:19,710
+مجموعات تدفع ، لسنا نتكلم هنا عن تدفعين متساويين ،
+
+313
+00:23:19,710 --> 00:23:24,590
+لسنا نتكلم عن تدفعين باعتبار عمل ، حركة ، عملي،
+
+314
+00:23:24,590 --> 00:23:26,050
+عملي، عملي، عملي، عملي، عملي، عملي، عملي، عملي،
+
+315
+00:23:26,050 --> 00:23:26,250
+عملي، عملي، عملي، عملي، عملي، عملي، عملي، عملي،
+
+316
+00:23:26,250 --> 00:23:28,600
+عملي، عملي، عملي، عملي، عملي، عملي، عمبمجرد تحسين
+
+317
+00:23:28,600 --> 00:23:35,160
+الانتجار بين الجمهور، نستطيع أيضًا تأثير على كيف
+
+318
+00:23:35,160 --> 00:23:41,860
+يتعامل الجمهور مع عملياتهم لتجعلهم يعتمدوا على
+
+319
+00:23:41,860 --> 00:23:49,960
+عملياتهم مرتبطة مع عملياتهم أي أسئلة بعد الآن؟أخر
+
+320
+00:23:49,960 --> 00:23:54,380
+مصطلح يجب أن نتحدث عنه هو الـ Cohesiveness بالطبع
+
+321
+00:23:54,380 --> 00:23:57,400
+عندما نتحدث عن كوهسفنس هنا، نتحدث عن أحد الأشياء
+
+322
+00:23:57,400 --> 00:24:08,200
+المهمة التي ستساعد تدفع الشخصيات أو المجموعات بشكل
+
+323
+00:24:08,200 --> 00:24:11,950
+عامنحن نعتبر أن أكثر المجموعات مرتبطة، أكتر
+
+324
+00:24:11,950 --> 00:24:15,530
+مجموعات مرتبطة، أكتر مرتبطة، أكتر مرتبطة، أكتر
+
+325
+00:24:15,530 --> 00:24:19,030
+مرتبطة، أكتر مرتبطة، أكتر مرتبطة، أكتر مرتبطة،
+
+326
+00:24:19,030 --> 00:24:19,570
+أكتر مرتبطة، أكتر مرتبطة، أكتر مرتبطة، أكتر
+
+327
+00:24:19,570 --> 00:24:20,390
+أكتر مرتبطة، أكتر مرتبطة، أكتر مرتبطة، أكتر
+
+328
+00:24:20,390 --> 00:24:24,590
+مرتبطة، أكتر مرتبطة، أكتر مرتبطولكن قدرتهم على
+
+329
+00:24:24,590 --> 00:24:28,450
+التعامل مع المشاكل، رغم أنها مشاكل شخصية أو مشاكل
+
+330
+00:24:28,450 --> 00:24:33,610
+عملية، عادة تكون أكتر. مرة أخرى، عندما نتحدث عن
+
+331
+00:24:33,610 --> 00:24:37,570
+مجتمعية، عادة يكون المجموعات المجتمعية تتفاهم أكتر
+
+332
+00:24:37,570 --> 00:24:42,410
+بمهارات وخطوات وما إلى ذلكعادةً أو مرة أخرى، هذا
+
+333
+00:24:42,410 --> 00:24:45,630
+واحد من أكتر .. نحن نتكلم عن خمس أدوات التي هي
+
+334
+00:24:45,630 --> 00:24:48,470
+جميعها مهمة، ولكن ربما تقريبًا عندما نتكلم عن
+
+335
+00:24:48,470 --> 00:24:53,950
+الواقعية، فهي تقريبًا أكتر مهمة في تقاريرها إلى
+
+336
+00:24:53,950 --> 00:24:58,250
+نقطة أخرى. الآن عندما نتكلم عن الواقعية هنا، نتكلم
+
+337
+00:24:58,250 --> 00:25:02,150
+عن مدى مدى مجموعات المجموعات مهتمة مع بعضها البعض.
+
+338
+00:25:02,310 --> 00:25:07,930
+مهتمة نعني هناهي لديها علاقة قوية مع بعضها البعض
+
+339
+00:25:07,930 --> 00:25:12,670
+أكثر علاقاتها مرتبطة أكثر هنا نقول إن هذا مجلد
+
+340
+00:25:12,670 --> 00:25:18,790
+مرتبط إذا كانت المجلد مختلفا هنا نتكلم عن مجلد
+
+341
+00:25:18,790 --> 00:25:21,450
+يوجد فيه الكثير من المشاكل هناك مشاكل
+
+342
+00:25:21,450 --> 00:25:25,890
+التcommunication مشاكل التعامل مشاكل التحكم وما
+
+343
+00:25:25,890 --> 00:25:29,530
+إلى ذلك وهذا يعني أن عملية مجلدين مثل هذا سيكون
+
+344
+00:25:29,530 --> 00:25:36,610
+عالي جدًاوهي واحدة من المواصفات هنا، لكي تزداد
+
+345
+00:25:36,610 --> 00:25:41,010
+المواصفات، هناك بعض التعليقات هنا، واحدة من
+
+346
+00:25:41,010 --> 00:25:45,030
+المهمات بالطبع هي الحصول على مجموعات أصغر، ولكن
+
+347
+00:25:45,030 --> 00:25:49,970
+مرة أخرى، لا أريد أن أكرر دائما نفس المواصفات، ليس
+
+348
+00:25:49,970 --> 00:25:52,910
+كل الوقت يمكننا أن نستخدم مجموعات أصغر، ولكن إذا
+
+349
+00:25:52,910 --> 00:25:58,410
+نستطيع فهيبالطبع هناك افضلات أكتر عندما نتحدث عن
+
+350
+00:25:58,410 --> 00:26:01,570
+مجموعات أصغر، المجموعات الأصغر هي أكتر مرتبطة من
+
+351
+00:26:01,570 --> 00:26:09,010
+المجموعات الأكتر كبيرة، كما أنه مهم أيضًا أن ندفع
+
+352
+00:26:09,010 --> 00:26:12,270
+اتفاق مع مهمات المجموعات، لهذا السبب عندما كنا
+
+353
+00:26:12,270 --> 00:26:19,340
+نتحدثمثلما قلنا في البداية أن هناك وقت ومكان
+
+354
+00:26:19,340 --> 00:26:23,240
+للتحدث عن مشاكل مرتبطة بالهدفات والهدفات للتصميم
+
+355
+00:26:23,240 --> 00:26:26,480
+ومشكلة التخطيط والهدفات والهدفات والهدفات والهدفات
+
+356
+00:26:26,480 --> 00:26:27,520
+والهدفات والهدفات والهدفات والهدفات والهدفات
+
+357
+00:26:27,520 --> 00:26:29,460
+والهدفات والهدفات والهدفات والهدفات والهدفات
+
+358
+00:26:29,460 --> 00:26:29,480
+والهدفات والهدفات والهدفات والهدفات والهدفات
+
+359
+00:26:29,480 --> 00:26:34,040
+والهدفات والهدفات والهدفات والهدفات والهوهذا يعني
+
+360
+00:26:34,040 --> 00:26:39,480
+أن الاتصال أقوى بين مجموعات مجتمعية. بالطبع أكثر
+
+361
+00:26:39,480 --> 00:26:42,380
+مجموعات مجتمعية تقضي وقت معاها أكتر، أكتر هم
+
+362
+00:26:42,380 --> 00:26:47,970
+سيفهموا بعضهم البعضو كما يفهموا قوتهم، أيضًا
+
+363
+00:26:47,970 --> 00:26:54,630
+يفهموا أسلوبهم وهذا سيساعدهم على معرفة .. على سبيل
+
+364
+00:26:54,630 --> 00:26:58,970
+المثال، إذا كنت أعرف واحد من صديقي ما هي الأشياء
+
+365
+00:26:58,970 --> 00:27:05,350
+التي ستغضب عليه، فأنا يجب أن أفقد هذه الأشياء، على
+
+366
+00:27:05,350 --> 00:27:09,670
+سبيل المثال أو إذا كان هناك مشاكل التي ستسبب فيها
+
+367
+00:27:09,670 --> 00:27:14,600
+بعض المشاكل، فسأحاول أن أساعدوالعزيزي والعزيزي
+
+368
+00:27:14,600 --> 00:27:14,940
+والعزيزي والعزيزي والعزيزي والعزيزي والعزيزي
+
+369
+00:27:14,940 --> 00:27:17,460
+والعزيزي والعزيزي والعزيزي والعزيزي والعزيزي
+
+370
+00:27:17,460 --> 00:27:21,680
+والعزيزي والعزيزي والعزيزي والعزيزي والعزيزي
+
+371
+00:27:21,680 --> 00:27:28,550
+والعزيزي والعزيزي والعزيزيأو مشاكل و في نفس الوقت
+
+372
+00:27:28,550 --> 00:27:32,450
+أكثر ما يمكنهم أن يحلوا أي مشاكل التي سوف يتعاملون
+
+373
+00:27:32,450 --> 00:27:41,190
+بها أيضًا إذا كانت المجموعة المدرسة صعبة الناس سوف
+
+374
+00:27:41,190 --> 00:27:46,800
+يشعرون بالمهمة من أن يكونوا أعضاء مجموعة معينةوهذا
+
+375
+00:27:46,800 --> 00:27:56,240
+يجعل الشخص يحب أن يكون مجلدًا ويفعل أفضل من نفسه
+
+376
+00:27:56,240 --> 00:28:01,040
+لتحافظ على مجلدته، وما إلى ذلك، فإنزعاج مجموعة
+
+377
+00:28:01,040 --> 00:28:07,800
+ومعرفة صعوبة يساعد أيضًا في زيادة التوافق بين
+
+378
+00:28:07,800 --> 00:28:09,720
+مجموعات مجتمع
+
+379
+00:28:12,920 --> 00:28:18,020
+مع المجموعات الأخرى أيضًا، ستتطور إلى نوع من
+
+380
+00:28:18,020 --> 00:28:23,340
+اعتبار لجمهور المجموعات وهم مثلًا، نستطيع أن نقول
+
+381
+00:28:23,340 --> 00:28:26,600
+إنهم سيكونوا أكثر فخورين بأن يكونوا مجموعات من
+
+382
+00:28:26,600 --> 00:28:31,740
+مجموعة معينة وهذا أيضًاوهو سيأثر على الوضع
+
+383
+00:28:31,740 --> 00:28:35,280
+التجاربي بطريقة إيجابية بالطبع هناك نقطة أخرى مثل
+
+384
+00:28:35,280 --> 00:28:38,680
+الهجوم على سبيل المثال بإضافة الانتجار بشكل شخصي
+
+385
+00:28:38,680 --> 00:28:43,320
+لكن عندما نتحدث عن الانتجار بشكل شخصي لا نتحدث عن
+
+386
+00:28:43,320 --> 00:28:47,810
+انتجار الانتجار تماما، نتحدث عن الانتجارمع مجموعات
+
+387
+00:28:47,810 --> 00:28:51,550
+أخرى، التواصل مع مجموعات أخرى مهم جدًا، لأن بعد كل
+
+388
+00:28:51,550 --> 00:28:55,150
+شيء نحن نتكلم عن مجموعات متعاملة، فيما يكون هناك
+
+389
+00:28:55,150 --> 00:28:57,750
+مجموعات وشركات مختلفة، ولكن في النهاية نحن نتكلم
+
+390
+00:28:57,750 --> 00:29:04,250
+عن محاولات متعاملة لإنهاء استخدام المجموعات بشكل
+
+391
+00:29:04,250 --> 00:29:09,440
+عامأنا أحتاج أن أعود إلى موضوع الهجوم، حسنًا، هنا
+
+392
+00:29:09,440 --> 00:29:17,960
+يبدو أن هناك نوع من التقارير بين الهجوم وكيف نتحدث
+
+393
+00:29:17,960 --> 00:29:21,600
+عن الهجوم في هذا الموضوع وكيف نتحدث عن الهجوم في
+
+394
+00:29:21,600 --> 00:29:26,940
+الموضوع السابق، في الموضوع السابق قالنا أنعن طريق
+
+395
+00:29:26,940 --> 00:29:31,540
+اجهزة اجتماعية تعتمد على اجهزة اجتماعية تعتمد على
+
+396
+00:29:31,540 --> 00:29:35,960
+اجهزة اجتماعية
+
+397
+00:29:35,960 --> 00:29:43,840
+تعتمد
+
+398
+00:29:43,840 --> 00:29:50,730
+علىبالتأكيد 100% بالنسبة للجمهور الشخصي ولكن في
+
+399
+00:29:50,730 --> 00:29:54,650
+النهاية، لكي تحصل على عرض، عليك أن تنجح المهمة
+
+400
+00:29:54,650 --> 00:29:58,190
+كجمهور كجمهور بعد أن تنجح المهمة كجمهور كجمهور
+
+401
+00:29:58,190 --> 00:29:58,850
+كجمهور كجمهور كجمهور كجمهور كجمهور كجمهور كجمهور
+
+402
+00:29:58,850 --> 00:30:01,650
+كجمهور كجمهور كجمهور كجمهور كجمهور كجمهور كجمهور
+
+403
+00:30:01,650 --> 00:30:02,370
+كجمهور كجمهور كجمهور كجمهور كجمهور كجمهور كجمهور
+
+404
+00:30:02,370 --> 00:30:05,390
+كجمهور كجمهور كجمهور كجمهور كجمهور كجمهور كجمهور
+
+405
+00:30:05,390 --> 00:30:10,570
+كجمهور كجعلى تجاربك وتجاربك وتجاربك تجاربك تجاربك
+
+406
+00:30:10,570 --> 00:30:12,810
+تجاربك تجاربك تجاربك تجاربك تجاربك تجاربك تجاربك
+
+407
+00:30:12,810 --> 00:30:15,410
+تجاربك تجاربك تجاربك تجاربك تجاربك تجاربك تجاربك
+
+408
+00:30:15,410 --> 00:30:15,610
+تجاربك تجاربك تجاربك تجاربك تجاربك تجاربك تجاربك
+
+409
+00:30:15,610 --> 00:30:15,650
+تجاربك تجاربك تجاربك تجاربك تجاربك تجاربك تجاربك
+
+410
+00:30:15,650 --> 00:30:16,110
+تجاربك تجاربك تجاربك تجاربك تجاربك تجاربك تجاربك
+
+411
+00:30:16,110 --> 00:30:34,370
+تجاربك تجاربك تجاربك تجاربك تج
+
+412
+00:30:35,480 --> 00:30:42,740
+كما قلنا أن التجارب مهمة للتجارب، هنا يجب أنتشير
+
+413
+00:30:42,740 --> 00:30:45,680
+إلى التواصل بين مجموعات التجارب والمجموعات
+
+414
+00:30:45,680 --> 00:30:46,780
+التجاربية والمجموعات التجاربية والمجموعات
+
+415
+00:30:46,780 --> 00:30:50,540
+التجاربية ومجموعات
+
+416
+00:30:50,540 --> 00:30:53,240
+التجاربية ومجموعات التجاربية ومجموعات التجاربية
+
+417
+00:30:53,240 --> 00:30:53,500
+التجاربية ومجموعات التجاربية ومجموعات التجاربية
+
+418
+00:30:53,500 --> 00:30:55,480
+ومجموعات التجاربية ومجموعات التجاربية ومجموعات
+
+419
+00:30:55,480 --> 00:30:58,680
+التجاربية ومجموعات التجاربية ومجموعات التجاربية
+
+420
+00:30:58,680 --> 00:31:01,780
+ومجموعات
+
+421
+00:31:01,780 --> 00:31:11,620
+التجاربية ومجموعات التجاربية ومجموعات
+
+422
+00:31:11,620 --> 00:31:15,160
+التجوالنظام التجاري السلبي نظام التجاري السلبي
+
+423
+00:31:15,160 --> 00:31:17,900
+نظام التجاري السلبي نظام التجاري السلبي نظام
+
+424
+00:31:17,900 --> 00:31:21,160
+التجاري السلبي نظام التجاري السلبي نظام التجاري
+
+425
+00:31:21,160 --> 00:31:22,940
+السلبي نظام التجاري السلبي نظام التجاري السلبي
+
+426
+00:31:22,940 --> 00:31:24,560
+نظام التجاري السلبي نظام التجاري السلبي نظام
+
+427
+00:31:24,560 --> 00:31:25,940
+التجاري السلبي نظام التجاري السلبي نظام التجاري
+
+428
+00:31:25,940 --> 00:31:28,120
+السلبي نظام التجاري السلبي نظام التجاري السلبي
+
+429
+00:31:28,120 --> 00:31:32,800
+نظام التجاري السلبي نظام التجاري السلبي نظام
+
+430
+00:31:32,800 --> 00:31:37,480
+التجاري السلبي نظام التجاري السلبي نظام التجاري
+
+431
+00:31:37,480 --> 00:31:47,660
+السلبي نظام التجاري السلبي نظلو كوهيسف ولو نقل
+
+432
+00:31:47,660 --> 00:32:00,920
+التطبيقات نحن نتكلم عن تطبيقات نقل التطبيقات نحن
+
+433
+00:32:00,920 --> 00:32:01,880
+نتكلم عن تطبيقات نقل
+
+434
+00:32:04,790 --> 00:32:09,050
+لأن حتى لو كنا نحب بعضنا بعض في غرفة وغرفة وغرفة
+
+435
+00:32:09,050 --> 00:32:09,690
+وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة
+
+436
+00:32:09,690 --> 00:32:11,390
+وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة
+
+437
+00:32:11,390 --> 00:32:12,190
+وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة
+
+438
+00:32:12,190 --> 00:32:17,570
+وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة
+
+439
+00:32:17,570 --> 00:32:18,890
+وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة
+
+440
+00:32:18,890 --> 00:32:29,250
+وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة وغرفة
+
+441
+00:32:29,250 --> 00:32:34,250
+وغرفة
+
+442
+00:32:34,250 --> 00:32:34,730
+و
+
+443
+00:32:38,520 --> 00:32:44,220
+لماذا؟ في مجموعات عالية ومع نظامات عالية تدفع،
+
+444
+00:32:44,220 --> 00:32:50,000
+أحيانًا تدفع أفضل من مجموعات عالية ومع نظامات
+
+445
+00:32:50,000 --> 00:32:51,920
+عالية تدفع
+
+446
+00:33:14,780 --> 00:33:23,620
+ماذا يمكن أن يكون؟ ما هي السببات الأخرى؟عندما
+
+447
+00:33:23,620 --> 00:33:28,560
+نتكلم عن مجموعات غير مرتبطة، نتكلم عن اعضاء اعضاء
+
+448
+00:33:28,560 --> 00:33:36,680
+اعضاء اعضاء يعملون ويعملون ويعملون
+
+449
+00:33:36,680 --> 00:33:39,960
+ويعملون ويعملون ويعملون ويعملون ويعملون ويعملون
+
+450
+00:33:39,960 --> 00:33:42,940
+ويعملون ويعملونوهو ما يرغبون أن يفعلونه، على ما
+
+451
+00:33:42,940 --> 00:33:45,920
+يبدو من مجموعات أخرى من المجموعات. لهذا السبب
+
+452
+00:33:45,920 --> 00:33:49,680
+نتوقع أحيانًا عندما يكون الوضع مرتبط، حتى لو كان
+
+453
+00:33:49,680 --> 00:33:54,180
+مستوى التجارب أقل، فالتجارب قد تكون ليست مرتبطة،
+
+454
+00:33:54,180 --> 00:33:58,980
+بل مدرعة. لماذا؟ لأن بعض الشخصيات في المجموعات
+
+455
+00:33:58,980 --> 00:34:04,530
+ستقوم بعمل أفراد أعلى.هذا ما يسمونه كذلك عندما
+
+456
+00:34:04,530 --> 00:34:09,190
+نتكلم عن مجموعة عالية ومدارس عالية نورك نورك نورك
+
+457
+00:34:09,190 --> 00:34:12,050
+نورك نورك نورك نورك نورك نورك نورك نورك نورك نورك
+
+458
+00:34:12,050 --> 00:34:12,150
+نورك نورك نورك نورك نورك نورك نورك نورك نورك نورك
+
+459
+00:34:12,150 --> 00:34:14,530
+نورك نورك نورك نورك نورك نورك نورك نورك نورك نورك
+
+460
+00:34:14,530 --> 00:34:17,250
+نورك نورك نورك نورك نورك نورك نورك نورك نورك نورك
+
+461
+00:34:17,250 --> 00:34:18,570
+نورك نورك نورك نورك نورك نورك نورك نورك نورك نورك
+
+462
+00:34:18,570 --> 00:34:27,670
+نورك نورك نورك نورك نورك نورك نورك نورك نورك نورك
+
+463
+00:34:27,670 --> 00:34:33,450
+نورربما يكون هناك منافسة، ولكن على الأقل سيكون
+
+464
+00:34:33,450 --> 00:34:38,690
+هناك مستوى عالي من الانقصاد بين أعضاء المجتمع، وهو
+
+465
+00:34:38,690 --> 00:34:41,350
+السبب في أن بعض الانقصاد سيستخدمون المزيد من
+
+466
+00:34:41,350 --> 00:34:42,130
+الاستفادة
+
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/dWqrRbe3QEE_raw.json b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/dWqrRbe3QEE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..3428c4f3fc11806f486be6146783d0f1d34238f7
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/dWqrRbe3QEE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2784, "start": 8.94, "end": 27.84, "text": "اليوم سوف نخلط 15 دقيقة لإنهاء هذه القصة وفي السبتانة سنبدأ بقصة جديدة في دراسة قبلها قررنا أن يكون هناك تقنيات مختلفة يمكن استخدامها", "tokens": [6027, 1829, 20498, 8608, 38688, 8717, 9778, 1211, 9566, 2119, 11778, 38436, 28671, 5296, 28814, 1863, 3224, 16606, 29538, 25062, 9381, 3660, 4032, 41185, 21136, 3555, 2655, 7649, 3660, 8608, 1863, 44510, 10721, 4724, 4587, 9381, 3660, 10874, 16254, 41891, 8978, 11778, 23557, 3794, 3660, 12174, 36150, 11296, 12174, 2288, 2288, 8315, 14739, 7251, 30544, 34105, 4117, 6055, 4587, 22653, 9307, 3714, 46456, 46538, 3660, 7251, 43020, 44713, 9778, 3215, 10943, 11296], "avg_logprob": -0.5470890410958904, "compression_ratio": 1.535031847133758, "no_speech_prob": 2.2649765014648438e-06, "words": [{"start": 8.939999999999998, "end": 10.14, "word": "اليوم", "probability": 0.6210123697916666}, {"start": 10.14, "end": 11.14, "word": " سوف", "probability": 0.43798828125}, {"start": 11.14, "end": 11.5, "word": " نخلط", "probability": 0.50054931640625}, {"start": 11.5, "end": 11.82, "word": " 15", "probability": 0.44140625}, {"start": 11.82, "end": 12.12, "word": " دقيقة", "probability": 0.90869140625}, {"start": 12.12, "end": 12.72, "word": " لإنهاء", "probability": 0.5877685546875}, {"start": 12.72, "end": 13.06, "word": " هذه", "probability": 0.35791015625}, {"start": 13.06, "end": 13.52, "word": " القصة", "probability": 0.5777180989583334}, {"start": 13.52, "end": 15.8, "word": " وفي", "probability": 0.33062744140625}, {"start": 15.8, "end": 16.38, "word": " السبتانة", "probability": 0.45611572265625}, {"start": 16.38, "end": 17.06, "word": " سنبدأ", "probability": 0.8590087890625}, {"start": 17.06, "end": 17.88, "word": " بقصة", "probability": 0.8154296875}, {"start": 17.88, "end": 18.42, "word": " جديدة", "probability": 0.9718424479166666}, {"start": 18.42, "end": 19.58, "word": " في", "probability": 0.79296875}, {"start": 19.58, "end": 22.28, "word": " دراسة", "probability": 0.62860107421875}, {"start": 22.28, "end": 22.6, "word": " قبلها", "probability": 0.4619140625}, {"start": 22.6, "end": 23.2, "word": " قررنا", "probability": 0.63037109375}, {"start": 23.2, "end": 23.34, "word": " أن", "probability": 0.138671875}, {"start": 23.34, "end": 24.48, "word": " يكون", "probability": 0.5924072265625}, {"start": 24.48, "end": 25.08, "word": " هناك", "probability": 0.9287109375}, {"start": 25.08, "end": 25.96, "word": " تقنيات", "probability": 0.78277587890625}, {"start": 25.96, "end": 25.96, "word": " مختلفة", "probability": 0.9542236328125}, {"start": 25.96, "end": 26.62, "word": " يمكن", "probability": 0.5433349609375}, {"start": 26.62, "end": 27.84, "word": " استخدامها", "probability": 0.820068359375}], "temperature": 1.0}, {"id": 2, "seek": 5479, "start": 28.01, "end": 54.79, "text": "بالطبع تلك التقنيات عندما نتكلم عن إفعالة تلك التقنيات بالطبع هي مختلفة و نستطيع أن نقوم بالمقارنة باستخدام القرص التالف مثلا هناك اختلافات في قيمة 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203.74, "word": " نقطة", "probability": 0.7298990885416666}, {"start": 203.74, "end": 204.6, "word": " مرتبطة", "probability": 0.721142578125}, {"start": 204.6, "end": 206.58, "word": " بالإشعارات", "probability": 0.5208028157552084}, {"start": 206.58, "end": 206.58, "word": " العالمية", "probability": 0.806396484375}, {"start": 206.58, "end": 207.32, "word": " هي", "probability": 0.46875}, {"start": 207.32, "end": 207.4, "word": " الـ", "probability": 0.4256591796875}, {"start": 207.4, "end": 207.76, "word": " social", "probability": 0.56982421875}, {"start": 207.76, "end": 208.42, "word": " looping", "probability": 0.864501953125}, {"start": 208.42, "end": 209.14, "word": " نقول", "probability": 0.474517822265625}, {"start": 209.14, "end": 209.44, "word": " إن", "probability": 0.26025390625}, {"start": 209.44, "end": 209.7, "word": " في", "probability": 0.41162109375}, {"start": 209.7, "end": 209.7, "word": " الـ", "probability": 0.47503662109375}, {"start": 209.7, "end": 210.02, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/fbxjV94XGiE_raw.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/fbxjV94XGiE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..322ce89fb5594303d3e77a44bc9df1a97ce1a6aa
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/fbxjV94XGiE_raw.srt
@@ -0,0 +1,1508 @@
+1
+00:00:05,990 --> 00:00:09,930
+هذا السبب بالطبع أن الانتباه يدفع إلى حركة
+
+2
+00:00:09,930 --> 00:00:13,670
+الاختيارأيضًا عندما نتكلم عن الاختيارات، يوجد
+
+3
+00:00:13,670 --> 00:00:18,090
+ممارسات مختلفة، وسنتكلم عن بعض هذه الممارسات،
+
+4
+00:00:18,090 --> 00:00:22,130
+ونعرف عن وقت استخدام كل ممارسة، وما هي أسلحة أو
+
+5
+00:00:22,130 --> 00:00:29,430
+أسلحة لكل ممارسة، ومع ذلك، وسنتكلم عن خطأات مختلفة
+
+6
+00:00:29,430 --> 00:00:34,350
+التي قد تؤثر على الاختيار والprocess، بالطبع بشكل
+
+7
+00:00:34,350 --> 00:00:38,800
+نقلي، وهو سيؤثر على الاختيار والprocessبالإضافة
+
+8
+00:00:38,800 --> 00:00:43,140
+إلى أشياء أخرى، فسنتحدث أكتر عن أشياء مرتبطة
+
+9
+00:00:43,140 --> 00:00:49,900
+بالإيقاع والتصريح في هذا الحلقه أولا، دعنا نتحدث
+
+10
+00:00:49,900 --> 00:00:59,540
+عن الإيقاع، ودعنا نبدأ هنا بالسؤال الرئيسي، ما هو
+
+11
+00:00:59,540 --> 00:01:02,320
+إيقاع؟ ما هو إيقاع؟
+
+12
+00:01:05,220 --> 00:01:10,840
+هو كيف يسيطر الإنسان ويعرف المعلومات حوله ويعرف
+
+13
+00:01:10,840 --> 00:01:14,880
+أنه لا يجب أن يكون هناك أي تغيير في حياته. حسنًا،
+
+14
+00:01:14,880 --> 00:01:19,900
+عندما نتحدث عن الوصول، نحن نتحدث عن ميكاليزم الذي
+
+15
+00:01:19,900 --> 00:01:25,500
+يسمح لنا أن نعرف مواقع مختلفة أو أشياء. الآن عندما
+
+16
+00:01:25,500 --> 00:01:32,740
+نتحدث عن الوصول، نتحدث ببساطة عن كيف نفهم الأشياء
+
+17
+00:01:32,740 --> 00:01:39,040
+اللي يجهزنا، حسنًا؟لتفهم هذه الحالات أو الأشياء
+
+18
+00:01:39,040 --> 00:01:44,520
+هنا نتحدث عن كيف نقوم بتفهيم هذه الحالات أو
+
+19
+00:01:44,520 --> 00:01:48,920
+الأشياء وفقًا لذلك نقوم بإطلاق القرارات وربما لهذا
+
+20
+00:01:48,920 --> 00:01:53,560
+السبب في هذه الكتابة على الأقل هناك نوع من الاتصال
+
+21
+00:01:53,560 --> 00:01:57,180
+هنا بين الانتظار والخيارات ربما في كتابات أخرى
+
+22
+00:01:57,180 --> 00:02:02,420
+سنجدها في قصص مختلفة ولكن هنا ربما يكون هناك مفهوم
+
+23
+00:02:02,420 --> 00:02:06,930
+أخر لأنبالطبع ليس فقط الملاحظة التي ستدفع قرارنا،
+
+24
+00:02:06,930 --> 00:02:12,150
+بل أيضًا عندما نتحدث عن قيم و قصص، كل شيء سيدفعنا
+
+25
+00:02:12,150 --> 00:02:17,050
+عندما نقوم بالقرارات، ولكن هنا بحسب كيف نشرح أو
+
+26
+00:02:17,050 --> 00:02:21,890
+نفسر الأشياء التي نتعامل معها، فسنردفع بطريقة
+
+27
+00:02:21,890 --> 00:02:29,070
+معينةهذا السبب في المناقشة هنا كيف نستخدم تقريرنا
+
+28
+00:02:29,070 --> 00:02:35,710
+لإعطاء معنى لجميع حياتنا أو حياتنا حولنا. حسنا؟
+
+29
+00:02:35,710 --> 00:02:41,150
+الآن عندما نتكلم عن الوصول أيضًا، هنا يوجد اتصالين
+
+30
+00:02:41,150 --> 00:02:44,510
+يجب أن نتكلم عنها. حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟
+
+31
+00:02:44,510 --> 00:02:45,770
+حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟
+
+32
+00:02:45,770 --> 00:02:49,330
+حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟
+
+33
+00:02:49,330 --> 00:02:49,990
+حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسنا؟
+
+34
+00:02:49,990 --> 00:02:55,780
+حسنا؟ حسنا؟ حسنا؟ حسنا؟ حسأسباب الحقيقة هنا، هناك
+
+35
+00:02:55,780 --> 00:03:00,980
+الأسباب التي نفهمها بحسب كيف نفهم الأشياء حولنا و
+
+36
+00:03:00,980 --> 00:03:08,880
+هناك الأسباب الحقيقية للوضع اللي سيأثر علينا أكتر
+
+37
+00:03:08,880 --> 00:03:14,900
+ليس الأسباب الحقيقية لأننا سنقوم بتحكم الناس
+
+38
+00:03:14,900 --> 00:03:21,540
+بحياتنا ومقالاتنا وقيماتنا للشخص، كيف نفهم هذا و
+
+39
+00:03:21,540 --> 00:03:27,660
+بعدها نحكمو لهذا السبب نقول أن كلمة ملاحظة هي كلمة
+
+40
+00:03:27,660 --> 00:03:34,360
+مهمة بشكل عام لأن الحقيقة نفسها إذا لم نفهمها أو
+
+41
+00:03:34,360 --> 00:03:41,920
+لا نفهمها أو دعوني أقول إن لم نراها، فلن تأثر على
+
+42
+00:03:41,920 --> 00:03:47,400
+طريقة كيف نفهم حالتين مختلفة، فالمهم هنا هو كيف
+
+43
+00:03:47,400 --> 00:03:53,080
+نفهم الأشياءالمهم هنا هو أن الحقيقة التي سوف تأثير
+
+44
+00:03:53,080 --> 00:03:57,680
+عاملنا بشكل عام هو ما نشعر به. لهذا السبب نقول أن
+
+45
+00:03:57,680 --> 00:04:04,040
+الانتصاف مهم جدًا وسوف يأثر عاملنا بشكل عام. وهذا
+
+46
+00:04:04,040 --> 00:04:10,260
+هو نقطة مهمة. الحقيقة نفسها ليست مهمة كمان كمان
+
+47
+00:04:10,260 --> 00:04:13,280
+كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+48
+00:04:16,000 --> 00:04:18,940
+هو كيف نتعامل أو نتعامل مع حالات مختلفة أو نتعامل
+
+49
+00:04:18,940 --> 00:04:19,680
+مع حالات مختلفة أو نتعامل مع حالات مختلفة أو
+
+50
+00:04:19,680 --> 00:04:22,740
+نتعامل مع حالات مختلفة أو نتعامل مع حالات مختلفة
+
+51
+00:04:22,740 --> 00:04:24,440
+أو نتعامل مع حالات مختلفة أو نتعامل مع حالات
+
+52
+00:04:24,440 --> 00:04:24,720
+مختلفة أو نتعامل مع حالات مختلفة أو نتعامل مع
+
+53
+00:04:24,720 --> 00:04:24,780
+حالات مختلفة أو نتعامل مع حالات مختلفة أو نتعامل
+
+54
+00:04:24,780 --> 00:04:24,780
+مع حالات مختلفة أو نتعامل مع حالات مختلفة أو
+
+55
+00:04:24,780 --> 00:04:24,880
+نتعامل مع حالات مختلفة أو نتعامل مع حالات مختلفة
+
+56
+00:04:24,880 --> 00:04:27,860
+أو نتعامل مع حالات مختلفة أو نتعامالثاني هو
+
+57
+00:04:27,860 --> 00:04:32,720
+الواقعات التي تأثر على الانتباه. عندما نتكلم عن
+
+58
+00:04:32,720 --> 00:04:36,100
+الانتباه، هناك ثلاث أساسي أساسي أساسي أساسي أساسي
+
+59
+00:04:36,100 --> 00:04:36,760
+أساسي أساسي أساسي أساسي أساسي أساسي أساسي أساسي
+
+60
+00:04:36,760 --> 00:04:39,020
+أساسي أساسي أساسي أساسي أساسي أساسي أساسي أساسي
+
+61
+00:04:39,020 --> 00:04:39,160
+أساسي أساسي أساسي أساسي أساسي أساسي أساسي أساسي
+
+62
+00:04:39,160 --> 00:04:39,680
+أساسي أساسي أساسي أساسي أساسي أساسي أساسي أساسي
+
+63
+00:04:39,680 --> 00:04:46,980
+أساسي أساسي أساسي أساسي أساسي أساسي أساسي
+
+64
+00:04:46,980 --> 00:04:51,960
+أساسي أساس
+
+65
+00:04:51,990 --> 00:04:56,970
+أو نحن و الآخرين بالإضافة إلى حياتنا أو حياتنا أو
+
+66
+00:04:56,970 --> 00:04:58,490
+حياتنا أو حياتنا أو حياتنا او حياتنا او حياتنا او
+
+67
+00:04:58,490 --> 00:04:59,090
+حياتنا او حياتنا او حياتنا او حياتنا او حياتنا او
+
+68
+00:04:59,090 --> 00:04:59,130
+حياتنا او حياتنا او حياتنا او حياتنا او حياتنا او
+
+69
+00:04:59,130 --> 00:04:59,130
+حياتنا او حياتنا او حياتنا او حياتنا او حياتنا او
+
+70
+00:04:59,130 --> 00:04:59,770
+حياتنا او حياتنا او حياتنا او حياتنا او حياتنا او
+
+71
+00:04:59,770 --> 00:05:01,070
+حياتنا او حياتنا او حياتنا او حياتنا او حياتنا او
+
+72
+00:05:01,070 --> 00:05:14,630
+حياتنا او حياتنا او حياتنا او
+
+73
+00:05:14,630 --> 00:05:18,750
+حي
+
+74
+00:05:21,960 --> 00:05:26,300
+هنا نتكلم عن جميع المواضيع التي نتكلم عنها سابقًا
+
+75
+00:05:26,300 --> 00:05:29,580
+في أضافة
+
+76
+00:05:29,580 --> 00:05:33,940
+إلى المواضيع التي سنتكلم عنها لاحقًا مثلًا، تجارب،
+
+77
+00:05:33,940 --> 00:05:35,900
+إتصالات وما إلى ذلك
+
+78
+00:05:40,190 --> 00:05:46,130
+أو الأشياء التي ستؤثر على كيف نقوم بتفهيم أشياء أو
+
+79
+00:05:46,130 --> 00:05:48,130
+نقوم بتفهيم أشياء أو نقوم بتفهيم أشياء أو نقوم
+
+80
+00:05:48,130 --> 00:05:48,190
+بتفهيم أشياء أو نقوم بتفهيم أشياء أو نقوم بتفهيم
+
+81
+00:05:48,190 --> 00:05:52,670
+أشياء أو نقوم بتفهيم أشياء أو نقوم بتفهيم أشياء أو
+
+82
+00:05:52,670 --> 00:05:54,310
+نقوم بتفهيم أشياء أو نقوم بتفهيم أشياء أو نقوم
+
+83
+00:05:54,310 --> 00:05:54,690
+بتفهيم أشياء أو نقوم بتفهيم أشياء أو نقوم بتفهيم
+
+84
+00:05:54,690 --> 00:05:57,230
+أشياء أو نقوم بتفهيم أشياء أو نقوم بتفهيم أشياء أو
+
+85
+00:05:57,230 --> 00:06:08,530
+نقوم بتفهيم أشياء أو نقوم بتفهيم أشياء أو
+
+86
+00:06:08,530 --> 00:06:12,430
+نقوم بتفهعند وضع العمل وعند وضع الاجتماعات اشياء
+
+87
+00:06:12,430 --> 00:06:17,010
+مرتبطة بالوضع
+
+88
+00:06:17,010 --> 00:06:22,550
+نفسه بالنسبة لجزء منه على سبيل المثال إذا كان هناك
+
+89
+00:06:22,550 --> 00:06:26,890
+تأثيرات اخرى على سبيل المثال وما إلى ذلك الثالث
+
+90
+00:06:26,890 --> 00:06:33,040
+فاكتر هنا او package هوالهدف نفسه أو الشيء اللي
+
+91
+00:06:33,040 --> 00:06:38,940
+نحاول ان نفهمه او نشرحه وهنا نتكلم عن مشاكل مختلفة
+
+92
+00:06:38,940 --> 00:06:45,760
+مرتبطة بالمشكلة نفسها مثلًا نفلتي، موشن، صوت،
+
+93
+00:06:45,760 --> 00:06:50,040
+صميم، وما إلى ذلك نحن هنا مرة أخرى نتكلم عن
+
+94
+00:06:50,040 --> 00:06:57,080
+المشكلة التي نحاول ان نفهمها
+
+95
+00:06:59,230 --> 00:07:02,470
+المعرفة هي المهمة عندما تتكلم عن الانتباه لأن
+
+96
+00:07:02,470 --> 00:07:07,290
+الانتباه في كلمات أخرى هي كيف نفهم الأشياء حولنا
+
+97
+00:07:07,290 --> 00:07:12,390
+باعتبار الانتباه أو التفسير أو أي شيء ما تحب أن
+
+98
+00:07:12,390 --> 00:07:16,450
+تسميه هنا في العامل هؤلاء هم المصادر الرئيسية التي
+
+99
+00:07:16,450 --> 00:07:22,090
+مرتبطة معمرة أخرى، الملاحظة هي كيف نقرر الأشياء
+
+100
+00:07:22,090 --> 00:07:27,170
+حولنا، وفقًا لذلك، سنقرر بعض القرارات المتعلقة
+
+101
+00:07:27,170 --> 00:07:31,190
+بالبيئة وكيف نتعامل مع البيئة عندما نتحدث عن
+
+102
+00:07:31,190 --> 00:07:36,310
+الملاحظة، هناك ما نشهده وحقيقة الأشياء، وما أهم
+
+103
+00:07:36,310 --> 00:07:41,350
+هنا هو كيف نشهد الأشياء، لأننا سنتعامل بحيث ما
+
+104
+00:07:41,350 --> 00:07:46,180
+نشهده، وليس بحيث كيف هي الأشياء حقًاعندما نتكلم عن
+
+105
+00:07:46,180 --> 00:07:50,420
+الملاحظة مرة أخرى، يوجد مصادر تأثير الملاحظة،
+
+106
+00:07:50,420 --> 00:07:53,640
+نستطيع أن نسمي هذه المصادر إلى ثلاثة مختلفة مختلفة
+
+107
+00:07:53,640 --> 00:07:55,220
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+108
+00:07:55,220 --> 00:07:56,180
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+109
+00:07:56,180 --> 00:07:58,140
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+110
+00:07:58,140 --> 00:08:00,080
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+111
+00:08:00,080 --> 00:08:06,140
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+112
+00:08:06,140 --> 00:08:14,760
+مختلفة مختلفة مختلفة مختلفة مختلفة مالأن، أحد
+
+113
+00:08:14,760 --> 00:08:21,520
+الحيوانات التي قد تساعدنا في التفكير عن كيف حدث
+
+114
+00:08:21,520 --> 00:08:25,220
+التفكير هو الحيوانات التجاربية، حسنًا، عندما نتكلم
+
+115
+00:08:25,220 --> 00:08:31,900
+عن الحيوانات التجاربية، نحن نحاول أن نشرح أسباب
+
+116
+00:08:31,900 --> 00:08:39,180
+التفكيرنحن نحاول أن نفهم ما هي السبب للإيقاع، وفي
+
+117
+00:08:39,180 --> 00:08:43,900
+نفس النظر لهذه النظرية، السبب يتم اعتباره إما
+
+118
+00:08:43,900 --> 00:08:50,300
+عاملات خارجية أو عاملات داخلية، لذلك هنا نقول إن
+
+119
+00:08:50,300 --> 00:08:54,900
+هناك اتجاهين
+
+120
+00:08:56,790 --> 00:09:02,970
+هناك أسباب خارجية وهناك أسباب خارجية الآن، نظرية
+
+121
+00:09:02,970 --> 00:09:10,790
+التعليم تشير إلى عملية عملية عملية عملية عملية
+
+122
+00:09:10,790 --> 00:09:12,010
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+123
+00:09:12,010 --> 00:09:12,130
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+124
+00:09:12,130 --> 00:09:14,070
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+125
+00:09:14,070 --> 00:09:15,030
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+126
+00:09:15,030 --> 00:09:15,030
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+127
+00:09:15,030 --> 00:09:15,030
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+128
+00:09:15,030 --> 00:09:15,070
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+129
+00:09:15,070 --> 00:09:15,070
+عملية عملية
+
+130
+00:09:24,350 --> 00:09:36,410
+و من هنا نستخدم قصة ومن هنا نستخدم قصة
+
+131
+00:09:36,410 --> 00:09:36,410
+ومن هنا نستخدم قصة ومن هنا نستخدم قصة ومن هنا
+
+132
+00:09:36,410 --> 00:09:36,410
+نستخدم قصة ومن هنا نستخدم قصة ومن هنا نستخدم قصة
+
+133
+00:09:36,410 --> 00:09:36,490
+ومن هنا نستخدم قصة ومن هنا نستخدم قصة ومن هنا
+
+134
+00:09:36,490 --> 00:09:36,970
+نستخدم قصة ومن هنا نستخدم قصة ومن هنا نستخدم قصة
+
+135
+00:09:36,970 --> 00:09:37,150
+ومن هنا نستخدم قصة ومن هنا نستخدم قصة ومن هنا
+
+136
+00:09:37,150 --> 00:09:37,150
+نستخدم قصة ومن هنا نستخدم قصة ومن هنا نستخدم قصة
+
+137
+00:09:37,150 --> 00:09:37,630
+ومن هنا نستخدم قصة ومن هنا نستخدم قصة ومن هنا
+
+138
+00:09:37,630 --> 00:09:43,910
+نستخدم قصة ومن هنا نستخدم قصة ومن هنا نستخدم قصة
+
+139
+00:09:43,910 --> 00:09:49,520
+ومن هنا نالأن، أولاً، نلاحظ الهواء، هذا هو
+
+140
+00:09:49,520 --> 00:09:56,040
+البرنامج الموجود هنا، نحتاج أن نرى الهواء، وفقًا
+
+141
+00:09:56,040 --> 00:10:00,400
+لهذا الهواء، نستطيع أن نحرر الهواء إذا كان مصطلحًا
+
+142
+00:10:00,400 --> 00:10:06,180
+لأهداف خارقة أو إهداف خارقة أو إهداف خارقة أو
+
+143
+00:10:06,180 --> 00:10:08,160
+إهداف خارقة أو إهداف خارقة أو إهداف خارقة أو إهداف
+
+144
+00:10:08,160 --> 00:10:08,160
+خارقة أو إهداف خارقة أو إهداف خارقة أو إهداف خارقة
+
+145
+00:10:08,160 --> 00:10:08,500
+أو إهداف خارقة أو إهداف خارقة أو إهداف خارقة أو
+
+146
+00:10:08,500 --> 00:10:08,840
+إهداف خارقة أو إهداف خارقة أو إهداف خارقة أو إهداف
+
+147
+00:10:08,840 --> 00:10:17,500
+خارقة أو إهداف خارقة أو إهثلاث حالات مختلفة، وفقًا
+
+148
+00:10:17,500 --> 00:10:23,420
+لتلك الحالات، نستطيع أن نقرر إذا كانت السبب داخلية
+
+149
+00:10:23,420 --> 00:10:30,040
+أو خارجية. الأول هو الواضحة، والثاني هو الواقع،
+
+150
+00:10:30,040 --> 00:10:36,600
+والثالث هو الواضحة. أولًا دعونا نتكلم عن ما هو
+
+151
+00:10:36,600 --> 00:10:39,000
+الواضحة وما هو الواقع.
+
+152
+00:10:42,110 --> 00:10:45,890
+at different situations they behave differently
+
+153
+00:10:45,890 --> 00:10:49,250
+okay now there are slight differences here between
+
+154
+00:10:49,250 --> 00:10:52,130
+the explanation of those terminologies let us
+
+155
+00:10:52,130 --> 00:10:54,070
+first يعني point by point
+
+156
+00:10:57,820 --> 00:11:04,420
+لذلك عندما نتكلم عن الواضحيات، هنا نتكلم عن حركتين
+
+157
+00:11:04,420 --> 00:11:10,940
+مختلفة في موقعين مختلفة عندما نتكلم عن الواقع، هنا
+
+158
+00:11:10,940 --> 00:11:19,650
+نتكلم عن مدى ما هو حركتنا مشابهة للحركةالشخص يعمل
+
+159
+00:11:19,650 --> 00:11:21,390
+مع أشخاص مختلفة مثلا مع أشخاص مختلفة مع أشخاص
+
+160
+00:11:21,390 --> 00:11:23,770
+مختلفة مع أشخاص مختلفة مع أشخاص مختلفة مع أشخاص
+
+161
+00:11:23,770 --> 00:11:25,470
+مختلفة مع أشخاص مختلفة مع أشخاص مختلفة مع أشخاص
+
+162
+00:11:25,470 --> 00:11:28,410
+مختلفة مع أشخاص مختلفة مع أشخاص مختلفة مع أشخاص
+
+163
+00:11:28,410 --> 00:11:34,270
+مختلفة مع أشخاص مختلفة مع أشخاص مختلفة مع أشخاص
+
+164
+00:11:34,270 --> 00:11:34,970
+مختلفة مع أشخاص مختلفة مع أشخاص مختلفة مع أشخاص
+
+165
+00:11:34,970 --> 00:11:35,150
+مختلفة مع أشخاص مختلفة مع أشخاص مختلفة مع أشخاص
+
+166
+00:11:35,150 --> 00:11:42,950
+مختلفة مع أشخاص مختلفة مع أشخاص مختلفة مع أشخاص
+
+167
+00:11:42,950 --> 00:11:46,890
+مختلف
+
+168
+00:11:47,400 --> 00:11:53,660
+الأن، إذا كانت الواضحة عالية، فهنا نقول إن الأسباب
+
+169
+00:11:53,660 --> 00:12:00,940
+خارجية، وإذا كانت عالية، فهنا نقول إنها خارجية
+
+170
+00:12:01,070 --> 00:12:05,810
+التفكير هو نفس الشيء، إذا كان التفكير عال، هنا نحن
+
+171
+00:12:05,810 --> 00:12:09,810
+نتكلم عن تأثيرات أو أسباب خارجية، و بالطبع إذا
+
+172
+00:12:09,810 --> 00:12:14,410
+كانت قوية، نحن نتكلم عن أسباب خارجية، و بالطبع إذا
+
+173
+00:12:14,410 --> 00:12:16,050
+كانت قوية، نحن نتكلم عن أسباب خارجية، و بالطبع إذا
+
+174
+00:12:16,050 --> 00:12:21,830
+كانت قوية، نحن نتكلم عن أسباب خارجية، و بالطبع إذا
+
+175
+00:12:21,830 --> 00:12:22,250
+كانت خارجية، نحن نتكلم عن أسباب خارجية، و بالطبع
+
+176
+00:12:22,250 --> 00:12:25,830
+إذا كانت خارجية، نحن نتكلم عن أسباب خارجية، و
+
+177
+00:12:25,830 --> 00:12:27,050
+بالطبع إذا كانت خارجية، نحن نتكلم عن أسباب خارجية،
+
+178
+00:12:27,050 --> 00:12:32,190
+و باللنأخذ الأولة على سبيل المثال، الواضحة، قلنا
+
+179
+00:12:32,190 --> 00:12:39,390
+إلى مدى مستوى الانسان يتعامل بشكل مختلف في موقعين
+
+180
+00:12:39,390 --> 00:12:43,250
+مختلفة. الآن، إذا كانت عالية، وهو يعني أن الانسان
+
+181
+00:12:43,250 --> 00:12:48,850
+يتعامل بشكل مختلف في موقعين مختلفة، قلنا هنا بأن
+
+182
+00:12:48,850 --> 00:12:53,210
+الأسباب خارجية.
+
+183
+00:12:55,090 --> 00:12:56,170
+لماذا؟
+
+184
+00:13:03,230 --> 00:13:07,350
+يعني think here about the two opinions okay now
+
+185
+00:13:07,350 --> 00:13:09,810
+you said first if someone is late for the work ten
+
+186
+00:13:09,810 --> 00:13:13,230
+minutes or for example okay here we are talking
+
+187
+00:13:13,230 --> 00:13:16,930
+about high distinctiveness or low distinctiveness
+
+188
+00:13:16,930 --> 00:13:21,350
+we cannot judge this unless we compare it with
+
+189
+00:13:21,350 --> 00:13:25,220
+other situations okay now يعني for exampleإذا كان
+
+190
+00:13:25,220 --> 00:13:31,900
+هذا الشخص متأخر يظهر للعمل ومتأخر يقابل مجلسات
+
+191
+00:13:31,900 --> 00:13:36,960
+ومتأخر يقابل
+
+192
+00:13:36,960 --> 00:13:37,980
+مجلسات ومتأخر يقابل مجلسات ومتأخر يقابل مجلسات
+
+193
+00:13:37,980 --> 00:13:38,460
+ومتأخر يقابل مجلسات ومتأخر يقابل مجلسات ومتأخر
+
+194
+00:13:38,460 --> 00:13:38,920
+يقابل مجلسات ومتأخر يقابل مجلسات ومتأخر يقابل
+
+195
+00:13:38,920 --> 00:13:40,620
+مجلسات ومتأخر يقابل مجلسات ومتأخر يقابل مجلسات
+
+196
+00:13:40,620 --> 00:13:45,460
+ومتأخر يقابل مجلسات ومتأخر يقابل مجلسات ومتأخر
+
+197
+00:13:45,460 --> 00:13:52,880
+يقابل مجلسات ومتأخر يقابل
+
+198
+00:13:52,880 --> 00:13:58,490
+مجمظهر للعمل، لكن عندما تتحدث عن مجلسات، هناك نوع
+
+199
+00:13:58,490 --> 00:14:01,830
+من مقرارات عندما تتحدث عن مقرارات، هناك أيضًا نوع
+
+200
+00:14:01,830 --> 00:14:06,910
+من مقرارات وما إلى ذلك، فالصحابة هنا مختلفة جدًا،
+
+201
+00:14:06,910 --> 00:14:09,970
+إنها مختلفة، إنها ليست نفسها في موقعات مختلفة،
+
+202
+00:14:09,970 --> 00:14:14,350
+لذلك هناك تأثيرات خارجية يجعل هذا الشخص يتصرف
+
+203
+00:14:14,350 --> 00:14:18,430
+بطريقة معينة أحيانًا أو بطريقة مختلفة أحيانًا،
+
+204
+00:14:18,430 --> 00:14:26,130
+حسنًا، نستطيع أن نشرح هذا في مجلس آخرعن طريق تفكير
+
+205
+00:14:26,130 --> 00:14:30,450
+الموضوع، ليس دائما الانفلوانات الخارجية مرتبطة
+
+206
+00:14:30,450 --> 00:14:35,330
+بشخص أخر، أحيانا الانفلوانات الخارجية مرتبطة
+
+207
+00:14:35,330 --> 00:14:39,810
+بالبيئة، دعوني أعود للأمثلة الأولى التي اقترحت،
+
+208
+00:14:39,810 --> 00:14:43,430
+ربما هذا الشخص اللذي كان متأخر، ربما كان هناك
+
+209
+00:14:43,430 --> 00:14:49,020
+مشكلة في التransportationلذلك كان عالقًا، ولم
+
+210
+00:14:49,020 --> 00:14:55,940
+يتأثر من .. لكن إذا كان عالقًا لكل شيء، مثل
+
+211
+00:14:55,940 --> 00:14:58,540
+المقابلات أو المقابلات أو المشاركة للعمل وما إلى
+
+212
+00:14:58,540 --> 00:15:02,260
+ذلك، فهنا نقول إن هناك اختلاف كبير، وهذه مسبوحية
+
+213
+00:15:02,260 --> 00:15:09,420
+الداخلية التي حصلت من نفسه أو نفسها. لكن إذا كانت
+
+214
+00:15:09,420 --> 00:15:15,330
+في تجارب معينةفي طريقة مختلفة من طريقة مختلفة من
+
+215
+00:15:15,330 --> 00:15:15,770
+طريقة مختلفة من طريقة مختلفة من طريقة مختلفة من
+
+216
+00:15:15,770 --> 00:15:17,690
+طريقة مختلفة من طريقة مختلفة من طريقة مختلفة من
+
+217
+00:15:17,690 --> 00:15:17,990
+طريقة مختلفة من طريقة مختلفة من طريقة مختلفة من
+
+218
+00:15:17,990 --> 00:15:18,230
+طريقة مختلفة من طريقة مختلفة من طريقة مختلفة من
+
+219
+00:15:18,230 --> 00:15:19,350
+طريقة مختلفة من طريقة مختلفة من طريقة مختلفة من
+
+220
+00:15:19,350 --> 00:15:19,530
+طريقة مختلفة من طريقة مختلفة من طريقة مختلفة من
+
+221
+00:15:19,530 --> 00:15:21,430
+طريقة مختلفة من طريقة مختلفة من طريقة مختلفة من
+
+222
+00:15:21,430 --> 00:15:27,050
+طريقة مختلفة من طريقة مختلفة من طريقة مختلفة من
+
+223
+00:15:27,050 --> 00:15:30,690
+طريقة مختلفة من طريقة مختلفة
+
+224
+00:15:36,940 --> 00:15:40,920
+نحن صحيحين عن هذا الموضوع، دعنا نتكلم عن الواقع
+
+225
+00:15:40,920 --> 00:15:45,080
+عندما نتكلم عن الواقع، فهو نفس القواعد، دعني أقول
+
+226
+00:15:45,080 --> 00:15:49,320
+هنا إذا كنا نتكلم عن عقوبة عالية، فنحن نتكلم هنا
+
+227
+00:15:49,320 --> 00:15:54,540
+عن الأسباب الخارجية، وإذا كنا نتكلم عن عقوبة
+
+228
+00:15:54,540 --> 00:15:58,620
+عالية، فهنا نتكلم عن الأسباب الداخلية، لماذا عندما
+
+229
+00:15:58,620 --> 00:16:02,900
+نتكلم عن عقوبة عالية، نتكلم عن الأسباب الخارجية؟
+
+230
+00:16:30,670 --> 00:16:35,610
+causes is related to the individualعندما نتكلم عن
+
+231
+00:16:35,610 --> 00:16:40,590
+السببات الخارجية، إما أنها مرتبطة بالبيئة أو البعض
+
+232
+00:16:40,590 --> 00:16:45,810
+يعمل مع الشخص وما إلى ذلك، وعندما نتكلم عن
+
+233
+00:16:45,810 --> 00:16:52,970
+الواضحة، فهي عكس، كيف؟ لأن الواضحة هي إلى مدى
+
+234
+00:16:52,970 --> 00:16:59,070
+مدرجة أن الشخص يتعامل بنفس الطريقة في حالات
+
+235
+00:16:59,070 --> 00:17:04,740
+متشابهة وما إلى ذلك، لذلك هنا نتكلم عنإذا كانت
+
+236
+00:17:04,740 --> 00:17:11,280
+قوية، فنحن نتكلم عن قوات خارقة، وإذا كانت قوية،
+
+237
+00:17:11,280 --> 00:17:18,100
+فنحن نتكلم عن قوات خارقة، وإذا
+
+238
+00:17:18,100 --> 00:17:22,020
+كانت قوية، فنحن نتكلم عن قوات خارقة
+
+239
+00:17:26,100 --> 00:17:32,860
+في نفس الطريقة في حالات متشابهة فهي شيء انتشرت من
+
+240
+00:17:32,860 --> 00:17:37,560
+الشخص لأن البيئة ليست نفسها هنا نحن نتكلم عن حالات
+
+241
+00:17:37,560 --> 00:17:43,200
+مختلفة في البيئة فكل مرة هذا الشخص يتعامل بنفس
+
+242
+00:17:43,200 --> 00:17:47,480
+الشيء لهذا السبب نقول هنا أنه يتم تأثيره بالداخل
+
+243
+00:17:47,480 --> 00:17:53,430
+من الشخص إذا هذا الشخص في حالات متشابهةتتعامل
+
+244
+00:17:53,430 --> 00:17:56,830
+بطريقة مختلفة، فنحن نعتبر الأسباب الموجودة هنا
+
+245
+00:17:56,830 --> 00:18:01,310
+لأسباب خارجية لأن بالنسبة للأسباب الموجودة هنا،
+
+246
+00:18:01,310 --> 00:18:05,410
+الانسان يتعامل بطريقات مختلفة، بما أن الوضع هو
+
+247
+00:18:05,410 --> 00:18:11,130
+نفسه، حسنًا؟ الآن، لماذا يجب أن نفهم إذا كانت
+
+248
+00:18:11,130 --> 00:18:18,850
+السبب للتعامل داخلي أو خارجي؟ ما هي أهمية نظر
+
+249
+00:18:18,850 --> 00:18:20,070
+التعامل؟
+
+250
+00:18:24,670 --> 00:18:28,250
+أو أشخاص أخرى، أعني عندما أنظر إلى الشخص و أقول إن
+
+251
+00:18:28,250 --> 00:18:34,210
+هذه أسباب خارجية، فإيجابيتي ستكون أنه أو أنها 100%
+
+252
+00:18:34,210 --> 00:18:38,070
+مسؤولة عن أفعاله أو أفعالها، لكن عندما أقول إن
+
+253
+00:18:38,070 --> 00:18:43,230
+هناك أسباب خارجية، فهي كأنني أعطيه بعض الشرح، أنا
+
+254
+00:18:43,230 --> 00:18:47,330
+أعطي هذا الشخص فرصة أخرى، لذلك يساعد كيف أقوم و
+
+255
+00:18:47,330 --> 00:18:53,190
+كيف أدعوا الناس يتعاملوهذا مهم عندما نحتاج ..
+
+256
+00:18:53,190 --> 00:18:57,610
+بالطبع قالنا في البداية للمجلس لماذا نحتاج أن ندرس
+
+257
+00:18:57,610 --> 00:19:00,970
+الهواء لأن إذا فهمنا الهواء نستطيع التغيير نستطيع
+
+258
+00:19:00,970 --> 00:19:03,810
+التحكم نستطيع تغيير الهواء وكذلكلذلك إذا كنا
+
+259
+00:19:03,810 --> 00:19:07,370
+نستطيع أن نستخدم الأسباب الداخلية أو الداخلية أو
+
+260
+00:19:07,370 --> 00:19:07,970
+الداخلية أو الداخلية أو الداخلية أو الداخلية أو
+
+261
+00:19:07,970 --> 00:19:08,290
+الداخلية أو الداخلية أو الداخلية أو الداخلية أو
+
+262
+00:19:08,290 --> 00:19:09,170
+الداخلية أو الداخلية أو الداخلية أو الداخلية أو
+
+263
+00:19:09,170 --> 00:19:09,790
+الداخلية أو الداخلية أو الداخلية أو الداخلية أو
+
+264
+00:19:09,790 --> 00:19:11,610
+الداخلية أو الداخلية أو الداخلية أو الداخلية أو
+
+265
+00:19:11,610 --> 00:19:14,010
+الداخلية أو الداخلية أو الداخلية أو الداخلية أو
+
+266
+00:19:14,010 --> 00:19:15,450
+الداخلية أو الداخلية أو الداخلية أو الداخلية أو
+
+267
+00:19:15,450 --> 00:19:15,450
+الداخلية أو الداخلية أو الداخلية أو الداخلية أو
+
+268
+00:19:15,450 --> 00:19:18,470
+الداخلية أو الداخلية أو الداخلية أو الداخلية أو
+
+269
+00:19:18,470 --> 00:19:23,390
+الداخلية أو الداخلية أو الداخليةإذا كنا نتكلم عن
+
+270
+00:19:23,390 --> 00:19:28,050
+الأسباب الخارجية، فهناك شيء مرتبط بالبيئة ويجب أن
+
+271
+00:19:28,050 --> 00:19:33,130
+نفعل شيء عنه لتحسين أو تغيير أو تغيير الهجوم أو أي
+
+272
+00:19:33,130 --> 00:19:37,910
+شيء نحتاجه هنا لنفعله مع الهجوم للشخص، فهو مهم أن
+
+273
+00:19:37,910 --> 00:19:43,500
+نفهم الأسباب لأن هذا جزء من فهم الهجوم نفسهوهذا
+
+274
+00:19:43,500 --> 00:19:47,420
+سيحفز قدرتنا على التعامل مع التعامل مع التعامل مع
+
+275
+00:19:47,420 --> 00:19:50,260
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+276
+00:19:50,260 --> 00:19:51,220
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+277
+00:19:51,220 --> 00:19:54,260
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+278
+00:19:54,260 --> 00:19:54,760
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+279
+00:19:54,760 --> 00:19:55,340
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+280
+00:19:55,340 --> 00:19:55,820
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+281
+00:19:55,820 --> 00:19:57,380
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+282
+00:19:57,380 --> 00:19:57,660
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+283
+00:19:57,660 --> 00:19:59,280
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+284
+00:19:59,280 --> 00:20:07,040
+التعامل مع التعامل مع التعامل
+
+285
+00:20:07,040 --> 00:20:08,000
+مع الت
+
+286
+00:20:12,920 --> 00:20:17,100
+الطريقة التي نفكر عن الأشياء ..يعني هناك بعض
+
+287
+00:20:17,100 --> 00:20:22,200
+الخطوات التي نفعلها و هنا سنتحدث عن اتجارات مختلفة
+
+288
+00:20:22,200 --> 00:20:28,880
+من الخطوات الأولة نسميها خطوة التعليم الأساسي الان
+
+289
+00:20:28,880 --> 00:20:33,460
+بالنسبة لخطوة التعليم الأساسي هنا عادة الشخص
+
+290
+00:20:38,500 --> 00:20:42,200
+focus on internal factors more than external
+
+291
+00:20:42,200 --> 00:20:47,060
+factors or they neglect or underestimate or
+
+292
+00:20:47,060 --> 00:20:51,220
+undermine the environmental factors okay and this
+
+293
+00:20:51,220 --> 00:20:56,380
+is a mistake okay why why we consider
+
+294
+00:20:59,050 --> 00:21:04,110
+Underestimating أو تغيير أفكار الخارجية هو شيء
+
+295
+00:21:04,110 --> 00:21:09,670
+نسميه خطأ لماذا؟ لأنك لا تستطيع أن تقول أن أي شخص
+
+296
+00:21:09,670 --> 00:21:13,350
+يتصرف لأنه يريد أن يفعل ذلك ربما هناك بعض الأفكار
+
+297
+00:21:13,350 --> 00:21:16,710
+الخارجية التي تأثر عليه و تأثر عمله لذلك يجب أن
+
+298
+00:21:16,710 --> 00:21:19,610
+تفهمك لذلك يمكنك أن تقوم بالحكم على الشخص الوحيد
+
+299
+00:21:19,610 --> 00:21:24,230
+حسنًا ، هذا صحيح ماذا أخر؟ لأن أحيانًا
+
+300
+00:21:29,000 --> 00:21:32,260
+وفي الكثير من الحالات، نحن مضطرين أن نفعل بعض
+
+301
+00:21:32,260 --> 00:21:35,800
+الأشياء التي لا نريدها أو لا نحبها وما إلى ذلك،
+
+302
+00:21:35,800 --> 00:21:39,580
+لكننا نجدها إما أنها محتاجة أو أحياناً نحن مضطرين
+
+303
+00:21:39,580 --> 00:21:43,740
+أن نفعل شيء لا نحبه وما إلى ذلك، فلا يمكننا أن
+
+304
+00:21:43,740 --> 00:21:50,740
+ننقل هنا الأشياء الخارجية، وطبعاً، كتلقاء أخطأ
+
+305
+00:21:50,740 --> 00:21:58,280
+أساسيعادةً هنا المسلحة للناس عادةً هي أعلى من
+
+306
+00:21:58,280 --> 00:22:03,540
+الشخص نفسه أو نفسها وهو السبب في تندنسية المسلحة
+
+307
+00:22:03,540 --> 00:22:07,900
+للناس هنا هي أعلى وهو مشكلة لأن بعض الأحيان كما
+
+308
+00:22:07,900 --> 00:22:12,160
+تحدثنا فقط الآن فهي خارج يدي المشخص و بعض الأحيان
+
+309
+00:22:12,160 --> 00:22:17,440
+يجب أن نفعل أشياء صحيح هذه ليست الموضوع اللي نتحدث
+
+310
+00:22:17,440 --> 00:22:23,510
+عنه نحن نتحدث عن حقيقة كيف حدث الأشياءالناس
+
+311
+00:22:23,510 --> 00:22:27,350
+أحيانًا تفعل الأشياء التي لا تريدها أن تفعلها أو
+
+312
+00:22:27,350 --> 00:22:33,210
+لا يؤمنوا بأنهم يجب أن يفعلوا هذا يحدث، لهذا السبب
+
+313
+00:22:33,210 --> 00:22:40,610
+نقول هنا إنه غير صحيح أن تبذل الناس لكل شيء، لأن
+
+314
+00:22:40,610 --> 00:22:45,430
+في بعض الأحيان هناك تأثيرات خارجية هنايعني تدفع
+
+315
+00:22:45,430 --> 00:22:51,550
+حياته الشخصية. الآن بياضة أخرى هنا أو خطأ نسميها
+
+316
+00:22:51,550 --> 00:22:54,750
+الـ self-serving bias. حسنا؟ الآن عندما نتحدث عن
+
+317
+00:22:54,750 --> 00:22:59,650
+الـ self-serving bias، هنا نتحدث عن كيف .. يعني
+
+318
+00:22:59,650 --> 00:23:04,220
+دعوني أعود إلى خطوات التجارب الأساسيةعندما نفكر
+
+319
+00:23:04,220 --> 00:23:07,400
+بالخطأات الأساسية في التعليم هنا، يمكن أن يكون في
+
+320
+00:23:07,400 --> 00:23:10,080
+بعض الأحيان أو في أغلب الأحيان، دعنا نحصل على مثال
+
+321
+00:23:10,080 --> 00:23:12,540
+هنا مثل الرئيسين، في بعض الأحيان يمكن أنهم
+
+322
+00:23:12,540 --> 00:23:18,760
+يتسامحوا بمعارفاتهم لأنهم لم يفعلوا بعض الأعمال أو
+
+323
+00:23:18,760 --> 00:23:22,320
+بعض البيانات، على سبيل المثال، ولم يتم إعطائها أو
+
+324
+00:23:22,320 --> 00:23:26,070
+كان هناك بعضوالأدوات المحتاجة أو المدينة أو أي شيء
+
+325
+00:23:26,070 --> 00:23:31,710
+ما .. فهم يفقدون هنا الأشياء الخارجية عندما نتكلم
+
+326
+00:23:31,710 --> 00:23:34,750
+عن الـself-serving bias نحن نتكلم هنا عن الـ bias
+
+327
+00:23:34,750 --> 00:23:38,910
+هنا نتكلم عن الهجوم الذي يتم إدارته من الشخص وليس
+
+328
+00:23:38,910 --> 00:23:44,010
+من أشخاص أخرين وخطأ وخطأ في التعامل بسبب الهجوم أو
+
+329
+00:23:44,010 --> 00:23:49,210
+هنا نتكلم عن تعامل أكتر من نتيجة نتيجة الهجوم نفسه
+
+330
+00:23:49,920 --> 00:23:55,220
+لذلك إذا كان هناك نجاح مرة أخرى، فهو عمل افضل من
+
+331
+00:23:55,220 --> 00:23:58,020
+نفسي، وإذا كان هناك خطأ هنا، فهنا نتحدث عن أشخاص
+
+332
+00:23:58,020 --> 00:24:02,360
+آخرين يسببون هذه الخطأ، وهذا ما نسميه نفسي يساعد
+
+333
+00:24:02,360 --> 00:24:02,900
+نفسي يساعد نفسي يساعد نفسي يساعد نفسي يساعد نفسي
+
+334
+00:24:02,900 --> 00:24:04,340
+يساعد نفسي يساعد نفسي يساعد نفسي يساعد نفسي يساعد
+
+335
+00:24:04,340 --> 00:24:05,760
+نفسي يساعد نفسي يساعد نفسي يساعد نفسي يساعد نفسي
+
+336
+00:24:05,760 --> 00:24:05,920
+يساعد نفسي يساعد نفسي يساعد نفسي يساعد نفسي يساعد
+
+337
+00:24:05,920 --> 00:24:14,660
+نفسي يساعد نفسي يساعد نفسي
+
+338
+00:24:15,640 --> 00:24:24,560
+مع نفسي، ماذا هي إتفاقات الإخطارات والخاطرات؟ ماذا
+
+339
+00:24:24,560 --> 00:24:29,920
+هي إتفاقات الإخطارات والخاطرات؟
+
+340
+00:24:32,810 --> 00:24:37,590
+لكن عندما نتكلم عن خطأ التصرف الأساسي، نقول أننا
+
+341
+00:24:37,590 --> 00:24:42,430
+نسيطر على الآخرين، ولكني كمدير أو كمشغل في
+
+342
+00:24:42,430 --> 00:24:45,230
+المؤسسة، لا أستطيع أن أستمر في تسييطر على الآخرين،
+
+343
+00:24:45,230 --> 00:24:49,550
+لأن هذا سيسبب في تخطيط أكتر لي أو لأشخاص أخرينو
+
+344
+00:24:49,550 --> 00:24:57,970
+بالطبع هذا سيأثر على عملهم أو عمل أشخاص أخرين ولكن
+
+345
+00:24:57,970 --> 00:25:00,730
+عندما يأتي الـself-serving bias إذا كنت أبقى فقط
+
+346
+00:25:00,730 --> 00:25:05,810
+أخبرها عن كل شيء جيد يحدث لها قد يسبب فيها نفسي أن
+
+347
+00:25:05,810 --> 00:25:11,970
+نفسي يرفع أو شيء مثل هذا وبالتالي فإن عملتي ستكون
+
+348
+00:25:11,970 --> 00:25:18,460
+أسفة ماذا يعني؟ نعمنحن فعلنا تقرارات غير صحيحة و
+
+349
+00:25:18,460 --> 00:25:21,380
+عندما نفعل هذا يعني أننا لم نفعلها بطريقة صحيحة
+
+350
+00:25:21,380 --> 00:25:25,400
+لنقوم بتجاربها و لنجعلها ممتازة و لكننا فعلنا
+
+351
+00:25:25,400 --> 00:25:29,800
+الموضوع بطريقة صحيحة حسنًا، في بداية هذه الدراسة
+
+352
+00:25:29,800 --> 00:25:35,080
+قلنا عندما نتحدث عن الانتصاف، هنا كيف تشعر الحقيقة
+
+353
+00:25:35,080 --> 00:25:43,730
+بشخص مهم أو أهم هنا، لكن الحقيقة الحقيقية ليستأو
+
+354
+00:25:43,730 --> 00:25:49,410
+أقل مهمة لماذا؟ لأن الناس عندما يتعامل أو يتعامل
+
+355
+00:25:49,410 --> 00:25:52,650
+بطريقة معينة، يتعامل بطريقة مناسبة لكيف تفهم
+
+356
+00:25:52,650 --> 00:25:56,750
+الحقيقة أو كيف تفهم الحقيقة، حسنًا، هنا نحن نتكلم
+
+357
+00:25:56,750 --> 00:26:04,310
+عن المفاهيم للحقيقة، حسنًا، هنا نتكلم عنمثلًا، إذا
+
+358
+00:26:04,310 --> 00:26:09,170
+كانت الوضعية مؤسسة على نوع من التفسير للموضوع ولكن
+
+359
+00:26:09,170 --> 00:26:13,730
+هذا التفسير أو الانتباه ليس حقيقي ولكن للشخصيات،
+
+360
+00:26:13,730 --> 00:26:18,950
+هذه هي الحقيقة هذا واحد من أهم خطوات أو غلطات
+
+361
+00:26:18,950 --> 00:26:22,890
+عندما نتكلم عن كيف يتعامل الناس مع رؤيتهم، حسنًا؟
+
+362
+00:26:22,890 --> 00:26:27,530
+إنه مثل .. يعني .. دعني أفسره بطريقة أخرى، بعض ..
+
+363
+00:26:27,530 --> 00:26:30,090
+لا أستطيع أن أقول فقط بعض الناس، الكثير من الناس
+
+364
+00:26:30,450 --> 00:26:34,170
+عندما يفكرون في الأشياء، لا يبحثون عن الصورة
+
+365
+00:26:34,170 --> 00:26:39,410
+الكامة أو الصورة كامة، يبحثون عن حصة .. يشاهدون
+
+366
+00:26:39,410 --> 00:26:46,200
+حصة الصورة أو الصورةلذلك لا يوجد فكرة مفهومة عن
+
+367
+00:26:46,200 --> 00:26:52,340
+جميع الأشياء المرتبطة بالوضع وهذا بالطبع سيسبب فيه
+
+368
+00:26:52,340 --> 00:26:56,980
+خطأ أو خطأ و بالطبع سيأثر على النتائج بدلا من
+
+369
+00:26:56,980 --> 00:27:01,600
+الحصول على نتائج positive يمكننا الحصول على نتائج
+
+370
+00:27:01,600 --> 00:27:01,600
+negative
+
+371
+00:27:05,780 --> 00:27:09,160
+التأثيرات الخاطئة من هؤلاء .. بشكل عام انا لا
+
+372
+00:27:09,160 --> 00:27:12,820
+اتكلم عن التفاصيل المحددة هنا حسنا؟ التي تفسرنا
+
+373
+00:27:12,820 --> 00:27:15,300
+عنها قبل قليل انا اتكلم عنها بشكل عام كيف هذا
+
+374
+00:27:15,300 --> 00:27:20,780
+سيؤثر على رؤيتنا انها ستدرس رؤيتنا بطريقة مختلفة
+
+375
+00:27:20,780 --> 00:27:25,080
+بدل اننا نفهم الحقيقة كمان كمان كمان كمان كمان
+
+376
+00:27:25,080 --> 00:27:30,920
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+377
+00:27:38,020 --> 00:27:40,060
+Okay okay this is enough for today
+
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/fuAsL4QgIn0_raw.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/fuAsL4QgIn0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..88635e30e19e5e10adc922af3ccf7a715f007d2d
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/fuAsL4QgIn0_raw.srt
@@ -0,0 +1,1664 @@
+1
+00:00:08,340 --> 00:00:13,280
+سنبدأ اليوم بقصة جديدة، القصة الثالثة. في هذه
+
+2
+00:00:13,280 --> 00:00:18,460
+القصة، سنتحدث عن طريقات وإنجاز العمل. إنها جزء من
+
+3
+00:00:18,460 --> 00:00:24,000
+ديناميكا الشخصية أو العامل. في القصة السابقة،
+
+4
+00:00:24,000 --> 00:00:30,680
+قررنا أشياء أخرى، مثل التعلم. قررنا أشياء
+
+5
+00:00:34,590 --> 00:00:39,470
+الاستخدامات والاستخدامات الانتجارية والاستخدامات
+
+6
+00:00:39,470 --> 00:00:41,950
+الانتجارية والاستخدامات الانتجارية والاستخدامات
+
+7
+00:00:41,950 --> 00:00:43,250
+الانتجارية والاستخدامات الانتجارية والاستخدامات
+
+8
+00:00:43,250 --> 00:00:43,250
+الانتجارية والاستخدامات الانتجارية والاستخدامات
+
+9
+00:00:43,250 --> 00:00:43,890
+الانتجارية والاستخدامات الانتجارية والاستخدامات
+
+10
+00:00:43,890 --> 00:00:44,830
+الانتجارية والاستخدامات الانتجارية والاستخدامات
+
+11
+00:00:44,830 --> 00:00:48,230
+الانتجارية والاستخدامات الانتجارية والاستخدامات
+
+12
+00:00:48,230 --> 00:00:54,270
+الانتجارية والاستخدامات الانتجارية والاستخدامات
+
+13
+00:00:54,270 --> 00:01:01,240
+الانتجارية والاستخدامات الانالأهمية التعليمية في
+
+14
+00:01:01,240 --> 00:01:02,140
+هذه القصة
+
+15
+00:01:05,420 --> 00:01:08,820
+كما ذكرت بالفعل، سنتحدث عن المواصفات المرتبطة
+
+16
+00:01:08,820 --> 00:01:13,100
+بالقيم العمل. عندما نتحدث عن القيم العمل، يوجد
+
+17
+00:01:13,100 --> 00:01:18,480
+مجموعات مختلفة مرتبطة أو قيم العمل، التي سنقوم
+
+18
+00:01:18,480 --> 00:01:23,520
+بتدريها. يجب أن نعرف، بالطبع، العلاقة بين القيم
+
+19
+00:01:23,520 --> 00:01:30,300
+العمل ورعاية الموظفين في المؤسسة.هناك مقالات عمل
+
+20
+00:01:30,300 --> 00:01:34,500
+مهمة عندما نتكلم عن المقالات، هناك الكثير من
+
+21
+00:01:34,500 --> 00:01:39,300
+المقالات، ولكننا سنتكلم عن المقالات المهمة مرتبطة
+
+22
+00:01:39,300 --> 00:01:46,870
+بالبيئة العملبعد ذلك سوف نبدأ بالإيجاب عن العمل
+
+23
+00:01:46,870 --> 00:01:51,090
+نفس الشيء سوف ندرس المصطلحات الرئيسية والأفكار
+
+24
+00:01:51,090 --> 00:01:56,490
+المرتبطة بالإيجاب عن العمل بإضافة إلى معرفة ما هي
+
+25
+00:01:56,490 --> 00:02:02,390
+السبب للإيجاب عن العمل وطبعا كيف يتجاوز العمليين
+
+26
+00:02:05,720 --> 00:02:10,200
+عشان عندما نتكلم عن الاطلاع يكون الموظفين سيكونون
+
+27
+00:02:10,200 --> 00:02:15,180
+مستمتعين أو مستمتعين إذا لم يكن الموظفين مستمتعين،
+
+28
+00:02:15,180 --> 00:02:18,580
+فهي ستتعامل بطريقة معينة، يجب أن نفهم كيف يتعامل
+
+29
+00:02:18,580 --> 00:02:25,440
+الموظفين وكيف نتعامل مع تلك التعاملات. الأن دعونا
+
+30
+00:02:25,440 --> 00:02:27,600
+نبدأ بالطرقات
+
+31
+00:02:29,980 --> 00:02:33,660
+نحن نتكلم عن اعتبارات ونقول ان اعتبار هو مصطلح
+
+32
+00:02:33,660 --> 00:02:44,240
+معين أو قرار يتعلق بالأشخاص أو الأحداث كيف نشرح
+
+33
+00:02:44,240 --> 00:02:45,440
+هذا؟
+
+34
+00:02:50,840 --> 00:02:56,960
+هنا نحن نتكلم عن اعتبارات، إنها نوع من تجارب أو
+
+35
+00:02:56,960 --> 00:03:04,360
+تقرار مني عن الاشخاص أو المؤسسات، على سبيل المثال،
+
+36
+00:03:04,360 --> 00:03:07,160
+وهذه ستكون أكتر مخصصة
+
+37
+00:03:18,410 --> 00:03:23,430
+Okay so يعني those judgments or evaluative
+
+38
+00:03:23,430 --> 00:03:28,170
+statements how employees usually are going to use
+
+39
+00:03:28,170 --> 00:03:31,410
+or how it is going to affect employees behavior
+
+40
+00:03:35,540 --> 00:03:40,820
+بسبب أن الجميع سيفرح بطريقة محددة باعتباره، بشكل
+
+41
+00:03:40,820 --> 00:03:46,360
+افضح او اقل لعمله، وهذا سيأثر على قيمة العمل أو
+
+42
+00:03:46,360 --> 00:03:49,000
+العاملات. فبعض الأكتبار، نستطيع أن نقول بأن
+
+43
+00:03:49,000 --> 00:03:55,970
+الاعتبار سيأثر على كيف سنأخذ قراراتنا.بعضًا نتحدث
+
+44
+00:03:55,970 --> 00:04:00,110
+عن شيء مرتبط بشأن كيف سيقرر الناس عن الأشياء وهذا
+
+45
+00:04:00,110 --> 00:04:03,510
+مضمون أيضًا في المستقبل عندما نتحدث عن القيم
+
+46
+00:04:03,510 --> 00:04:07,750
+بطريقة أكتر مدهشة حتى لذلك عندما نتحدث عن اعتقاد
+
+47
+00:04:07,750 --> 00:04:12,170
+نحن نتحدث هنا عن مجزرة التي ستأثر على كيف سنقوم
+
+48
+00:04:12,170 --> 00:04:15,990
+باختيار خياراتنا باتجاه أشخاص أو أشخاص أو حيوانات
+
+49
+00:04:15,990 --> 00:04:20,150
+أو أي شيء آخر هنا مرة أخرى نحن نتحدث عن اعتبار أو
+
+50
+00:04:20,150 --> 00:04:25,850
+قيمةالتي سوف تأثير على كيف نتعامل مع الأشخاص
+
+51
+00:04:25,850 --> 00:04:30,090
+والناس والأشخاص والأشخاص والأشخاص والأشخاص
+
+52
+00:04:30,090 --> 00:04:30,090
+والأشخاص والأشخاص والأشخاص والأشخاص والأشخاص
+
+53
+00:04:30,090 --> 00:04:30,610
+والأشخاص والأشخاص والأشخاص والأشخاص والأشخاص
+
+54
+00:04:30,610 --> 00:04:31,830
+والأشخاص والأشخاص والأشخاص والأشخاص والأشخاص
+
+55
+00:04:31,830 --> 00:04:31,890
+والأشخاص والأشخاص والأشخاص والأشخاص والأشخاص
+
+56
+00:04:31,890 --> 00:04:31,970
+والأشخاص والأشخاص والأشخاص والأشخاص والأشخاص
+
+57
+00:04:31,970 --> 00:04:31,970
+والأشخاص والأشخاص والأشخاص والأشخاص والأشخاص
+
+58
+00:04:31,970 --> 00:04:41,310
+والأشخاص والأشخاص والأشخاص والأشخاص والأشخاص
+
+59
+00:04:41,310 --> 00:04:45,270
+والأشخاص
+
+60
+00:04:46,860 --> 00:04:52,000
+في طريقة أكتر مباشرة، سنقرر عن أشياء أو الناس أو
+
+61
+00:04:52,000 --> 00:04:56,880
+الأحداث، يمكننا أن نقول إنه شيء مفيد يجب أن نتعامل
+
+62
+00:04:56,880 --> 00:05:00,620
+معه أو يمكن أن يكون شيء نقلي يجب أن نتعامل معه
+
+63
+00:05:00,730 --> 00:05:05,030
+avoid أو هنا يمكن أن يكون هناك إجابة لذلك يمكن أن
+
+64
+00:05:05,030 --> 00:05:08,090
+نكون مرتبطين في هذه العملية أو يمكن أن يكون هناك
+
+65
+00:05:08,090 --> 00:05:13,010
+نوع من خسارة أو نتيجة مخاطرة لذلك سنا ناقض وما إلى
+
+66
+00:05:13,010 --> 00:05:18,970
+ذلك، فهنا مرة أخرى، سيساعدنا في القرار عن مشاكل
+
+67
+00:05:18,970 --> 00:05:21,150
+مختلفة، حيث أشياء وما إلى ذلك. عندما نتكلم عن
+
+68
+00:05:21,150 --> 00:05:26,700
+القصص، هناك جزءين مختلفين من القصصattitude يعني it
+
+69
+00:05:26,700 --> 00:05:31,100
+is not like a one step process we are talking
+
+70
+00:05:31,100 --> 00:05:34,460
+about process with multi components let me say not
+
+71
+00:05:34,460 --> 00:05:37,260
+steps okay so when you talk about attitude there
+
+72
+00:05:37,260 --> 00:05:40,060
+are different components there are three main
+
+73
+00:05:40,060 --> 00:05:43,120
+components the first one is the cognitive
+
+74
+00:05:43,120 --> 00:05:47,060
+component the second one is the affective
+
+75
+00:05:47,060 --> 00:05:50,100
+component and the third one is the behavioral
+
+76
+00:05:50,100 --> 00:05:54,870
+componentعندما نتكلم عن الوضع الكوجيني، هنا نتكلم
+
+77
+00:05:54,870 --> 00:06:00,890
+عن كيف نرى أشياء أو أشخاص أو حالات نفكر بطريقة
+
+78
+00:06:00,890 --> 00:06:08,630
+معينة، نحن لدينا فكرة، نحن لدينا فكرة عن أشياء،
+
+79
+00:06:08,630 --> 00:06:15,550
+أشخاص، حالات وما إلى ذلك، فهذا هو الوضع الأول هنا
+
+80
+00:06:15,550 --> 00:06:21,340
+نتكلم عن بعضماذا عن المعلومات الخلفية نستطيع أن
+
+81
+00:06:21,340 --> 00:06:25,120
+نقولها نستطيع أن نقولها عن الانتقال بعض الأحيان
+
+82
+00:06:25,120 --> 00:06:28,940
+نستطيع أن نقولها عن أفكار و رؤية كل هذه الأشياء
+
+83
+00:06:28,940 --> 00:06:35,440
+ستأثر على كيف نشهد الأشياء الناس و الوضع و الوضع و
+
+84
+00:06:35,440 --> 00:06:36,460
+مرة أخرى و مرة أخرى و مرة أخرى و مرة أخرى و مرة
+
+85
+00:06:36,460 --> 00:06:38,380
+أخرى و مرة أخرى و مرة أخرى و مرة أخرى و مرة أخرى و
+
+86
+00:06:38,380 --> 00:06:38,440
+مرة أخرى و مرة أخرى و مرة أخرى و مرة أخرى و مرة
+
+87
+00:06:38,440 --> 00:06:38,660
+أخرى و مرة أخرى و مرة أخرى و مرة أخرى و مرة أخرى و
+
+88
+00:06:38,660 --> 00:06:47,750
+مرة أخرى و مرة أخرى و مرة أخرى و مرة أخرى وفي
+
+89
+00:06:47,750 --> 00:06:51,830
+المرحلة التالية أو عندما نقوم بمرحلة التالية،
+
+90
+00:06:51,830 --> 00:06:57,990
+سنقرر إذا كنا نحب أو نكره هذه الشيء أو هذه الموضوع
+
+91
+00:06:57,990 --> 00:07:02,230
+وما إلى ما يعتمد على ماذا؟
+
+92
+00:07:04,610 --> 00:07:09,870
+هو شعور، ولكن يعتمد على ما نصدر هنا عن هذه
+
+93
+00:07:09,870 --> 00:07:16,170
+الأشياء. نحن سنظهر شعورنا إذا كنا نحب أو نكره شيء.
+
+94
+00:07:16,490 --> 00:07:21,990
+فأولا نحن لدينا فكرة هنا أو نحن لدينا فكرة. سنخلص
+
+95
+00:07:21,990 --> 00:07:30,200
+فكرة هنا ثم سنختار كيف نشعر بشأن هذاأي حدث مرة
+
+96
+00:07:30,200 --> 00:07:34,520
+أخرى أو شيء ما على ما يبدو على ما يبدو على ما يبدو
+
+97
+00:07:34,520 --> 00:07:36,200
+على ما يبدو على ما يبدو على ما يبدو على ما يبدو
+
+98
+00:07:36,200 --> 00:07:36,200
+على ما يبدو على ما يبدو على ما يبدو على ما يبدو
+
+99
+00:07:36,200 --> 00:07:36,220
+على ما يبدو على ما يبدو على ما يبدو على ما يبدو
+
+100
+00:07:36,220 --> 00:07:37,820
+على ما يبدو على ما يبدو على ما يبدو على ما يبدو
+
+101
+00:07:37,820 --> 00:07:40,400
+على ما يبدو على ما يبدو على ما يبدو على ما يبدو
+
+102
+00:07:40,400 --> 00:07:40,880
+على ما يبدو على ما يبدو على ما يبدو على ما يبدو
+
+103
+00:07:40,880 --> 00:07:46,500
+على ما يبدو على ما يبدو على ما يبدو على ما يبدو
+
+104
+00:07:46,500 --> 00:07:51,720
+على ما
+
+105
+00:07:51,720 --> 00:07:59,540
+يبدو على ما يبدوأفكار أو نصيحة التي خلقناها عن هذه
+
+106
+00:07:59,540 --> 00:08:06,540
+الوضع. يمكننا أن نعرف هذا من ناحية التفاصيل. أولا
+
+107
+00:08:06,540 --> 00:08:13,980
+سوف نتعامل مع الموضوع ثم سوف نخلق شعور عن الموضوع
+
+108
+00:08:13,980 --> 00:08:15,760
+ثم أخيرا سوف نضيف
+
+109
+00:08:19,520 --> 00:08:24,000
+عندما نتكلم عن اعتبارات في بعض الكتبات تدفع
+
+110
+00:08:24,000 --> 00:08:29,420
+اعتبارات كما هو الشعور لشيء وهو حقيقي لأنه أحد
+
+111
+00:08:29,420 --> 00:08:35,340
+أساسي المشكلة هنا ولكن باعتبار ما ندرسه هنا نقول
+
+112
+00:08:35,340 --> 00:08:41,020
+أن هناك ثلاث أساسي، لكن مرة أخرى جزء مهم من أي
+
+113
+00:08:41,020 --> 00:08:46,310
+اعتبار هو كيف نشعر بالأشياء أوأشخاص أخرين أو
+
+114
+00:08:46,310 --> 00:08:47,150
+مجتمعين أو مجتمعين أو مجتمعين أو مجتمعين أو
+
+115
+00:08:47,150 --> 00:08:48,230
+مجتمعين أو مجتمعين أو مجتمعين أو مجتمعين أو
+
+116
+00:08:48,230 --> 00:08:52,290
+مجتمعين أو مجتمعين أو مجتمعين أو مجتمعين أو
+
+117
+00:08:52,290 --> 00:08:54,710
+مجتمعين أو مجتمعين أو مجتمعين أو مجتمعين أو
+
+118
+00:08:54,710 --> 00:08:55,550
+مجتمعين أو مجتمعين أو مجتمعين أو مجتمعين أو
+
+119
+00:08:55,550 --> 00:08:55,890
+مجتمعين أو مجتمعين أو مجتمعين أو مجتمعين أو
+
+120
+00:08:55,890 --> 00:08:56,330
+مجتمعين أو مجتمعين أو مجتمعين أو مجتمعين أو
+
+121
+00:08:56,330 --> 00:08:58,730
+مجتمعين أو مجتمعين أو مجتمعين أو مجتمعين أو
+
+122
+00:08:58,730 --> 00:09:04,700
+مجتمعين أو مجتمعين أو مجتمعين أو مجتمعين أودعوني
+
+123
+00:09:04,700 --> 00:09:07,180
+أعود إلى النقطة الأولى التي قد تحدثنا عنها، القصص
+
+124
+00:09:07,180 --> 00:09:12,600
+مهمة جدًا لأنها ستساعدنا في قرار كيف نتعامل في
+
+125
+00:09:12,600 --> 00:09:17,120
+حالة معينة، لذلك ستتأثر على قراراتنا التي تم
+
+126
+00:09:17,120 --> 00:09:24,120
+إختيارها لكي نتعامل مع حالات مختلفة. أحد المشكلات
+
+127
+00:09:24,120 --> 00:09:32,620
+التي مرتبطة بقصصنا هي ما نسميه اتصال كوجنية، في
+
+128
+00:09:32,620 --> 00:09:38,420
+اتصال كوجينيWe do not have one attitude. We have a
+
+129
+00:09:38,420 --> 00:09:42,520
+package of attitudes and those attitudes are mixed
+
+130
+00:09:42,520 --> 00:09:46,460
+and sometimes it is contradictory to each other.
+
+131
+00:09:47,280 --> 00:09:52,140
+So whenever there are two or more attitudes which
+
+132
+00:09:52,140 --> 00:09:54,980
+is not compliant to each other, we say that there
+
+133
+00:09:54,980 --> 00:09:57,340
+is a cognitive dissonance situation.
+
+134
+00:10:00,430 --> 00:10:04,250
+إذا كان هناك مشكلة بين مقالات مختلفة أو إذا كان
+
+135
+00:10:04,250 --> 00:10:07,870
+هناك بعض المقالات التي لا تتناسب مع بعضها أو
+
+136
+00:10:07,870 --> 00:10:12,130
+أحيانًا ربما مقالة لا تتناسب لعبارة عن عبارة عن
+
+137
+00:10:12,130 --> 00:10:12,290
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+138
+00:10:12,290 --> 00:10:13,630
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+139
+00:10:13,630 --> 00:10:14,450
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+140
+00:10:14,450 --> 00:10:14,830
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+141
+00:10:14,830 --> 00:10:14,870
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+142
+00:10:14,870 --> 00:10:22,690
+عن عبارة عن عبارة عن عبارة
+
+143
+00:10:22,690 --> 00:10:22,890
+عن
+
+144
+00:10:29,390 --> 00:10:33,910
+هذا بالتأكيد سيؤثر على قيمة الشخص لأنه سيحصل عبارة
+
+145
+00:10:33,910 --> 00:10:36,590
+عن مشاركة وإتفاقات عن الموضوع
+
+146
+00:10:40,460 --> 00:10:43,460
+and how people are going to react or behave
+
+147
+00:10:43,460 --> 00:10:46,140
+according to those decisions okay so sometimes
+
+148
+00:10:46,140 --> 00:10:49,340
+people due to cognitive disorders they find it
+
+149
+00:10:49,340 --> 00:10:56,840
+difficult to respond in a certain way and
+
+150
+00:10:56,840 --> 00:10:59,720
+sometimes maybe they are going to respond in a way
+
+151
+00:10:59,720 --> 00:11:02,740
+that which is not according to what they believe
+
+152
+00:11:02,740 --> 00:11:09,760
+okayوهذا سيفزح مشاكل أخرى التي سنتحدث عنها أيضًا،
+
+153
+00:11:09,760 --> 00:11:13,440
+فعندما نتحدث عن اتصال كوجنيفي، فهنا نتحدث عن نوع
+
+154
+00:11:13,440 --> 00:11:19,040
+من الانتقام بين اتفاقين او اكتر او أحيانًا يمكن أن
+
+155
+00:11:19,040 --> 00:11:24,780
+يكون بين اتفاقين وبعامل، أحيانًا يكون بين اتفاقين
+
+156
+00:11:24,780 --> 00:11:31,450
+وأحيانًا بين اتفاقين وبعامل، مرة أخرىقلنا إن هذه
+
+157
+00:11:31,450 --> 00:11:37,970
+حالة خاطئة وعادةً ستسبب فيها نسبات خاطئة وهو السبب
+
+158
+00:11:37,970 --> 00:11:40,990
+في أن الناس يجب أن يجدوا طريقة لتعامل مع هذه
+
+159
+00:11:40,990 --> 00:11:44,890
+الحالة كيفية التعامل مع هذه الحالة سنتكلم عنها
+
+160
+00:11:44,890 --> 00:11:48,230
+لاحقًا ولكن أولًا دعنا نتكلم عن الانعكاس التعقيدي
+
+161
+00:11:48,230 --> 00:11:52,970
+نفسه و قبل أن نتكلم أكتر عن انعكاس التعقيدي دعنا
+
+162
+00:11:52,970 --> 00:11:58,370
+نعود إلى المصطلح الرئيسي وهو هل الهدف دائم يتبعif
+
+163
+00:11:58,370 --> 00:12:02,170
+law follow from attitudes okay and usually or the
+
+164
+00:12:02,170 --> 00:12:09,410
+right answer is no why it is no why
+
+165
+00:12:09,410 --> 00:12:14,950
+behavior not always follow from attitudes
+
+166
+00:12:18,840 --> 00:12:23,200
+because of as you just mentioned that because that
+
+167
+00:12:23,200 --> 00:12:25,960
+we have a lot of reasons that might affect our
+
+168
+00:12:25,960 --> 00:12:28,700
+behavior maybe the contradictions between the
+
+169
+00:12:28,700 --> 00:12:32,200
+behavior and the attitudes and so why behave in a
+
+170
+00:12:32,200 --> 00:12:36,180
+way that is not what we believe in or the way we
+
+171
+00:12:36,180 --> 00:12:41,160
+speak okay this is one of the reasons are there
+
+172
+00:12:41,160 --> 00:12:45,380
+any other reasons maybe some kind of weird
+
+173
+00:12:50,120 --> 00:12:58,840
+وأنا مضطر أن أفعل شيء لا أصدقه في هذه الحالة، فإن
+
+174
+00:12:58,840 --> 00:13:03,740
+حركتي ليس من نفسي، لأنني مضطر أن أفعل هذه الأشياء
+
+175
+00:13:03,740 --> 00:13:07,940
+من خلال الرئيس، هذا هو السبب في تسمية هذا الفيديو،
+
+176
+00:13:07,940 --> 00:13:12,480
+لكي نتكلم عن الانتقام الكغناطي، ولكن ما أريد فعله
+
+177
+00:13:12,480 --> 00:13:15,920
+هو نقطة أخرى،already يعني from the beginning
+
+178
+00:13:15,920 --> 00:13:18,960
+attitudes is not the only factor which is
+
+179
+00:13:18,960 --> 00:13:22,580
+influencing individual behavior we have values, we
+
+180
+00:13:22,580 --> 00:13:24,500
+have perception, we have abilities, we have
+
+181
+00:13:24,500 --> 00:13:28,160
+learning etc okay so this is the first point this
+
+182
+00:13:28,160 --> 00:13:30,080
+is the first point that we need to understand it
+
+183
+00:13:30,080 --> 00:13:32,280
+okay then we can go back and discuss what is
+
+184
+00:13:32,280 --> 00:13:35,140
+related to this title here according to this
+
+185
+00:13:35,140 --> 00:13:39,840
+chapterالقصص مختلفة
+
+186
+00:13:39,840 --> 00:13:42,300
+بين قصص مختلفة من قصص مختلفة من قصص مختلفة من قصص
+
+187
+00:13:42,300 --> 00:13:43,940
+مختلفة من قصص مختلفة من قصص مختلفة من قصص مختلفة
+
+188
+00:13:43,940 --> 00:13:44,040
+من قصص مختلفة من قصص مختلفة من قصص مختلفة من قصص
+
+189
+00:13:44,040 --> 00:13:49,360
+مختلفة من قصص مختلفة من
+
+190
+00:13:49,360 --> 00:13:51,780
+قصص
+
+191
+00:13:59,190 --> 00:14:01,990
+لقد قمنا بالدراسة في الحلقه الثانية و سوف ندرسها
+
+192
+00:14:01,990 --> 00:14:04,390
+في الحلقه الثالثة اربع اربع اربع اربع اربع اربع
+
+193
+00:14:04,390 --> 00:14:10,600
+اربع اربع اربع اربع اربع اربعهناك ديناميات مختلفة،
+
+194
+00:14:10,600 --> 00:14:15,200
+ولكن دعنا نعود الان لـ Attitudes، لأن هناك في بعض
+
+195
+00:14:15,200 --> 00:14:20,120
+الحالات اتفاق عقلي، فلا يكون الاتفاق دائمًا يدفع
+
+196
+00:14:20,120 --> 00:14:24,820
+تجاربنا، حتى عندما يتعلق الاتفاق، ولكن بعض الأحيان
+
+197
+00:14:24,820 --> 00:14:28,620
+هناك نوع من الانتفاق بين اتفاقين مختلفة أو بين
+
+198
+00:14:28,620 --> 00:14:33,240
+اتفاق والحياة الصحيحة التي يجب أن تكون في حالة
+
+199
+00:14:33,240 --> 00:14:37,940
+معينة وما إلى ذلك ، لذلك هناك بعض الاتصالات
+
+200
+00:14:37,940 --> 00:14:45,060
+المعارضة في بعض الحالات التي ستجعلنا نتعامل بطريقة
+
+201
+00:14:45,060 --> 00:14:49,280
+مختلفة وليس بإتصال مع اعتبارنا ولكن مرة أخرى عندما
+
+202
+00:14:49,280 --> 00:14:55,660
+نتحدث عن اتصالات معينة نتحدث عن حالةوالناس لا
+
+203
+00:14:55,660 --> 00:15:00,820
+تتعامل على ما يشعرون بأنهم يجب أن يتعاملوا على ما
+
+204
+00:15:00,820 --> 00:15:00,880
+يشعرون بأنهم يجب أن يتعاملوا على ما يشعرون بأنهم
+
+205
+00:15:00,880 --> 00:15:03,260
+يجب أن يتعاملوا على ما يشعرون بأنهم يجب أن
+
+206
+00:15:03,260 --> 00:15:04,480
+تتعاملوا على ما يشعرون بأنهم يجب أن تتعاملوا على
+
+207
+00:15:04,480 --> 00:15:05,120
+ما يشعرون بأنهم يجب أن تتعاملوا على ما يشعرون
+
+208
+00:15:05,120 --> 00:15:06,520
+بأنهم يجب أن تتعاملوا على ما يشعرون بأنهم يجب أن
+
+209
+00:15:06,520 --> 00:15:07,440
+تتعاملوا على ما يشعرون بأنهم يجب أن تتعاملوا على
+
+210
+00:15:07,440 --> 00:15:11,300
+ما يشعرون
+
+211
+00:15:11,300 --> 00:15:18,600
+بأنهم يجب أن تتعاملوا على ما يشعرون بأنهم يجب أن
+
+212
+00:15:19,250 --> 00:15:22,630
+التعامل التعامل التعامل التعامل التعامل التعامل
+
+213
+00:15:22,630 --> 00:15:23,750
+التعامل التعامل التعامل التعامل التعامل التعامل
+
+214
+00:15:23,750 --> 00:15:27,290
+التعامل التعامل التعامل التعامل التعامل التعامل
+
+215
+00:15:27,290 --> 00:15:27,290
+التعامل التعامل التعامل التعامل التعامل التعامل
+
+216
+00:15:27,290 --> 00:15:27,990
+التعامل التعامل التعامل التعامل التعامل التعامل
+
+217
+00:15:27,990 --> 00:15:30,390
+التعامل التعامل التعامل التعامل التعامل التعامل
+
+218
+00:15:30,390 --> 00:15:30,390
+التعامل التعامل التعامل التعامل التعامل التعامل
+
+219
+00:15:30,390 --> 00:15:30,430
+التعامل التعامل التعامل التعامل التعامل التعامل
+
+220
+00:15:30,430 --> 00:15:36,310
+التعامل التعامل التعامل التعامل التعامل التعامل
+
+221
+00:15:36,310 --> 00:15:40,270
+التعامل التعام
+
+222
+00:15:41,290 --> 00:15:47,970
+الناس عندما تكون لديها غيابات وانتصارات غير مناسبة
+
+223
+00:15:47,970 --> 00:15:55,450
+ستفكرون في ما ستفعلونه وما سنفعله هو أننا نحتاج أن
+
+224
+00:15:55,450 --> 00:16:00,890
+نتعامل مع هذه الوضع نحتاج لدينا حلول لتحل الوضع
+
+225
+00:16:00,890 --> 00:16:06,870
+غير مناسب اللي نتعامل معه كيف نفعل ذلك؟ نحتاج أن
+
+226
+00:16:06,870 --> 00:16:11,860
+نسيطر على التغيير نحتاج أن نسيطر علىVariables.
+
+227
+00:16:12,060 --> 00:16:16,260
+What variables we are talking about here? What
+
+228
+00:16:16,260 --> 00:16:23,420
+variables we are talking about here? For example,
+
+229
+00:16:24,080 --> 00:16:27,060
+how we think about attitudes, how we think about
+
+230
+00:16:27,060 --> 00:16:30,580
+situation. When we discussed attitude, we said
+
+231
+00:16:30,580 --> 00:16:33,160
+that there are three main components, okay? There
+
+232
+00:16:33,160 --> 00:16:35,600
+is the cognitive component, the feeling component,
+
+233
+00:16:35,840 --> 00:16:39,340
+and finally the behavioral component, okay?لذلك
+
+234
+00:16:39,340 --> 00:16:44,220
+يجب أن نفكر في حالتنا و أحيانًا يجب أن نحرر كيف
+
+235
+00:16:44,220 --> 00:16:50,960
+نشعر بالحالة وما إلى ذلك لكي نحرر حالة غير مناسبة.
+
+236
+00:16:51,180 --> 00:16:54,160
+لذلك مرة أخرى عندما نتحدث عن اتفاق كوجنية نحن
+
+237
+00:16:54,160 --> 00:16:58,900
+نتحدث هنا عن غيابة أو غيابة بين اتين او اكتر
+
+238
+00:16:59,160 --> 00:17:02,500
+attitudes or between attitudes and behaviors okay
+
+239
+00:17:02,500 --> 00:17:05,940
+this is going to create uncomfortable situation
+
+240
+00:17:05,940 --> 00:17:10,140
+for the individual people usually think about how
+
+241
+00:17:10,140 --> 00:17:14,240
+to resolve such situation and to do that we need
+
+242
+00:17:14,240 --> 00:17:17,820
+to do something which is related to the variable
+
+243
+00:17:17,820 --> 00:17:21,760
+we need to moderate the variables and this we call
+
+244
+00:17:21,760 --> 00:17:29,790
+moderatingمدرسات مدرسات هي شيء أو ميكانيزم
+
+245
+00:17:29,790 --> 00:17:35,150
+المستخدم يستخدمه الشخصية لتحرير الموضوع المشكلة
+
+246
+00:17:35,150 --> 00:17:41,490
+التي تحدثنا عنها لذلك نحتاج لمدرسات مدرسات مرتبطة
+
+247
+00:17:41,490 --> 00:17:47,440
+بالتواصل بينattitude and the behavior in order to
+
+248
+00:17:47,440 --> 00:17:52,460
+reach a normal relation between attitudes and
+
+249
+00:17:52,460 --> 00:17:57,400
+behaviors okay now how to do that okay here I'm
+
+250
+00:17:57,400 --> 00:18:00,260
+not talking about a process I'm talking about some
+
+251
+00:18:00,260 --> 00:18:09,400
+requirements خلي
+
+252
+00:18:09,400 --> 00:18:12,800
+الجوال على جانبه اللي لعب في الجوال نكمل
+
+253
+00:18:18,970 --> 00:18:24,230
+ممكن نقول أن هناك أربع مصادر التي يجب أن نتكلم
+
+254
+00:18:24,230 --> 00:18:28,870
+عنها، فإن فهم هذه المصادر سيساعدنا على إيجاد طريقة
+
+255
+00:18:28,870 --> 00:18:33,910
+لتحسين علاقات بين حركتين وحركتين. واحدة من هذه
+
+256
+00:18:33,910 --> 00:18:39,170
+الحركتين مرتبطة بمهمة الحركتينAs attitude is very
+
+257
+00:18:39,170 --> 00:18:42,310
+important for us so it will affect our behavior if
+
+258
+00:18:42,310 --> 00:18:47,070
+it's related directly to our personality and it's
+
+259
+00:18:47,070 --> 00:18:49,030
+very important for us so it will affect directly
+
+260
+00:18:49,030 --> 00:18:51,050
+and have a strong relationship with the media
+
+261
+00:18:51,050 --> 00:18:54,570
+either negatively or positively So when you talk
+
+262
+00:18:54,570 --> 00:18:57,470
+about attitudes which is highly important for us
+
+263
+00:18:57,470 --> 00:19:01,880
+usually such attitudesIt's not easy to change and
+
+264
+00:19:01,880 --> 00:19:05,040
+usually such attitudes are based on beliefs for
+
+265
+00:19:05,040 --> 00:19:07,600
+example and sometimes even it is based on values
+
+266
+00:19:07,600 --> 00:19:12,090
+and so onهذه الطبقات عادية يكون لديها مقارنة عالية
+
+267
+00:19:12,090 --> 00:19:19,810
+مع الهواء اللي نتعامل معه بشكل مرتبط إذا كانت
+
+268
+00:19:19,810 --> 00:19:25,470
+الطبقات مهمة لنا عادية هنا العلاقة بين الطبقات و
+
+269
+00:19:25,470 --> 00:19:31,540
+الهواء عادية هي علاقة افضل المهم هوالكثير من
+
+270
+00:19:31,540 --> 00:19:34,600
+الاعتبار اللي موجود هنا هو العلاقة بين الاعتبار
+
+271
+00:19:34,600 --> 00:19:36,980
+والتعامل اللي موجود هنا هو الاعتبار اللي موجود هنا
+
+272
+00:19:36,980 --> 00:19:37,580
+هو الاعتبار اللي موجود هنا هو الاعتبار اللي موجود
+
+273
+00:19:37,580 --> 00:19:38,140
+هنا هو الاعتبار اللي موجود هنا هو الاعتبار اللي
+
+274
+00:19:38,140 --> 00:19:38,640
+موجود هنا هو الاعتبار اللي موجود هنا هو الاعتبار
+
+275
+00:19:38,640 --> 00:19:38,700
+اللي موجود هنا هو الاعتبار اللي موجود هنا هو
+
+276
+00:19:38,700 --> 00:19:39,580
+الاعتبار اللي موجود هنا هو الاعتبار اللي موجود هنا
+
+277
+00:19:39,580 --> 00:19:39,880
+هو الاعتبار اللي موجود هنا هو الاعتبار اللي موجود
+
+278
+00:19:39,880 --> 00:19:41,540
+هنا هو الاعتبار اللي موجود هنا هو الاعتبار اللي
+
+279
+00:19:41,540 --> 00:19:43,960
+موجود هنا هو الاعتبار اللي موجود هنا هو الاعتبار
+
+280
+00:19:43,960 --> 00:19:46,540
+اللي موجود هنا هو الاعتبار اللي موجود هنا هو
+
+281
+00:19:46,770 --> 00:19:49,590
+attitudes and usually such attitudes it is stable
+
+282
+00:19:49,590 --> 00:19:54,350
+and again it is compatible with the behaviors that
+
+283
+00:19:54,350 --> 00:19:57,890
+we behave another one is correspondence to
+
+284
+00:19:57,890 --> 00:20:00,210
+behavior correspondence to behavior here we are
+
+285
+00:20:00,210 --> 00:20:03,390
+talking about up to what extent there is match
+
+286
+00:20:03,390 --> 00:20:07,550
+between the attitudes and the behavior so if the
+
+287
+00:20:07,550 --> 00:20:10,590
+attitude is corresponding to the behavior then
+
+288
+00:20:10,590 --> 00:20:12,770
+here we are talking about again a healthy relation
+
+289
+00:20:13,020 --> 00:20:18,480
+إذا كانت التصرفات ليست متصرفة، فهنا نتكلم عن علاقة
+
+290
+00:20:18,480 --> 00:20:26,140
+نقية، حيث يجب أن ندرس الميزانيات لكي نصل إلى علاقة
+
+291
+00:20:26,140 --> 00:20:30,380
+صحية أو صحية بين التصرفات والعاملات.
+
+292
+00:20:32,280 --> 00:20:37,140
+الجزء هنا هو الاستخدام، الاستخدام مرتبط بالذكاء
+
+293
+00:20:37,140 --> 00:20:45,380
+هنا، حتى ما نتذكر أن في تلك اللحظات يوجد مرتبط ما
+
+294
+00:20:45,380 --> 00:20:50,960
+بين الحركة والمصطلح وما إلى ذلك، الجزء الرابع
+
+295
+00:20:50,960 --> 00:20:56,600
+مرتبط بالضغط الاجتماعيالضغط الاجتماعي، هنا نتحدث
+
+296
+00:20:56,600 --> 00:21:00,860
+عن ضغط يتم إجراءه من أشخاص أخرين، مع المجتمع، مع
+
+297
+00:21:00,860 --> 00:21:03,640
+المعارفين، مع المديرات، ربما عندما نتحدث عن
+
+298
+00:21:03,640 --> 00:21:09,540
+المؤسسة وما إلى ذلك. في حالتين مثل هذه، ما هي رولة
+
+299
+00:21:09,540 --> 00:21:13,400
+ضغط اجتماعي؟ كيف سوف تأثر علاقة بين القصص
+
+300
+00:21:13,400 --> 00:21:15,280
+والعاملين؟
+
+301
+00:21:17,320 --> 00:21:20,720
+هو كيف سوف يؤثر علاقات بين حركتين ومصالحين
+
+302
+00:21:20,720 --> 00:21:28,220
+ومصالحين ومصالحين ومصالحين ومصالحين ومصالحين
+
+303
+00:21:28,220 --> 00:21:38,300
+ومصالحين
+
+304
+00:21:38,680 --> 00:21:42,340
+one case but there might be other cases yes if
+
+305
+00:21:42,340 --> 00:21:45,100
+there is disagreement there will be disagreement
+
+306
+00:21:45,100 --> 00:21:47,960
+because social pressure is affecting negatively on
+
+307
+00:21:47,960 --> 00:21:52,300
+the one attitude or behavior they may act in in
+
+308
+00:21:52,300 --> 00:21:55,620
+the way that he he didn't say that it's right he
+
+309
+00:21:55,620 --> 00:21:57,840
+didn't say that it's right but he must behave
+
+310
+00:21:57,840 --> 00:22:02,680
+because of this pressure which is on him okay yes
+
+311
+00:22:02,680 --> 00:22:06,500
+despite she was not always in agreementthis
+
+312
+00:22:06,500 --> 00:22:12,160
+depends on the situation itself right it
+
+313
+00:22:12,160 --> 00:22:15,980
+depends on the pressure itself and what is the
+
+314
+00:22:15,980 --> 00:22:19,540
+real component here or content of the pressure yes
+
+315
+00:22:20,410 --> 00:22:23,270
+I think that once we are impressed in something
+
+316
+00:22:23,270 --> 00:22:26,210
+and we want to do it but sometimes the pressure
+
+317
+00:22:26,210 --> 00:22:29,130
+can affect you because it shapes your decision
+
+318
+00:22:29,130 --> 00:22:32,390
+making process because we are affected so much by
+
+319
+00:22:32,390 --> 00:22:34,550
+those people and sometimes this pressure is
+
+320
+00:22:34,550 --> 00:22:37,490
+positive and sometimes this pressure is negative
+
+321
+00:22:37,490 --> 00:22:39,890
+but whenever there is a pressure this means that
+
+322
+00:22:39,890 --> 00:22:42,610
+we are not going to behave according to our
+
+323
+00:22:42,610 --> 00:22:47,020
+actions okayلذلك هنا مرة أخرى إذا كانت كذلك فإنها
+
+324
+00:22:47,020 --> 00:22:50,560
+ستجعلها تخلق اي نوع من اتفاق كوجنيف الآن يجب أن
+
+325
+00:22:50,560 --> 00:22:54,620
+نتعامل مع هذه الضغط لكي نسيطر على الانتجارات حسنًا
+
+326
+00:22:54,620 --> 00:22:59,620
+، لذلك عادة .. الآن لا مهما كانت مصطلحاتنا جيدة أو
+
+327
+00:22:59,620 --> 00:23:03,140
+مخاطرة، هذا ليس المشكلة هنا نتحدث عن العلاقة بين
+
+328
+00:23:03,140 --> 00:23:06,680
+مصطلحاتنا ومصطلحات الحياة حسنًا ، لدينا بعض
+
+329
+00:23:06,680 --> 00:23:09,240
+المصطلحات الجيدة ، لدينا بعض المصطلحات المخاطرة
+
+330
+00:23:09,470 --> 00:23:12,890
+attitudes and so on and all the people are alike
+
+331
+00:23:12,890 --> 00:23:16,190
+in this situation okay but again I'm not talking
+
+332
+00:23:16,190 --> 00:23:19,310
+about the attitude itself whether it is positive
+
+333
+00:23:19,310 --> 00:23:23,210
+or negative okay though the social pressure it
+
+334
+00:23:23,210 --> 00:23:26,050
+might be in some cases positive and it might be in
+
+335
+00:23:26,050 --> 00:23:31,030
+some cases negative according to theالوضع نفسه،
+
+336
+00:23:31,030 --> 00:23:34,090
+ولكن ما نتكلم عنه هنا هو الـ cognitive dissonance
+
+337
+00:23:34,090 --> 00:23:37,370
+وكيف نتعامل مع الـ cognitive dissonance. لذلك، لكي
+
+338
+00:23:37,370 --> 00:23:39,830
+نتعامل مع الـ cognitive dissonance، يجب أن ندرس
+
+339
+00:23:39,830 --> 00:23:43,150
+الميزانيات. كل مرة يكون هناك ضغط مجتمع، يجب أن
+
+340
+00:23:43,150 --> 00:23:48,310
+نتعامل مع هذا الضغط، لكي نصنع مقاومة بين القصة
+
+341
+00:23:48,310 --> 00:23:53,190
+والبيئة. هذه هي الموضوع مرة أخرى.الخاصة الأخيرة هي
+
+342
+00:23:53,190 --> 00:23:57,190
+أنه لا يوجد منافسة أو لا يوجد منافسة بين القصص
+
+343
+00:23:57,190 --> 00:24:02,470
+والعبارات، لذلك لكي نحل هذه اللحظة، علينا إنشاء
+
+344
+00:24:02,470 --> 00:24:08,670
+هذه المنافسة بين القصص والعباراتالمشكلة مرتبطة مع
+
+345
+00:24:08,670 --> 00:24:17,310
+تجاربنا وكيف .. وإذا كان هناك تجارب قبلية مرتبطة
+
+346
+00:24:17,310 --> 00:24:24,770
+مع الحالة وكيف هذا سيجعلنا نفكر في الحالة وهذا
+
+347
+00:24:24,770 --> 00:24:29,790
+مرتبط بالجزء الكognitive أو يغير أشعارنا عن الحالة
+
+348
+00:24:29,790 --> 00:24:35,700
+وهذا مرتبط معوالثانية التي مرتبطة بالشعور وهذا
+
+349
+00:24:35,700 --> 00:24:41,080
+سينتهي أخيرًا في نوع من التجارب وما إلى ذلك، لذلك
+
+350
+00:24:41,080 --> 00:24:46,640
+تجاربنا يجب أن نتعامل معها لكي .. بالطبع ليس
+
+351
+00:24:46,640 --> 00:24:51,640
+دائمًا الـ five factors، يعتمد على الوضع نفسه، لكن
+
+352
+00:24:51,640 --> 00:24:57,520
+هؤلاء هم مثال للجزء اللي يجب أن نتعامل معه لكي نقل
+
+353
+00:24:57,520 --> 00:25:04,580
+المشابهة بين القصص وعن طريق التعامل مع التعامل مع
+
+354
+00:25:04,580 --> 00:25:07,160
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+355
+00:25:07,160 --> 00:25:07,160
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+356
+00:25:07,160 --> 00:25:07,920
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+357
+00:25:07,920 --> 00:25:09,520
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+358
+00:25:09,520 --> 00:25:10,220
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+359
+00:25:10,220 --> 00:25:10,300
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+360
+00:25:10,300 --> 00:25:10,320
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+361
+00:25:10,320 --> 00:25:10,440
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+362
+00:25:10,440 --> 00:25:11,640
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+363
+00:25:11,640 --> 00:25:17,260
+التعامل مع التعامل مع التعامل مع التعامل مع
+
+364
+00:25:17,260 --> 00:25:22,260
+التعامل مع التعامل
+
+365
+00:25:32,870 --> 00:25:39,150
+بالنسبة لكيف يشعر الناس بالوضع و كيف يتطوروا نفسهم
+
+366
+00:25:39,150 --> 00:25:42,510
+و يفعلوا نفسهم و يفعلوا نفسهم و يفعلوا نفسهم و
+
+367
+00:25:42,510 --> 00:25:42,670
+يفعلوا نفسهم و يفعلوا نفسهم و يفعلوا نفسهم و
+
+368
+00:25:42,670 --> 00:25:44,210
+يفعلوا نفسهم و يفعلوا نفسهم و يفعلوا نفسهم و
+
+369
+00:25:44,210 --> 00:25:44,770
+يفعلوا نفسهم و يفعلوا نفسهم و يفعلوا نفسهم و
+
+370
+00:25:44,770 --> 00:25:44,770
+يفعلوا نفسهم و يفعلوا نفسهم و يفعلوا نفسهم و
+
+371
+00:25:44,770 --> 00:25:44,770
+يفعلوا نفسهم و يفعلوا نفسهم و يفعلوا نفسهم و
+
+372
+00:25:44,770 --> 00:25:45,350
+يفعلوا نفسهم و يفعلوا نفسهم و يفعلوا نفسهم و
+
+373
+00:25:45,350 --> 00:26:01,230
+يفعلوا نفسهم و يفعلوا نفسهم و يفعلوا نفسهم و
+
+374
+00:26:01,230 --> 00:26:01,230
+ي
+
+375
+00:26:04,330 --> 00:26:07,370
+to performance okay and of course this is related
+
+376
+00:26:07,370 --> 00:26:09,730
+to job environment to the organization okay but
+
+377
+00:26:09,730 --> 00:26:12,730
+this is related to performance and productivity
+
+378
+00:26:12,730 --> 00:26:17,890
+and so on okay now one of those attitudes is job
+
+379
+00:26:17,890 --> 00:26:21,270
+satisfaction okay now when you talk about job
+
+380
+00:26:21,270 --> 00:26:23,570
+satisfaction here we are talking about feeling
+
+381
+00:26:23,570 --> 00:26:26,530
+related to work but whenever there is job
+
+382
+00:26:26,530 --> 00:26:29,410
+satisfaction we are talking here about positive
+
+383
+00:26:29,410 --> 00:26:35,610
+work exactly okay so some peopleهم يحكموا عملهم
+
+384
+00:26:35,610 --> 00:26:40,970
+بطريقة إيجابية، وهذا سيطور فيه نوع من الإستمتاع،
+
+385
+00:26:40,970 --> 00:26:46,350
+إستمتاع عالي، وفي بعض الأحيان ربما سنطور فيه فكرة
+
+386
+00:26:46,350 --> 00:26:54,750
+نقلي، وهذا سيكون نتيجة للإستمتاع. ما هي علاقة بين
+
+387
+00:26:54,750 --> 00:26:59,300
+الإستمتاع والدراسة؟سنتحدث عن هذا في أكتر تفاصيل،
+
+388
+00:26:59,300 --> 00:27:04,040
+ولكن دعنا على الأقل نصنع مصطلح لها، ما هي علاقة ما
+
+389
+00:27:04,040 --> 00:27:07,940
+بين الإتصال والإدارة؟ أولا، إذا كانت الإتصال عالي،
+
+390
+00:27:07,940 --> 00:27:11,260
+فسيكون الهجوم مؤثر على الناس، يؤثر عليهم،
+
+391
+00:27:15,050 --> 00:27:19,170
+Are you sure about this يعني؟ I think it's like
+
+392
+00:27:19,170 --> 00:27:22,270
+most of the times, we cannot like generalize that
+
+393
+00:27:22,270 --> 00:27:24,330
+there is a positive relationship between job
+
+394
+00:27:24,330 --> 00:27:26,750
+satisfaction and performance because again it's
+
+395
+00:27:26,750 --> 00:27:30,010
+not the only factor that affects performance, so I
+
+396
+00:27:30,010 --> 00:27:32,150
+might have a very high job satisfaction but there
+
+397
+00:27:32,150 --> 00:27:35,670
+are other forces or other factors that affect my
+
+398
+00:27:35,670 --> 00:27:40,030
+performanceوفي نهاية اليوم فإن عملتي ستكون ممتازة
+
+399
+00:27:40,030 --> 00:27:46,110
+و أحد هؤلاء عمليات، فبعض الأشخاص مستمتعين ولكنهم
+
+400
+00:27:46,110 --> 00:27:50,590
+لاعرفوا عملياتهم، لذا فلن يفعلوا بأي مستويات
+
+401
+00:27:50,590 --> 00:27:56,370
+المتوقع، و بعض الأشخاص مستمتعين ولكنهم سيفعلوا
+
+402
+00:27:56,370 --> 00:27:59,570
+بشكل جيد، لماذا؟ لأن هناك بعض التحكم الذي يتم
+
+403
+00:27:59,570 --> 00:28:03,560
+تحكيه الوظيفة وكانوا مجردهم أن يفعلوا أفضل شيءSo
+
+404
+00:28:03,560 --> 00:28:06,080
+again here there is no direct relation between
+
+405
+00:28:06,080 --> 00:28:09,320
+satisfaction and performance, but there is a
+
+406
+00:28:09,320 --> 00:28:11,780
+relation between satisfaction and other things
+
+407
+00:28:11,780 --> 00:28:14,460
+Like for example between satisfaction and
+
+408
+00:28:14,460 --> 00:28:18,060
+absenteeism, between satisfaction and turnover,
+
+409
+00:28:18,500 --> 00:28:23,510
+and this is going to affect productivityهذا سيأثر
+
+410
+00:28:23,510 --> 00:28:27,470
+عاليًا، لهذا السبب إنه مهم، واحدة من أهم مصادر
+
+411
+00:28:27,470 --> 00:28:34,690
+العمل هي إتصال العمل، طبعًا لاحقًا سنتحدث أكتر عن
+
+412
+00:28:34,690 --> 00:28:40,630
+إتصال لأنه جزء ثاني من هذه القصة، طبعًا هناك مصادر
+
+413
+00:28:40,630 --> 00:28:48,230
+أخرى التي سنتحدث عنها لاحقًاin the coming lecture
+
+414
+00:28:48,230 --> 00:28:51,330
+بكف
+
+415
+00:28:51,330 --> 00:28:54,030
+اليوم okay بس في assignment اللي اعطيكوايا خلينا
+
+416
+00:28:54,030 --> 00:28:56,210
+نحكي فيها الحين الخمس دقايق اللي نحتاجها
+
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/khaKiKuZmtw_raw.json b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/khaKiKuZmtw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..3e1083b1c836e62b7fb10cdc6c2290c57b93da96
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/khaKiKuZmtw_raw.json
@@ -0,0 +1 @@
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وقد تحدثنا سابقًا في المعلومة السابقة أنه عندما نتكلم عن عملية الاختيارات وعندما نتكلم عن الخطوط", "tokens": [2407, 3224, 2407, 19446, 7251, 7435, 3555, 14739, 8717, 5016, 36520, 9154, 16490, 1211, 6027, 6225, 42213, 10632, 2423, 47283, 31371, 9640, 9307, 4032, 28543, 6055, 24401, 12984, 8315, 8608, 16758, 4587, 14111, 995, 8978, 9673, 3615, 1211, 20498, 3660, 21136, 16758, 28671, 14739, 3224, 43242, 15042, 8717, 2655, 4117, 19528, 18871, 6225, 42213, 10632, 2423, 47283, 31371, 9640, 9307, 4032, 3615, 41260, 15042, 8717, 2655, 4117, 19528, 18871, 33962, 9566, 2407, 9566], "avg_logprob": -0.5967060979959127, "compression_ratio": 1.8962962962962964, "no_speech_prob": 1.2516975402832031e-05, "words": [{"start": 859.58, "end": 859.92, "word": "وهو", "probability": 0.2779134114583333}, {"start": 859.92, "end": 859.92, "word": " ما", "probability": 0.51123046875}, {"start": 859.92, "end": 860.14, "word": " يجب", "probability": 0.8017578125}, {"start": 860.14, "end": 860.22, "word": " أن", 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"probability": 0.37353515625}, {"start": 1864.13, "end": 1865.59, "word": " هذا", "probability": 0.2252197265625}, {"start": 1865.59, "end": 1865.97, "word": " الموضوع", "probability": 0.8543701171875}, {"start": 1865.97, "end": 1866.31, "word": " اللي", "probability": 0.67626953125}, {"start": 1866.31, "end": 1867.21, "word": " نتكلم", "probability": 0.6966552734375}, {"start": 1867.21, "end": 1867.39, "word": " عنه.", "probability": 0.95361328125}, {"start": 1867.47, "end": 1867.75, "word": " إذا", "probability": 0.60626220703125}, {"start": 1867.75, "end": 1868.63, "word": " لم", "probability": 0.26953125}, {"start": 1868.63, "end": 1870.25, "word": " ينجح", "probability": 0.70782470703125}, {"start": 1870.25, "end": 1871.17, "word": " المؤسسة", "probability": 0.600048828125}, {"start": 1871.17, "end": 1871.53, "word": " في", "probability": 0.322509765625}, {"start": 1871.53, "end": 1871.65, "word": " القيام", "probability": 0.669921875}, {"start": 1871.65, "end": 1872.43, "word": " بذلك،", "probability": 0.63543701171875}, {"start": 1872.43, "end": 1872.89, "word": " فسيكون", "probability": 0.630096435546875}, {"start": 1872.89, "end": 1873.63, "word": " الموظفين", "probability": 0.73349609375}, {"start": 1873.63, "end": 1873.95, "word": " في", "probability": 0.326416015625}, {"start": 1873.95, "end": 1874.55, "word": " المستقبل", "probability": 0.8226318359375}, {"start": 1874.55, "end": 1875.55, "word": " أكثر", "probability": 0.73583984375}, {"start": 1875.55, "end": 1876.13, "word": " مستعدين", "probability": 0.399505615234375}, {"start": 1876.13, "end": 1877.71, "word": " لتتعامل", "probability": 0.5209147135416666}, {"start": 1877.71, "end": 1877.83, "word": " في", "probability": 0.2318115234375}, {"start": 1877.83, "end": 1878.91, "word": " أي", "probability": 0.7431640625}, {"start": 1878.91, "end": 1879.37, "word": " من", "probability": 0.54736328125}, {"start": 1879.37, "end": 1879.85, "word": " تلك", "probability": 0.6708984375}, {"start": 1879.85, "end": 1880.81, "word": " التجارب", "probability": 0.68682861328125}, {"start": 1880.81, "end": 1881.45, "word": " أو", "probability": 0.96923828125}, {"start": 1881.45, "end": 1882.51, "word": " حالة.", "probability": 0.5270182291666666}, {"start": 1884.85, "end": 1886.05, "word": " بكفي", "probability": 0.5703125}, {"start": 1886.05, "end": 1886.35, "word": " اليوم،", "probability": 0.7242838541666666}, {"start": 1886.35, "end": 1886.65, "word": " يعطيكوا", "probability": 0.67939453125}, {"start": 1886.65, "end": 1886.99, "word": " العافية", "probability": 0.9617513020833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1890.475875, "duration_after_vad": 1863.0899999999967}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/pn2OeT0s4Kg.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/pn2OeT0s4Kg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..47c40c24147b38975c9ec1e8f3ca341cf537627a
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/pn2OeT0s4Kg.srt
@@ -0,0 +1,1763 @@
+1
+00:00:00,000 --> 00:00:02,680
+موسيقى
+
+2
+00:00:09,060 --> 00:00:13,840
+اليوم سنبدأ مع حلقة جديدة، حلقة نمبر 9، إنها عن
+
+3
+00:00:13,840 --> 00:00:19,200
+مؤسسة تصريح مجموعات، سنبدأ في هذه الحلقة مع مجموعة
+
+4
+00:00:19,200 --> 00:00:23,360
+جديدة لتعليم تصريح مجموعة، في هذه المجموعة سنتحدث 
+
+5
+00:00:23,360 --> 00:00:28,700
+عن تصريح مجموعة، سنتحدث عن حلقة نمبر 9، ثم حلقة
+
+6
+00:00:28,700 --> 00:00:32,580
+نمبر 10، وهي عن مجموعات، لكن أولا يجب أن نتحدث عن
+
+7
+00:00:32,580 --> 00:00:37,150
+مجموعات بالنسبة للجامعات الجامعية
+
+8
+00:00:37,150 --> 00:00:39,250
+الجامعية 
+
+9
+00:00:39,250 --> 00:00:42,730
+الجامعية 
+
+10
+00:00:42,730 --> 00:00:46,330
+الجامعية 
+
+11
+00:00:46,330 --> 00:00:46,350
+الجامعية
+
+12
+00:00:46,350 --> 00:00:46,410
+الجامعية
+
+13
+00:00:46,410 --> 00:00:48,050
+الجامعية
+
+14
+00:00:48,050 --> 00:00:50,070
+الجامعية
+
+15
+00:00:50,070 --> 00:01:00,530
+الجامعية 
+
+16
+00:01:01,320 --> 00:01:05,140
+بالإضافة إلى أشياء أخرى مرتبطة بالجروب مثلًا
+
+17
+00:01:05,140 --> 00:01:13,420
+نظامات، يجب أن نعرف ما هي أسلحة أو أهداف أو أدوات 
+
+18
+00:01:13,420 --> 00:01:18,700
+كيف نستخدم الجروب؟ ماذا هو المهم من الجروب في مجال
+
+19
+00:01:18,700 --> 00:01:26,200
+الحوار؟ أيضًا سنتحدث عن كيف يأخذ الجروب قرارات، هذا 
+
+20
+00:01:26,200 --> 00:01:31,020
+أيضًا أحد الأشياء المهمة التي يجب أن نفعلها أولا 
+
+21
+00:01:31,020 --> 00:01:35,240
+نتكلم عن كيف يأخذ الأحداث القرارات في هذه الحلقة
+
+22
+00:01:35,240 --> 00:01:40,060
+أيضًا نتكلم عن كيف تأخذ مجموعات قرارات، فهناك
+
+23
+00:01:40,060 --> 00:01:45,620
+مواضيع مختلفة التي سنتكلم عنها في هذا المجال، أولا 
+
+24
+00:01:45,620 --> 00:01:51,240
+دعنا نبدأ بالموضوع الرئيسي هنا وهو مجموعات، ما هي 
+
+25
+00:01:51,240 --> 00:01:58,030
+مجموعة؟ إذا كان علينا أن نُدير مجموعة، كيف يمكننا أن 
+
+26
+00:01:58,030 --> 00:02:06,710
+ندير مجموعة؟ عندما نتكلم عن مجموعة، نتكلم عادة أو
+
+27
+00:02:06,710 --> 00:02:10,950
+دائمًا، نتكلم عن أكثر من شخص واحد، نتكلم عن اثنين
+
+28
+00:02:10,950 --> 00:02:14,470
+أو أكثر مجموعة، لكن لماذا المجموعات تتجمع إلى
+
+29
+00:02:14,470 --> 00:02:21,050
+مجموعة؟ وهذا جزء من الوصفة، لماذا المجموعات تتجمع
+
+30
+00:02:21,050 --> 00:02:22,110
+إلى مجموعة؟
+
+31
+00:02:26,610 --> 00:02:30,450
+في بعض الأحيان يحتاجون للانتماء لشيء مثل هذا 
+
+32
+00:02:30,450 --> 00:02:36,370
+يحتاجون أن يكونوا جزء من شيء يعتقدونه مثل الـ
+
+33
+00:02:36,370 --> 00:02:41,250
+value system أو شيء مثل ذلك، حسنًا، لكن ما تتكلم
+
+34
+00:02:41,250 --> 00:02:49,550
+عنه هو لماذا الجمهور يتعاملون بالجمهورية، ما تتكلم 
+
+35
+00:02:49,550 --> 00:02:53,190
+عنه هو لماذا الجمهور يتعاملون بالجمهورية، لكن هنا 
+
+36
+00:02:53,190 --> 00:03:00,020
+علينا أولًا في مجتمع نحن نتكلم عن أو أكثر شخصية في
+
+37
+00:03:00,020 --> 00:03:05,260
+هذا المجال، نحن نتكلم عن الوصول للهدف أو الأهداف
+
+38
+00:03:05,260 --> 00:03:09,040
+الواضحة، وهو السبب أن المجموعات عادة تتصرف لإنهاء
+
+39
+00:03:09,040 --> 00:03:14,960
+أهداف أو أهداف، ولكن الذين يعملون معهم لإنهاء أهداف
+
+40
+00:03:14,960 --> 00:03:20,120
+وأهداف، هناك نقطة مهمة يجب أن نتكلم عنها هنا، أولا 
+
+41
+00:03:20,120 --> 00:03:27,310
+يجب أن يتعاملوا مع بعضهم، هنا نتكلم عن التعامل بين
+
+42
+00:03:27,310 --> 00:03:30,590
+الإنسانين، يحتاجون إلى التعامل، يحتاجون إلى 
+
+43
+00:03:30,590 --> 00:03:31,970
+التعامل، يحتاجون إلى التعامل، يحتاجون إلى التعامل،
+
+44
+00:03:31,970 --> 00:03:32,290
+يحتاجون إلى التعامل، يحتاجون إلى التعامل، يحتاجون 
+
+45
+00:03:32,290 --> 00:03:32,450
+إلى التعامل، يحتاجون إلى التعامل، يحتاجون إلى
+
+46
+00:03:32,450 --> 00:03:33,690
+التعامل، يحتاجون إلى التعامل، يحتاجون إلى التعامل،
+
+47
+00:03:33,690 --> 00:03:36,910
+يحتاجون إلى التعامل، يحتاجون إلى التعامل، يحتاجون
+
+48
+00:03:36,910 --> 00:03:37,410
+إلى التعامل، يحتاجون إلى التعامل، يحتاجون إلى 
+
+49
+00:03:37,410 --> 00:03:40,930
+التعامل، يحتاجون إلى التعامل، يحتاجون
+
+50
+00:03:40,930 --> 00:03:46,070
+إلى التعامل، يحتاجون إلى التعامل،
+
+51
+00:03:46,070 --> 00:03:51,020
+يحتاجون إلى التعامل، يحتاجون إلى التعامل في حالات 
+
+52
+00:03:51,020 --> 00:03:55,440
+معينة، وهو السبب أن في حالات معينة، الإنسان بدل من
+
+53
+00:03:55,440 --> 00:03:58,660
+العمل وحده يفضل العمل مع مجموعات معينة، لماذا؟
+
+54
+00:03:58,660 --> 00:04:01,940
+لأنهم لديهم فرصة أفضل هنا لإنهاء أهدافهم، بالطبع
+
+55
+00:04:01,940 --> 00:04:05,220
+ليس كل العمليات التي نحتاجها مجموعات أو فريق، لكن
+
+56
+00:04:05,220 --> 00:04:10,840
+هناك عمليات أو حالات أو ظروف حيث أن النتيجة 
+
+57
+00:04:10,840 --> 00:04:14,700
+الأخيرة لا يمكن أن تكون حاصلة بدون مجموعة، في حالات 
+
+58
+00:04:14,700 --> 00:04:19,150
+مثل هذه، نحتاج مجموعة لإنهاء العمل، عندما نتكلم عن 
+
+59
+00:04:19,150 --> 00:04:23,210
+مجموعة، هنا نتكلم مرة أخرى عن أكثر من شخصين
+
+60
+00:04:23,210 --> 00:04:28,250
+المتعاملين والمتعاملين الذين أتوا مع بعضهم لإنهاء 
+
+61
+00:04:28,250 --> 00:04:31,670
+مهام معينة، لذا إذا لم يكن هناك مهام، لا يوجد 
+
+62
+00:04:31,670 --> 00:04:37,910
+حاجة لإنشاء مجموعة، فهذه واحدة من الأساسيات
+
+63
+00:04:37,910 --> 00:04:44,610
+المحتاجة لإنشاء مجموعة، يجب أن يكون هناك مهام
+
+64
+00:04:45,810 --> 00:04:51,910
+للتحقيق من قبل كل الذين يصنعون مجموعة، عندما نتحدث عن 
+
+65
+00:04:51,910 --> 00:04:57,610
+مجموعات، نحن نتحدث عن مجموعات مختلفة وخاصة هناك 
+
+66
+00:04:57,610 --> 00:04:59,710
+أنواع مختلفة وخاصة هناك أنواع مختلفة وخاصة
+
+67
+00:04:59,710 --> 00:05:01,630
+هناك أنواع مختلفة وخاصة هناك أنواع مختلفة
+
+68
+00:05:01,630 --> 00:05:05,190
+وخاصة هناك أنواع مختلفة وخاصة هناك أنواع
+
+69
+00:05:05,190 --> 00:05:05,550
+مختلفة وخاصة هناك أنواع مختلفة وخاصة هناك
+
+70
+00:05:05,550 --> 00:05:06,310
+أنواع مختلفة وخاصة هناك أنواع مختلفة وخاصة
+
+71
+00:05:06,310 --> 00:05:09,410
+هناك أنواع مختلفة وخاصة هناك أنواع مختلفة
+
+72
+00:05:09,410 --> 00:05:13,100
+وخاصة هناك أنواع في أي مؤسسة، هناك مجموعات عامة
+
+73
+00:05:13,100 --> 00:05:17,980
+ومجموعات غير عامة، ما هي الفروقات بين مجموعات عامة
+
+74
+00:05:17,980 --> 00:05:20,180
+وغير عامة؟
+
+75
+00:05:22,600 --> 00:05:26,560
+المجموعات التجارية تسمح للمجموعات التجارية التي
+
+76
+00:05:26,560 --> 00:05:32,200
+يتم تجربتها وتجربة نفسها، لكي تصل إلى أحد أو اثنين
+
+77
+00:05:32,200 --> 00:05:35,780
+مهمات. ولكن عندما يتعلق الأمر بالمجموعات التجارية، إنها 
+
+78
+00:05:35,780 --> 00:05:42,300
+بين مجلس المجموعات أو المشاركين، ولكن بدون تجارب
+
+79
+00:05:42,300 --> 00:05:47,080
+تتعامل معهم. حسنًا، هناك مجموعات
+
+80
+00:05:52,250 --> 00:05:59,470
+وهو خلقها من المؤسسة، وعادة أو دائمًا يتم اكتشافها من
+
+81
+00:05:59,470 --> 00:06:06,570
+خلق المؤسسة، وهناك مجموعات أخرى، والتواصل بين
+
+82
+00:06:06,570 --> 00:06:11,930
+الموظفين الذين يعملون في المؤسسة. في كلا الحالتين،
+
+83
+00:06:11,930 --> 00:06:15,350
+نحن نتكلم عن مجتمع ومجتمع، ولكن هناك مجموعات
+
+84
+00:06:15,350 --> 00:06:20,710
+أساسية التي هي جزء من أساسية المؤسسة، وهي موضح أو
+
+85
+00:06:20,710 --> 00:06:27,420
+مُسماة بأساسية المؤسسة أو المؤسسة. وطبعًا هم مع بعض
+
+86
+00:06:27,420 --> 00:06:32,340
+لإنهاء مهام، عمليات، وعمليات وما إلى ذلك، وفي نفس
+
+87
+00:06:32,340 --> 00:06:36,120
+الوقت، هناك مجموعات غير عاملة، هنا نحن نتحدث عن
+
+88
+00:06:36,120 --> 00:06:41,320
+مجموعة من داخل المؤسسة التي لديها نوع من علاقات
+
+89
+00:06:41,320 --> 00:06:47,200
+وفقًا لذلك هم اكتشفوها كمجموعة، طبعًا ما هي مجموعات
+
+90
+00:06:47,200 --> 00:06:51,520
+غير عاملة وغير عاملة، سنتحدث عن ذلك لاحقًا، ولكن 
+
+91
+00:06:51,520 --> 00:06:58,220
+هنا مرة أخرى، الاختلاف الرئيسي هنا هو أنه عندما
+
+92
+00:06:58,220 --> 00:07:02,960
+نتحدث عن مجموعات عامة، نتحدث عن مؤسسة ومؤسسة نفسها
+
+93
+00:07:02,960 --> 00:07:08,860
+وكيف يوجد اختلافات في مجموعة، ومجموعة ومجموعة وما
+
+94
+00:07:08,860 --> 00:07:12,000
+إلى ذلك، عندما نتحدث عن مجموعات غير عامة، نتحدث عن 
+
+95
+00:07:12,000 --> 00:07:19,700
+مجموعة أو علاقات أو أي علاقة التي ليست مؤسسة من
+
+96
+00:07:19,700 --> 00:07:26,520
+نفس المؤسسة، حسنًا، عندما نتكلم عن هذين الاسمين
+
+97
+00:07:26,520 --> 00:07:30,820
+الرئيسيين، الواقعي والمؤسسي، هناك مجموعات. حسنًا، 
+
+98
+00:07:30,820 --> 00:07:34,440
+عندما نتكلم عن مجموعات واقعية، نحن نتكلم هنا عن 
+
+99
+00:07:34,440 --> 00:07:37,640
+مجموعات عمليات ومجموعات وظيفية. هؤلاء هم بعض
+
+100
+00:07:37,640 --> 00:07:42,020
+مجموعات المجموعات الواقعية. حسنًا، عندما نتكلم عن
+
+101
+00:07:42,020 --> 00:07:49,930
+مجموعة عمليات، بعض الأحيان، عندما أتكلم عن الجمهور،
+
+102
+00:07:49,930 --> 00:07:56,430
+قلت إنه موجود في أسلوب المؤسسة، عادةً هناك مجموعات
+
+103
+00:07:56,430 --> 00:08:00,870
+موجودة 
+
+104
+00:08:00,870 --> 00:08:04,450
+بالمؤسسة نفسها، هذه المجموعات، عندما نتكلم عن
+
+105
+00:08:04,450 --> 00:08:08,610
+مجالس أو مجموعات أو أي شيء، هنا نتكلم عن مجموعات
+
+106
+00:08:08,610 --> 00:08:12,140
+الوظيفية، لذلك عندما نتكلم عن المجموعات الوظيفية،
+
+107
+00:08:12,140 --> 00:08:16,300
+عادةً نتكلم عن مجموعات أكثر استمرارية، هؤلاء 
+
+108
+00:08:16,300 --> 00:08:20,660
+المجموعات مستمرين بشكل مباشر، بالطبع لسنا نتكلم عن
+
+109
+00:08:20,660 --> 00:08:22,580
+مجموعات مستمرة بشكل مباشر، لن نتكلم عن مجموعات
+
+110
+00:08:22,580 --> 00:08:26,840
+مستمرة بشكل مباشر، لذلك هؤلاء المجموعات عادةً 
+
+111
+00:08:26,840 --> 00:08:33,720
+يتبعون بعض الأفعال، هو ليس مجرد عمليات أو عمليات
+
+112
+00:08:33,720 --> 00:08:36,980
+التي ستنتهي في وقت قصير، نعم، نحن نتكلم هنا عن
+
+113
+00:08:36,980 --> 00:08:42,600
+المشروع مثلًا مجلس التسويق، نحن نتكلم عن عمليات، إذا
+
+114
+00:08:42,600 --> 00:08:46,500
+كنا نتحدث عن مجلس موارد الإنسان أو أي مجلس أو مجلس
+
+115
+00:08:46,500 --> 00:08:52,440
+داخل المؤسسة، هنا نتحدث عن مجلس وظيفي، هناك مجلس من
+
+116
+00:08:52,440 --> 00:08:58,300
+الإنسان ومدير أو رئيس، وعادة هذا المدير أو رئيس 
+
+117
+00:08:58,300 --> 00:09:04,670
+يسيطر على مجلس المجلس، وإنهم يقومون بإنهاء عمليات
+
+118
+00:09:04,670 --> 00:09:09,230
+محتاجة من المؤسسة، عندما نتكلم عن عمليات عملية
+
+119
+00:09:09,230 --> 00:09:11,670
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+120
+00:09:11,670 --> 00:09:11,810
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+121
+00:09:11,810 --> 00:09:11,850
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+122
+00:09:11,850 --> 00:09:14,410
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+123
+00:09:14,410 --> 00:09:17,090
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+124
+00:09:17,090 --> 00:09:17,710
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+125
+00:09:17,710 --> 00:09:18,350
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+126
+00:09:18,350 --> 00:09:23,250
+عملية عملية عملية عملية عملية
+
+127
+00:09:26,860 --> 00:09:31,420
+وهي محتاجة لإيقاف عمليات أو عمليات أو عمليات أو 
+
+128
+00:09:31,420 --> 00:09:31,700
+عمليات أو عمليات أو عمليات أو عمليات أو عمليات أو
+
+129
+00:09:31,700 --> 00:09:32,280
+عمليات أو عمليات أو عمليات أو عمليات أو عمليات أو
+
+130
+00:09:32,280 --> 00:09:35,080
+عمليات أو عمليات أو عمليات أو عمليات أو عمليات أو
+
+131
+00:09:35,080 --> 00:09:35,620
+عمليات أو عمليات أو عمليات أو عمليات أو عمليات أو
+
+132
+00:09:35,620 --> 00:09:36,900
+عمليات أو عمليات أو عمليات أو عمليات أو عمليات أو
+
+133
+00:09:36,900 --> 00:09:39,280
+عمليات أو عمليات أو عمليات أو عمليات أو عمليات أو
+
+134
+00:09:39,280 --> 00:09:39,680
+عمليات أو عمليات أو عمليات أو عمليات أو عمليات أو
+
+135
+00:09:39,680 --> 00:09:47,080
+عمليات أو عمليات أو عمليات أو عمليات أو عمليات، الآن على
+
+136
+00:09:47,080 --> 00:09:50,780
+الجانب الآخر، هناك مجموعات غير عاملة، هنا مجددًا 
+
+137
+00:09:50,780 --> 00:09:55,980
+هناك مجموعات غير عاملة، واحدة منها هي المجموعات
+
+138
+00:09:55,980 --> 00:10:02,020
+المهتمة والثانية هي المجموعات المصطلحية، عادةً بين
+
+139
+00:10:02,020 --> 00:10:06,080
+أي مجموعة، رغم أنها عاملة أو غير عاملة، هناك نتيجة 
+
+140
+00:10:06,280 --> 00:10:11,100
+وهذا ما قلنا أنه مجرد تأثير لتصميم جمهور أي جمهور
+
+141
+00:10:11,100 --> 00:10:13,500
+أنه يكون هناك نوع من موضوع تتعامل معه أو تتعامل 
+
+142
+00:10:13,500 --> 00:10:14,060
+معه أو تتعامل معه أو تتعامل معه أو تتعامل معه أو
+
+143
+00:10:14,060 --> 00:10:16,380
+تتعامل معه أو تتعامل معه أو تتعامل معه أو تتعامل
+
+144
+00:10:16,380 --> 00:10:16,780
+معه أو تتعامل معه أو تتعامل معه أو تتعامل معه أو
+
+145
+00:10:16,780 --> 00:10:18,760
+تتعامل معه أو تتعامل معه أو تتعامل معه أو تتعامل
+
+146
+00:10:18,760 --> 00:10:23,620
+معه أو تتعامل معه أو تتعامل معه أو تتعامل معه أو
+
+147
+00:10:23,620 --> 00:10:33,060
+تتعامل معه أو تتعامل معه أو تتعامل معه أو 
+
+148
+00:10:33,060 --> 00:10:39,550
+نتعامل، نتكلم عن علاقات مؤسسة ومؤسسة، ولكنهم 
+
+149
+00:10:39,550 --> 00:10:44,250
+يعملون في نفس المؤسسة. عندما نتكلم عن مجموعات
+
+150
+00:10:44,250 --> 00:10:50,370
+مهتمة، هؤلاء المجموعات تتعامل على مهتمة معينة
+
+151
+00:10:50,370 --> 00:10:52,830
+مرتبطة بالعمل،
+
+152
+00:10:54,390 --> 00:10:57,990
+they are not a formal group, they are informal 
+
+153
+00:10:57,990 --> 00:11:01,130
+group. يعني for example, they have a common interest 
+
+154
+00:11:01,130 --> 00:11:05,310
+but when we talk about friendship group, usually 
+
+155
+00:11:05,310 --> 00:11:08,890
+they have common characteristics, people become
+
+156
+00:11:08,890 --> 00:11:13,370
+friends because they have common characteristics 
+
+157
+00:11:13,370 --> 00:11:16,530
+or personal traits and so on, and sometimes because 
+
+158
+00:11:16,530 --> 00:11:20,450
+they have interests, but when they have interest, we
+
+159
+00:11:20,450 --> 00:11:24,070
+call this an interest group, okay. الشركات الصحيحة
+
+160
+00:11:24,070 --> 00:11:28,770
+العادية تكون أكثر مرتبطة، لماذا؟ لأنها تحتوي على
+
+161
+00:11:28,770 --> 00:11:34,470
+أشكال عامة، وهو أيضا يعني أن الشركات الصحيحة إذا 
+
+162
+00:11:34,470 --> 00:11:37,950
+كنا نتحدث عن شركات مستمرين أو مستقلين، فهي مرتبطة
+
+163
+00:11:38,790 --> 00:11:42,950
+مقارنة بتلك المجموعات بالمجموعات المهتمة، لأن
+
+164
+00:11:42,950 --> 00:11:48,310
+المجموعات المهتمة هي مجموعات عمل، عندما ينتهي
+
+165
+00:11:48,310 --> 00:11:52,330
+العمل، فلا تحتاج المجموعة للعمل، وعندما يتوفر 
+
+166
+00:11:52,330 --> 00:11:55,850
+المهتمة، فلا تحتاج المجموعة للعمل، ولكن عندما نتحدث
+
+167
+00:11:55,850 --> 00:11:59,110
+عن مجتمعات أصدقاء، فنحن نتحدث عن بعض الناس الذين
+
+168
+00:11:59,110 --> 00:12:01,970
+يتواصلون مع بعضهم البعض، أو الشخصيات أو الشخصيات أو الشخصيات
+
+169
+00:12:01,970 --> 00:12:03,630
+أو الشخصيات أو الشخصيات أو الشخصيات أو الشخصيات أو
+
+170
+00:12:03,630 --> 00:12:05,190
+الشخصيات أو الشخصيات أو الشخصيات أو الشخصيات أو
+
+171
+00:12:05,190 --> 00:12:05,990
+الشخصيات أو الشخصيات أو الشخصيات أو الشخصيات أو
+
+172
+00:12:05,990 --> 00:12:06,410
+الشخصيات أو الشخصيات أو الشخصيات أو الشخصيات أو
+
+173
+00:12:06,410 --> 00:12:09,690
+الشخصيات أو الشخصيات أو الشخصيات أو الشخصيات أو
+
+174
+00:12:09,690 --> 00:12:11,650
+الشخصيات أو الشخصيات أو الشخصيات أو الشخصيات أو
+
+175
+00:12:11,650 --> 00:12:18,970
+الشخصيات أو الشخصيات أو الشخصيات أو
+
+176
+00:12:19,560 --> 00:12:23,200
+الآن، قلنا، دعنا نعود لبعض المراحل هنا، قلنا أن
+
+177
+00:12:23,200 --> 00:12:27,600
+هناك مجموعات عامة ومجموعات غير عامة، ونحن نتحدث عن 
+
+178
+00:12:27,600 --> 00:12:32,680
+عامة ومجموعات عامة ومجموعات غير عامة ومجموعات غير
+
+179
+00:12:32,680 --> 00:12:32,900
+عامة ومجموعات غير عامة ومجموعات غير عامة ومجموعات
+
+180
+00:12:32,900 --> 00:12:33,160
+ومجموعات غير عامة ومجموعات غير عامة ومجموعات غير
+
+181
+00:12:33,160 --> 00:12:37,540
+عامة ومجموعات غير عامة ومجموعات غير عامة ومجموعات
+
+182
+00:12:37,540 --> 00:12:44,080
+غير عامة ومجموعات 
+
+183
+00:12:44,080 --> 00:12:48,700
+غير
+
+184
+00:12:48,700 --> 00:12:54,570
+عامة، وما الفرق بين الـ formal  والـ informal groups؟ لماذا
+
+185
+00:12:54,570 --> 00:12:57,890
+الـ informal groups أيضا مهمة؟
+
+186
+00:13:01,680 --> 00:13:07,740
+هؤلاء الأشخاص دائما يتعاملون مع بعضهم البعض، وإذا
+
+187
+00:13:07,740 --> 00:13:11,520
+كنا نتعامل مع المجتمع، لا يمكننا فقط أن نتعامل مع
+
+188
+00:13:11,520 --> 00:13:17,220
+الجانب الاجتماعي لذلك، لأن العلاقات الاجتماعية
+
+189
+00:13:17,220 --> 00:13:21,700
+والتعامل الاجتماعي سوف يؤثر على الأداء، على سبيل
+
+190
+00:13:21,700 --> 00:13:25,540
+المثال، فهو مهم أن نتعامل مع كلا الجانبين، لأننا لا 
+
+191
+00:13:25,540 --> 00:13:30,160
+نستطيع أن نتعامل معهم كمشركين أو عاملين أو مخلوقات
+
+192
+00:13:33,310 --> 00:13:38,730
+لماذا من المهم أن تقوم بالدراسة في مجموعات عامة؟ 
+
+193
+00:13:38,730 --> 00:13:44,990
+أعتقد أن المجموعات العامة هي تجارب، والتعامل مع 
+
+194
+00:13:44,990 --> 00:13:49,630
+الناس، فبالطبع هذا سيؤثر على رأي الموظفين، 
+
+195
+00:13:49,630 --> 00:13:55,730
+عقلياتهم، رأيهم في العالم، وخلاصة، رقمهم. حسنًا، 
+
+196
+00:13:55,730 --> 00:13:59,650
+لكن المجموعات العامة ستؤثر على أشياء أكثر، مثل 
+
+197
+00:13:59,650 --> 00:14:00,030
+ماذا؟
+
+198
+00:14:02,940 --> 00:14:08,760
+عن طريق المشاركين، أنا لا أتكلم عن كيف يتعامل
+
+199
+00:14:08,760 --> 00:14:14,900
+الجروب مع بعضهم البعض، عندما
+
+200
+00:14:14,900 --> 00:14:20,280
+نتكلم عن جروبات غير إعلانية، نحن نتكلم عن قيمة
+
+201
+00:14:20,280 --> 00:14:25,040
+مهمة في تجارب التجارب، وهذا السبب لا نستطيع أن 
+
+202
+00:14:25,040 --> 00:14:27,620
+نتكلم عن جروبات غير إعلانية عندما نتكلم عن تجارب 
+
+203
+00:14:27,620 --> 00:14:31,230
+التجارب، أو عندما نتكلم عن الوظيفة بشكل عام، الآن
+
+204
+00:14:31,230 --> 00:14:34,590
+عندما نتحدث عن التواصلات، على سبيل المثال، في بعض
+
+205
+00:14:34,590 --> 00:14:36,010
+الأحيان، يمكن أن تكون المجموعات التجارية التجارية 
+
+206
+00:14:36,010 --> 00:14:39,190
+التجارية التجارية التجارية التجارية التجارية
+
+207
+00:14:39,190 --> 00:14:40,750
+التجارية التجارية التجارية التجارية التجارية
+
+208
+00:14:40,750 --> 00:14:42,030
+التجارية التجارية التجارية التجارية التجارية
+
+209
+00:14:42,030 --> 00:14:47,850
+التجارية التجارية التجارية التجارية التجارية
+
+210
+00:14:47,850 --> 00:14:57,010
+التجارية التجارية التجارية
+
+211
+00:14:57,010 --> 00:14:59,610
+التجار
+
+212
+00:15:00,360 --> 00:15:04,280
+وهذه المجموعات سوف تؤثر على تجارب التجارب بشكل عام 
+
+213
+00:15:04,280 --> 00:15:09,300
+بشكل عام، يعني لا يهم كمية المجموعات لديها أموال
+
+214
+00:15:09,300 --> 00:15:13,940
+مثلًا، أسلحة، خطوط جيدة، أسلحة، جميع هذه المجموعات
+
+215
+00:15:13,940 --> 00:15:20,260
+مطالبات مهمة، لكن إذا كانت المجموعات المجلسية مثلًا
+
+216
+00:15:20,950 --> 00:15:25,110
+تقرر أن تقاتل المؤسسة، فهي ستدمر المؤسسة، أنا
+
+217
+00:15:25,110 --> 00:15:28,690
+أتكلم عن مثال راديكالي، ولكنه سيساعدنا في فهم لماذا
+
+218
+00:15:28,690 --> 00:15:33,130
+الجروبات غير مؤسسة مهمة. الآن عندما نتكلم عن عملية
+
+219
+00:15:33,130 --> 00:15:38,390
+المؤسسة، بعض الدراسات المتعارفة هناك يسمونها 
+
+220
+00:15:38,390 --> 00:15:41,490
+سوشيومترا، وفي سوشيومترا يتكلمون عن علاقات غير
+
+221
+00:15:41,490 --> 00:15:45,790
+مؤسسة بين الشخصيات في المؤسسة، لماذا؟ لأن هذا يجب
+
+222
+00:15:45,790 --> 00:15:49,240
+أن يساعد المؤسسة. على سبيل المثال، تدخل مجموعات
+
+223
+00:15:49,240 --> 00:15:53,400
+أساسية لماذا؟ لأن الناس الذين لديهم علاقات جيدة مع 
+
+224
+00:15:53,400 --> 00:15:56,520
+بعضهم البعض، يستطيعون فهم بعضهم البعض بشكل أفضل، 
+
+225
+00:15:56,520 --> 00:16:00,180
+يستطيعون التعامل بسهولة، هم سيساعدون بعضهم البعض، 
+
+226
+00:16:00,180 --> 00:16:03,100
+على سبيل المثال، وكذلك. عندما يرغبون في إعادة
+
+227
+00:16:03,100 --> 00:16:07,740
+هيكلة المؤسسة، من المهم أن نفهم نوع التواصلات
+
+228
+00:16:07,740 --> 00:16:13,420
+المتوافرة في المؤسسة. ونحتاج، على سبيل المثال، تصميم
+
+229
+00:16:13,420 --> 00:16:20,380
+فريق أو مجلس مهم جدا
+
+230
+00:16:20,380 --> 00:16:25,340
+لفهم من يتفاهم بشكل أفضل مع بعضهم البعض، أو يتفاهم
+
+231
+00:16:25,340 --> 00:16:27,340
+بشكل أفضل مع بعضهم البعض، أو يتفاهم بشكل أفضل مع
+
+232
+00:16:27,340 --> 00:16:27,380
+بعضهم البعض، أو يتفاهم بشكل أفضل مع بعضهم البعض، أو
+
+233
+00:16:27,380 --> 00:16:28,800
+يتفاهم بشكل أفضل مع بعضهم البعض، أو يتفاهم بشكل
+
+234
+00:16:28,800 --> 00:16:31,460
+أفضل مع بعضهم البعض، أو يتفاهم بشكل أفضل مع بعضهم
+
+235
+00:16:31,460 --> 00:16:32,480
+البعض، أو يتفاهم بشكل أفضل مع بعضهم البعض، أو يتفاهم
+
+236
+00:16:32,480 --> 00:16:40,460
+بشكل أفضل مع بعضهم البعض، أو يتفاهم بشكل أفضل مع
+
+237
+00:16:40,460 --> 00:16:45,050
+بعضهم البعض، أو يت… وأحيانًا سيؤثر على تجارب المجموعات 
+
+238
+00:16:45,050 --> 00:16:49,230
+العامة، لهذا السبب يجب أن ندرس مجموعات عامة عامة 
+
+239
+00:16:49,230 --> 00:16:56,750
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+240
+00:16:56,750 --> 00:16:57,050
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+241
+00:16:57,050 --> 00:17:00,390
+عامة عامة عامة عامة عامة عامة عامة عامة
+
+242
+00:17:06,480 --> 00:17:10,820
+الآن، لماذا الناس تتجمع في المجموعات، هذا ربما ما 
+
+243
+00:17:10,820 --> 00:17:14,940
+تحدثت عنه سابقًا، هناك أسباب مختلفة لماذا الناس 
+
+244
+00:17:14,940 --> 00:17:19,780
+تتجمد في المجموعات، واحدة منها هي الحماية، بالطبع
+
+245
+00:17:19,780 --> 00:17:29,420
+إذا نتحدث عنها بشكل بسيط، أو أكثر شخصية، فهي أكثر
+
+246
+00:17:29,420 --> 00:17:34,570
+كفاءة في التعامل مع حاجة مختلفة أو مشكلة، أفضل من واحد
+
+247
+00:17:34,570 --> 00:17:38,830
+شخصيًا، لذلك بدلًا من البقاء وحيدًا مع مشكلة
+
+248
+00:17:38,830 --> 00:17:42,590
+معينة، يمكننا أن نساعد بعضنا البعض في التعامل مع
+
+249
+00:17:42,590 --> 00:17:46,370
+المشكلة، بالطبع، هناك أسباب أخرى مثلًا، مثلًا، 
+
+250
+00:17:46,370 --> 00:17:52,070
+الوظيفة، كل فريق بمجموعاته، مهمته، مهمته، وما إلى 
+
+251
+00:17:52,070 --> 00:17:59,970
+ذلك، ستحصل على وظيفة تحترم، وهذا بسبب مجموعته
+
+252
+00:17:59,970 --> 00:18:06,200
+أيضًا. بالطبع، احترام الذات، هنا نتحدث عن شخصين يشعرون
+
+253
+00:18:06,200 --> 00:18:10,240
+أنهم يستطيعون أن ينجحوا إن هم أشخاص من فريق مهم،
+
+254
+00:18:10,240 --> 00:18:14,720
+على سبيل المثال، ما هو نوع العمليات أو العمليات
+
+255
+00:18:14,720 --> 00:18:19,160
+التي يتعاملون بها لأنهم أشخاص من فريق معين،
+
+256
+00:18:19,160 --> 00:18:22,420
+بالإضافة إلى التواصل، نتحدث عن علاقات مجتمعية، هنا 
+
+257
+00:18:22,420 --> 00:18:23,680
+بالطبع قوة 
+
+258
+00:18:27,200 --> 00:18:32,500
+لأن تأثيرنا أفضل عندما نكون مجتمعًا من مجموعات، لأن
+
+259
+00:18:32,500 --> 00:18:38,600
+المجموعات يجب أن تساعد مجموعاتها، بالطبع لإنهاء
+
+260
+00:18:38,600 --> 00:18:40,120
+مهمات مختلفة، أو لإنهاء مهمات مختلفة، أو لإنهاء
+
+261
+00:18:40,120 --> 00:18:40,560
+مهمات مختلفة، أو لإنهاء مهمات مختلفة، أو لإنهاء
+
+262
+00:18:40,560 --> 00:18:41,520
+مهمات مختلفة، أو لإنهاء مهمات مختلفة، أو لإنهاء
+
+263
+00:18:41,520 --> 00:18:42,880
+مهمات مختلفة، أو لإنهاء مهمات مختلفة، أو لإنهاء
+
+264
+00:18:42,880 --> 00:18:44,540
+مهمات مختلفة، أو لإنهاء مهمات مختلفة، أو لإنهاء
+
+265
+00:18:44,540 --> 00:18:50,220
+مختلفة، أو لإنهاء مختلفة، أو لإنهاء مختلفة، أو لإنهاء
+
+266
+00:18:50,220 --> 00:18:56,920
+مختلفة، أو لإ… إذا لم يكن هناك هدف معين بين الأشخاص
+
+267
+00:18:56,920 --> 00:19:00,680
+الذين يكونون أعضاء أي فريق، فعادة لا يوجد سبب
+
+268
+00:19:00,680 --> 00:19:05,360
+لاتصال الفريق، وإذا كان الفريق مجتمعًا، فعادة
+
+269
+00:19:05,360 --> 00:19:13,860
+علاقات الفريق ضعيفة وليس هناك اتجاه يتبعه، وهو
+
+270
+00:19:13,860 --> 00:19:18,300
+السبب في عادة الفريق لا يوجد هدف أو هدف، عادةً ليس
+
+271
+00:19:18,300 --> 00:19:24,800
+مفيدًا، بل غير مفيد، لأن هنا لا يوجد شيء يمكن أن 
+
+272
+00:19:24,800 --> 00:19:27,820
+تنجح بسبب هذا. قبل قليل قلت أنها واحدة من
+
+273
+00:19:27,820 --> 00:19:31,180
+الاحتياجات، أنه عندما نتحدث عن مجموعة يجب أن يكون 
+
+274
+00:19:31,180 --> 00:19:37,520
+هناك مهمة مشتركة لجميع أعضاء مجموعة محددة. 
+
+275
+00:19:39,980 --> 00:19:46,880
+عندما نتكلم عن كيف تتشكل المجموعات، يوجد ممارسات
+
+276
+00:19:46,880 --> 00:19:51,080
+مختلفة، اليوم دعنا نتكلم عن واحدة من هذه الممارسات
+
+277
+00:19:51,080 --> 00:19:57,660
+هذه الممارسة تدعى الممارسة الخمس مراحل أو الممارسة
+
+278
+00:19:57,660 --> 00:20:03,040
+التطورية، وهو مسمى آخر للممارسة. في المدارس الخمس
+
+279
+00:20:03,040 --> 00:20:07,560
+المدرسية، هناك خمس مدارس رئيسية تعتمد على
+
+280
+00:20:07,560 --> 00:20:11,980
+المدارس التي ستتخلص منها أي مجموعة بينما تتجمع 
+
+281
+00:20:11,980 --> 00:20:15,820
+المجموعة. باعتبار المدارس الخامسة **المدارس** المدرسية،
+
+282
+00:20:15,820 --> 00:20:20,520
+المدارس الأولى يدعى Forming. عندما نتحدث عن
+
+283
+00:20:20,520 --> 00:20:26,120
+Forming، عادةً، المجموعات هنا تتعامل مع الكثير من
+
+284
+00:20:26,120 --> 00:20:32,460
+الاضطراب وما إلى ذلك، وهو **الذي** المجموعة **التي** الجمهور
+
+285
+00:20:32,460 --> 00:20:39,380
+يدخل الجمهور وهنا نحن نتحدث عن الشعور بالضروري وما
+
+286
+00:20:39,380 --> 00:20:43,060
+إلى ذلك. الآن، المرحلة الثانية هي **الاستقرار**. الآن
+
+287
+00:20:43,060 --> 00:20:47,220
+عندما نتحدث عن **الاستقرار**، هنا نتحدث عن الكثير من
+
+288
+00:20:47,220 --> 00:20:53,540
+المعاقبة بين أعضاء الجمهور. طبعًا، هناك بعض **القلق**
+
+289
+00:20:53,540 --> 00:20:58,540
+بعد ذلك، هناك معاقبة بين أعضاء الجمهور. الآن،
+
+290
+00:20:58,540 --> 00:21:03,460
+المرحلة الثالثة هي التخطيط.عندما تتكلم عن **العاملية**
+
+291
+00:21:03,460 --> 00:21:03,720
+عاملية عاملية عاملية عاملية عاملية عاملية عاملية
+
+292
+00:21:03,720 --> 00:21:06,420
+عاملية عاملية عاملية عاملية عاملية عاملية عاملية
+
+293
+00:21:06,420 --> 00:21:07,500
+عاملية عاملية عاملية عاملية عاملية عاملية عاملية
+
+294
+00:21:07,500 --> 00:21:10,240
+عاملية عاملية عاملية عاملية عاملية عاملية عاملية
+
+295
+00:21:10,240 --> 00:21:10,660
+عاملية عاملية عاملية عاملية عاملية عاملية عاملية
+
+296
+00:21:10,660 --> 00:21:12,020
+عاملية عاملية عاملية عاملية عاملية عاملية عاملية
+
+297
+00:21:12,020 --> 00:21:15,760
+عاملية عاملية عاملية عاملية عاملية عاملية عاملية
+
+298
+00:21:15,760 --> 00:21:28,480
+عاملية عاملية عاملية عاملية
+
+299
+00:21:30,000 --> 00:21:35,400
+والخطوة الخامسة هي الانتقال، هنا نتحدث عن انتقال
+
+300
+00:21:35,400 --> 00:21:39,120
+المجموعات، خاصة عندما نتحدث عن مجموعات مقتصرة
+
+301
+00:21:39,120 --> 00:21:44,940
+دعونا نعود إلى تلك المرات ونتحدث عن لماذا في المرة
+
+302
+00:21:44,940 --> 00:21:50,940
+الأولى يوجد شعور **بالـ**غير متأكد؟ لماذا في المرة
+
+303
+00:21:50,940 --> 00:21:59,180
+القادمة يوجد شعور **بالـ**غير متأكد؟ربما في البداية
+
+304
+00:21:59,180 --> 00:22:02,520
+الناس اللي لا يعرفوا بعضهم البعض بطريقة جيدة،
+
+305
+00:22:02,520 --> 00:22:07,340
+لا يعرفوا إذا كانوا يستطيعوا تحقيق **هذا** الجمهور أو
+
+306
+00:22:07,340 --> 00:22:11,660
+تحقيق **هذا** الهدف اللي يريدون أن تحقيقه أو لا، لذلك
+
+307
+00:22:11,660 --> 00:22:18,440
+ربما يكونوا متأكدين أو غير متأكدين أو غير متأكدين
+
+308
+00:22:18,440 --> 00:22:19,040
+أو غير متأكدين أو غير متأكدين أو غير متأكدين أو
+
+309
+00:22:19,040 --> 00:22:19,060
+متأكدين أو غير متأكدين أو غير متأكدين أو غير
+
+310
+00:22:19,060 --> 00:22:19,260
+متأكدين أو غير متأكدين أو غير متأكدين أو غير
+
+311
+00:22:19,260 --> 00:22:24,440
+متأكدين أو غير متأكدين أو
+
+312
+00:22:24,440 --> 00:22:24,560
+غير متأ
+
+313
+00:22:35,110 --> 00:22:37,770
+والمهم **أكثر** هو النقطة الأولى، على الرغم من أن جميع
+
+314
+00:22:37,770 --> 00:22:41,230
+النقطة التي تحدثت عنها مهمة متساومة، ولكن عادةً
+
+315
+00:22:41,230 --> 00:22:44,350
+عندما نتكلم عن الهدف نفسه، عادةً الجمهور في هذه
+
+316
+00:22:44,350 --> 00:22:47,930
+المجال **غير** متأكد عن الهدف، الواجهة، النتيجة
+
+317
+00:22:47,930 --> 00:22:52,650
+الأخيرة التي يحتاجها لتحقيقها، وهو أحد الأسباب **أهم**
+
+318
+00:22:52,650 --> 00:22:56,170
+لماذا
+
+319
+00:22:56,170 --> 00:23:00,650
+هناك بعض الانتقال. بالإضافة إلى نقطة أخرى، مثلما
+
+320
+00:23:00,650 --> 00:23:04,060
+نتكلم عن كيف نستطيع **أن** ماذا سيحدث عندما تصل إلى هذا
+
+321
+00:23:04,060 --> 00:23:08,540
+الهدف أو تلقي **هذا** الهدف؟ ماذا سيحدث عندما تصل إلى
+
+322
+00:23:08,540 --> 00:23:09,640
+إلى هذا الهدف أو تلقي **هذا** الهدف؟ ماذا سيحدث عندما
+
+323
+00:23:09,640 --> 00:23:12,060
+تصل إلى هذا الهدف أو تلقي **هذا** الهدف؟ ماذا سيحدث
+
+324
+00:23:12,060 --> 00:23:13,380
+عندما تصل إلى هذا الهدف أو تلقي **هذا** الهدف؟ ماذا
+
+325
+00:23:13,380 --> 00:23:15,200
+سيحدث عندما تصل إلى هذا الهدف أو تلقي **هذا** الهدف؟
+
+326
+00:23:15,200 --> 00:23:18,660
+ماذا سيحدث عندما تصل إلى هذا الهدف أو تلقي **هذا**
+
+327
+00:23:18,660 --> 00:23:24,000
+الهدف؟ ماذا سيحدث عندما تصل إلى هذا الهدف أو تلقي
+
+328
+00:23:24,000 --> 00:23:27,580
+**هذا**
+
+329
+00:23:27,580 --> 00:23:33,500
+الهدف؟ ماذا سيحدث **عندما** وهو لأن المشكلة تتطور بسبب
+
+330
+00:23:33,500 --> 00:23:37,780
+المشكلة **المُحكمة**، من **غير** محكمة، من سيكون على أعلى
+
+331
+00:23:37,780 --> 00:23:43,500
+**المستوى**، لذلك لإيقاف **المستوى** من **الجمهور** ومن **المدير** أو
+
+332
+00:23:43,500 --> 00:23:47,720
+من **المُحكمة**، يجب أن تكون المشكلة **المُحكمة**. وإذا كنا
+
+333
+00:23:47,720 --> 00:23:52,920
+نعود إلى تلك المناطق التي جعلتها
+
+334
+00:23:52,920 --> 00:23:59,960
+غير متأكدة، فهذه المناطق يجب أن تكون **حلول** هنا يجب
+
+335
+00:23:59,960 --> 00:24:03,640
+أن نصل إلى حلول أو أن نتفاهم في هذه الحلول، ما هي
+
+336
+00:24:03,640 --> 00:24:09,800
+مهمتنا، لذلك سيكون هناك **هناك** نقاط مختلفة وفي بعض
+
+337
+00:24:09,800 --> 00:24:16,160
+الأحيان نقاط مختلفة وفي بعض الأحيان نقاط مختلفة
+
+338
+00:24:16,160 --> 00:24:17,720
+وفي بعض الأحيان نقاط مختلفة وفي بعض الأحيان نقاط
+
+339
+00:24:17,720 --> 00:24:19,900
+مختلفة وفي بعض الأحيان نقاط مختلفة وفي بعض الأحيان
+
+340
+00:24:19,900 --> 00:24:20,320
+نقاط مختلفة وفي بعض الأحيان نقاط مختلفة وفي بعض
+
+341
+00:24:20,320 --> 00:24:20,820
+الأحيان نقاط مختلفة وفي بعض الأحيان نقاط مختلفة
+
+342
+00:24:20,820 --> 00:24:26,020
+وفي بعض الأحيان نقاط مختلفة وفي بعض الأحيان نقاط
+
+343
+00:24:26,020 --> 00:24:31,540
+مختلفة وفي بعض الأحيان نقاط مختلفة وفي بعض الأحيان
+
+344
+00:24:31,540 --> 00:24:39,970
+نقاط مختلفة وفي بعض **الأحيان** خاصة بالنسبة للأشخاص،
+
+345
+00:24:39,970 --> 00:24:44,650
+كيف تتعامل مع المصادر، ماذا يجب أن تفعل لإنجاز
+
+346
+00:24:44,650 --> 00:24:50,140
+الهدف، **الـ**هدف الواضح وما إلى ذلك **المشاكل** يجب أن يتم
+
+347
+00:24:50,140 --> 00:24:55,380
+حلّها، وهذا السبب **في** المجتمع أن هناك مشاكل بين
+
+348
+00:24:55,380 --> 00:25:00,600
+المجتمعين، وكل هذه المشاكل يجب أن تتم حلّها في
+
+349
+00:25:00,600 --> 00:25:04,300
+الثالث مرحلة، هنا نتحدث عن التنمية، في هذه المرحلة
+
+350
+00:25:04,400 --> 00:25:13,180
+عادةً يتمكن **الجمهور** من إنشاء مصطلحات أساسية
+
+351
+00:25:13,180 --> 00:25:18,680
+يتفاوضون على أشياء وهذا
+
+352
+00:25:18,680 --> 00:25:26,400
+هو نتيجة **الـ**ثانوية مرحلة هنا **الجمهور** تطور مصطلحات
+
+353
+00:25:26,400 --> 00:25:33,640
+أساسية **أكثر**. تبدأ عملها، علاقات **الأعضاء** تكون **أكثر**
+
+354
+00:25:33,640 --> 00:25:38,600
+عادلة، نستطيع أن نقول هنا، لماذا؟ لأن في أولين
+
+355
+00:25:38,600 --> 00:25:42,920
+مرتين، كانت هناك الكثير من التحدثات ومقابلات، على
+
+356
+00:25:42,920 --> 00:25:47,880
+سبيل المثال، وكذلك، وعادة في ذلك الوقت، **الأعضاء**
+
+357
+00:25:47,880 --> 00:25:52,760
+**يفهمون** بعضها البعض بشكل أفضل، يستطيعوا
+
+358
+00:25:52,760 --> 00:26:00,350
+التعامل بشكل **أكثر** وهي قادرة على التعامل مع المشاكل
+
+359
+00:26:00,350 --> 00:26:03,070
+المختلفة وإيجاد حلول **لـ**أولاد المشاكل المختلفة
+
+360
+00:26:03,070 --> 00:26:05,130
+وإيجاد حلول **لـ**أولاد المشاكل المختلفة وإيجاد حلول
+
+361
+00:26:05,130 --> 00:26:05,930
+المختلفة وإيجاد حلول **لـ**أولاد المشاكل المختلفة
+
+362
+00:26:05,930 --> 00:26:12,790
+وإيجاد حلول **لـ**أولاد المشاكل المختلفة وإيجاد حلول
+
+363
+00:26:12,790 --> 00:26:16,510
+**لـ**أولاد المشاكل المختلفة وإيجاد حلول **لـ**أولاد المشاكل
+
+364
+00:26:16,510 --> 00:26:19,570
+المختلفة وإيجاد حلول **لـ**أولاد المشاكل المختلفة
+
+365
+00:26:19,570 --> 00:26:24,350
+وإيجاد حلول
+
+366
+00:26:24,350 --> 00:26:26,050
+**لـ**أولاد المشاكل المختلفة وإيجو**اد** مهارات ومهارات
+
+367
+00:26:26,050 --> 00:26:26,430
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+368
+00:26:26,430 --> 00:26:29,930
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+369
+00:26:29,930 --> 00:26:30,010
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+370
+00:26:30,010 --> 00:26:31,270
+ومهارات ومهارات ومهارات ومهارات ومهارات ومهارات
+
+371
+00:26:31,270 --> 00:26:40,630
+ومهارات ومهارات ومهارات ومهارات ومهارات
+
+372
+00:26:40,630 --> 00:26:44,270
+ومهارات
+
+373
+00:26:50,230 --> 00:26:54,470
+و كما ذكرت في **الـ**مجموعات التجارية، هنا نتكلم عن
+
+374
+00:26:54,470 --> 00:26:57,530
+كيفية إضافة **أفعال**، لماذا؟ لأن في **الـ**مجموعات
+
+375
+00:26:57,530 --> 00:27:02,610
+التجارية، نحتاج أن ننهي العمل و نذهب إلى مهمة أخرى
+
+376
+00:27:02,610 --> 00:27:05,910
+أو نعود إلى مجموعات **الـ**قواعد الخاص بنا، على سبيل
+
+377
+00:27:05,910 --> 00:27:11,010
+المثال، حسنًا؟ هنا، عادةً، هناك مرحلة رابعة، وهي
+
+378
+00:27:11,010 --> 00:27:15,090
+مرحلة **جارية**، حسنًا؟ لكن إذا كنا نتكلم عن مجموعات
+
+379
+00:27:15,090 --> 00:27:19,680
+**الـ**قواعد، على سبيل المثال، وهي **بشكل** مستمر، لذلك سوف
+
+380
+00:27:19,680 --> 00:27:25,560
+نتوقف هنا في المرحلة الرابعة حسنًا، على الرغم من
+
+381
+00:27:25,560 --> 00:27:32,320
+أن هذا يبدو منطقيًا، لكن هناك الكثير من **الاعتبارات**
+
+382
+00:27:32,320 --> 00:27:37,080
+هنا عندما نتحدث عن **المدخلة** الخامس من **الـ**مرحلة قد
+
+383
+00:27:37,080 --> 00:27:41,520
+يكون واضحًا أن هناك نوع من **إشارات** عملية **الـ**تجارب
+
+384
+00:27:41,520 --> 00:27:47,320
+نفسها عندما نتحدث عن تطوير **الـ**مجموعة **لسنا نتحدث عن**
+
+385
+00:27:47,320 --> 00:27:53,460
+.. ببساطة كما ذكرنا **الـ**موضوع، **الـ**موضوع هو **أكثر** ..
+
+386
+00:27:53,460 --> 00:28:01,420
+مضغوط هنا .. لماذا؟ إنه **أكثر** مضغوط نعم؟ لأن الكثير
+
+387
+00:28:01,420 --> 00:28:03,900
+من الناس .. الكثير من الناس مرتبطين في **هذا**
+
+388
+00:28:03,900 --> 00:28:07,540
+**البرنامج** نحن نتكلم عن **الإبداع البشري** بعد كل شيء
+
+389
+00:28:07,540 --> 00:28:13,450
+و لا يمكننا أن **نسهم** في **الإبداع البشري** يكون هناك
+
+390
+00:28:13,450 --> 00:28:19,030
+معلومات مختلفة ويجب أن نعتمد على ذلك لذلك ليس مثل
+
+391
+00:28:19,030 --> 00:28:23,090
+1,2,3,4,5 ومن ثم **الجمهور** يكون مجموعته هناك الكثير
+
+392
+00:28:23,090 --> 00:28:27,810
+من **التفاصيل** التي مرتبطة بكيف يتعامل **الجمهور** مع كل
+
+393
+00:28:27,810 --> 00:28:32,650
+مرحلة **هذا** السبب أننا نعتبر أن **الـ**برنامج **الـ**مصطلح
+
+394
+00:28:32,650 --> 00:28:38,930
+**يسهم** في كيف حدثت الأشياء حقًا. الآن، السبب الثاني
+
+395
+00:28:38,930 --> 00:28:47,650
+هنا في **هذه** التجارب، عندما نتكلم عن **الـ**مصادر، عادةً
+
+396
+00:28:47,650 --> 00:28:50,750
+نتكلم عن إثنين من **الـ**مصادر، نحن لدينا ما نسميه
+
+397
+00:28:50,750 --> 00:28:53,290
+مصادر **إيجابية** ونحن لدينا ما نسميه مصادر **سلبية**.
+
+398
+00:28:54,090 --> 00:28:58,150
+عندما نتحدث عن اتفاقات **أفضل**، نتوقع اتفاقات **أفضل**،
+
+399
+00:28:58,150 --> 00:29:01,510
+لهذا السبب نسميها اتفاقات **أفضل** عندما نتحدث عن
+
+400
+00:29:01,510 --> 00:29:05,370
+اتفاقات **أفضل**، نتوقع اتفاقات **أفضل**، لهذا السبب
+
+401
+00:29:05,370 --> 00:29:09,810
+نسميها اتفاقات **أفضل**، لهذا السبب نسميها اتفاقات
+
+402
+00:29:09,810 --> 00:29:10,050
+**أفضل**، لهذا السبب نسميها اتفاقات **أفضل**، لهذا السبب
+
+403
+00:29:10,050 --> 00:29:11,150
+نسميها اتفاقات **أفضل**، لهذا السبب نسميها اتفاقات
+
+404
+00:29:11,150 --> 00:29:15,370
+**أفضل**، لهذا السبب نسميها اتفاقات **أفضل**، لهذا السبب
+
+405
+00:29:15,370 --> 00:29:20,640
+نسميها اتفاقات **أفضل** أحيانًا تكون **هذه** الانتجارات
+
+406
+00:29:20,640 --> 00:29:28,400
+**تسيطر** على تجارب عالية أو هي ستساعد **الـ**مجتمع لإنجاز
+
+407
+00:29:28,400 --> 00:29:33,640
+**أفضل**، فهذا يعتمد على **الـ**انتجار نفسه، طبيعة
+
+408
+00:29:33,640 --> 00:29:38,820
+**الـ**انتجار، **أما** أنه انتجار **مفيد** أو **غير مفيد**. الأسباب
+
+409
+00:29:38,820 --> 00:29:46,390
+الثالثة هنا **الـ**برنامج ليس دائمًا عملية أو **غير عملية**، ليس
+
+410
+00:29:46,390 --> 00:29:50,130
+دائمًا .. مثلما تحدثنا عن **الـ**قوة **العالمية**، **الـ**قوة
+
+411
+00:29:50,130 --> 00:29:54,410
+**العالمية**، نقول أنه ليس فقط أننا سنفعل ما نحتاجه في
+
+412
+00:29:54,410 --> 00:29:57,390
+**الـ**سطح الأول و بعدها نذهب إلى **الـ**سطح الثاني، وهو نفس
+
+413
+00:29:57,390 --> 00:30:01,210
+الشيء هنا، حسنًا؟ هؤلاء هما مواضعين مختلفة، لكن
+
+414
+00:30:01,210 --> 00:30:05,950
+**الـ**مفهوم هو نفس الشيء هنا، ليس كأننا سننتهي بطريقة
+
+415
+00:30:05,950 --> 00:30:10,180
+واحدة تمامًا و بعدها سنبدأ **ولكن** عندما نتكلم عن
+
+416
+00:30:10,180 --> 00:30:14,280
+مرحلة جديدة، مثلًا عندما نتكلم عن **الـ**مرحلة التالية
+
+417
+00:30:14,280 --> 00:30:18,000
+وما إلى ذلك، أحيانًا **هذه** المراحل ستتعامل مع بعضها
+
+418
+00:30:18,000 --> 00:30:24,240
+البعض، لذلك ليس دائمًا برنامج **مستمر** أو برنامج
+
+419
+00:30:24,240 --> 00:30:30,040
+**متقطع**، أحيانًا **هذا** البرنامج سيكون **مزدوج** عندما
+
+420
+00:30:30,040 --> 00:30:31,640
+نتكلم عن مراحل مختلفة 
+
+421
+00:30:34,550 --> 00:30:39,850
+هذا السبب في بعض الأحيان عندما تتجمد تجاربها أو 
+
+422
+00:30:39,850 --> 00:30:42,310
+تتجمد تجاربها تتجمد تجاربها تتجمد تجاربها تتجمد 
+
+423
+00:30:42,310 --> 00:30:46,450
+تجاربها تتجمد تجاربها تتجمد تجاربها تتجمد تجاربها
+
+424
+00:30:46,450 --> 00:30:47,070
+تتجمد تجاربها تتجمد تجاربها تتجمد تجاربها تتجمد
+
+425
+00:30:47,070 --> 00:30:47,090
+تجاربها تتجمد تجاربها تتجمد تجاربها تتجمد تجاربها
+
+426
+00:30:47,090 --> 00:30:58,910
+تجاربها تتجمد تجاربها تتجمد تجارب
+
+427
+00:30:59,100 --> 00:31:03,520
+أو أننا سنجد أننا فشلنا في تحقيق المرحلات الأولى 
+
+428
+00:31:03,520 --> 00:31:09,160
+وأننا نحتاج لتعامل مع المرحلات الأولى أو بأي سبب 
+
+429
+00:31:09,160 --> 00:31:15,280
+موجود ولكن لأسباب مختلفة، المجمهدين قد يعودوا إلى 
+
+430
+00:31:15,280 --> 00:31:19,360
+المرحلات الأولى لأن هناك شيء جديد أو شيء غير صحيح 
+
+431
+00:31:19,360 --> 00:31:21,660
+أو أي شيء أيه أيه أيه أيه أيه أيه أيه أيه أيه أيه
+
+432
+00:31:21,660 --> 00:31:23,820
+أيه أيه أيه أيه أيه أيه أيه أيه أيه أيه أيه
+
+433
+00:31:26,770 --> 00:31:31,770
+هنا، إذا رأيتِ، عندما تحدثنا عن المرحلات، كنا 
+
+434
+00:31:31,770 --> 00:31:36,330
+نتحدث فقط عن المجموعات وما يحدث داخل المجموعات، لم 
+
+435
+00:31:36,330 --> 00:31:42,070
+نتحدث عن كيفية تأثير المؤسسات على ما يحدث داخل 
+
+436
+00:31:42,070 --> 00:31:45,330
+المجموعات، وهذه المجموعات، نحن نتحدث عن الوظيفة 
+
+437
+00:31:45,330 --> 00:31:49,540
+ونحن نتحدث عن المجموعات داخل المؤسسات  المجلد
+
+438
+00:31:49,540 --> 00:31:55,960
+المجلدي هنا مهم جدًا عندما نتكلم عن عملية تصميم 
+
+439
+00:31:55,960 --> 00:32:00,340
+المجلد لماذا؟ لأننا لسنا نتكلم عن مجلد مختلف نحن 
+
+440
+00:32:00,340 --> 00:32:08,140
+نتكلم هنا عن شيء ممتع بالمجلد إنه جزء أو جزء من 
+
+441
+00:32:08,140 --> 00:32:12,380
+مجلد المجلد حسنًا، هل لديكم أسئلة؟ 
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/rLUs1b-eyH8.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/rLUs1b-eyH8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9e796f165846e1edce90a4f601072dbeb3eb868b
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/rLUs1b-eyH8.srt
@@ -0,0 +1,2204 @@
+1
+00:00:05,420 --> 00:00:09,500
+وفي هذا المجال، قلنا إن هناك أدوات أساسية يمكننا
+
+2
+00:00:09,500 --> 00:00:13,400
+استخدامها أولاً هي استخدام مقارنة عالمية واحدة
+
+3
+00:00:13,400 --> 00:00:18,500
+وبسيطة، قلنا إنها سؤال واحد مع إجابة واحدة، نعم أو 
+
+4
+00:00:18,500 --> 00:00:23,120
+لا، وإذا كانوا موظفين مستمتعين أو لا، وأداة أخرى،
+
+5
+00:00:23,120 --> 00:00:29,990
+قلنا إنه يمكننا استخدام مقارنة، وهنا نتكلم عن مثلًا
+
+6
+00:00:29,990 --> 00:00:34,250
+سؤال أو شريحة حيث يكون هناك أو ربما مقابلة أيضًا
+
+7
+00:00:34,250 --> 00:00:38,150
+حيث يكون هناك الكثير من الأسئلة، من تلك الأسئلة 
+
+8
+00:00:38,150 --> 00:00:41,650
+نحاول أن نتعامل معها أو نتعامل معها، إذا كانت
+
+9
+00:00:41,650 --> 00:00:45,810
+الموظفين مستمتعين أو لا، قلنا أيضًا بأننا نستطيع
+
+10
+00:00:45,810 --> 00:00:52,250
+استخدام كلا الأداتين، ولكن يكون أفضل استخدام الأولى
+
+11
+00:00:52,250 --> 00:00:53,410
+هي رقم مجتمعي يخبرنا لماذا 
+
+12
+00:00:53,410 --> 00:00:54,310
+لا يكونوا
+
+13
+00:00:54,310 --> 00:01:01,270
+غاضبين، وما هي المصادر التي تسبب في هذا الانزعاج.
+
+14
+00:01:01,270 --> 00:01:02,090
+لهذا السبب،
+
+15
+00:01:02,090 --> 00:01:02,270
+يمكن استخدام 
+
+16
+00:01:02,270 --> 00:01:04,430
+كلا الأداتين، 
+
+17
+00:01:04,430 --> 00:01:04,910
+كمشاركة 
+
+18
+00:01:04,910 --> 00:01:11,280
+لبعضنا البعض. نستطيع استخدام الأولى لإنقاذ الوقت
+
+19
+00:01:11,280 --> 00:01:16,660
+والاستفادة، لديه إشارة عن إذا كانوا مستمتعين أو لا.
+
+20
+00:01:16,880 --> 00:01:22,560
+ثم نستطيع استخدام التجارب الثانية، اللي هي تجارب
+
+21
+00:01:22,560 --> 00:01:25,820
+المقاييس، لتعرف ما هي المناطق اللي جعلت الموظفين
+
+22
+00:01:25,820 --> 00:01:30,560
+غاضبين، قلنا مرة أخرى أن هناك تجارب مختلفة يمكن
+
+23
+00:01:30,900 --> 00:01:35,210
+استخدامها، عندما نتكلم عن الأدوات، فنحن نتكلم هنا
+
+24
+00:01:35,210 --> 00:01:40,050
+إما عن مقابلات أو استبيانات أو رحلات وما إلى ذلك،
+
+25
+00:01:40,050 --> 00:01:47,000
+هؤلاء هم الأدوات التي يمكن استخدامها لإطلاق أي 
+
+26
+00:01:47,000 --> 00:01:49,360
+واحد من هذه التجارب. الآن، مشكلة أخرى هنا، هي
+
+27
+00:01:49,360 --> 00:01:53,780
+السؤال المهم، إن الناس مستمرة أو لا مستمرة بعملهم
+
+28
+00:01:53,780 --> 00:01:58,660
+وهذا شيء لا يمكننا أن نحكمه بدون استخدام نوع من
+
+29
+00:01:58,660 --> 00:02:04,020
+التجارب التجريبية مثل التي قد تحدثنا عنها لكي نعرف 
+
+30
+00:02:04,020 --> 00:02:11,560
+إن الموظفين مستمرة أو لا، ولكن عادةً
+
+31
+00:02:11,560 --> 00:02:18,440
+أحد أهم القرارات هنا التي يجب أن تساعدنا في اكتشاف
+
+32
+00:02:18,440 --> 00:02:24,860
+إذا كانوا موظفين أم لا، هو طريقة كيف نقوم بتحسين
+
+33
+00:02:24,860 --> 00:02:28,460
+موظفينا، 
+
+34
+00:02:31,890 --> 00:02:37,810
+فبإمكاننا أن نحصل على إجابة عن إذا كانت موظفة 
+
+35
+00:02:37,810 --> 00:02:42,790
+مبتهجة أو لا، هذا أول جزء من الموضوع. الجزء الثاني
+
+36
+00:02:42,790 --> 00:02:43,690
+هنا، يجب أن نكون متأكدين عن ما هي المصادر أو 
+
+37
+00:02:43,690 --> 00:02:44,650
+المواصفات من الأدوات التي يتم استخدامها لكل مجال، 
+
+38
+00:02:44,650 --> 00:02:46,150
+خصوصًا عندما نتكلم عن المجال الثاني، نستطيع، على 
+
+39
+00:02:46,150 --> 00:02:46,370
+ سبيل المثال، أن نبحث عن بعض الأسباب،
+
+40
+00:02:46,370 --> 00:02:49,410
+ولكن ربما هذه 
+
+41
+00:02:49,410 --> 00:02:52,670
+السببات ليست مرتبطة بالنسبة للتسلسل والانتساب من
+
+42
+00:02:52,670 --> 00:02:56,590
+الموظفين، لذلك هنا مرة أخرى، ليس فقط باستخدام
+
+43
+00:02:56,590 --> 00:03:01,810
+طرقات كتبية أو علمية، بل أيضًا كيف تستخدم تلك 
+
+44
+00:03:01,810 --> 00:03:06,530
+الطرقات، كيف تم تصميمها، ما هي محتوى تلك، نستخدم
+
+45
+00:03:06,530 --> 00:03:13,170
+أيضًا أحد أهم أدوات ما إذا كانت الموظفين
+
+46
+00:03:13,170 --> 00:03:16,810
+مستمتعين أو لا، مرة أخرى، هذا يتعلق إلى النقطة 
+
+47
+00:03:16,810 --> 00:03:20,430
+الأولى هنا، قبل أننا قلنا أننا نستخدم رقمًا عالميًا
+
+48
+00:03:20,430 --> 00:03:24,670
+واحدًا، هي تساعدنا في إيجابنا إذا كان الموظفين 
+
+49
+00:03:24,670 --> 00:03:29,790
+مستمتعين أو مستمتعين بشكل عام، ولكن باستخدام
+
+50
+00:03:29,790 --> 00:03:33,490
+التجارب الثانوية هنا هي ستساعدنا في إيجابنا ما هي 
+
+51
+00:03:33,490 --> 00:03:38,010
+المناطق التي يسبب فيها الاستمتاع. لهذا السبب نقول
+
+52
+00:03:38,010 --> 00:03:45,990
+هنا أن النتائج تتعامل مع كيفية تجارب الاستمتاع. إذا 
+
+53
+00:03:45,990 --> 00:03:49,790
+استخدمنا الأدوات الصحيحة، وليس فقط الأدوات
+
+54
+00:03:49,790 --> 00:03:53,670
+الصحيحة، الأدوات الصحيحة، هذه الأدوات ستساعدنا في
+
+55
+00:03:53,670 --> 00:03:57,070
+اكتشاف بطريقة واضحة ما إذا كانت الموظفين مستمتعين 
+
+56
+00:03:57,070 --> 00:04:02,250
+أو لا مستمتعين، وما هي سبب الانزعاج، خاصة إذا كان
+
+57
+00:04:02,250 --> 00:04:05,630
+هناك انزعاج، غير مستمتع، في هذا المجال أيضًا يوجد
+
+58
+00:04:05,630 --> 00:04:11,490
+أشياء مختلفة سيسبب فيها الانزعاج، وفي نفس الوقت
+
+59
+00:04:11,490 --> 00:04:14,950
+لا يوجد تلك المصادر فهو سيسبب فيها الانزعاج،
+
+60
+00:04:14,950 --> 00:04:18,070
+الانزعاج، الانزعاج، أحد أهم من الأشياء المشكلة هنا
+
+61
+00:04:18,070 --> 00:04:20,770
+هي المساعدة والدفع، عندما نتحدث عن تجارب التجارب في 
+
+62
+00:04:20,770 --> 00:04:28,460
+الجامعة، لكننا نقول إنها مشكلة بسبب أنها ليست 
+
+63
+00:04:28,460 --> 00:04:32,600
+الوحيدة، الوحيدة، هناك الكثير من الوحيدات، ربما هذه 
+
+64
+00:04:32,600 --> 00:04:39,200
+واحدة من الوحيدات المهمة، وربما هي واحدة من 
+
+65
+00:04:39,200 --> 00:04:43,740
+الوحيدات المهمة، ولكنها ليست الوحيدة، الوحيدة،
+
+66
+00:04:43,740 --> 00:04:48,400
+الوحيدة، يعني الناس ربما يكونوا satisfied عندما 
+
+67
+00:04:48,400 --> 00:04:51,860
+يكونوا مدفوعين، ولكن ليس بالطبع أنهم دائمًا مدفوعين
+
+68
+00:04:51,860 --> 00:04:59,160
+عندما يكونوا مدفوعين، لماذا؟ 
+
+69
+00:04:59,160 --> 00:05:02,860
+لماذا؟ الدفع والدفعات، أو الترقية، بطريقة الانتشار
+
+70
+00:05:02,860 --> 00:05:10,010
+التي تم تطبيقها في المؤسسة هي واحدة من الأشياء أو 
+
+71
+00:05:10,010 --> 00:05:13,830
+المواصفات المهمة التي ستتأكد إذا كانت الموظفين
+
+72
+00:05:13,830 --> 00:05:17,670
+مستمتعين أو لا مستمتعين، ولكن مرة أخرى، هذه ليست
+
+73
+00:05:17,670 --> 00:05:21,670
+الوحيدة، الوحيدة، الآن، على سبيل المثال، الموظفين 
+
+74
+00:05:21,670 --> 00:05:25,190
+يمكن أن يكونوا satisfied بعمل عمل مع مجتمعهم، مع 
+
+75
+00:05:25,190 --> 00:05:30,070
+مجتمعهم، مع مجتمعهم، مع مجتمعهم، مع مجتمعهم، مع 
+
+76
+00:05:30,070 --> 00:05:35,390
+مجتمعهم، مع مجتمعهم، مع مجتمعهم، مع مجتمعهم، مع
+
+77
+00:05:35,390 --> 00:05:41,050
+مجتمعهم، مع مجتمعهم، مع مجتمعهم، مع مجتمعهم، مع 
+
+78
+00:05:41,050 --> 00:05:45,750
+مجتمعهم، مع مجتمعهم، مع مجتمع
+
+79
+00:05:45,750 --> 00:05:49,670
+لأن الناس تحصل على  satisfied  بطريقة مختلفة، ربما أنا 
+
+80
+00:05:49,670 --> 00:05:53,250
+مدعوم بشكل جيد، لكن ربما سأرى الآخرين كيف يكونوا 
+
+81
+00:05:53,250 --> 00:05:58,690
+مدعومين، وربما أعتقد أنهم مدعومين أكثر من ما 
+
+82
+00:05:58,690 --> 00:06:01,210
+يستحقونه، وفي مقارنة مع نفسي معهم، سأجد أن هناك 
+
+83
+00:06:01,210 --> 00:06:02,930
+نوع من التعامل غير صحيح وما إلى ذلك، فهذا سيأثر
+
+84
+00:06:02,930 --> 00:06:03,550
+على الانزعاج، وهو واحد الجانب، 
+
+85
+00:06:03,550 --> 00:06:04,230
+عندما نتكلم عن 
+
+86
+00:06:04,230 --> 00:06:07,090
+الترقية، 
+
+87
+00:06:07,090 --> 00:06:13,210
+عندما نتكلم عن كيفية تجارب التجارب، وكيف يتم 
+
+88
+00:06:13,210 --> 00:06:19,310
+تطبيقها،  أعتقد أن هناك
+
+89
+00:06:20,630 --> 00:06:25,770
+الكثير من الحالات الأخرى لإيجابك، مثلًا، ربما الوظيفة
+
+90
+00:06:25,770 --> 00:06:29,470
+مدفوعة بشكل جيد، ولكن في نفس الشركة لا يعجبها
+
+91
+00:06:29,470 --> 00:06:32,390
+القواعد أو القيادة من المؤسسة كمثال، أو ربما طريقة
+
+92
+00:06:32,390 --> 00:06:37,150
+القيادة ليست مناسبة للوظيفة، نحن نتحدث، على سبيل 
+
+93
+00:06:37,150 --> 00:06:41,330
+المثال، إن كان هناك مستوى عالي من التركيز على سبيل 
+
+94
+00:06:41,330 --> 00:06:43,970
+المثال، أو أحيانًا ربما الوظيفة ليست مناسبة، على
+
+95
+00:06:43,970 --> 00:06:47,490
+سبيل المثال، هنا هناك الكثير من الأسباب، عندما تتكلم 
+
+96
+00:06:47,490 --> 00:06:48,150
+عن مجال التجارب اللي هو مجال التجارب،
+
+97
+00:06:48,150 --> 00:06:49,970
+مجال التجارب،
+
+98
+00:06:49,970 --> 00:06:51,690
+مجال التجارب،
+
+99
+00:06:51,690 --> 00:06:52,830
+مجال التجارب،
+
+100
+00:06:52,830 --> 00:06:54,090
+مجال التجارب،
+
+101
+00:06:54,090 --> 00:06:55,150
+مجال التجارب،
+
+102
+00:06:55,150 --> 00:06:58,460
+مجال التجارب، مجال التجارب، 
+
+103
+00:06:58,460 --> 00:07:03,900
+عادةً هم سيقررون أيضًا إذا كانوا 
+
+104
+00:07:03,900 --> 00:07:07,380
+satisfied أو لا، بالإضافة إلى ذلك، كما ذكرت أيضًا،
+
+105
+00:07:07,380 --> 00:07:11,660
+هناك الكثير من الحالات والحالات الأخرى التي يجب
+
+106
+00:07:11,660 --> 00:07:16,660
+أن تكون اعتمادها، نحن نتحدث عن مجموعة هنا، التطبيق 
+
+107
+00:07:16,660 --> 00:07:19,720
+ليس واحد حالة أو واجهة الحالة، إنه مجموعة من
+
+108
+00:07:19,720 --> 00:07:24,200
+الكثير من الحالات، ربما بعض من هذه الحالات مهمة 
+
+109
+00:07:24,200 --> 00:07:27,700
+أكثر، ولكن مرة أخرى نحن نتكلم هنا عن علاقات مرتبطة
+
+110
+00:07:27,700 --> 00:07:31,080
+نحن لسنا نتكلم عن واحد محدد، وهناك أشياء أخرى ليست 
+
+111
+00:07:31,080 --> 00:07:32,340
+مهمة، لا، كل هذه الأشياء مرتبطة ستكون affect the
+
+112
+00:07:32,340 --> 00:07:32,360
+satisfaction 
+
+113
+00:07:32,360 --> 00:07:34,640
+level of employees 
+
+114
+00:07:34,640 --> 00:07:35,220
+whether they are 
+
+115
+00:07:35,220 --> 00:07:35,840
+satisfied or not، 
+
+116
+00:07:35,840 --> 00:07:38,120
+yes؟ 
+
+117
+00:07:38,120 --> 00:07:44,680
+But also at some point the 
+
+118
+00:07:44,680 --> 00:07:50,720
+employee gets fully satisfied about his payment,
+
+119
+00:07:50,720 --> 00:07:56,100
+his or her payment or promotion، I mean any 
+
+120
+00:07:56,100 --> 00:08:00,380
+further payment، any extra payments he will 
+
+121
+00:08:00,380 --> 00:08:04,660
+receive، it's not going to affect his satisfaction
+
+122
+00:08:04,660 --> 00:08:09,200
+أو إنّها لن تضيف شيء جديد للعملاء، لذا حتى عندما 
+
+123
+00:08:09,200 --> 00:08:14,240
+نتكلم عن الاستمتاع بشأن تلك المواقع، المواقع الجيدة
+
+124
+00:08:14,240 --> 00:08:19,490
+التي ستسبب في استمتاع، هي ستسبب في استمتاع حتى نقطة 
+
+125
+00:08:19,490 --> 00:08:22,890
+معينة، ولكن ربما خارج هذه النقطة، هي لن تكون نفسية
+
+126
+00:08:22,890 --> 00:08:27,450
+كما كانت في beginning، and here also we need to 
+
+127
+00:08:27,450 --> 00:08:34,270
+differentiate between the financial package which 
+
+128
+00:08:34,270 --> 00:08:36,810
+might motivate employees but not necessarily 
+
+141
+00:09:22,020 --> 00:09:26,380
+satisfy employees يعني maybe due to the financial
+
+142
+00:09:26,380 --> 00:09:28,640
+package offered by the organization maybe the
+
+143
+00:09:28,640 --> 00:09:31,300
+employees are going to be motivated to exert
+
+144
+00:09:31,300 --> 00:09:34,680
+maximum effort but not necessarily that they are
+
+145
+00:09:34,680 --> 00:09:37,200
+satisfied. Of course, in some cases they might be, in
+
+146
+00:09:37,200 --> 00:09:40,160
+other cases they might not be. That's why I said
+
+147
+00:09:40,160 --> 00:09:43,100
+that we need to differentiate here between the
+
+148
+00:09:43,100 --> 00:09:45,860
+role of the compensation package offered by the
+
+149
+00:09:45,860 --> 00:09:49,200
+organization in motivating employees and the role
+
+150
+00:09:49,200 --> 00:09:55,500
+of this package in satisfying the employees. الأهم
+
+151
+00:09:55,500 --> 00:10:01,740
+مشكلة هنا بالطبع هي إذا كان هناك نوع من الغضب وفي
+
+152
+00:10:01,740 --> 00:10:04,540
+حين أن نتكلم عن هذا الموضوع أولا يجب أن نعرف ماذا
+
+153
+00:10:04,540 --> 00:10:08,220
+يسبب في الانزعاج. بالطبع أحد أهم المشاكل التي قد
+
+154
+00:10:08,220 --> 00:10:13,660
+تحدثنا عنها قبل قليل هي تأثير الدفع ومشاركة العمل
+
+155
+00:10:13,660 --> 00:10:19,480
+فقط إلى نقطة. وهذه هي النقطة التي قد تحدثنا عنها 
+
+156
+00:10:19,480 --> 00:10:24,810
+مرة أخرى. مشكلة هنا مرتبطة بالشخصية. Okay, now when
+
+157
+00:10:24,810 --> 00:10:29,630
+you talk about people, as an example, there are some
+
+158
+00:10:29,630 --> 00:10:33,210
+positive traits in the personality, and some people
+
+159
+00:10:33,210 --> 00:10:36,050
+they are negative by nature, okay? And in this
+
+160
+00:10:36,050 --> 00:10:39,210
+regard, we say that there are people who have
+
+161
+00:10:39,210 --> 00:10:43,050
+positive core self-evaluation, and others who have
+
+162
+00:10:43,050 --> 00:10:46,350
+negative core self-evaluation, okay? هؤلاء الناس
+
+163
+00:10:46,350 --> 00:10:48,670
+الذين لديهم تجارب اجتماعية 
+
+164
+00:10:48,670 --> 00:10:50,170
+ 
+165
+00:10:50,170 --> 00:10:50,730
+ 
+166
+00:10:50,730 --> 00:10:54,150
+ 
+167
+00:10:54,150 --> 00:10:54,670
+ 
+168
+00:10:54,670 --> 00:10:54,850
+ 
+169
+00:10:54,850 --> 00:11:01,350
+ 
+170
+00:11:01,350 --> 00:11:15,310
+ 
+171
+00:11:15,710 --> 00:11:21,550
+هي لديها الكثير من أحداث شخصية خاطئة، خاصة عندما ي
+
+172
+00:11:21,550 --> 00:11:26,470
+... أو كيف يشعرون بأنفسهم. لهذا السبب قلنا أن هناك
+
+173
+00:11:26,470 --> 00:11:31,130
+أشخاص مع تقدير أساسي نفسي، وهناك أشخاص مع تقدير
+
+174
+00:11:31,130 --> 00:11:36,730
+أساسي نفسي خاطئ. والناس مع تقدير أساسي نفسي هم
+
+175
+00:11:36,730 --> 00:11:40,190
+أكثر  ممكن أن يكونوا مستمتعين بشكل كبير. على الجانب 
+
+176
+00:11:40,190 --> 00:11:43,590
+الآخر، الناس مع الشخص اللي بيعمل نقاط أساسية، نقاط
+
+177
+00:11:43,590 --> 00:11:48,930
+أساسية، هو أكثر ... أكثر  ممكن أنهم سيكونوا غاضبين.
+
+178
+00:11:48,930 --> 00:11:51,990
+لماذا؟ لماذا الناس اللي بيعمل نقاط أساسية، نقاط
+
+179
+00:11:51,990 --> 00:11:58,210
+أساسية، عادةً، إنجازاتهم أقل من أولئك اللي بيعمل
+
+180
+00:11:58,210 --> 00:12:06,480
+نقاط أساسية، نقاط أساسية؟ أعتقد أن السبب فيهم ... هم
+
+181
+00:12:06,480 --> 00:12:09,640
+لا يرغبون أن يفعلوا ذلك، لذلك كل ما يفعلونه لن
+
+182
+00:12:09,640 --> 00:12:12,640
+يكونوا ممتعين لأنهم لا يثقون بأنفسهم، و لا يعرفون
+
+183
+00:12:12,640 --> 00:12:17,420
+أنهم لن ينجحوا في هذا العالم، لذلك عملهم تقريبًا
+
+184
+00:12:17,420 --> 00:12:23,680
+كانت غير ... وعادةً يشعرون بأنفسهم ضعفاء بطريقة ما
+
+185
+00:12:23,680 --> 00:12:24,800
+و بطريقة ما و بطريقة ما و بطريقة ما و بطريقة ما و
+
+186
+00:12:24,800 --> 00:12:27,140
+بطريقة ما و بطريقة ما و بطريقة ما و بطريقة ما و
+
+187
+00:12:27,140 --> 00:12:33,530
+بطريقة ما. ماذا يمكن نضيف إلى هذا الموضوع؟ نعم، لأنهم
+
+188
+00:12:33,530 --> 00:12:38,390
+دائمًا يتوقعون المزيد من المزيد من المزيد من المزيد
+
+189
+00:12:38,390 --> 00:12:39,870
+من المزيد من المزيد من المزيد من المزيد من المزيد
+
+190
+00:12:39,870 --> 00:12:41,690
+من المزيد من المزيد من المزيد من المزيد من المزيد
+
+191
+00:12:41,690 --> 00:12:45,510
+من المزيد من المزيد من المزيد من المزيد من المزيد
+
+192
+00:12:45,510 --> 00:12:46,950
+من المزيد من المزيد من المزيد من المزيد من المزيد
+
+193
+00:12:46,950 --> 00:12:46,970
+ 
+194
+00:12:46,970 --> 00:12:47,330
+ 
+195
+00:12:47,330 --> 00:12:48,550
+ 
+196
+00:12:48,550 --> 00:12:53,370
+ 
+197
+00:12:53,370 --> 00:12:55,990
+من
+
+198
+00:12:56,690 --> 00:13:06,610
+هذه المقالات تأثر على تجارب  
+
+199
+00:13:12,430 --> 00:13:15,550
+أولًا، قبل ذلك قررنا ما هي العلاقة الحقيقية ما بين
+
+200
+00:13:15,550 --> 00:13:22,590
+الاستمتاع والإنجاز، حسنًا؟ الوضع التقليدي لهذا الموضوع،
+
+201
+00:13:22,590 --> 00:13:27,010
+عادة الناس، أعوام من السنين، أنا أتكلم عن المحققين
+
+202
+00:13:27,010 --> 00:13:31,070
+وما إلى ذلك، يعتبرون أن الاستمتاع يؤدي إلى
+
+203
+00:13:31,070 --> 00:13:37,490
+الإنجاز، حسنًا؟ الوضع التقليدي related to the field
+
+204
+00:13:37,490 --> 00:13:40,450
+that we are studying suggesting that performance
+
+205
+00:13:40,450 --> 00:13:44,970
+leads to satisfaction. So, usually those people who
+
+206
+00:13:44,970 --> 00:13:47,890
+believe in themselves, who believe that they have
+
+207
+00:13:47,890 --> 00:13:51,070
+the competences, who believe they have an
+
+208
+00:13:51,070 --> 00:13:53,730
+opportunity to improve their situation and so on,
+
+209
+00:13:53,730 --> 00:13:57,690
+usually such people they are going to يجب أن تقوموا
+
+210
+00:13:57,690 --> 00:14:02,910
+بعمل أفعال أكثر لتحسين تجاربهم. إذا كنا نتحدث عن
+
+211
+00:14:02,910 --> 00:14:07,510
+أسلوب صوتي في المؤسسة، في أي مؤسسة عملية، فالناس
+
+212
+00:14:07,510 --> 00:14:09,810
+اللي يقوموا بعمل أفعال جيدًا، يجب أن يكونوا
+
+213
+00:14:09,810 --> 00:14:11,870
+محفوظين، يجب أن يكونوا محفوظين، يجب أن يكونوا
+
+214
+00:14:11,870 --> 00:14:13,330
+محفوظين.
+
+215
+00:14:17,040 --> 00:14:22,460
+باعتبار لأجهزتهم من أجل المؤسسة، وهذا يعتمد عادة
+
+216
+00:14:22,460 --> 00:14:26,960
+على التحسين المستمرة. وعندما تتكلم عن أشخاص
+
+217
+00:14:26,960 --> 00:14:33,220
+يشعرون بأنفسهم بطريقة نقية أو تقدير نفسهم كما
+
+218
+00:14:33,220 --> 00:14:38,460
+ذكرنا، عادةً أشخاص كذلك ليسوا قادرين على يقوموا
+
+219
+00:14:38,460 --> 00:14:39,640
+بعملية تحسين 
+
+220
+00:14:39,640 --> 00:14:45,540
+ 
+221
+00:14:45,540 --> 00:14:48,640
+ 
+222
+00:14:48,640 --> 00:14:54,260
+ 
+223
+00:14:54,260 --> 00:14:54,600
+ 
+224
+00:14:54,600 --> 00:14:57,920
+ 
+225
+00:14:57,920 --> 00:15:03,760
+وهو نفسه غير صحيح بالطبع، فهنا مرة أخرى،
+
+226
+00:15:03,760 --> 00:15:08,700
+يجب أن ننظر إلى موضوع الانزعاج والانزعاج والذي
+
+227
+00:15:08,700 --> 00:15:13,300
+سيسبب في ماذا؟ مرة أخرى، المصادر التقليدية
+
+228
+00:15:13,300 --> 00:15:18,090
+المرتبطة بهذه النقطة عادةً كانت الوصولة الرئيسية
+
+229
+00:15:18,090 --> 00:15:23,630
+كانت أن الانطلاق يدفع إلى الواجهة، التي ليست صحيحة
+
+230
+00:15:23,630 --> 00:15:28,150
+مرة أخرى. التجارب التقليدية تتضمن أن الواجهة يجب أن
+
+231
+00:15:28,150 --> 00:15:33,510
+تدفع إلى الانطلاق. ولكن لكي تدفع الواجهة إلى الانطلاق
+
+232
+00:15:33,510 --> 00:15:38,310
+مرة أخرى يجب أن نتحدث عن مؤسسة عملية. وهناك نظامات
+
+233
+00:15:38,310 --> 00:15:45,190
+وقوانين ومشروعات جيدة ومشروعات
+
+234
+00:15:45,190 --> 00:15:47,350
+ 
+235
+00:15:47,350 --> 00:15:53,810
+ 
+236
+00:15:53,810 --> 00:15:54,890
+ 
+237
+00:15:54,890 --> 00:15:54,910
+ 
+238
+00:15:54,910 --> 00:15:54,930
+ 
+239
+00:15:54,930 --> 00:15:55,750
+ 
+240
+00:15:55,750 --> 00:16:05,370
+ 
+241
+00:16:05,480 --> 00:16:09,120
+وهم أقل ما يعجبون أنفسهم، وهكذا، لهذا السبب تفكير
+
+242
+00:16:09,120 --> 00:16:14,180
+الناس عادةً عن أنفسهم أقل. لهذا السبب مرة أخرى هم
+
+243
+00:16:14,180 --> 00:16:18,320
+في أغلب الحالات غير مستمتعين، حسنًا؟ مرة أخرى هنا
+
+244
+00:16:18,320 --> 00:16:21,640
+لسنا نتحدث عن واحد factor فقط، لسنا نتحدث عن أفعال
+
+245
+00:16:21,640 --> 00:16:25,340
+مختلفة، لسنا نتحدث عن مشاكل مرتبطة بالدفع والمقاومة،
+
+246
+00:16:25,340 --> 00:16:30,320
+لسنا نتكلم عن مشاكل مرتبطة بالشخصية، ولا يجب أن نفتقر
+
+247
+00:16:30,320 --> 00:16:33,280
+المشاكل التي قبل أن نتكلم عنها. عندما نتكلم عن
+
+248
+00:16:33,280 --> 00:16:37,820
+الانطلاق، فالأسباب ليست محدودة فقط لـ compensation، و
+
+249
+00:16:37,820 --> 00:16:43,040
+ليس فقط أيضًا للشخصية، هناك أشياء أخرى، لكن هنا فقط
+
+250
+00:16:43,040 --> 00:16:48,680
+لنتكلم عن الاثنين هنا، شيء مرتبط بالـ organization
+
+251
+00:16:48,680 --> 00:16:54,930
+وشيء مرتبط بالشخصيات في المؤسسة، ولكن أيضًا هناك
+
+252
+00:16:54,930 --> 00:16:58,970
+أشكال أخرى، بعضها مرتبطة بالمؤسسة، وربما أشكال
+
+253
+00:16:58,970 --> 00:17:02,890
+أخرى مرتبطة بالإنسان، وربما هناك أشكال أخرى أكثر
+
+254
+00:17:02,890 --> 00:17:08,010
+من حدد المؤسسة، بعض الأشكال الاجتماعية والأشكال،
+
+255
+00:17:08,010 --> 00:17:10,990
+وهناك الكثير من الأشكال التي يمكن أن تلعب دورًا في
+
+256
+00:17:10,990 --> 00:17:13,850
+تسبب الاتفاق والمتفاجأة
+
+257
+00:17:26,430 --> 00:17:32,370
+ولكن لا يوجد شيء مثل full satisfaction. يعني هذا
+
+258
+00:17:32,370 --> 00:17:40,230
+ليس مثل شيء نأكله ونشعر أن قلبنا مليء. حتى عندما
+
+259
+00:17:40,230 --> 00:17:44,370
+نأكل يعني بعد وقت ما سنشعر أننا غاضبين مرة أخرى.
+
+260
+00:17:44,370 --> 00:17:48,680
+نستطيع أن نتخيل الاتفاق بالطريقة اللي هينصل إلى
+
+261
+00:17:48,680 --> 00:17:52,500
+مستوى محدد للاستمتاع، ولكن مرة أخرى، احتياجاتنا
+
+262
+00:17:52,500 --> 00:17:59,480
+دائمًا تتطور، تتغير، تزداد وما إلى ذلك، لذلك لا
+
+263
+00:17:59,480 --> 00:18:05,150
+يوجد شيء مثل استمتاع مليء up to a point ... to a
+
+264
+00:18:05,150 --> 00:18:07,390
+point you are going to feel that we are satisfied
+
+265
+00:18:07,390 --> 00:18:12,070
+but next day after some time we are going to find
+
+266
+00:18:12,070 --> 00:18:14,650
+that there are other needs that we need to satisfy
+
+267
+00:18:14,650 --> 00:18:18,150
+so it is an ongoing process. It is not going to reach
+
+268
+00:18:18,150 --> 00:18:21,970
+a certain limit. What is the importance of studying
+
+269
+00:18:21,970 --> 00:18:26,790
+satisfaction? بسبب عملاء غير مستمتعين، سنتحدث عن ما
+
+270
+00:18:26,790 --> 00:18:30,150
+هي ... ما هي ... ما هي ... ما هي ... ما هي ... ما هي ...
+
+271
+00:18:30,150 --> 00:18:30,550
+ما هي ... ما هي ... ما هي ... ما هي ... ما هي ... ما هي
+
+272
+00:18:30,550 --> 00:18:31,110
+... ما هي ... ما هي ... ما هي ... ما هي ... ما هي ... ما
+
+273
+00:18:31,110 --> 00:18:31,530
+ما هي ... ما هي ... ما هي ... ما هي ... ما هي ... ما هي
+
+274
+00:18:31,530 --> 00:18:34,630
+... ما هي ... ما هي ... ما هي ... ما هي ... ما هي ... ما
+
+275
+00:18:34,630 --> 00:18:34,650
+هي ... ما هي ... ما هي ... ما هي ... ما هي ... ما هي ...
+
+276
+00:18:34,650 --> 00:18:34,830
+... ما هي ... ما هي ... ما هي ... ما هي ... ما هي ... ما
+
+277
+00:18:34,830 --> 00:18:36,370
+ما هي ... ما هي ... ما هي ... ما هي ... ما هي ... ما هي
+
+278
+00:18:36,370 --> 00:18:47,630
+... ما هي ... ما هي ... ما هي ... ما هي ... ما هي ... ما
+
+279
+00:18:50,990 --> 00:18:55,930
+نحن نتكلم عن الإبداع الإنساني في مؤسسات  هي
+
+280
+00:18:55,930 --> 00:19:00,410
+لا شيء بدون مصادر الإنسان. حسنًا، لذلك كيف يتعامل 
+
+281
+00:19:00,410 --> 00:19:05,370
+الناس هو واحد من الأشياء المهمة التي مرتبطة
+
+282
+00:19:05,370 --> 00:19:09,590
+بالمؤسسات ومصادر الإنسان حسنًا، لذلك عندما نتكلم
+
+283
+00:19:09,590 --> 00:19:14,870
+عن المال، باستخدام كم مصادر، مصادر أخرى لديها
+
+284
+00:19:14,870 --> 00:19:19,450
+المؤسسة كيف يتعامل الناس، كيف يتعاملون وما هي
+
+285
+00:19:19,450 --> 00:19:25,410
+ممارساتهم وما إلى ذلك هو أهم قيمة هنا إلى مدى ما
+
+286
+00:19:25,410 --> 00:19:29,190
+سيكون هناك استخدام للوصول إلى مصادر أخرى إذا كان
+
+287
+00:19:29,190 --> 00:19:34,390
+لدينا مصادر إنسانية جيدة فسنستخدم المصادر الأخرى
+
+288
+00:19:34,390 --> 00:19:38,430
+إذا كانت المصادر الإنسانية في المؤسسة ضعيفة فسنخسر
+
+289
+00:19:38,430 --> 00:19:41,970
+المصادر الأخرى، حسنًا؟ لذلك، نحن نتحدث هنا عن
+
+290
+00:19:41,970 --> 00:19:45,910
+المنابع الأهم عندما نتحدث عن المصادر الإنسانية،
+
+291
+00:19:45,910 --> 00:19:51,980
+مرة أخرى عندما نتكلم عن امتلاك العمل وكيف يتجاوز
+
+292
+00:19:51,980 --> 00:19:56,100
+العميل لهذه الامتلاكة، هنا يوجد نموذج يجب أن نتكلم
+
+293
+00:19:56,100 --> 00:20:00,040
+عنه، وفقًا لهذا النموذج، هنا يوجد اتصالات مختلفة،
+
+294
+00:20:00,040 --> 00:20:06,260
+واحد منهم يتعلق بالنوع أو الطبيعة التجريبية، وإذا
+
+295
+00:20:06,260 --> 00:20:11,480
+كانت ستكون مصممة أو مغلقة، ويمكننا أن نقول كيف
+
+296
+00:20:11,480 --> 00:20:15,180
+ستتجاوز الناس، وإذا كانوا سيكونون مهتمين أو
+
+297
+00:20:15,180 --> 00:20:21,960
+غاضبين، هنا يوجد أربعة أنواع من الإجابات لـ
+
+298
+00:20:21,960 --> 00:20:25,020
+Dissatisfaction بالطبع هذا ليس عملية عامة مرة
+
+299
+00:20:25,020 --> 00:20:29,400
+أخرى، فهو فقط موديل يساعدنا في التحدث عن الفكرة،
+
+300
+00:20:29,400 --> 00:20:31,760
+حسنًا؟ واحدة من هذه الفكرة هي الـ Exit عندما نتحدث
+
+301
+00:20:31,760 --> 00:20:35,480
+عن الـ Exit، نحن نتحدث عن حركة مخيفة ومحركة عامة
+
+302
+00:20:35,480 --> 00:20:40,220
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+303
+00:20:40,220 --> 00:20:40,260
+عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+304
+00:20:40,260 --> 00:20:40,680
+عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+305
+00:20:40,680 --> 00:20:45,420
+عامة عامة عامة عامة عامة عامة
+
+306
+00:20:47,700 --> 00:20:52,840
+وهم سيغادرون المؤسسة، حسنًا؟ لذلك في حالات مثل
+
+307
+00:20:52,840 --> 00:20:56,740
+هذه، عادةً لأعمال مثل هذه يشعرون أنه لا يوجد أمل
+
+308
+00:20:56,740 --> 00:21:02,820
+لإنهاء استمتاعهم أو المشكلة التي تسبب في استمتاعهم
+
+309
+00:21:02,820 --> 00:21:07,990
+ومشاكلهم، لهذا السبب عاملون مثل هؤلاء في النهاية هم
+
+310
+00:21:07,990 --> 00:21:12,730
+يبحثون عن عمل آخر، يبحثون عن فرصة أخرى، هم هم هم
+
+311
+00:21:12,730 --> 00:21:14,290
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+312
+00:21:14,290 --> 00:21:14,890
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+313
+00:21:14,890 --> 00:21:15,650
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+314
+00:21:15,650 --> 00:21:17,450
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+315
+00:21:17,450 --> 00:21:18,750
+هم هم هم هم هم هم هم هم هم هم هم هم هم هم هم
+
+316
+00:21:18,750 --> 00:21:27,490
+هم هم هم هم هم هم هم هم هم
+
+317
+00:21:27,490 --> 00:21:36,750
+ه
+
+318
+00:21:37,470 --> 00:21:43,410
+الأشياء أو المشكلة التي تسبب فيها غضبهم يحاولون
+
+319
+00:21:43,410 --> 00:21:50,030
+أن يفعلوا شيئًا في المؤسسة لكي يتحركوا من منطقة غضب
+
+320
+00:21:50,030 --> 00:21:56,770
+أو منطقة نفسية إلى نفسية أخرى لديهم
+
+321
+00:21:56,770 --> 00:22:03,650
+إجابات مختلفة واحدة منها مبنية ونسميها وليالية وفي
+
+322
+00:22:03,650 --> 00:22:08,940
+الوليالية الناس مختلفون، لن يفعلوا أي شيء ولكنهم
+
+323
+00:22:08,940 --> 00:22:13,440
+ينتظرون التغيير، ولكنهم لن يشاركوا في التغيير، على
+
+324
+00:22:13,440 --> 00:22:17,560
+الأقل الـ Voice، أشخاص مثلها سيشاركوا في التغيير، في
+
+325
+00:22:17,560 --> 00:22:22,330
+الحقيقة هم مفيدون للشركات التي تستثمر في التغيير
+
+326
+00:22:22,330 --> 00:22:25,670
+هي تستثمر في التغيير وفي بعض الأحيان قد يقوموا
+
+327
+00:22:25,670 --> 00:22:29,550
+بالتغيير ويقوموا بعمل شيء ولكن الولائية هنا هي
+
+328
+00:22:29,550 --> 00:22:31,570
+الناس التي تستثمر في التغيير ويقوموا بالتغيير و
+
+329
+00:22:31,570 --> 00:22:34,750
+تعمل شيء ولكن الناس التي تستثمر في التغيير و
+
+330
+00:22:34,750 --> 00:22:45,320
+تقوموا بالتغيير وهنا نحن نتكلم عن نجلة وإذا
+
+331
+00:22:45,320 --> 00:22:50,960
+كان لديهم فرصة لإيقاف شيء نفسي نفسي نفسي نفسي نفسي
+
+332
+00:22:50,960 --> 00:22:52,520
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+333
+00:22:52,520 --> 00:22:54,140
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+334
+00:22:54,140 --> 00:22:54,840
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+335
+00:22:54,840 --> 00:22:54,960
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي 
+
+336
+00:23:07,870 --> 00:23:12,990
+هي مرتبطة بشكل كيف سيشارك الناس في الموضوع، وفقًا
+
+337
+00:23:12,990 --> 00:23:18,950
+لذلك، سنقرر إذا كانوا مستثمرين أو مستثمرين، وما هي
+
+338
+00:23:18,950 --> 00:23:23,690
+طبيعة تجاربهم، وإذا كانت مصطلحية أو غير مصطلحية،
+
+339
+00:23:23,690 --> 00:23:28,270
+حسنًا؟ ولكن هنا، لسنا نتحدث عن مصطلحات مرتبطة
+
+340
+00:23:28,270 --> 00:23:33,870
+بالتسلسل، هنا نسمح بالمصطلحات الآن إذا كان هناك
+
+341
+00:23:33,870 --> 00:23:40,450
+مستمتع أو لا مستمتع، نستطيع أن نشارك هذا في النقطة
+
+342
+00:23:40,450 --> 00:23:45,340
+التي سنتحدث عنها هنا على سبيل المثال، تجارب
+
+343
+00:23:45,340 --> 00:23:48,560
+الوظيفة، نحن قد تحدثنا عن هذا الموضوع عدة مرات
+
+344
+00:23:48,560 --> 00:23:51,880
+أعتقد أنه يجب أن يكون واضحًا كفاية لأنه لا يوجد
+
+345
+00:23:51,880 --> 00:23:57,780
+علاقة مباشرة أو أكثر بين الوظيفة والتجارب ولكن
+
+346
+00:23:57,780 --> 00:24:03,360
+هناك علاقة بين الوظيفة والتجارب والنسبة للوظيفة،
+
+347
+00:24:03,360 --> 00:24:07,400
+الوظيفة مرتبطة مع تجارب الوظيفة، أكثر من أن
+
+348
+00:24:07,400 --> 00:24:12,300
+الموظفين موظفين، أكثر من أن نستطيع هو نوع من مهارات
+
+349
+00:24:12,300 --> 00:24:20,620
+مؤسساتنا، لكنها ليست مرتبطة بالإدارة الشخصية،
+
+350
+00:24:20,620 --> 00:24:26,860
+لأن إدارة الشخصية مرتبطة بكثير من النقاط الأخرى،
+
+351
+00:24:26,860 --> 00:24:29,120
+مثل مهارة الشخصية، مهارات الشخصية، مهارات الشخصية
+
+352
+00:24:29,120 --> 00:24:33,570
+مرتبطة بكثير من النقاط الأخرى ولكن مرة أخرى، إنها
+
+353
+00:24:33,570 --> 00:24:37,270
+مرتبطة بـ Productivity وقد تحدثنا عن نقطة واحدة
+
+354
+00:24:37,270 --> 00:24:41,770
+قبل أن نقول أن الـ performance يجب أن يؤدي إلى
+
+355
+00:24:41,770 --> 00:24:46,590
+الاطلاع ولكن مرة أخرى، لكي يؤدي الوظيفة إلى
+
+356
+00:24:46,590 --> 00:24:51,710
+الاطلاع، اقترحنا أن يكون لدينا مؤسسة جيدة مؤسسة
+
+357
+00:24:51,710 --> 00:24:53,390
+جيدة مؤسسة جيدة مؤسسة جيدة مؤسسة جيدة مؤسسة جيدة
+
+358
+00:24:53,390 --> 00:24:55,730
+مؤسسة جيدة مؤسسة جيدة مؤسسة جيدة مؤسسة جيدة مؤسسة
+
+359
+00:24:55,730 --> 00:24:59,090
+جيدة مؤسسة جيدة مؤسسة جيدة مؤسسة جيدة مؤسسة جيدة
+
+360
+00:24:59,090 --> 00:25:04,360
+مؤسسة جيدة مؤسسة جيدة واتفاق أو اتفاق مقبل وما إلى
+
+361
+00:25:04,360 --> 00:25:08,840
+ذلك، يعني حتى لو كان الموظفين يتوافقون بشكل جيد ولم
+
+362
+00:25:08,840 --> 00:25:13,900
+يكن هناك إعجاب من الوظيفة، لن يكون هناك اتفاق أو
+
+363
+00:25:13,900 --> 00:25:21,000
+الموظفين لن يشعروا بأنهم اتفقوا، لذلك لكي يتوافقوا
+
+364
+00:25:21,000 --> 00:25:24,780
+بشكل جيد هنا يجب أن يكون لدينا مؤسسة مشروع عملي
+
+365
+00:25:24,780 --> 00:25:28,640
+جداً فيها القوانين والحكومات تدعم المشاركين عندما
+
+366
+00:25:28,640 --> 00:25:30,620
+يقوموا بشكل مناسب للقوانين والحكومات تدعم
+
+367
+00:25:30,620 --> 00:25:31,020
+والحكومات تدعم المشاركين عندما يقوموا بشكل مناسب
+
+368
+00:25:31,020 --> 00:25:31,740
+للقوانين والحكومات تدعم المشاركين عندما يقوموا
+
+369
+00:25:31,740 --> 00:25:32,260
+بشكل مناسب للقوانين والحكومات تدعم المشاركين عندما
+
+370
+00:25:32,260 --> 00:25:33,300
+يقوموا بشكل مناسب للقوانين والحكومات تدعم
+
+371
+00:25:33,300 --> 00:25:35,240
+المشاركين عندما يقوموا بشكل مناسب للقوانين
+
+372
+00:25:35,240 --> 00:25:36,640
+والحكومات تدعم المشاركين
+
+373
+00:25:38,370 --> 00:25:43,510
+Organizational Citizenship behavior دعوني أفسره بكلمة بسيطة، إنه كتاب
+
+374
+00:25:43,510 --> 00:25:47,830
+يتكلم عن أفضل شيء في مؤسسة دائمًا، في داخل المؤسسة
+
+375
+00:25:47,830 --> 00:25:50,930
+وفي الخارج من المؤسسة، نحن نتكلم عن الناس التي
+
+376
+00:25:50,930 --> 00:25:56,410
+مستمتعين بسبب أنهم مستمتعين، عادةً لا يتكلمون
+
+377
+00:25:56,410 --> 00:26:00,570
+بطريقة سلبية عن المؤسسة، يتكلمون بطريقة أفضل عن
+
+378
+00:26:00,570 --> 00:26:04,230
+المؤسسة، حتى عندما يريدون أن يتكلموا عن شيء،
+
+379
+00:26:04,230 --> 00:26:08,530
+يتكلمون عن شيء in a positive way not in a
+
+380
+00:26:08,530 --> 00:26:11,590
+destructive way no it should be in a constructive
+
+381
+00:26:11,590 --> 00:26:14,970
+way so in simple words Organizational Citizenship
+
+382
+00:26:14,970 --> 00:26:19,230
+it is related to how people reflect the image of
+
+383
+00:26:19,230 --> 00:26:22,490
+the organization okay in addition to other
+
+384
+00:26:22,490 --> 00:26:25,670
+attitudes okay for example let me give a very
+
+385
+00:26:25,670 --> 00:26:29,510
+simple example okay those people for example when
+
+386
+00:26:29,510 --> 00:26:32,230
+they go out of a room they switch off the lights
+
+387
+00:26:32,230 --> 00:26:36,790
+and so on this is سلوك مرتبط بشكل أو يمكننا أن
+
+388
+00:26:36,790 --> 00:26:40,870
+نسميها مرتبطة بشكل جيد مرتبطة بشكل جيد بشكل جيد
+
+389
+00:26:40,870 --> 00:26:42,730
+بشكل جيد بشكل جيد بشكل جيد بشكل جيد بشكل جيد بشكل
+
+390
+00:26:42,730 --> 00:26:43,930
+جيد بشكل جيد بشكل جيد بشكل جيد بشكل جيد بشكل جيد
+
+391
+00:26:43,930 --> 00:26:45,410
+بشكل جيد بشكل جيد بشكل جيد بشكل جيد بشكل جيد بشكل
+
+392
+00:26:45,410 --> 00:26:46,510
+جيد بشكل جيد بشكل جيد بشكل جيد بشكل جيد بشكل جيد
+
+393
+00:26:46,510 --> 00:26:47,550
+بشكل جيد بشكل جيد بشكل جيد بشكل جيد بشكل جيد بشكل
+
+394
+00:26:47,550 --> 00:26:52,210
+جيد بشكل جيد بشكل جيد بشكل جيد بشكل
+
+395
+00:26:52,210 --> 00:26:57,670
+جيد بشكل جيد بشكل جيد بشكل جيد بش
+
+396
+00:27:02,770 --> 00:27:06,350
+Okay, now this is one of the outcomes of job
+
+397
+00:27:06,350 --> 00:27:08,890
+satisfaction, people who are satisfied usually
+
+398
+00:27:08,890 --> 00:27:11,730
+they are more willing to talk in a positive manner
+
+399
+00:27:11,730 --> 00:27:14,830
+about the organization, the more there is
+
+400
+00:27:14,830 --> 00:27:17,110
+dissatisfaction, the more there is going to be
+
+401
+00:27:17,110 --> 00:27:22,370
+negative appreciation to the organization آخر نتيجة
+
+402
+00:27:22,370 --> 00:27:25,870
+لإنجاز العمل وبالطبع يجب أن تكون النتيجة نتيجة
+
+403
+00:27:25,870 --> 00:27:30,290
+الانتصاف، نحن نتحدث في نفس الوقت عن الانتصاف و
+
+404
+00:27:30,290 --> 00:27:35,630
+بالطبع انتصاف هذا هو انتصاف العميل، ما هي العلاقة
+
+405
+00:27:35,630 --> 00:27:43,620
+بين إرضاء العميل وإرضاء الموظف؟ إذا كانت الموظفين
+
+406
+00:27:43,620 --> 00:27:47,640
+مستمتعين وعملوا عملهم، فهذا سيظهر بشكل أفضل لإنجاز
+
+407
+00:27:47,640 --> 00:27:50,900
+المستخدم لأنهم سيساعدونهم بشكل أفضل، خاصة إذا كانت
+
+408
+00:27:50,900 --> 00:27:50,960
+الموظفين مستمتعين وعملوا عملهم، فهذا سيساعدهم بشكل
+
+409
+00:27:50,960 --> 00:27:53,800
+أفضل لإنجاز المستخدم إذا كانت الموظفين مستمتعين
+
+410
+00:27:53,800 --> 00:27:54,600
+وعملوا عملهم، فهذا سيساعدهم بشكل أفضل لإنجاز المستخدم
+
+411
+00:27:54,600 --> 00:27:57,660
+إذا كانت الموظفين مستمتعين وعملوا عملهم، فهذا سيساعدهم
+
+412
+00:27:57,660 --> 00:27:59,100
+بشكل أفضل لإنجاز المستخدم
+
+413
+00:28:04,900 --> 00:28:08,520
+أو مستخدمين وأفضل أن المستخدمين يتعاملوا مع مستخدمين
+
+414
+00:28:08,520 --> 00:28:13,120
+أكثر المستخدمين سيكونون مستمتعين بالطبع ليس فقط ..
+
+415
+00:28:13,120 --> 00:28:19,420
+ما قلته مهم جدًا كيف المستخدمين يتعاملون ويتعاملون
+
+416
+00:28:19,420 --> 00:28:24,000
+مع المستخدمين لكن مشكلة أخرى التي مرتبطة هنا هي كيف
+
+417
+00:28:24,000 --> 00:28:26,800
+المستخدمين أو إلى مدى ما المستخدمين المستخدمين المستخدمين
+
+418
+00:28:26,800 --> 00:28:28,560
+المستخدمين المستخدمين المستخدمين المستخدمين المستخدمين
+
+419
+00:28:28,560 --> 00:28:31,180
+المستخدمين المستخدمين المستخدمين المستخدمين بطريقة عامة و
+
+420
+00:28:31,180 --> 00:28:31,740
+بطريقة عامة و بطريقة عامة و بطريقة عامة و بطريقة 
+
+421
+00:28:31,740 --> 00:28:33,380
+عامة و بطريقة عامة و بطريقة عامة و بطريقة عامة و
+
+422
+00:28:33,380 --> 00:28:35,180
+بطريقة عامة و بطريقة عامة و بطريقة عامة و بطريقة 
+
+423
+00:28:35,180 --> 00:28:38,120
+عامة و بطريقة عامة و بطريقة عامة و بطريقة عامة و
+
+424
+00:28:38,120 --> 00:28:39,700
+بطريقة عامة و بطريقة عامة و بطريقة عامة و بطريقة
+
+425
+00:28:39,700 --> 00:28:40,020
+عامة و بطريقة عامة و بطريقة عامة و بطريقة عامة و
+
+426
+00:28:40,020 --> 00:28:45,160
+بطريقة عامة و بطريقة عامة و بطريقة عامة و بطريقة
+
+427
+00:28:45,160 --> 00:28:50,920
+عامة و بطريقة عامة و بطريقة 
+
+428
+00:28:50,920 --> 00:28:57,200
+عامة وسيرمز أو up to what extent they are going to
+
+429
+00:28:57,200 --> 00:29:04,660
+work as .. to work in a professional way or use 
+
+430
+00:29:04,660 --> 00:29:06,940
+professional methods and so on.. so we are
+
+431
+00:29:06,940 --> 00:29:10,300
+talking here again how employees are going to
+
+432
+00:29:10,300 --> 00:29:15,120
+interact in all dimensions with  أكثر الموظفين
+
+433
+00:29:15,120 --> 00:29:18,940
+يكونوا مبتسعين، أكثر الموظفين يتعاملون بشكل أفضل
+
+434
+00:29:18,940 --> 00:29:25,980
+مع مستخدمين آخر نتيجة هنا هي Absentism عندما نتكلم
+
+435
+00:29:25,980 --> 00:29:30,340
+.. و هذا واحد من النقاط اللي نتكلم عنه كثير من
+
+436
+00:29:30,340 --> 00:29:35,360
+الوقت، نقول أن عادة مستخدمين غاضبين يكونوا أكثر 
+
+437
+00:29:35,360 --> 00:29:37,040
+مستخدمين يكونوا مستخدمين يكونوا مستخدمين يكونوا
+
+438
+00:29:37,040 --> 00:29:38,060
+مستخدمين مستخدمين مستخدمين مستخدمين مستخدمين
+
+439
+00:29:38,060 --> 00:29:38,360
+مستخدمين مستخدمين مستخدمين مستخدمين مستخدمين
+
+440
+00:29:38,360 --> 00:29:40,620
+مستخدمين مستخدمين مستخدمين مستخدمين مستخدمين
+
+441
+00:29:40,620 --> 00:29:40,760
+مستخدمين مستخدمين مستخدمين مستخدمين مستخدمين
+
+442
+00:29:40,760 --> 00:29:47,320
+مستخدمين مستخدمين مستخدمين
+
+443
+00:29:47,320 --> 00:29:52,900
+مستخدمين مستخدمين مستخدمين مستخدمين مستخدمين
+
+444
+00:29:52,900 --> 00:29:56,700
+مستخدمين مستI do not like to show at work. This is 
+
+445
+00:29:56,700 --> 00:29:57,660
+absenteeism.
+
+446
+00:30:01,620 --> 00:30:04,500
+Why؟ Because I think this is what it means don't
+
+447
+00:30:04,500 --> 00:30:11,620
+care enough to be attentive to every work day It
+
+448
+00:30:11,620 --> 00:30:14,200
+is the same question, why يعني؟
+
+449
+00:30:17,850 --> 00:30:25,890
+سؤال عن مهمات الوظيفة لتحرر من الرئيس أو الرئيس من
+
+450
+00:30:25,890 --> 00:30:33,630
+داخل المؤسسة أنهم ليسوا ممتازين من داخل المؤسسة؟
+
+451
+00:30:33,630 --> 00:30:36,810
+ربما أنهم ممتازين من أنهم ليسوا ممتازين من أنهم 
+
+452
+00:30:36,810 --> 00:30:37,850
+ليسوا ممتازين من أنهم ليسوا ممتازين من أنهم ليسوا
+
+453
+00:30:37,850 --> 00:30:37,970
+ممتازين من أنهم ليسوا ممتازين من أنهم ليسوا
+
+454
+00:30:37,970 --> 00:30:39,090
+ممتازين من أنهم ليسوا ممتازين من أنهم ليسوا
+
+455
+00:30:39,090 --> 00:30:39,170
+ممتازين من أنهم ليسوا ممتازين من أنهم ليسوا
+
+456
+00:30:39,170 --> 00:30:39,490
+ممتازين من أنهم ليسوا ممتازين من أنهم ليسوا
+
+457
+00:30:39,490 --> 00:30:42,670
+ممتازين من أنهم ليسوا ممتازين من أنهم ليسوا
+
+458
+00:30:42,670 --> 00:30:43,450
+ممتازين من أنهم لي
+
+459
+00:30:46,650 --> 00:30:50,950
+forget this how they are going to feel maybe okay 
+
+460
+00:30:50,950 --> 00:30:53,490
+so usually when they are at work maybe they are
+
+461
+00:30:53,490 --> 00:30:57,290
+more stressed due to dissatisfaction and so on so
+
+462
+00:30:57,290 --> 00:31:02,430
+sometimes it is like a relief وعندما يكون هناك 
+
+463
+00:31:02,430 --> 00:31:06,150
+مستوى أكثر من  الانتصاف، عادةً في حالات مثل هذه،
+
+464
+00:31:06,150 --> 00:31:09,850
+الموظفين سيفكرون في الخروج من المؤسسة، لذلك مرة
+
+465
+00:31:09,850 --> 00:31:13,470
+أخرى، الانتصاف هو أيضاً اعناق هنا للموظفين بأنهم 
+
+466
+00:31:13,470 --> 00:31:16,810
+غير مستمتعين، على الأقل، الانتصاف هو واحد من 
+
+467
+00:31:16,810 --> 00:31:21,330
+المشكلات، ربما بعض الناس مستمتعين، ولكنهم يجدون بتر
+
+468
+00:31:21,330 --> 00:31:26,990
+فرصة، ولكن هنا نتحدث عن افتتاح وانتصاف، عادةً
+
+469
+00:31:26,990 --> 00:31:31,330
+عندما نتحدث عن ابسنطيزم و Turnover يظهر العمل عادةً
+
+470
+00:31:31,330 --> 00:31:34,690
+أنه مرتبط بالانتصاف، هذا سيخلق
+
+471
+00:31:38,500 --> 00:31:42,040
+إذا كان هناك ضغط إضافي دعوني أقول هنا عامة
+
+472
+00:31:42,040 --> 00:31:46,660
+الموظفين يحاولون أن يتجاوز هذه السببات وإحدى
+
+473
+00:31:46,660 --> 00:31:49,840
+المنابع اللي يمكن استخدامها هنا ليست تظهر للعمل 
+
+474
+00:31:49,840 --> 00:31:54,800
+وفي حالة أعظم هم سيفكرون في تركة المؤسسة إذا كان
+
+475
+00:31:54,800 --> 00:32:01,190
+لديهم فرصة أخرى وما إلى ذلك آخر نتيجة هنا هي
+
+476
+00:32:01,190 --> 00:32:08,250
+تغييرات المجلد، قلنا أن هناك تغييرات في المجلد،
+
+477
+00:32:08,250 --> 00:32:12,130
+إنها تغييرات نقية، إنها مرتبطة بالتغييرات
+
+478
+00:32:12,130 --> 00:32:16,250
+والمقالات وما إلى ذلك، في حالات مثل هذه، عادةً
+
+479
+00:32:16,250 --> 00:32:19,050
+أكثر الموظفين يكونوا غاضبين، أكثر ما سيكون لدينا
+
+480
+00:32:19,050 --> 00:32:24,460
+تغييرات في المجلد، أكثر ما يكونوا وأكثر مستمرة، أكثر
+
+481
+00:32:24,460 --> 00:32:32,040
+مستمرة، أكثر مستمرة، أكثر مستمرة، أكثر مستمرة،
+
+482
+00:32:32,040 --> 00:32:35,240
+أكثر مستمرة، أكثر مستمرة، أكثر مستمرة، أكثر
+
+483
+00:32:35,240 --> 00:32:35,260
+مستمرة، أكثر مستمرة، أكثر مستمرة، أكثر مستمرة،
+
+484
+00:32:35,260 --> 00:32:35,280
+أكثر مستمرة، أكثر مستمرة، أكثر مستمرة، أكثر
+
+485
+00:32:35,280 --> 00:32:42,020
+مستمرة، أكثر مستمرة، أكثر مستمرة، أكثر مستمرة
+
+486
+00:32:43,000 --> 00:32:45,880
+Satisfaction is very important and maybe you have
+
+487
+00:32:45,880 --> 00:32:48,340
+asked why we need to study satisfaction and we
+
+488
+00:32:48,340 --> 00:32:51,840
+have answered this question but in real life
+
+489
+00:32:51,840 --> 00:32:56,780
+عادةً معظم المدراء يفشلون أن يتعاملون
+
+490
+00:32:56,780 --> 00:33:02,340
+بالإستمتاع أو أن يفهموا مستوى الإستمتاع للموظفين
+
+491
+00:33:02,340 --> 00:33:07,260
+أو حتى أحياناً لو أشعروا أن هناك نوع من المفاجأة،
+
+492
+00:33:07,260 --> 00:33:14,060
+يفشلون أن يشعروا بأسباب المفاجأة في المنطقة، 
+
+493
+00:33:14,060 --> 00:33:17,280
+لماذا؟ Why when you talk about practical
+
+494
+00:33:17,280 --> 00:33:21,020
+application here, not in all organizations, not
+
+495
+00:33:21,020 --> 00:33:25,160
+all managers succeed in dealing professionally,
+
+496
+00:33:25,480 --> 00:33:30,120
+positively with the satisfaction issue؟ Yes؟ I
+
+497
+00:33:30,120 --> 00:33:32,280
+think there are many reasons, maybe the most
+
+498
+00:33:32,280 --> 00:33:36,560
+important reason is maybe the aspects or the
+
+499
+00:33:36,560 --> 00:33:39,400
+content they used to measure this satisfaction is
+
+500
+00:33:39,400 --> 00:33:43,660
+wrong alreadyو أحيانًا ربما لا يعرفوا ما هي
+
+501
+00:33:43,660 --> 00:33:46,380
+الأدوات التي يستخدموها، و أحيانًا عندما يستخدموا
+
+502
+00:33:46,380 --> 00:33:48,720
+الأدوات، يستخدموا الأدوات الخاطئة أو أحيانًا
+
+503
+00:33:48,720 --> 00:33:51,640
+المشاركين التي يستخدموها قد تكون في بعض الحالات 
+
+504
+00:33:51,640 --> 00:33:56,560
+قيمية على سبيل المثال، يستخدمون أساسهم الخاصة، مثل
+
+505
+00:33:56,560 --> 00:34:03,090
+ما نرى في الحكومة اليوم، بعض المدراء يعتقدون أن
+
+506
+00:34:03,090 --> 00:34:07,130
+الناس تحبهم، لكن في الواقع لا يفعلون ذلك، فهم 
+
+507
+00:34:07,130 --> 00:34:14,070
+يشعرون بالوضع في .. يعني .. إنها فرصة جدًا، و نحن
+
+508
+00:34:14,070 --> 00:34:17,450
+نتكلم عن الرئيسية هنا و الهدف، حتى إذا كنا نتكلم
+
+509
+00:34:17,450 --> 00:34:20,330
+عن مستوى الدولي أو إذا كنا نتكلم عن المؤسسة 
+
+510
+00:34:27,530 --> 00:34:30,230
+أو مستوى مستوى مستوى مستوى مستوى مستوى مستوى مستوى
+
+511
+00:34:30,230 --> 00:34:33,470
+مستوى مستوى مستوى مستوى مستوى مستوى مستوى مستوى
+
+512
+00:34:33,470 --> 00:34:33,610
+مستوى مستوى مستوى مستوى مستوى مستوى مستوى مستوى
+
+513
+00:34:33,610 --> 00:34:33,630
+مستوى مستوى مستوى مستوى مستوى مستوى مستوى مستوى
+
+514
+00:34:33,630 --> 00:34:33,650
+مستوى مستوى مستوى مستوى مستوى مستوى مستوى مستوى
+
+515
+00:34:33,650 --> 00:34:39,430
+مستوى مستوى مستوى مستوى مستوى مستوى مستوى
+
+516
+00:34:39,430 --> 00:34:47,970
+مست
+
+517
+00:34:48,140 --> 00:34:52,760
+معرفة الإنتصار، أعني أن تنظر إلى رئيس يستخدم مؤسسة
+
+518
+00:34:52,760 --> 00:34:58,020
+مركزية ومؤسسة مختلفة وما يعني أنه لا يهتم 
+
+519
+00:34:58,020 --> 00:35:03,840
+بالإنتصار؟ حسناً، بعض المدراء ينقلون كل الفكرة، 
+
+520
+00:35:03,840 --> 00:35:10,200
+ولا يجدون أنها مهمة أو مهمة لتعرف إن موظفينهم
+
+521
+00:35:10,200 --> 00:35:15,080
+مستمتعين أو لا وهم فقط ينقلون الوضع ولا يهتمون
+
+522
+00:35:15,080 --> 00:35:17,080
+بالإنتصار، نعم 
+
+523
+00:35:20,180 --> 00:35:23,460
+العمال كانوا يتعاملون مع بعضهم البعض في مجالات
+
+524
+00:35:23,460 --> 00:35:27,640
+مختلفة، مثل العمال اللي كانوا يتعاملون مع 
+
+525
+00:35:27,640 --> 00:35:28,500
+العمال اللي كانوا يتعاملون مع العمال اللي 
+
+526
+00:35:28,500 --> 00:35:30,580
+كانوا يتعاملون مع العمال اللي كانوا يتعاملون مع 
+
+527
+00:35:30,580 --> 00:35:33,920
+العمال بعض الأحيان يكون هناك مفاوضة في النظام،
+
+528
+00:35:33,920 --> 00:35:39,720
+دعوني أقول ذلك، الأدوات التي تستخدمها، هناك اختلاف
+
+529
+00:35:39,720 --> 00:35:44,680
+كبير هنا بين مؤسسة ومؤسسة ومؤسسة ومؤسسة ومؤسسة
+
+530
+00:35:44,680 --> 00:35:44,740
+ومؤسسة ومؤسسة ومؤسسة ومؤسسة ومؤسسة ومؤسسة ومؤسسة
+
+531
+00:35:44,740 --> 00:35:46,360
+ومؤسسة ومؤسسة ومؤسسة ومؤسسة ومؤسسة ومؤسسة ومؤسسة
+
+532
+00:35:46,360 --> 00:35:52,480
+ومؤسسة ومؤسسة ومؤأشخاص أخرى من المؤسسات التي كانت
+
+533
+00:35:52,480 --> 00:35:57,060
+تنقل الموضوع، وليس فقط المدراء، وحتى أحيانًا
+
+534
+00:35:57,060 --> 00:36:01,100
+عندما .. إذا لم يكن هناك نظام صوت أو أي ميكانيزم
+
+535
+00:36:01,100 --> 00:36:07,840
+يستخدمه من المؤسسة، فهذا لن يحرر
+
+536
+00:36:07,840 --> 00:36:11,260
+المدير أن يتعامل مع الموضوع، ولكن إذا كانت واحدة
+
+537
+00:36:11,260 --> 00:36:17,590
+من العلمية من العمل داخل المؤسسة، ثم العاملين هنا
+
+538
+00:36:17,590 --> 00:36:21,430
+سيستخدمون الوقت، سيستخدمون الأدوات أو الميكانيزمات
+
+539
+00:36:21,430 --> 00:36:27,330
+التي تم إعطائها للمؤسسة، وهذا موضوع مهم، وليس
+
+540
+00:36:27,330 --> 00:36:30,990
+دائماً يمكننا أن نتخلص من الأنشطة التي تأخذها
+
+541
+00:36:30,990 --> 00:36:34,670
+الموظفين والعاملين، المنظمة يجب أن تدعم الموظفين
+
+542
+00:36:34,670 --> 00:36:39,150
+لتأخذ الأنشطة Okay this is important يعني if the
+
+543
+00:36:39,150 --> 00:36:42,170
+organization itself did not motivate employees or
+
+544
+00:36:42,170 --> 00:36:45,530
+managers to go through certain practices or to
+
+545
+00:36:45,530 --> 00:36:48,170
+consider certain practices the employees and the
+
+546
+00:36:48,170 --> 00:36:50,570
+managers not always they are going to take the
+
+547
+00:36:50,570 --> 00:36:53,090
+initiative so here we need support when we talk
+
+548
+00:36:53,090 --> 00:36:55,350
+about support the organization must provide the 
+
+549
+00:36:55,350 --> 00:36:58,450
+mechanisms the organization must provide the 
+
+550
+00:36:58,450 --> 00:37:04,160
+motivation mechanisms to help على الأقل المدراء
+
+551
+00:37:04,160 --> 00:37:07,880
+يأخذون الأنشطة ولكن مرة أخرى لا يمكننا أن نعتمد
+
+552
+00:37:07,880 --> 00:37:11,800
+فقط على أخذ الأنشطة، يجب أن يكون لدينا نظام 
+
+553
+00:37:11,800 --> 00:37:16,860
+نفسه، لذلك هناك اختلافات بين المؤسسات التي يعتبر
+
+554
+00:37:16,860 --> 00:37:21,300
+هذه المشكلة مشكلة مهمة ومشكلة المؤسسات التي لا
+
+555
+00:37:21,300 --> 00:37:24,940
+تعتبرها مشكلة مهمة، عادةً المجموعة الأولى من 
+
+556
+00:37:24,940 --> 00:37:30,100
+المؤسسات هي يعملون أكثر عملية إنشاء أسلوب أو نظام 
+
+557
+00:37:31,900 --> 00:37:37,380
+تعتمد على ميكانيزمات مثلها، تبحث عن إشارات مثلها، 
+
+558
+00:37:37,380 --> 00:37:42,560
+وفي حالة طبعاً لتجارب، تجارب بطريقة مناسبة جدًا 
+
+559
+00:37:42,560 --> 00:37:46,640
+لتلك الحالات، وهذا سيساعد المدراء ليتعاملوا أكثر مع
+
+560
+00:37:46,640 --> 00:37:49,280
+الحالة، ولكن مرة أخرى، إذا كنا نتحدث عن المدير، 
+
+561
+00:37:49,280 --> 00:37:52,160
+أحيانًا يتعلق بالنظام، وأحيانًا يتعلق بالنظام
+
+562
+00:37:52,160 --> 00:37:56,020
+بطريقة عقلية، وإن هناك تجارب كاملة في الحالة،
+
+563
+00:37:56,020 --> 00:38:01,750
+وأحيانًا لا يعرفوا المعرفة to deal with such 
+
+564
+00:38:01,750 --> 00:38:07,230
+situations, sometimes they use tools or mechanisms 
+
+565
+00:38:07,230 --> 00:38:09,690
+which are not well prepared or professionally 
+
+566
+00:38:09,690 --> 00:38:13,390
+prepared. Usually, in such cases the results are
+
+567
+00:38:13,390 --> 00:38:18,850
+going to be negative. Any questions?
+
+568
+00:38:18,850 --> 00:38:21,990
+okay يعطيكم العافية إن شاء الله المحاضرة الجاية
+
+569
+00:38:21,990 --> 00:38:24,190
+بنبدأ بال chapter أربعة 
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/sGYtwI1XK0E_postprocess.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/sGYtwI1XK0E_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..97e93a0494481448af0142d5b88d9eb9c167df39
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/sGYtwI1XK0E_postprocess.srt
@@ -0,0 +1,1512 @@
+1
+00:00:09,020 --> 00:00:12,640
+سنستمر اليوم بالتحدث عن قيم ومن ثم سنتحدث عن علاقة
+
+2
+00:00:12,640 --> 00:00:18,500
+بين قيم وشخصية هناك
+
+3
+00:00:18,500 --> 00:00:22,200
+بعض الأشياء التي يجب أن نتحدث عنها أو نتحدث عنها
+
+4
+00:00:22,200 --> 00:00:27,700
+وهي مرتبطة بالقيم واحدة منها هي علاقة بين قيم أو
+
+5
+00:00:27,700 --> 00:00:32,580
+يجب أن نختار بين قيم وقيم أسلوبية بالطبع هذا
+
+6
+00:00:32,580 --> 00:00:37,620
+استخدم في محاولة معينةوهو روكتش فاليو صحيفة في هذا
+
+7
+00:00:37,620 --> 00:00:43,480
+الصحيفة نستطيع أن نختار بين اتين قيمالأن عندما
+
+8
+00:00:43,480 --> 00:00:47,260
+نتكلم عن القيم التقليدية أكتر أننا نتكلم عن القيم
+
+9
+00:00:47,260 --> 00:00:51,200
+التقليدية أو القيم التي سوف تأثر عاملنا على طريق
+
+10
+00:00:51,200 --> 00:00:53,080
+طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ
+
+11
+00:00:53,080 --> 00:00:54,320
+طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ
+
+12
+00:00:54,320 --> 00:00:55,280
+طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ
+
+13
+00:00:55,280 --> 00:00:57,340
+طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ
+
+14
+00:00:57,340 --> 00:00:59,960
+طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ طوارئ
+
+15
+00:00:59,960 --> 00:01:09,360
+طوارئ طوارئ طوارئ
+
+16
+00:01:10,980 --> 00:01:16,700
+أولا نحن نتكلم عن موضوع واحد وهو الهيراركيا للقيم
+
+17
+00:01:16,700 --> 00:01:22,380
+ونقول أن هناك قيم مهمة أو مهمة عالية وهناك قيم
+
+18
+00:01:22,380 --> 00:01:27,860
+أخرى ليست مهمة لنابالطبع في ذلك الوقت قررنا إلى أي
+
+19
+00:01:27,860 --> 00:01:31,400
+مستوى نستطيع تغيير القيم ولكننا أيضا نحتاج لنشارك
+
+20
+00:01:31,400 --> 00:01:35,300
+الهيراريكيا للقيم للقيم التجارية ضد القيم التجارية
+
+21
+00:01:35,300 --> 00:01:44,600
+لأن هذه القيم التجارية أكثر مهمة لنا هذا لا يعني
+
+22
+00:01:44,600 --> 00:01:49,240
+أن القيم التجارية أقل مهمة لكن يعني أن القيم
+
+23
+00:01:49,240 --> 00:01:55,840
+التجارية أقل مهمةمهمة او اكتر مهمة لنا الان قبل
+
+24
+00:01:55,840 --> 00:01:58,280
+ذلك قبل قبل قبل قبل قبل قبل قبل قبل قبل قبل قبل
+
+25
+00:02:10,940 --> 00:02:14,340
+مزيد من الموضوع اللي يجب أن نتكلم عنه وهو أيضًا
+
+26
+00:02:14,340 --> 00:02:19,620
+مرتبط بالقيم هو القيم الجيلية القيم الجيلية هي
+
+27
+00:02:19,620 --> 00:02:24,000
+مدالة تتم تطبيقها في الولايات المتحدة بالنسبة لهذه
+
+28
+00:02:24,000 --> 00:02:27,560
+المدالة، إنهم يحاولون أن يختلفوا بين الهوايبير،
+
+29
+00:02:27,560 --> 00:02:32,440
+الهوايبير من الجيلين مختلفة وطبعًا، يتعلمون كيف
+
+30
+00:02:32,440 --> 00:02:35,460
+تتغير الهوايبير في الجيلين مختلفة
+
+31
+00:02:39,910 --> 00:02:45,010
+بالنسبة للمدالة القيم الجيلية، هناك أربع جيل
+
+32
+00:02:45,010 --> 00:02:49,410
+أساسيًا، مثلًا الـ Veterans، Boomers، Xers
+
+33
+00:02:49,410 --> 00:02:58,590
+وNexters هنا نحن نتحدث عن الجيل الأسوأ الذين كانوا
+
+34
+00:02:58,590 --> 00:03:04,550
+جزء من القوة العمل بين عام 1950 و1964، لا نتحدث
+
+35
+00:03:04,550 --> 00:03:09,560
+هنا عن الولادة، نتحدث عنعندما كانت هذه الجيلة
+
+36
+00:03:09,560 --> 00:03:13,560
+مرتبطة في القوة العملية أو عندما كانت جزء من القوة
+
+37
+00:03:13,560 --> 00:03:16,400
+العملية أكتر من الممكن أن هؤلاء الناس اليوم هم
+
+38
+00:03:16,400 --> 00:03:21,340
+أكتر من 65 سنة، حسنا؟ الآن، في ذلك الوقت، أهم
+
+39
+00:03:21,340 --> 00:03:26,740
+القيم في ذلك الوقت كانت مشاكل مثل العمل صعب، مشاكل
+
+40
+00:03:26,740 --> 00:03:31,020
+مثل .. هؤلاء الناس كانوا أكتر مخصصين وما إلى ذلك،
+
+41
+00:03:31,020 --> 00:03:38,470
+حسنا؟ لذلك، بين كل جيلةهناك تغييرات في القيم وهذا
+
+42
+00:03:38,470 --> 00:03:43,730
+مشكلة مهمة ويعني أن القيم ليسوا مستقلين وهو ما
+
+43
+00:03:43,730 --> 00:03:49,870
+نكتشفه قبلها ولكن يمكنك أن ترى هنا كم وقت يحتاجه
+
+44
+00:03:49,870 --> 00:03:54,170
+لتغيير القيم هنا عندما نتحدث عن عملية العمل
+
+45
+00:03:54,170 --> 00:04:00,090
+الأمريكيةوكان هناك عامات أو عامات كثيرة كانت
+
+46
+00:04:00,090 --> 00:04:04,230
+محتاجة لتغيير هذه القيم ومن الواضح أن هذه القيم تم
+
+47
+00:04:04,230 --> 00:04:08,570
+تغييرها بسبب العديد من الأسباب والأفكار. بعض من
+
+48
+00:04:08,570 --> 00:04:11,270
+هذه الأسباب مرتبطة بالثقافة نفسها، بعض من هذه
+
+49
+00:04:11,270 --> 00:04:16,470
+الأسباب مرتبطة بالبيئة نفسهاربما التكنولوجيا أيضًا
+
+50
+00:04:16,470 --> 00:04:21,430
+مرتبطة في تغيير هذه القيم بإضافة إلى أشياء أخرى لا
+
+51
+00:04:21,430 --> 00:04:28,010
+يمكننا أن نغلق هنا تجارب التعليم والتعلم وما إلى
+
+52
+00:04:28,010 --> 00:04:32,590
+ذلك وهو ما قلت قبلها هناك الكثير من الأشياء
+
+53
+00:04:32,590 --> 00:04:38,110
+التجاربية المرتبطة في هذا الموضوع هنا يمكننا أن
+
+54
+00:04:38,110 --> 00:04:45,100
+نرى أن بين تلك الجيلاتهنا عامة نحن نتكلم عن القيم
+
+55
+00:04:45,100 --> 00:04:50,140
+المناسبة ومن هذه القيم التي مرتبطة بالبيئة، لكن
+
+56
+00:04:50,140 --> 00:04:55,840
+نستطيع أن نرى هنا إلى أي نقطة تتغير هذه القيم، إذا
+
+57
+00:04:55,840 --> 00:05:01,160
+كنا نتكلم عن المهندسين هنا، فإن قيمة المؤسسة كانت
+
+58
+00:05:01,160 --> 00:05:07,140
+عالية جدًا، في جيل أخركان هناك مشكلة مرتبطة
+
+59
+00:05:07,140 --> 00:05:09,140
+بالعلاقة بالعلاقة بالعلاقة بالعلاقة بالعلاقة
+
+60
+00:05:09,140 --> 00:05:09,540
+بالعلاقة بالعلاقة بالعلاقة بالعلاقة بالعلاقة
+
+61
+00:05:09,540 --> 00:05:09,740
+بالعلاقة بالعلاقة بالعلاقة بالعلاقة بالعلاقة
+
+62
+00:05:09,740 --> 00:05:12,700
+بالعلاقة بالعلاقة بالعلاقة بالعلاقة بالعلاقة
+
+63
+00:05:12,700 --> 00:05:12,820
+بالعلاقة بالعلاقة بالعلاقة بالعلاقة بالعلاقة
+
+64
+00:05:12,820 --> 00:05:12,840
+بالعلاقة بالعلاقة بالعلاقة بالعلاقة بالعلاقة
+
+65
+00:05:12,840 --> 00:05:12,860
+بالعلاقة بالعلاقة بالعلاقة بالعلاقة بالعلاقة
+
+66
+00:05:12,860 --> 00:05:13,220
+بالعلاقة بالعلاقة بالعلاقة بالعلاقة بالعلاقة
+
+67
+00:05:13,220 --> 00:05:17,120
+بالعلاقة بالعلاقة بالعلاقة بالعلاقة بالعلاقة
+
+68
+00:05:17,120 --> 00:05:26,120
+بالعلاقة بالعلاقة بالعلاقة
+
+69
+00:05:26,120 --> 00:05:26,520
+بال
+
+70
+00:05:33,500 --> 00:05:38,840
+في هذه القيم و بالطبع هذا ممكن للقيم الأخرى أيضًا
+
+71
+00:05:38,840 --> 00:05:46,680
+لذلك هنا من جيل إلى جيل أخر كان هناك قيم التي قد
+
+72
+00:05:46,680 --> 00:05:52,560
+تغيرت من .. ربما أحيانًا القيم نفسها تم تغييرها و
+
+73
+00:05:52,560 --> 00:05:57,620
+أحيانًا ربما كان هناك قيم جديدة تغيير القيم الأخرى
+
+74
+00:05:57,620 --> 00:06:01,480
+أو القيم القديمة وهذا هو اثبات أن القيم يمكن أن
+
+75
+00:06:01,480 --> 00:06:06,960
+تتغيرولكن مرة أخرى، هذا يحتاج إلى وقت. القيم لا
+
+76
+00:06:06,960 --> 00:06:10,780
+يمكن تغييرها بسهولة. لهذا السبب نقول إنه أكثر صعب
+
+77
+00:06:10,780 --> 00:06:15,820
+تغيير القيم ومقارنةها إلى ديناميكا محددة لعبارة عن
+
+78
+00:06:15,820 --> 00:06:20,300
+التعامل. نعم؟ ما هي الاختلاف بين الـAI ومجتمعها؟
+
+79
+00:06:22,270 --> 00:06:24,550
+When you talk about loyalty to career and
+
+80
+00:06:24,550 --> 00:06:26,890
+especially when we talk about the modern or
+
+81
+00:06:26,890 --> 00:06:31,450
+contemporary perspective of career planning, years
+
+82
+00:06:31,450 --> 00:06:36,250
+ago, twenty or fifteen years ago, the career
+
+83
+00:06:36,250 --> 00:06:38,770
+planning process was mainly depending on the
+
+84
+00:06:38,770 --> 00:06:42,720
+organization itselfاليوم، بالطبع عندما نتكلم عن
+
+85
+00:06:42,720 --> 00:06:47,680
+المجال الخاص والأمريكا المتطورة وما إلى ذلك، نتكلم
+
+86
+00:06:47,680 --> 00:06:52,540
+أكتر عن طريقة المشاركة بين المؤسسة والموظفين، لذا
+
+87
+00:06:52,540 --> 00:06:57,940
+هناك حركة هنا ومكان للموظفين لتشاركوا في اختيار
+
+88
+00:06:57,940 --> 00:07:04,400
+طريقة عملهم، ولكن بالطبع باستخدام طريقة مخطوطة بين
+
+89
+00:07:04,400 --> 00:07:12,800
+المؤسسة والموظفينهذه اكتشافات على الوثبات على
+
+90
+00:07:12,800 --> 00:07:17,460
+نفسها بإضافة إلى الوثبات على العلاقات أو المؤسسات
+
+91
+00:07:17,460 --> 00:07:21,400
+لأن هنا نحن نتكلم عن أكتشافات أكتشافات على
+
+92
+00:07:21,400 --> 00:07:24,120
+الموظفين للموظفين للمشاركة في ميكانيزمات مختلفة
+
+93
+00:07:24,120 --> 00:07:28,440
+حتى مثل الوظيفة القرارية بإضافة إلى الاختيارات
+
+94
+00:07:28,440 --> 00:07:33,460
+والميكانيزمات المستخدمة من المؤسساتSo again there
+
+95
+00:07:33,460 --> 00:07:39,040
+are changes, this is a good example that values is
+
+96
+00:07:39,040 --> 00:07:42,400
+changeable but again we need to understand here
+
+97
+00:07:42,400 --> 00:07:48,200
+that it needs time in order to change values When
+
+98
+00:07:48,200 --> 00:07:52,400
+we talk about changing values, isn't it about
+
+99
+00:07:52,400 --> 00:07:58,290
+changing values individually?Okay now of course
+
+100
+00:07:58,290 --> 00:08:01,290
+later on maybe next lecture we are going to study
+
+101
+00:08:01,290 --> 00:08:04,110
+the global implications and we are going to study
+
+102
+00:08:04,110 --> 00:08:09,190
+whether personality is related to culture and
+
+103
+00:08:09,190 --> 00:08:11,630
+whether values is related to culture and how
+
+104
+00:08:11,630 --> 00:08:14,370
+culture is going to affect personality or how
+
+105
+00:08:14,370 --> 00:08:21,190
+culture is going to affectوطبعا هناك نوع من علاقة
+
+106
+00:08:21,190 --> 00:08:27,050
+هنا بين تغيير ايضا شخصية او قيم وليس فقط
+
+107
+00:08:27,050 --> 00:08:30,750
+الميكانيزم الوحيد هنا او الديناميكا انها مرتبطة
+
+108
+00:08:30,750 --> 00:08:37,630
+ايضا بشكل اخر نحن لا نستطيعما نتحدث عنه هو
+
+109
+00:08:37,630 --> 00:08:40,650
+العاملية والعاملية بشكل عام من أشخاص من الوضع
+
+110
+00:08:40,650 --> 00:08:46,130
+البيئي والعاملية
+
+111
+00:08:46,130 --> 00:08:51,630
+من أشخاص من الوضع البيئي والعاملية من أشخاص من
+
+112
+00:08:51,630 --> 00:08:53,470
+الوضع البيئي والعاملية من الوضع البيئي والعاملية
+
+113
+00:08:53,470 --> 00:08:53,850
+من الوضع البيئي والعاملية من الوضع البيئي
+
+114
+00:08:53,850 --> 00:08:54,530
+من الوضع البيئي والعاملية من الوضع البيئي
+
+115
+00:08:54,530 --> 00:08:57,300
+والعاملية من الوضوهي تأثير عالي وفي بعض الأحيان
+
+116
+00:08:57,300 --> 00:09:01,040
+نحن نتحدث عن أقل درجة وما إلى ذلك ولكن مرة أخرى،
+
+117
+00:09:01,040 --> 00:09:05,920
+ليس فقط مرتبط بشخصيات، بل نحن نتحدث عن ديناميكا
+
+118
+00:09:05,920 --> 00:09:08,280
+واحدة ولكننا لا نستطيع أن نفرق أيضًا تلك
+
+119
+00:09:08,280 --> 00:09:11,020
+الديناميكا واحدة من أشخاص أخرين من مصادر البيئة،
+
+120
+00:09:11,020 --> 00:09:15,840
+دائمًا هناك نوع من التواصل، إلى مدى مدرجة تتواصل
+
+121
+00:09:15,840 --> 00:09:20,780
+هذه التواصل مع ما نتحدث عنه، هناك اختلافات بالطبع
+
+122
+00:09:22,680 --> 00:09:28,820
+الان دعنا نتكلم عن الوصول لقصة شخصية شخصية وقيم
+
+123
+00:09:28,820 --> 00:09:33,560
+للعمل في مكان عمل بالطبع لكي نتكلم عن هذه الأشياء،
+
+124
+00:09:33,560 --> 00:09:36,940
+يجب أن نتكلم أولا عن ما يسمى كـ personality job
+
+125
+00:09:36,940 --> 00:09:40,130
+fit عندما نتكلم عن personality job fitOkay
+
+126
+00:09:40,130 --> 00:09:42,810
+personality job fit theory here we are talking
+
+127
+00:09:42,810 --> 00:09:46,630
+about up to what extent the personality of
+
+128
+00:09:46,630 --> 00:09:51,410
+individual is matching with the job itself of
+
+129
+00:09:51,410 --> 00:09:54,230
+course after few minutes we are going to discuss
+
+130
+00:09:54,230 --> 00:09:58,480
+the person organization thingوعندما نتكلم عن شخصية
+
+131
+00:09:58,480 --> 00:10:05,080
+ومؤسسة مناسبة، سنتكلم عن مدى مدى شخصية الشخصية
+
+132
+00:10:05,080 --> 00:10:09,580
+المناسبة للمؤسسة ومناسبة للمؤسسة ومناسبة للمؤسسة
+
+133
+00:10:09,580 --> 00:10:09,880
+ومناسبة للمؤسسة ومناسبة للمؤسسة ومناسبة للمؤسسة
+
+134
+00:10:09,880 --> 00:10:10,800
+ومناسبة للمؤسسة ومناسبة للمؤسسة ومناسبة للمؤسسة
+
+135
+00:10:10,800 --> 00:10:19,060
+ومناسبة للمؤسسة ومناسبة للمؤسسة ومناسبة للمؤسسة
+
+136
+00:10:19,060 --> 00:10:23,100
+ومناسبة للمؤسسة ومناسبة
+
+137
+00:10:25,080 --> 00:10:32,700
+التواصل هنا او التواصل بين الشخصية و العمل و
+
+138
+00:10:32,700 --> 00:10:38,860
+بالطبع بين الشخصية و الانجلاز اللي سنتحدث عنه
+
+139
+00:10:38,860 --> 00:10:48,600
+لاحقا نتوقع انه يكون هناك تأثير جيد أو نتوقع أن
+
+140
+00:10:48,600 --> 00:10:55,880
+نحصل على نتيجة جيدة تلك التأثيراتسيكون مرتبط بشيء
+
+141
+00:10:55,880 --> 00:11:01,320
+ما، يعني في أي مجال نتوقع النتائج هنا، إذا كان
+
+142
+00:11:01,320 --> 00:11:07,500
+هناك شخصية عالية مناسبة للعمل، نعم؟ ربما الوضع
+
+143
+00:11:07,500 --> 00:11:12,820
+المناسب للعمل ومن ثم الوضع المناسب للعمل، لأن إذا
+
+144
+00:11:12,820 --> 00:11:17,820
+كانت شخصيتي مناسبة لعمل أو عمل يعني أنني أستطيع
+
+145
+00:11:17,820 --> 00:11:22,340
+الحصول على أفضل في هذا العمل، فسأكون أكتر مناسبة
+
+146
+00:11:24,280 --> 00:11:28,000
+ولكننا قررنا قبل قليل أنه لايوجد علاقة مباشرة أو
+
+147
+00:11:28,000 --> 00:11:32,420
+محددة بين الواجهة والإبتسام ولكن بالتأكيد عندما
+
+148
+00:11:32,420 --> 00:11:37,180
+يكون الواجهة أعلى، فسيكون هناك تأثير افضل على
+
+149
+00:11:37,180 --> 00:11:39,600
+الوظيفة على سبيل المثال أو إذا كنا نتحدث عن
+
+150
+00:11:39,600 --> 00:11:43,710
+الواجهة والإبتسام فيو أحيانًا يمكن أن يؤثر على
+
+151
+00:11:43,710 --> 00:11:47,110
+التجارب، ولكن هنا نتحدث عن أنه لا يوجد علاقة أكتر،
+
+152
+00:11:47,110 --> 00:11:52,870
+لا علاقة أكتر بين التجارب، ولكن مرة أخرى، كلمة
+
+153
+00:11:52,870 --> 00:11:56,730
+المهمة هنا هي الاطلاع، وعندما نتحدث عن الاطلاع،
+
+154
+00:11:56,730 --> 00:12:00,850
+نتوقع هنا أشياء أضافية أخرى، مثلًا، حرارة
+
+155
+00:12:00,850 --> 00:12:06,130
+الانتقال، حرارة الانتقال وحرارة الانتقال وحرارة
+
+156
+00:12:06,130 --> 00:12:06,590
+الانتقال وحرارة الانتقال وحرارة الانتقال وحرارة
+
+157
+00:12:06,590 --> 00:12:09,350
+الانتقال وحرارة الانتقال وحرارة الانتقال وحرارة
+
+158
+00:12:09,350 --> 00:12:14,230
+الانتقاللكن ليس لأن التجارب تتحسن بسبب أن الموظفين
+
+159
+00:12:14,230 --> 00:12:18,110
+يعطون المزيد من الوقت للعمل لذلك ستزداد النتيجة
+
+160
+00:12:18,110 --> 00:12:22,690
+ولكن ليس بالطبع أننا نتحدث عن القوة على الرغم من
+
+161
+00:12:22,690 --> 00:12:27,250
+أنها تأثر على الموظفين غير مستمتعين يمكن أن يدمروا
+
+162
+00:12:27,250 --> 00:12:35,770
+أو يقوموا بشيء غير صحيح لأننا قلنا بأنه بسبب
+
+163
+00:12:35,770 --> 00:12:40,120
+المستمتعين يوجد أربع نوع من الحياة المتوقعةعلى هذا
+
+164
+00:12:40,120 --> 00:12:43,800
+الشعور، نقول إن الخروج وما إلى ذلك، لذلك أحيانًا
+
+165
+00:12:43,800 --> 00:12:48,600
+نتوقع أنهيار ناجحة بسبب هذا الشعور. الآن عندما
+
+166
+00:12:48,600 --> 00:12:52,980
+نتحدث عن شخصيتك المناسبة، هنا نتحدث عن مدى مدى
+
+167
+00:12:52,980 --> 00:13:00,090
+شخصية الشخص المناسبةالعمل نفسه، لكي نتكلم عن هذا،
+
+168
+00:13:00,090 --> 00:13:05,230
+و بالطبع كما ذكرنا، نقول أن هذا مرتبط بالإهتمام
+
+169
+00:13:05,230 --> 00:13:08,090
+والتحرك، هنا لكي نتكلم عن تقنية personality job
+
+170
+00:13:08,090 --> 00:13:11,870
+fit تقنية واحدة من أكتر نموذجات معروفة هي
+
+171
+00:13:11,870 --> 00:13:18,050
+الـHorace personality job fit test، تجارب كل هذه
+
+172
+00:13:18,050 --> 00:13:27,830
+الأسئلةوفقًا لإجابتها، الجسم سيكون اكتشف من خمس
+
+173
+00:13:27,830 --> 00:13:32,390
+مجموعات جسمية مختلفة. الان هنا نحن نتكلم عن تلك
+
+174
+00:13:32,390 --> 00:13:39,470
+الخمس مجموعات جسمية مختلفة. او او او او او او او
+
+175
+00:13:39,470 --> 00:13:39,930
+او او او او او او او او او او او او او او او او او
+
+176
+00:13:39,930 --> 00:13:40,130
+او او او او او او او او او او او او او او او او او
+
+177
+00:13:40,130 --> 00:13:42,890
+او او او او او او او او او او او او او او او او او
+
+178
+00:13:42,890 --> 00:13:53,160
+او او اوالان بالنسبة لهولندا مدالة الوظيفة الوظيفة
+
+179
+00:13:53,160 --> 00:13:55,100
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+180
+00:13:55,100 --> 00:13:58,900
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+181
+00:13:58,900 --> 00:14:00,700
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+182
+00:14:00,700 --> 00:14:01,360
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+183
+00:14:01,360 --> 00:14:01,580
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+184
+00:14:01,580 --> 00:14:03,000
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+185
+00:14:03,000 --> 00:14:07,020
+الوظيفة الوظيفة الوظيفة الوظيفةوهو مستعمل على
+
+186
+00:14:07,020 --> 00:14:12,340
+الانترنت ويمكنك إيجاده بسهولة وإذا قمت بإجابة هذه
+
+187
+00:14:12,340 --> 00:14:16,080
+المسألة أو الوصفة باعتبار الشخصية
+
+188
+00:14:19,070 --> 00:14:22,630
+والتعليقات المناسبة للعديد من العمل المناسب يتم
+
+189
+00:14:22,630 --> 00:14:28,230
+إعطائها من خلال موقع الإنترنت نفسه طبعا كل واحد
+
+190
+00:14:28,230 --> 00:14:31,830
+مننا لا يوجد شخصية واحدة عندما نتكلم عن نظرية
+
+191
+00:14:31,830 --> 00:14:32,370
+هولندا
+
+192
+00:14:35,890 --> 00:14:39,990
+personality type and we have other sub types يعني
+
+193
+00:14:39,990 --> 00:14:43,990
+usually answering the questionnaire there is going
+
+194
+00:14:43,990 --> 00:14:48,370
+to be some sort of ranking for those personality
+
+195
+00:14:48,370 --> 00:14:53,730
+types personality types that we have and according
+
+196
+00:14:53,730 --> 00:14:56,350
+to those some recommendations are going to be
+
+197
+00:14:56,350 --> 00:14:58,990
+given here what are the most likely jobs that you
+
+198
+00:14:58,990 --> 00:15:02,290
+are going to be comfortable with and those jobs of
+
+199
+00:15:02,290 --> 00:15:04,350
+course if you have a challenge
+
+200
+00:15:16,590 --> 00:15:22,850
+وهذا يتوقع أن يعطينا نتيجة افضل التي مرتبط بـ
+
+201
+00:15:22,850 --> 00:15:29,550
+productivity افعالية افعالية افعالية افعالية
+
+202
+00:15:29,550 --> 00:15:30,110
+افعالية
+
+203
+00:15:32,850 --> 00:15:37,830
+الان بالطبع عندما نتكلم عن مدالة هولندا، واحد من
+
+204
+00:15:37,830 --> 00:15:43,370
+الأشياء المفاجئة هنا هي المشكلة الاخرى، هنا فقط
+
+205
+00:15:43,370 --> 00:15:49,850
+نتكلم عن شخصية الشخصية وما هي العمل المناسب، لكن
+
+206
+00:15:49,850 --> 00:15:54,370
+بالطبع هناك أشياء أخرى يجب أن تكون اعتمادها، مثل
+
+207
+00:15:54,370 --> 00:15:54,910
+ماذا؟
+
+208
+00:15:58,150 --> 00:16:00,970
+Exactly education and qualifications and so on
+
+209
+00:16:00,970 --> 00:16:05,860
+okay maybe I like to workon a certain job but
+
+210
+00:16:05,860 --> 00:16:07,800
+maybe I do not have the skills or education
+
+211
+00:16:07,800 --> 00:16:10,920
+qualifications or experiences and so on okay so
+
+212
+00:16:10,920 --> 00:16:13,460
+there are other factors which must be taken into
+
+213
+00:16:13,460 --> 00:16:16,300
+consideration that's why most people when they use
+
+214
+00:16:16,300 --> 00:16:20,720
+the Holland personality job fit they use it in
+
+215
+00:16:20,720 --> 00:16:23,260
+order to identify what are their future
+
+216
+00:16:23,260 --> 00:16:26,380
+opportunities and it is a good test for those
+
+217
+00:16:26,380 --> 00:16:28,910
+people who are searching for a jobWhy? Because
+
+218
+00:16:28,910 --> 00:16:33,390
+they can identify what jobs they can search for at
+
+219
+00:16:33,390 --> 00:16:37,210
+the same time they can work on developing their
+
+220
+00:16:37,210 --> 00:16:41,310
+competences skills other qualifications if needed
+
+221
+00:16:41,310 --> 00:16:44,070
+and so on okay and usually we use it in a training
+
+222
+00:16:44,070 --> 00:16:47,610
+use such test in order to increase their awareness
+
+223
+00:16:47,610 --> 00:16:50,570
+about where they should search okay but of course
+
+224
+00:16:50,570 --> 00:16:56,210
+there is also something else which is we need to
+
+225
+00:16:56,210 --> 00:17:04,080
+knowما هي مهارتها؟ مهارتها هي مهارة نحن نحتاجها
+
+226
+00:17:04,080 --> 00:17:08,280
+لكي نكون
+
+227
+00:17:08,280 --> 00:17:15,540
+نجحين أو نحوز فرصتنا لإيجاد عمل مثل هذا بالإضافة
+
+228
+00:17:15,540 --> 00:17:20,780
+إلى أشياء أخرى مثلبالطبع هذا ليس مرتبط، ولكن
+
+229
+00:17:20,780 --> 00:17:25,500
+بالنسبة لك، إنه مهم، أتمنى في المستقبل، بإضافة إلى
+
+230
+00:17:25,500 --> 00:17:29,440
+أننا نحتاج لنعرف ما هي العمل المتوفر على السوق،
+
+231
+00:17:29,440 --> 00:17:33,420
+يعني لا يجب أن أبحث عن عمل ليس متوفر، حسنًا، لذلك
+
+232
+00:17:33,420 --> 00:17:39,260
+يجب أن نعرف ما نحبهما نحتاجه لتطويره في مجال
+
+233
+00:17:39,260 --> 00:17:42,860
+مهارات ومهارات وما إلى ذلك كذلك يجب أن نفهم ماذا
+
+234
+00:17:42,860 --> 00:17:47,320
+موجود في السوق حسنا فهؤلاء هم الاثرين المهمات
+
+235
+00:17:47,320 --> 00:17:50,320
+المهمة عندما نتحدث عنها بالطبع نحن نتحدث عن
+
+236
+00:17:50,320 --> 00:17:52,620
+الهولندا personality job fit theory هنا نحن نتحدث
+
+237
+00:17:52,620 --> 00:17:56,940
+عن المرحلة الأولى فإننا نفهم ما هي احتياطاتنا
+
+238
+00:17:56,940 --> 00:18:01,260
+عندما نتحدث عن العمل هنا حسنا فبالطبع بالنسبة لهذا
+
+239
+00:18:01,260 --> 00:18:08,120
+المodel نستطيع أن نجد هنا أن هناكof course a lot
+
+240
+00:18:08,120 --> 00:18:10,940
+of differences when it comes to the personality of
+
+241
+00:18:10,940 --> 00:18:14,040
+people and not all people like the same thing and
+
+242
+00:18:14,040 --> 00:18:16,760
+this is of course is something overrated,
+
+243
+00:18:16,880 --> 00:18:20,220
+lesbianism, increasing productivity in addition to
+
+244
+00:18:20,220 --> 00:18:23,720
+other benefits of course okay this is one of the
+
+245
+00:18:23,720 --> 00:18:25,800
+theories which is helpful to understand the
+
+246
+00:18:25,800 --> 00:18:28,820
+relation between job and personality another issue
+
+247
+00:18:28,820 --> 00:18:31,200
+that we need to discuss is the relation between
+
+248
+00:18:35,000 --> 00:18:40,860
+الشركة و الشخصية
+
+249
+00:18:40,860 --> 00:18:48,600
+بالطبع هذه المناطق المتشابهه هناك
+
+250
+00:18:48,600 --> 00:18:53,800
+هناك مرتبط
+
+251
+00:18:53,800 --> 00:19:06,170
+بين الشخصية و الشركة هناك نتوقعبالطبع عندما نتكلم
+
+252
+00:19:06,170 --> 00:19:12,450
+عن تشبيه الشخصية للorganization أكتر ما نتكلم عن
+
+253
+00:19:12,450 --> 00:19:20,050
+ثقافة الوظيفة إلى مدى ما ثقافة الوظيفة تتعامل مع
+
+254
+00:19:20,050 --> 00:19:28,850
+قيم شخصية عملاء الوظيفة فهنا مرة أخرى نتوقع نتائج
+
+255
+00:19:28,850 --> 00:19:36,850
+مفيدةالان اتفقنا على اي نوع من الاختصارات
+
+256
+00:19:53,570 --> 00:19:56,890
+maybe customer service dealing with customers
+
+257
+00:19:56,890 --> 00:20:00,130
+market okay earlier we have discussed issues like
+
+258
+00:20:00,130 --> 00:20:02,150
+satisfied employees they are going to deal with
+
+259
+00:20:02,150 --> 00:20:05,010
+customers in more appropriate manner and of course
+
+260
+00:20:05,010 --> 00:20:07,770
+the opposite is true also okay what else?
+
+261
+00:20:14,950 --> 00:20:19,650
+in the production area okay what else?
+
+262
+00:20:25,310 --> 00:20:29,250
+ممكن تلك الناس تشعر بالتعامل مع مؤسساتها و تكون
+
+263
+00:20:29,250 --> 00:20:33,390
+أكتر قادرة على هذه المؤسسة التي ستتحسن حالة
+
+264
+00:20:33,390 --> 00:20:38,390
+مؤسساتها و تجعلها .. و ستزال تزال تزال تزال تزال
+
+265
+00:20:38,390 --> 00:20:39,270
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+266
+00:20:39,270 --> 00:20:39,290
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+267
+00:20:39,290 --> 00:20:39,770
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+268
+00:20:39,770 --> 00:20:39,790
+تزال تزال تزال تزال تزال تزال تزال تزال تزال تزال
+
+269
+00:20:39,790 --> 00:20:45,350
+تزال تزال تزال تزال تزال تزال تزال تزال تهل نتوقع
+
+270
+00:20:45,350 --> 00:20:47,730
+نتائج مناسبة هنا مرتبط بالتعامل مع المجتمع على
+
+271
+00:20:47,730 --> 00:20:50,850
+سبيل المثال؟ نعم بالطبع نحن نتكلم .. هذا هو السبب
+
+272
+00:20:50,850 --> 00:20:53,790
+اللي قلته في البداية أنه عندما نتكلم عن الوظيفة
+
+273
+00:20:53,790 --> 00:20:56,630
+الشخصية أكتر نتكلم عن الأشياء المرتبطة بالمؤسسة
+
+274
+00:20:56,630 --> 00:21:01,070
+والثقافة وعلى ما يستخدم قيم الأعمال المناسبة أو
+
+275
+00:21:01,070 --> 00:21:05,980
+موافقة بالمؤسسةهنا نتوقع الكثير من النتائج، واحدة
+
+276
+00:21:05,980 --> 00:21:10,420
+منها مرتبطة بالزيادة في مؤسسة وإلى مدى مدى
+
+277
+00:21:10,420 --> 00:21:14,500
+الموظفين سيتعاملوا بسهولة مع بعضهم البعض، والتعامل
+
+278
+00:21:14,500 --> 00:21:20,620
+مع بعضهم بسهولة مع
+
+279
+00:21:20,620 --> 00:21:21,400
+بعضهم بسهولة مع بعضهم بسهولة مع بعضهم بسهولة مع
+
+280
+00:21:21,400 --> 00:21:21,440
+بعضهم بسهولة مع بعضهم بسهولة مع بعضهم بسهولة مع
+
+281
+00:21:21,440 --> 00:21:21,460
+بعضهم بسهولة مع بعضهم بسهولة مع بعضهم بسهولة مع
+
+282
+00:21:21,460 --> 00:21:22,020
+بعضهم بسهولة مع بعضهم بسهولة مع بعضهم بسهولة مع
+
+283
+00:21:22,020 --> 00:21:25,560
+بعضهم بسهولة مع بعضهم بسهولة مع بعضهم بسهولة مع
+
+284
+00:21:25,560 --> 00:21:26,440
+بعضهم ب
+
+285
+00:21:31,930 --> 00:21:37,090
+بالطبع هؤلاء هم المشكلة التي نتحدث عنها هنا، وهو
+
+286
+00:21:37,090 --> 00:21:42,750
+السبب لإن الشركات عندما تبدأ الانتجار للعمل المهم
+
+287
+00:21:42,750 --> 00:21:45,410
+أو المهم للعمل، واحد من المشكلة التي يحتاجها
+
+288
+00:21:45,410 --> 00:21:50,210
+التجارب هي إلى مدى مدى قيم الانتجارات المناسبة
+
+289
+00:21:50,210 --> 00:21:54,360
+للشركات مع قيم والثقافةلماذا؟ لأن أشخاص مثلها
+
+290
+00:21:54,360 --> 00:22:00,220
+يعملون مع المجلد أو في المجلد، أشخاص مثلها هم ..
+
+291
+00:22:00,220 --> 00:22:03,540
+يعني نحن نحصل على جميع نتائج المشاهدة التي نتكلم
+
+292
+00:22:03,540 --> 00:22:07,260
+عنها، حسنًا؟ لذلك، إنه مهم عندما تتكلم عن
+
+293
+00:22:07,260 --> 00:22:11,260
+الاختيار، وعادةً الناس .. هم أكتر بالطبع مرتاحين
+
+294
+00:22:11,260 --> 00:22:16,610
+مع مجلدات مناسبة لشركتهمValues okay so here again
+
+295
+00:22:16,610 --> 00:22:19,370
+we are talking about up to what extent the
+
+296
+00:22:19,370 --> 00:22:22,370
+matching is important between personal values and
+
+297
+00:22:22,370 --> 00:22:26,550
+the organization itself okay again this will
+
+298
+00:22:26,550 --> 00:22:31,310
+increase productivity it is going to reduce
+
+299
+00:22:31,310 --> 00:22:37,090
+turnover absenteeism in addition to other issues
+
+300
+00:22:37,090 --> 00:22:43,450
+okay now of course one of the instrumentsوهو
+
+301
+00:22:43,450 --> 00:22:54,430
+استخدامه لتحقق إلى مدى ما يتم تحقيق قيم محتاجة أو
+
+302
+00:22:54,430 --> 00:23:00,820
+موافقة مع ثقافة المؤسسة أو مؤسسة الوظيفةهذه واحدة
+
+303
+00:23:00,820 --> 00:23:04,540
+من الأدوات التي يمكن استخدامها بالطبع بالإضافة إلى
+
+304
+00:23:04,540 --> 00:23:09,400
+الـ Big Five Trade Survey هناك أدوات أو أدوات أخرى
+
+305
+00:23:09,400 --> 00:23:14,900
+يمكن استخدامها هنا لتحقق إلى مدى قيمة الموظفين
+
+306
+00:23:14,900 --> 00:23:22,580
+التي يحتاجونهاالتي ستجعلها تنام بين قيم أو شخصية
+
+307
+00:23:22,580 --> 00:23:26,840
+أو قيم ومن الواضح أن مجتمعها مناسبة هنا مرة أخرى
+
+308
+00:23:26,840 --> 00:23:32,120
+نحن نتكلم عن مزيج الاتصال أو اكتشاف الاتصال بين
+
+309
+00:23:32,120 --> 00:23:41,000
+شخصية وقيموهي قيمة الشخص وقيمه ومن خلال المجتمع،
+
+310
+00:23:41,000 --> 00:23:46,240
+إلى مدى مدى، هذا سيؤثر على ميكانيزمات مختلفة تتعلق
+
+311
+00:23:46,240 --> 00:23:52,440
+بالعمل في المجتمع، مثل مصممة أبسنتزم، تحول، وكذلك
+
+312
+00:23:54,580 --> 00:23:57,460
+أشياء أخرى التي يجب أن نتكلم عنها اليوم و أعتقد
+
+313
+00:23:57,460 --> 00:24:04,080
+أننا سنستمر في نهاية هذا الحلقه هي الـ
+
+314
+00:24:04,080 --> 00:24:09,200
+Implications إحدى الأشياء التي يجب أن نتكلم عنها
+
+315
+00:24:09,200 --> 00:24:12,560
+هنا هو إذا كانت الـ Frameworks مثل الـ Big Five
+
+316
+00:24:12,560 --> 00:24:17,940
+تتعامل عبر الثانوية ثانوية ثانوية ثانوية ثانوية
+
+317
+00:24:17,940 --> 00:24:19,760
+ثانوية ثانوية ثانوية
+
+318
+00:24:23,770 --> 00:24:30,690
+هو سيكون مختلف؟ لماذا؟
+
+319
+00:24:37,250 --> 00:24:40,130
+فضل. Because when we were talking about the big
+
+320
+00:24:40,130 --> 00:24:44,110
+five, he said it has something to do with
+
+321
+00:24:44,110 --> 00:24:48,550
+agreeableness, extroversion, nauseousness, etc.
+
+322
+00:24:48,710 --> 00:24:51,310
+And I don't think that these stuff are affected by
+
+323
+00:24:51,310 --> 00:24:54,590
+the culture because it is directly related to the
+
+324
+00:24:54,590 --> 00:24:58,530
+person him or herself. I mean if I were in Gaza
+
+325
+00:24:58,530 --> 00:25:02,470
+and I was like agreeable and this wouldn't change
+
+326
+00:25:02,470 --> 00:25:07,100
+if I don't do itOkay but it might be different in
+
+327
+00:25:07,100 --> 00:25:11,000
+Africa itself Okay it might be different when it
+
+328
+00:25:11,000 --> 00:25:15,600
+comes to dealing with other people How am I going
+
+329
+00:25:15,600 --> 00:25:18,300
+to deal with different characters who share .. who
+
+330
+00:25:18,300 --> 00:25:22,480
+have different culture behaviors or whatever But
+
+331
+00:25:22,480 --> 00:25:24,800
+when it comes to myself I don't think that this
+
+332
+00:25:24,800 --> 00:25:28,420
+will change Now if you are talking about yourself
+
+333
+00:25:28,420 --> 00:25:34,430
+maybe it is going to be less changeable okayولكننا
+
+334
+00:25:34,430 --> 00:25:40,470
+لا نتكلم عن نفسي أو أنت إذا كنا في بلد أخرى، إذا
+
+335
+00:25:40,470 --> 00:25:45,930
+كانت تلك القيم أو أهداف شخصية هنا، نحن نتكلم عن
+
+336
+00:25:45,930 --> 00:25:50,790
+إذا كانت هي تتغير أو لا، نحن نتكلم عن إدارة هذا
+
+337
+00:25:50,790 --> 00:25:55,660
+المجلدفي البلد A و البلد B إذا كنا نحصل على نفس
+
+338
+00:25:55,660 --> 00:26:00,240
+النتائج أو لا و بالطبع ليس بالطبع أننا نحصل على
+
+339
+00:26:00,240 --> 00:26:05,760
+نفس النتائج، لذا ربما عندما نتكلم عن .. إذا كنت
+
+340
+00:26:05,760 --> 00:26:10,840
+أتكلم عن نفسي، ربما من بلد إلى بلد أخر، لن يكون
+
+341
+00:26:10,840 --> 00:26:14,020
+هناك تغييرات عامة، حسنًا أنا أتفق معك، ربما
+
+342
+00:26:14,020 --> 00:26:19,630
+بالطبع، ليس بالطبع، لكن عندما نتكلم عن تطبيقهؤلاء
+
+343
+00:26:19,630 --> 00:26:24,350
+الأجهزة من مدينة إلى مدينة أخرى لأن هناك دائما
+
+344
+00:26:24,350 --> 00:26:29,770
+أفعال خارجية في كل مدينة، فإن الشخصية مختلفة بسبب
+
+345
+00:26:29,770 --> 00:26:36,050
+هذه الوضعيات و لأن الجميع بسبب مجتمعه يتجاوز بشكل
+
+346
+00:26:36,050 --> 00:26:41,580
+مختلف من الناس الأخرىلذلك نتوقع أن يكون هناك رأي
+
+347
+00:26:41,580 --> 00:26:46,000
+في التواصل الاجتماعي بشكل كبير لكي نتعرف على هذه
+
+348
+00:26:46,000 --> 00:26:49,940
+الحالة، هذا ما أريد أن أقول عن الـ Big Five على
+
+349
+00:26:49,940 --> 00:26:57,700
+سبيل المثال، إنها ثقافة في الثقافات الوحيدة من
+
+350
+00:26:57,700 --> 00:27:03,710
+ثقافات التجاربيةعندما نتكلم عن الثقافة الوطنية،
+
+351
+00:27:03,710 --> 00:27:09,010
+نتكلم أكتر عن البلدان الغربية، على سبيل المثال،
+
+352
+00:27:09,010 --> 00:27:15,710
+حيث أن مهمة الوطنين هي الـMORE، هذا ليس مرتبط
+
+353
+00:27:15,710 --> 00:27:22,730
+بـTeamwork، لأنه قد يكون مشكلة مهمة للوطن أن يعمل
+
+354
+00:27:22,730 --> 00:27:28,990
+داخل الـTeamلذلك عندما نتحدث عن ثقافات محددة ليس
+
+355
+00:27:28,990 --> 00:27:30,810
+بالطبع أننا نتحدث عن عملية عملية عملية عملية عملية
+
+356
+00:27:30,810 --> 00:27:31,450
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+357
+00:27:31,450 --> 00:27:32,790
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+358
+00:27:32,790 --> 00:27:34,450
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+359
+00:27:34,450 --> 00:27:37,150
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+360
+00:27:37,150 --> 00:27:37,710
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+361
+00:27:37,710 --> 00:27:37,750
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+362
+00:27:37,750 --> 00:27:49,740
+عملية عملية عملية عملفهي ليست مرتبطة ولكن هنا مهمة
+
+363
+00:27:49,740 --> 00:27:54,600
+الشخص هو أنه يتم إعجابه بشخصية أنه أو انه يتعامل
+
+364
+00:27:54,600 --> 00:27:56,980
+مع الشخصية نفس الموضوع يجب أن نتكلم عنه عندما
+
+365
+00:27:56,980 --> 00:28:02,400
+نتكلم عن قيم طبعا عندما نتكلم عن قيم فهي مختلفة
+
+366
+00:28:02,400 --> 00:28:03,900
+عبر ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+367
+00:28:03,900 --> 00:28:05,040
+ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+368
+00:28:05,040 --> 00:28:07,720
+ثانوية ثانوية ثانوية ثانوية
+
+369
+00:28:13,940 --> 00:28:22,020
+ماذا هي المصطلحات في التعليقات التالية؟ ماذا هي
+
+370
+00:28:22,020 --> 00:28:27,920
+المصطلحات لـ Hofstede Framework؟ هناك خمس مصطلحات
+
+371
+00:28:27,920 --> 00:28:31,280
+الرئيسية التي سوف نتكلم عنها لأننا نتكلم عن
+
+372
+00:28:31,280 --> 00:28:34,520
+الثقافات كثير يعني لذا في التعليقات التالية سوف
+
+373
+00:28:34,520 --> 00:28:38,520
+نتكلم عن مصطلحات Hofstede Framework وماذا هي
+
+374
+00:28:38,520 --> 00:28:42,700
+المصطلحات المختلفة لـ Hofstede Framework لكي نفهم
+
+375
+00:28:43,200 --> 00:28:47,060
+كيف تختلف قيم من مجتمع إلى مجتمع آخر؟ هنا نحن
+
+376
+00:28:47,060 --> 00:28:52,100
+نتكلم عن القيم التي ستكون هناك اختلافات في القيم،
+
+377
+00:28:52,100 --> 00:28:55,480
+ليس بالطبع انها مختلفة تماما، لكن سيكون هناك
+
+378
+00:28:55,480 --> 00:29:00,120
+اختلافات في أسلوب القيم أو المجموعة.
+
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/x9I54_ZTBE8_raw.json b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/x9I54_ZTBE8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ab561108e29d551f8e17f116c811d77ec6f48ab9
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/x9I54_ZTBE8_raw.json
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ان نقول ان هناك افعالية افعالية هي", "tokens": [3555, 28814, 2304, 41361, 16095, 16472, 7251, 1863, 7435, 5016, 14407, 8978, 6225, 42213, 20449, 9957, 4032, 3615, 41260, 15042, 8717, 2655, 4117, 19528, 18871, 6156, 16572, 4587, 31439, 8717, 36178, 25124, 1829, 38207, 35525, 19452, 8315, 8717, 2655, 4117, 19528, 34105, 18871, 6156, 16572, 4587, 30731, 3714, 3215, 7578, 3714, 3215, 7578, 6156, 16572, 4587, 7251, 33604, 27842, 16472, 7251, 43020, 16095, 16472, 7251, 1863, 7435, 5016, 14407, 8978, 18863, 42213, 34051, 7251, 1863, 7435, 5016, 14407, 8978, 18863, 42213, 1975, 4117, 49115, 16472, 7251, 33604, 27842, 14407, 4724, 8848, 23275, 1975, 4117, 2655, 2288, 16472, 8717, 39648, 16472, 34105, 4117, 1975, 5172, 3615, 6027, 10632, 1975, 5172, 3615, 6027, 10632, 39896], "avg_logprob": -0.47889255719226703, "compression_ratio": 2.225988700564972, "no_speech_prob": 1.537799835205078e-05, "words": [{"start": 1371.45, "end": 1372.03, "word": "بإمكانهم", "probability": 0.55797119140625}, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/zmLKpJD8yWc_postprocess.srt b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/zmLKpJD8yWc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f9ef499c242bf4c0404a2cbd7bc5a57fc026d3f5
--- /dev/null
+++ b/PL9fwy3NUQKwYZpwQq4bZ2ZHrcLS4E9xUm/zmLKpJD8yWc_postprocess.srt
@@ -0,0 +1,1948 @@
+1
+00:00:06,870 --> 00:00:13,270
+سننتهي الحلقة الأولى، في دراسة قبلها، أخر شيء قد
+
+2
+00:00:13,270 --> 00:00:19,350
+تحدثنا عن عملية الهجوم، كمصطلح، كمصطلح، بإضافة إلى
+
+3
+00:00:19,350 --> 00:00:25,110
+.. كذلك، قد تحدثنا عن مجالات مختلفة التي تشجع إلى
+
+4
+00:00:25,110 --> 00:00:29,750
+مجال عملية الهجوم، اليوم سنتحدث عن مجال عملية
+
+5
+00:00:29,750 --> 00:00:36,540
+الهجوممزيد من المفاهيم التي سنتحدث عنها. بعض
+
+6
+00:00:36,540 --> 00:00:40,800
+المفاهيم المهمة المرتبطة لشركة Organization
+
+7
+00:00:40,800 --> 00:00:45,520
+Behavior هي أنه لا يوجد أبسلوت عندما نتحدث عن شركة
+
+8
+00:00:45,520 --> 00:00:48,620
+Organization Behavior. عندما نقول أنه لا يوجد
+
+9
+00:00:48,620 --> 00:00:54,240
+أبسلوت، هذا يعني أنه لا يوجد أسطاندرات. لا يمكننا
+
+10
+00:00:54,240 --> 00:01:02,400
+أن ندعي الناس في مصطلحات حولبعنوان عملية عملية
+
+11
+00:01:02,400 --> 00:01:03,720
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+12
+00:01:03,720 --> 00:01:03,900
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+13
+00:01:03,900 --> 00:01:06,920
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+14
+00:01:06,920 --> 00:01:09,780
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+15
+00:01:09,780 --> 00:01:11,520
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+16
+00:01:11,520 --> 00:01:14,520
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+17
+00:01:14,520 --> 00:01:14,540
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+18
+00:01:14,540 --> 00:01:17,480
+عملية عملية عملية عملية عملية عملية عملية
+
+19
+00:01:25,570 --> 00:01:30,650
+بسبب أننا نتكلم عن الإنسان و إنهم مختلفين، لذلك
+
+20
+00:01:30,650 --> 00:01:35,310
+الناس في موقع مختلف، ربما اتو ناس مختلفة مختلفة في
+
+21
+00:01:35,310 --> 00:01:41,150
+موقع مختلف أو الناس نفسه سيفعل أشياء مختلفة في
+
+22
+00:01:41,150 --> 00:01:46,930
+موقع مختلف، لذلك إنها مختلفة ومشكلةو أحيانًا أيضًا
+
+23
+00:01:46,930 --> 00:01:50,030
+نفس الناس يتصرفون بشكل مختلف في حالات مشابقة
+
+24
+00:01:50,030 --> 00:01:54,090
+أيضًا، وهذا يضيف المزيد من المشكلة عندما نتحدث عن
+
+25
+00:01:54,090 --> 00:01:58,010
+OB، لذلك عندما نتحدث عن الهجوم، فهو مختلف جدًا،
+
+26
+00:01:58,010 --> 00:02:02,930
+لماذا؟ لأننا نتحدث عن علاقات خاطئة وخاطئة، هنا
+
+27
+00:02:02,930 --> 00:02:08,910
+هناك بعض النقطات التي يجب أن نعتمد عليها، حسنًا
+
+28
+00:02:08,910 --> 00:02:12,630
+عندما نتحدث عن علاقات خاطئة وخاطئة، هنا نتحدث عن
+
+29
+00:02:12,630 --> 00:02:20,060
+الخطأ أو السببوالـ output أو الـ إفاق نفسه عندما
+
+30
+00:02:20,060 --> 00:02:24,420
+نتكلم عن الأسباب هنا نتكلم عن أشخاص مستقلين أو
+
+31
+00:02:24,420 --> 00:02:25,840
+أشخاص مستقلين ومستقلين ومستقلين ومستقلين ومستقلين
+
+32
+00:02:25,840 --> 00:02:27,000
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين
+
+33
+00:02:27,000 --> 00:02:30,840
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين
+
+34
+00:02:30,840 --> 00:02:31,760
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين
+
+35
+00:02:31,760 --> 00:02:32,020
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين
+
+36
+00:02:32,020 --> 00:02:34,980
+ومستقلين ومستقلين ومستقلين ومستقلين ومستقلين و
+
+37
+00:02:35,180 --> 00:02:39,800
+استخدام واستخدام مصادر او هناك أسباب وإتصالات؟ لا
+
+38
+00:02:39,800 --> 00:02:45,660
+ماهي أهم هنا هو أن هناك مصادر أخرى تتعانى في كل
+
+39
+00:02:45,660 --> 00:02:50,080
+حالة هذا هو السبب عندما تتحدث عن عملية التجارب كل
+
+40
+00:02:50,080 --> 00:02:55,340
+حالة تحتوي على أفكارها الخاصة هناك بعض المصادر
+
+41
+00:02:55,340 --> 00:03:00,500
+التي ستتعانى لذلك هناك مصادر مصادر مصادر مصادر
+
+42
+00:03:00,500 --> 00:03:02,220
+مصادر مصادر مصادر مصادر مصادر مصادر مصادر مصادر
+
+43
+00:03:02,220 --> 00:03:04,780
+مصادر مصادر مصادر مصادر مصادر مصادر مصادر مصادر
+
+44
+00:03:04,810 --> 00:03:09,230
+it is changeable okay more there are other
+
+45
+00:03:09,230 --> 00:03:12,290
+variables which will interfere in each situation
+
+46
+00:03:12,290 --> 00:03:15,830
+that's why we say in addition to the cause and
+
+47
+00:03:15,830 --> 00:03:20,070
+defectفاكتورات أو مستقلات ومستقلات مستقلات
+
+48
+00:03:20,070 --> 00:03:23,110
+ومستقلات ومستقلات مستقلات مستقلات مستقلات مستقلات
+
+49
+00:03:23,110 --> 00:03:30,810
+مستقلات مستقلات مستقلات مستقلات مستقلات
+
+50
+00:03:30,810 --> 00:03:41,770
+مستقلات
+
+51
+00:03:47,250 --> 00:03:52,430
+في حالة أخرى، يظهروا سعادتهم بطريقة مختلفة، لماذا؟
+
+52
+00:03:52,430 --> 00:03:56,990
+لأن في بعض الأحيان، رغم أن الواضحات البيئية أو
+
+53
+00:03:56,990 --> 00:03:59,130
+الواضحات البيئية أو الواضحات البيئية أو الواضحات
+
+54
+00:03:59,130 --> 00:04:00,430
+الواضحات البيئية أو الواضحات البيئية أو الواضحات
+
+55
+00:04:00,430 --> 00:04:01,130
+البيئية أو الواضحات البيئية أو الواضحات البيئية أو
+
+56
+00:04:01,130 --> 00:04:01,610
+الواضحات البيئية أو الواضحات البيئية أو الواضحات
+
+57
+00:04:01,610 --> 00:04:03,550
+البيئية أو الواضحات البيئية أو الواضحات البيئية أو
+
+58
+00:04:03,550 --> 00:04:08,600
+الواضحات البيئية أو الواضحات البيئيةالحالة
+
+59
+00:04:08,600 --> 00:04:12,540
+الانتقالية التي يمكن انتقالها كل مرة لا نحن نتحدث
+
+60
+00:04:12,540 --> 00:04:18,960
+عن حالة مستغربة جدًا هناك مصادر ومصادر داخلية
+
+61
+00:04:18,960 --> 00:04:22,360
+مستغربة ومستغربة وفي نفس الوقت هناك مصادر داخلية
+
+62
+00:04:22,360 --> 00:04:26,540
+مستغربة أيضًا وهي مستغربة حسنًا لهذا السبب نقول أن
+
+63
+00:04:26,540 --> 00:04:31,840
+هناك عدد من أبساط عندما نتحدث عن حياة مؤسسة حسنًا
+
+64
+00:04:31,840 --> 00:04:33,380
+الآن عندما نتحدث عن
+
+65
+00:04:36,340 --> 00:04:40,000
+العمل و المحاولات التي تم صنعها لعبارة عن الهجوم
+
+66
+00:04:40,000 --> 00:04:45,180
+الوضعي هناك الكثير من المحاولات نحتاج أن نتعامل مع
+
+67
+00:04:45,180 --> 00:04:48,900
+هذه المحاولات لأن هذه المحاولات يجب أن تساعدنا في
+
+68
+00:04:48,900 --> 00:04:53,620
+كيف نشعر بالعبارة عن الهجوم الوضعي أو كيف يجب أن
+
+69
+00:04:53,620 --> 00:04:58,640
+نتعامل مع عبارة عن الهجوم الوضعي هذه المحاولات
+
+70
+00:04:58,640 --> 00:05:06,430
+تجعل بعض الشركاتالتغيير عندما يتعلق بالإستعمال
+
+71
+00:05:06,430 --> 00:05:12,450
+للعبارة المجلدية، أعني هنا استعمال في مجلد مجلد
+
+72
+00:05:12,450 --> 00:05:17,610
+مجلد، على سبيل المثال، نحتاج للإجابة للجمهورية
+
+73
+00:05:17,840 --> 00:05:24,640
+الاستجابة للجمهورية تجارب بعض المهاجمات، كيف يجب
+
+74
+00:05:24,640 --> 00:05:30,700
+أن يتم تطبيق المهاجمين في المجتمع. وعندما نتكلم عن
+
+75
+00:05:30,700 --> 00:05:34,440
+الجمهورية، نتكلم عن الدخول إلى مؤسسات جديدة،
+
+76
+00:05:34,440 --> 00:05:38,120
+الدخول إلى مؤسسات جديدة هنا، نتكلم عن مجموعات عمل
+
+77
+00:05:38,120 --> 00:05:42,760
+مختلفة في هذا أو في هذا البلد، وفي نفس الوقت،
+
+78
+00:05:42,760 --> 00:05:46,340
+نتكلم عن أشخاص مختلفة بالنسبة للثقافة، على سبيل
+
+79
+00:05:46,340 --> 00:05:51,230
+المثالهناك المزيد من المجتمع لأننا نتكلم عن دول
+
+80
+00:05:51,230 --> 00:05:57,180
+مختلفة وما إلى ذلك، لذلك الجمهوريةبعض التغييرات
+
+81
+00:05:57,180 --> 00:06:04,020
+كيف يجب أن تتعامل استخدام OB من مديرات مختلفة
+
+82
+00:06:04,020 --> 00:06:07,420
+ومؤسسات ومؤسسات مختلفة ومؤسسات مؤسسات مؤسسات
+
+83
+00:06:07,420 --> 00:06:24,960
+مؤسسات مؤسسات مؤسسات مؤسسات مؤسسات مؤسسات
+
+84
+00:06:25,510 --> 00:06:30,590
+والتي يجب أن تكون اعتمادها من مديرات مختلفة في
+
+85
+00:06:30,590 --> 00:06:38,390
+أضافة لقبوليزيات ومديرات مجتمع مختلفة في أي بلد في
+
+86
+00:06:38,390 --> 00:06:43,970
+أي مؤسسة هناك ما يسمى كمختلفة مختلفة هنا نحن نتحدث
+
+87
+00:06:43,970 --> 00:06:49,530
+عن اختلافات في مجموعات العمل في بعض البلدين ربما
+
+88
+00:06:49,530 --> 00:06:51,950
+المختلفة تم تخلصها بسبب
+
+89
+00:06:55,670 --> 00:06:59,550
+Infinity or there are differences which is related
+
+90
+00:06:59,550 --> 00:07:03,230
+to race for example, sometimes to origin,
+
+91
+00:07:03,630 --> 00:07:07,990
+language, religion and so on okay Now sometimes
+
+92
+00:07:07,990 --> 00:07:12,150
+those differences are created through other
+
+93
+00:07:12,640 --> 00:07:17,680
+فاكتوريات، حسنا؟ ليس بالطبع دين، اثنية، ورحلة وما
+
+94
+00:07:17,680 --> 00:07:21,040
+إلى ذلك، أحيانًا ربما تكون هذه الفرقات مرتبطة
+
+95
+00:07:21,040 --> 00:07:26,420
+بالدراسة على سبيل المثال أو بعض الفاكتوريات
+
+96
+00:07:26,420 --> 00:07:30,060
+الثقافية على سبيل المثال، وما إلى ذلك، حسنا؟ لذلك،
+
+97
+00:07:30,060 --> 00:07:34,020
+مختلفة العمليات هي محاولة أخرى، لماذا؟ لأنه عندما
+
+98
+00:07:34,020 --> 00:07:39,900
+نتحدث عن الorganization نحن نتحدث عن جسد متعاملوكل
+
+99
+00:07:39,900 --> 00:07:43,680
+شخص في المؤسسة يجب أن يعمل معًا لإيقاف مهارات
+
+100
+00:07:43,680 --> 00:07:46,140
+ومهارات مؤسسة ومهارات مؤسسة ومهارات مؤسسة ومهارات
+
+101
+00:07:46,140 --> 00:07:49,020
+مؤسسة ومهارات مؤسسة ومهارات مؤسسة ومهارات مؤسسة
+
+102
+00:07:49,020 --> 00:07:50,880
+ومهارات مؤسسة ومهارات مؤسسة ومهارات مؤسسة ومهارات
+
+103
+00:07:50,880 --> 00:07:51,660
+ومهارات مؤسسة ومهارات مؤسسة ومهارات مؤسسة ومهارات
+
+104
+00:07:51,660 --> 00:07:59,030
+مؤسسة ومهارات مؤسسة ومهارالذين قادرين على تحقيق
+
+105
+00:07:59,030 --> 00:08:01,750
+مهارات مختلفة ومهارات مختلفة ومهارات مختلفة
+
+106
+00:08:01,750 --> 00:08:01,790
+ومهارات مختلفة ومهارات مختلفة ومهارات مختلفة
+
+107
+00:08:01,790 --> 00:08:03,270
+ومهارات مختلفة ومهارات مختلفة ومهارات مختلفة
+
+108
+00:08:03,270 --> 00:08:03,590
+ومهارات مختلفة ومهارات مختلفة ومهارات مختلفة
+
+109
+00:08:03,590 --> 00:08:05,170
+ومهارات مختلفة ومهارات مختلفة ومهارات مختلفة
+
+110
+00:08:05,170 --> 00:08:05,970
+ومهارات مختلفة ومهارات مختلفة ومهارات مختلفة
+
+111
+00:08:05,970 --> 00:08:07,910
+ومهارات مختلفة ومهارات مختلفة ومهارات مختلفة
+
+112
+00:08:07,910 --> 00:08:12,850
+ومهارات مختلفة ومهارات مختلفة ومهارات م
+
+113
+00:08:12,880 --> 00:08:19,340
+Productivity، it is important to have output which
+
+114
+00:08:19,340 --> 00:08:24,600
+is according to standards or which is .. we are
+
+115
+00:08:24,600 --> 00:08:28,360
+talking of course here about better quality، okay؟
+
+116
+00:08:28,360 --> 00:08:30,980
+Those are also other challenges. When we talk
+
+117
+00:08:30,980 --> 00:08:34,820
+about improving the quality of .. quality and
+
+118
+00:08:34,820 --> 00:08:39,410
+productivityهنا مرة أخرى، نحتاج أحيانًا ربما تغيّر
+
+119
+00:08:39,410 --> 00:08:43,530
+الوصول للموظفين، كيف يجب أن يتعاملوا بطرق عمل
+
+120
+00:08:43,530 --> 00:08:45,990
+مختلفة، على سبيل المثال، أعطيهم تدريب دراسي،
+
+121
+00:08:45,990 --> 00:08:53,710
+أعطيهم أحيانًا تدريب دراسي، لكي يجعلهم يتعاملوا
+
+122
+00:08:53,710 --> 00:08:55,510
+بشكل جيد، يجعلهم يتعاملوا بشكل جيد،
+
+123
+00:08:59,860 --> 00:09:04,500
+أو شيء مثل هذا هذا هو السبب لما قلت أننا أحيانًا
+
+124
+00:09:04,500 --> 00:09:07,580
+ربما يجب أن نتطور بعض التغييرات عندما يتعلق
+
+125
+00:09:07,580 --> 00:09:10,360
+بالرؤية العمليين الآن ما هي الميكانيزمات أو
+
+126
+00:09:10,360 --> 00:09:14,780
+أحيانًا حتى قيمهم أو أحيانًا حتى كيف يأخذوا
+
+127
+00:09:14,780 --> 00:09:18,840
+القرارات على سبيل المثال أو يتعاملوا مع بعضهم
+
+128
+00:09:18,840 --> 00:09:22,240
+البعض نحن قد نحصل على هذا باستخدام التدريب على
+
+129
+00:09:22,240 --> 00:09:26,540
+سبيل المثال أو أي ميكانيزم آخر وهو صح بالطبع في
+
+130
+00:09:26,540 --> 00:09:31,000
+أضافة إلى تحسينقيمة ومصالحية يجب أن نحرر عملية
+
+131
+00:09:31,000 --> 00:09:31,220
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+132
+00:09:31,220 --> 00:09:32,340
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+133
+00:09:32,340 --> 00:09:34,040
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+134
+00:09:34,040 --> 00:09:35,440
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+135
+00:09:35,440 --> 00:09:38,220
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+136
+00:09:38,220 --> 00:09:38,860
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+137
+00:09:38,860 --> 00:09:44,960
+عملية عملية عملية عملية
+
+138
+00:09:54,990 --> 00:09:59,370
+أو مصطلح لإيقاف المستخدم بالطبع إنه مهم جدًا
+
+139
+00:09:59,370 --> 00:10:04,730
+دائمًا نحتاج لنقل هذه التحديات إلى مشاكل مرتبطة
+
+140
+00:10:04,730 --> 00:10:09,590
+بشركة ومبادرة يعني دائمًا يجب أن نتخيل كيف نستطيع
+
+141
+00:10:09,590 --> 00:10:14,610
+أن نرتبط هذا لإيقاف المستخدم أوالقيم التي تحتاجها
+
+142
+00:10:14,610 --> 00:10:20,710
+العميل أو على سبيل المثال، ما هي الخاصية التي مهمة
+
+143
+00:10:20,710 --> 00:10:24,610
+أن تتعامل مع تحديات مثل هذه أو عندما تتحدث عن
+
+144
+00:10:24,610 --> 00:10:28,150
+عملية الجروب، ما هي رولة الجروب، الشركات،
+
+145
+00:10:28,150 --> 00:10:32,050
+الرئيسية، التcommunication، وما إلى ذلك، فهذه هي
+
+146
+00:10:32,050 --> 00:10:35,010
+الطريقة التي يجب أن نفكر في هذه التحديات، وليس
+
+147
+00:10:35,010 --> 00:10:39,080
+الموضوع أننا نعرف أنها تحدياتهي الموضوع في معرفة
+
+148
+00:10:39,080 --> 00:10:47,320
+كيف تصنع هذه المحاولات محاولة لتطبيق OB في المؤسسة
+
+149
+00:10:47,320 --> 00:10:51,100
+بالطبع هناك الكثير من المحاولات بعضها متعلقة
+
+150
+00:10:51,100 --> 00:10:55,600
+لتحسين مهارات الناس محاولات متعلقة بالنسبة للإدارة
+
+151
+00:10:55,600 --> 00:11:01,440
+أكتر المعملين يمتلكوا محاولات أكتر يستطيعوا تحسين
+
+152
+00:11:01,440 --> 00:11:07,230
+نسبة للإدارةبالطبع من المؤسسة بشكل عام تدفع
+
+153
+00:11:07,230 --> 00:11:11,250
+الإبتكار والتغيير نحن نعيش في منطقة دينامية جدًا،
+
+154
+00:11:11,250 --> 00:11:18,970
+نحتاج لإنشاء ثقافة تتجه إلى التغيير وهذا موضوع مهم
+
+155
+00:11:18,970 --> 00:11:23,850
+جدًا، ومثلًا عندما نتحدث عن التعامل مع الوقت نحن
+
+156
+00:11:23,850 --> 00:11:27,730
+لسنا نتحدث عن منطقة مستقل أو مستقل، نحن نتحدث عن
+
+157
+00:11:29,150 --> 00:11:34,090
+البيئة، حسنا؟ لذلك التعامل مع التغيير هو ميكانيزم
+
+158
+00:11:34,090 --> 00:11:36,830
+مهم جدًا .. ميكانيزم مهم جدًا عندما نتحدث عن
+
+159
+00:11:36,830 --> 00:11:41,350
+محاولات OBA، حسنا؟ بالطبع، هناك الكثير من
+
+160
+00:11:41,350 --> 00:11:46,690
+المحاولات، مرة أخرى، ببساطة التحدث هنا، يجب أن
+
+161
+00:11:46,690 --> 00:11:52,090
+نجعل هذه المحاولات متعلقة بالتطبيق التجاري، حسنا؟
+
+162
+00:11:52,090 --> 00:11:53,250
+أي أسئلة حتى الآن؟
+
+163
+00:12:00,950 --> 00:12:05,070
+Coping it means يعني how to handleطيب، كيف تتعامل
+
+164
+00:12:05,070 --> 00:12:09,010
+بسهولة؟ كيف تتعامل حتى إذا .. يجب أن نتعامل بكل
+
+165
+00:12:09,010 --> 00:12:11,630
+هذه المشاكل بسهولة بسهولة، نعم الـ temporariness
+
+166
+00:12:11,630 --> 00:12:16,970
+هنا، نحن دائما نتعامل مع حالات مقتصرة، ليس حالات
+
+167
+00:12:16,970 --> 00:12:19,910
+مستمرة، لذا كيف يمكن العمليين أن يتعاملوا مع هذه
+
+168
+00:12:19,910 --> 00:12:23,270
+الحالات، أو في كلمة أخرى، كيف يمكنهم أن يتعاملوا
+
+169
+00:12:23,270 --> 00:12:28,110
+بشكل افتتاحي،
+
+170
+00:12:28,110 --> 00:12:32,270
+حسنا؟ مرة أخرى، كما ذكرت، هناك أشخاص مختلفين
+
+171
+00:12:33,520 --> 00:12:37,920
+التحديات نحتاج دائما تتعلق بالتحديات الموجودة في
+
+172
+00:12:37,920 --> 00:12:40,300
+التطبيقات الانتجارية
+
+173
+00:12:43,740 --> 00:12:49,560
+ساعدت في تطور ممارسات معينة قبل قليل من الوقت، قبل
+
+174
+00:12:49,560 --> 00:12:50,420
+قليل من الوقت، قبل قليل من الوقت، قبل قليل من
+
+175
+00:12:50,420 --> 00:12:52,700
+الوقت، قبل قليل من الوقت، قبل قليل من الوقت، قبل
+
+176
+00:12:52,700 --> 00:12:52,860
+قليل من الوقت، قبل قليل من الوقت، قبل قليل من
+
+177
+00:12:52,860 --> 00:12:52,960
+الوقت، قبل قليل من الوقت، قبل قليل من الوقت، قبل
+
+178
+00:12:52,960 --> 00:12:56,600
+قليل من الوقت، قبل قليل من الوقت، قبل قليل من
+
+179
+00:12:56,600 --> 00:13:03,240
+الوقت، قبل قليل من الوقت،
+
+180
+00:13:03,240 --> 00:13:10,660
+قبل قليل
+
+181
+00:13:10,660 --> 00:13:17,160
+من الوقالان عندما نتكلم عن مدالة OB نحن لدينا
+
+182
+00:13:17,160 --> 00:13:23,220
+اثنين مهمات مختلفة هنا او مجموعات مختلفة يجب ان
+
+183
+00:13:23,220 --> 00:13:32,880
+نعتمد عليها مختلفات مختلفة نسميها X ومختلفة نسميها
+
+184
+00:13:32,880 --> 00:13:38,940
+Y ماهي الفرق بين مختلفة ومختلفة مختلفة مختلفة
+
+185
+00:13:38,940 --> 00:13:39,060
+مختلفة مختلفة
+
+186
+00:13:45,200 --> 00:13:51,020
+أو اشياء اخرى ممكن تساعدنا في تنظيم الانتجارات
+
+187
+00:13:51,020 --> 00:13:58,740
+الانتجارات الانتجارات الانتجارات ممكن تساعدنا في
+
+188
+00:13:58,740 --> 00:14:00,640
+تنظيم الانتجارات الانتجارات ممكن تساعدنا في تنظيم
+
+189
+00:14:00,640 --> 00:14:03,740
+الانتجارات الانتجارات ممكن تساعدنا في تنظيم
+
+190
+00:14:03,740 --> 00:14:05,880
+الانتجارات الانتجارات ممكن تساعدنا في تنظيم
+
+191
+00:14:05,880 --> 00:14:06,240
+الانتجارات الانتجارات ممكن تساعدنا في تنظيم
+
+192
+00:14:06,240 --> 00:14:07,040
+الانتجارات الانتجارات ممكن تساعدنا في تنظيم
+
+193
+00:14:07,040 --> 00:14:09,560
+الانتجارات الانتجارات ممكن تساعدنا في تنظيم
+
+194
+00:14:09,560 --> 00:14:13,240
+الانتجارات الانتجارات ممكن تساعدنا في تنظ
+
+195
+00:14:16,440 --> 00:14:20,080
+إذا نعود إلى علاقة خطأ وإدارة عندما نتكلم عن مصادر
+
+196
+00:14:20,080 --> 00:14:24,760
+مستقل هنا نتكلم عن الخطأ المستقل المستقل نتكلم عن
+
+197
+00:14:24,760 --> 00:14:28,720
+إدارة أو في كلمات أخرى نستطيع أن نقول المدخل
+
+198
+00:14:28,720 --> 00:14:35,180
+والمخرج أو الانفلوان والنتيجة نستطيع أن نفسر هذا
+
+199
+00:14:35,180 --> 00:14:39,640
+إلى كلمات مختلفة لكن على أية حال عندما نتكلم عن
+
+200
+00:14:39,640 --> 00:14:43,280
+المصادر المستقل مرة أخرى هنا نتكلم عن المصادر التي
+
+201
+00:14:43,280 --> 00:14:49,760
+نتكلم عنهاوهو ما نستخدمه وهو
+
+202
+00:14:49,760 --> 00:14:57,440
+ما نستخدمه وهو ما نستخدمه وهو ما نستخدمه وهو ما
+
+203
+00:14:57,440 --> 00:14:58,920
+نستخدمه وهو ما نستخدمه وهو ما نستخدمه وهو ما
+
+204
+00:14:58,920 --> 00:15:06,690
+نستخدمه وهو ما نستخدمه وهو ما نستخدممختلفة أيضًا
+
+205
+00:15:06,690 --> 00:15:12,390
+نحن نتكلم عن المصادر البيئية التي قد تأثير علاقة
+
+206
+00:15:12,390 --> 00:15:16,050
+ما بين السبب والإفاق، حسنًا؟ لذلك المصادر
+
+207
+00:15:16,050 --> 00:15:19,670
+المستقلية ليست المصادر الوضعية، لا، المصادر
+
+208
+00:15:19,670 --> 00:15:26,850
+الوضعية هي مصادر أخرى التي قد تأثير علاقة ما بين
+
+209
+00:15:26,850 --> 00:15:30,510
+المصادر والإفاق، وهذا السبب لمناقشتنا قبل أن هناك
+
+210
+00:15:30,510 --> 00:15:34,980
+بعض الأفعال عندما نتكلم عن العاملات العاملةبسبب
+
+211
+00:15:34,980 --> 00:15:40,420
+تلك المقالات التحكمية اللي هي الانتبناد في الكثير
+
+212
+00:15:40,420 --> 00:15:47,530
+من الحالات انها تأثر على مصادر حاليةيسبب فيها بعض
+
+213
+00:15:47,530 --> 00:15:52,310
+التغييرات أو سيؤثر على الانتقالات أو النتيجة التي
+
+214
+00:15:52,310 --> 00:15:57,310
+نراها. حسنًا، عندما نتكلم عن الانتقالات، هنا نتكلم
+
+215
+00:15:57,310 --> 00:16:03,450
+عن الإجابة على الانتقالات أو النتائج التي يمكننا
+
+216
+00:16:03,450 --> 00:16:06,630
+أن نحصل عليها أو الانتقال. مرة أخرى، نتكلم عن
+
+217
+00:16:06,630 --> 00:16:12,390
+الوضع و العلاقة. حسنًا، عادةً، هؤلاء هم الانتقالات
+
+218
+00:16:12,390 --> 00:16:17,090
+التي يجب أن نحكم عليها.هنا انا اتكلم عن العاملات
+
+219
+00:16:17,090 --> 00:16:22,170
+الهيوغوية لماذا يجب علينا التحكم في هذه العاملات؟
+
+220
+00:16:22,170 --> 00:16:27,990
+لماذا يجب علينا التحكم في العاملات الانتقالية؟
+
+221
+00:16:30,930 --> 00:16:35,530
+The initial input to gain the dependent variables,
+
+222
+00:16:35,710 --> 00:16:38,570
+the output. So if you want to get a higher quality
+
+223
+00:16:38,570 --> 00:16:41,510
+or better results for the dependent variables, we
+
+224
+00:16:41,510 --> 00:16:45,610
+have to draw the independent variables. Okay. What
+
+225
+00:16:45,610 --> 00:16:48,530
+else? Yes. Maybe to avoid the deviations from our
+
+226
+00:16:48,530 --> 00:16:52,290
+own model. To avoid? Deviations from the model.
+
+227
+00:16:52,870 --> 00:16:53,550
+What else?
+
+228
+00:16:59,150 --> 00:17:02,810
+What is the definition of organization behavior? I
+
+229
+00:17:02,810 --> 00:17:07,770
+know that it is a field of study. What else? Yes.
+
+230
+00:17:28,140 --> 00:17:30,980
+وهو يساعدنا على محافظة التعامل التجاربي بطريقة ما
+
+231
+00:17:30,980 --> 00:17:37,560
+وبالتالي دعنا نعرف .. دعنا نستخدم علمنا لكي نحصل
+
+232
+00:17:37,560 --> 00:17:42,020
+على أفعال أعلى لأنهم مستخدمين للتحكم كما قلنا ولكن
+
+233
+00:17:42,020 --> 00:17:44,780
+المواصفات المستخدمة على سبيل المثال ليست مستخدمة
+
+234
+00:17:44,780 --> 00:17:49,500
+للتحكم بطريقة معينة أو شيء آخر لذلك سيكون أسهل لنا
+
+235
+00:17:49,500 --> 00:17:53,280
+أن نتعامل مع المواصفات المستخدمة بدلا من المواصفات
+
+236
+00:17:53,280 --> 00:17:58,630
+المستخدمة طبعا المواصفات المستخدمةوهو الـ output
+
+237
+00:17:58,630 --> 00:18:02,910
+نحن لا نتحكم بشكل مباشر ولكن إذا تحكمنا على
+
+238
+00:18:02,910 --> 00:18:05,630
+القوانين الانتقالية نستطيع أن نتحكم على النتائج
+
+239
+00:18:05,630 --> 00:18:08,550
+وهو السبب المهم أن نتحكم على القوانين الانتقالية
+
+240
+00:18:08,550 --> 00:18:13,670
+لماذا؟ لأنها مصادر اللي نعتمد عليها لكي نحرر
+
+241
+00:18:13,670 --> 00:18:19,050
+النتائج، حسنا؟ كنت تريد أن تقول شيء؟ نعم، أريد فقط
+
+242
+00:18:19,050 --> 00:18:22,470
+أن أقول ما قلته قبل ذلك إذا أخذنا القوانين
+
+243
+00:18:22,470 --> 00:18:22,750
+الانتقالية
+
+244
+00:18:29,140 --> 00:18:33,080
+نعم، نعم، نعم،
+
+245
+00:18:33,080 --> 00:18:39,580
+نعم،
+
+246
+00:18:39,580 --> 00:18:46,240
+نعم،
+
+247
+00:18:46,240 --> 00:18:49,280
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+248
+00:18:49,280 --> 00:18:49,880
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+249
+00:18:49,880 --> 00:18:50,440
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+250
+00:18:50,440 --> 00:18:50,660
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+251
+00:18:50,660 --> 00:18:51,220
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+252
+00:18:51,220 --> 00:18:53,500
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم
+
+253
+00:18:54,400 --> 00:18:59,160
+هنا نتكلم عن كيف نتعامل مع الهجوم الوحيد أو الهجوم
+
+254
+00:18:59,160 --> 00:19:00,840
+الجمهوري أو الهجوم الأساسي أو الهجوم الأساسي أو
+
+255
+00:19:00,840 --> 00:19:02,660
+الهجوم الوحيد أو الهجوم الوحيد أو الهجوم الوحيد أو
+
+256
+00:19:02,660 --> 00:19:04,600
+الهجوم الوحيد أو الهجوم الوحيد أو الهجوم الوحيد أو
+
+257
+00:19:04,600 --> 00:19:04,780
+الهجوم الوحيد أو الهجوم الوحيد أو الهجوم الوحيد أو
+
+258
+00:19:04,780 --> 00:19:06,200
+الهجوم الوحيد أو الهجوم الوحيد أو الهجوم الوحيد أو
+
+259
+00:19:06,200 --> 00:19:08,520
+الهجوم الوحيد أو الهجوم الوحيد أو الهجوم الوحيد أو
+
+260
+00:19:08,520 --> 00:19:13,740
+الهجوم الوحيد أو الهجوم الوحيد أو الهجوم الوحيد أو
+
+261
+00:19:13,740 --> 00:19:19,640
+الهجوم الوحيد أوأنا قلت قبل أن الوظيفة الوظيفة
+
+262
+00:19:19,640 --> 00:19:25,880
+مرتبطة بالتخيل والفهم الوظيفة الوظيفة الوظيفة
+
+263
+00:19:25,880 --> 00:19:28,660
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+264
+00:19:28,660 --> 00:19:31,400
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+265
+00:19:31,400 --> 00:19:31,500
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+266
+00:19:31,500 --> 00:19:33,400
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+267
+00:19:33,400 --> 00:19:34,680
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة
+
+268
+00:19:34,680 --> 00:19:44,460
+الوظيفة الوظيفة الوظيفة الوظيفة الوظيفة الوظيف
+
+269
+00:19:44,490 --> 00:19:46,530
+هي عملية التعامل الإنساني في مجال التعامل
+
+270
+00:19:46,530 --> 00:19:50,850
+الإجتماعي وهذا مسبب آخر لماذا نحتاج أن نتعامل مع
+
+271
+00:19:50,850 --> 00:19:54,890
+مواصفات مستقل أو نحاول التحكم بمواصفات مستقل لأن
+
+272
+00:19:54,890 --> 00:19:59,590
+إذا تحكمنا بمواصفات مستقل نستطيع أن نتعاملالخروج
+
+273
+00:19:59,590 --> 00:20:01,930
+اللي هو الهيومان الهيومان الهيومان الهيومان
+
+274
+00:20:01,930 --> 00:20:02,630
+الهيومان الهيومان الهيومان الهيومان الهيومان
+
+275
+00:20:02,630 --> 00:20:04,850
+الهيومان الهيومان الهيومان الهيومان الهيومان
+
+276
+00:20:04,850 --> 00:20:06,030
+الهيومان الهيومان الهيومان الهيومان الهيومان
+
+277
+00:20:06,030 --> 00:20:09,870
+الهيومان الهيومان الهيومان الهيومان الهيومان
+
+278
+00:20:09,870 --> 00:20:10,030
+الهيومان الهيومان الهيومان الهيومان الهيومان
+
+279
+00:20:10,030 --> 00:20:13,250
+الهيومان الهيومان الهيومان الهيومان الهيومان
+
+280
+00:20:13,250 --> 00:20:26,330
+الهيومان الهيومان اله
+
+281
+00:20:26,840 --> 00:20:34,920
+Input هنا ماذا يجب أن يساعد في تصميم النتيجة، كيف
+
+282
+00:20:34,920 --> 00:20:39,960
+تعمل الorganization؟وإذا كنا نستخدم المدخل، فهذا
+
+283
+00:20:39,960 --> 00:20:45,280
+سيأثر على النتيجة التي تم إجراءها من المؤسسة مرة
+
+284
+00:20:45,280 --> 00:20:50,960
+أخرى هنا نتحدث عن X وهو سيقوم بإدارتنا إلى Y إذا
+
+285
+00:20:50,960 --> 00:20:56,200
+كنا نجح في فهم هذه العلاقة، فنستطيع أن نتوقع
+
+286
+00:20:56,200 --> 00:21:00,980
+حياتنا المستقبلية وماذا سيحدث من خلال الموظفين،
+
+287
+00:21:00,980 --> 00:21:04,300
+وبالطبع هذا يساعد المؤسسة
+
+288
+00:21:05,760 --> 00:21:11,100
+أعطني مثلًا للميزانيين المستغربين المستغربين، الـ
+
+289
+00:21:11,100 --> 00:21:15,600
+output، الـ effect، نعم؟ نعم، نعم، نعم، نعم، نعم،
+
+290
+00:21:15,600 --> 00:21:16,000
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+291
+00:21:16,000 --> 00:21:17,560
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+292
+00:21:17,560 --> 00:21:17,700
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+293
+00:21:17,700 --> 00:21:17,740
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+294
+00:21:17,740 --> 00:21:19,980
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+295
+00:21:19,980 --> 00:21:29,300
+نعم، نعم، نعم، نعم، نعم، نعم،
+
+296
+00:21:29,300 --> 00:21:31,780
+نعم، ن
+
+297
+00:21:40,310 --> 00:21:44,970
+إذا كل شيء تم فعله بشكل صحيح من أجل المؤسسة، وإذا
+
+298
+00:21:44,970 --> 00:21:52,130
+كانت أشياء أخرى كانت في طريقة أفضل، فهو يجب أن
+
+299
+00:21:52,130 --> 00:21:53,470
+يدفع إلى إجتماع
+
+300
+00:21:56,910 --> 00:21:59,430
+when you talk about productivity it is important
+
+301
+00:21:59,430 --> 00:22:02,990
+to be effective and efficient okay it's not the
+
+302
+00:22:02,990 --> 00:22:05,550
+issue only of producing something we need to
+
+303
+00:22:05,550 --> 00:22:09,230
+produce effectively and efficiently what else yes
+
+304
+00:22:11,180 --> 00:22:13,700
+Okay, now when you talk about absenteeism, we need
+
+305
+00:22:13,700 --> 00:22:17,240
+to reduce or increase? Of course reduce
+
+306
+00:22:17,240 --> 00:22:19,840
+absenteeism, when you talk about satisfaction, we
+
+307
+00:22:19,840 --> 00:22:22,940
+need to increase satisfaction Okay, so there are
+
+308
+00:22:22,940 --> 00:22:25,520
+some dependent variables which we need to increase
+
+309
+00:22:25,520 --> 00:22:28,660
+and there are other dependent variables which we
+
+310
+00:22:28,660 --> 00:22:32,580
+need to decreaseالان مرة أخرى هنا يوجد اتجارات
+
+311
+00:22:32,580 --> 00:22:37,780
+مختلفة ومختلفة ومختلفة ومختلفة ومختلفة ومختلفة
+
+312
+00:22:37,780 --> 00:22:38,460
+ومختلفة ومختلفة ومختلفة ومختلفة ومختلفة ومختلفة
+
+313
+00:22:38,460 --> 00:22:39,120
+ومختلفة ومختلفة ومختلفة ومختلفة ومختلفة ومختلفة
+
+314
+00:22:39,120 --> 00:22:40,920
+ومختلفة ومختلفة ومختلفة ومختلفة ومختلفة ومختلفة
+
+315
+00:22:40,920 --> 00:22:50,960
+ومختلفة ومختلفة ومختلفة ومختلفة ومختلفة
+
+316
+00:22:50,960 --> 00:22:57,280
+ومختلف
+
+317
+00:22:57,300 --> 00:23:01,360
+المزيد من الناس غير موجودة، المزيد من المجلدات
+
+318
+00:23:01,360 --> 00:23:06,440
+ستفقد أيام العمل، هذه أيام العمل مرتبطة بالنسبة
+
+319
+00:23:06,440 --> 00:23:07,100
+للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة
+
+320
+00:23:07,100 --> 00:23:10,340
+للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة
+
+321
+00:23:10,340 --> 00:23:11,780
+للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة
+
+322
+00:23:11,780 --> 00:23:12,180
+للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة
+
+323
+00:23:12,180 --> 00:23:12,240
+للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة
+
+324
+00:23:12,240 --> 00:23:14,820
+للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة للنسبة
+
+325
+00:23:14,820 --> 00:23:19,840
+للنسبة
+
+326
+00:23:19,840 --> 00:23:26,290
+للنسبة للنوإذا كانوا مقفلين من المؤسسة أو إذا
+
+327
+00:23:26,290 --> 00:23:31,590
+كانوا يرحلون بطريقتهم الخاصة لأي حسب السبب طبعا
+
+328
+00:23:31,590 --> 00:23:36,610
+تغيير المساعدة في تغيير المساعدة هذا يعني أنه يكون
+
+329
+00:23:36,610 --> 00:23:42,410
+هناك أكتر اختار من المؤسسة والناس المختارة جديد
+
+330
+00:23:42,410 --> 00:23:45,970
+لعمل في المؤسسة يحتاجون المزيد من الوقت لتتعامل مع
+
+331
+00:23:45,970 --> 00:23:50,790
+البيئة الداخلية وما إلى ذلك، فهو أيضا مهم لتقليد
+
+332
+00:23:50,790 --> 00:23:55,630
+تغيير المساعدةمختلفة مختلفة مختلفة مختلفة مختلفة
+
+333
+00:23:55,630 --> 00:24:05,990
+مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة مختلفة
+
+334
+00:24:05,990 --> 00:24:16,190
+مختلفة
+
+335
+00:24:21,830 --> 00:24:25,270
+ومن داخل المؤسسة ومن خلال الوظيفة العملية، حسنا؟
+
+336
+00:24:25,270 --> 00:24:28,510
+من المهم دائما أن نزعل مستوى مستوى الوظيفة العملية
+
+337
+00:24:28,510 --> 00:24:31,910
+لماذا يجب أن نعمل على مستوى مستوى الوظيفة العملية؟
+
+338
+00:24:31,910 --> 00:24:35,010
+بالطبع، كل هذه المشاكل التي سنتحدث عنها لاحقا في
+
+339
+00:24:35,010 --> 00:24:38,870
+أكتر تفاصيل، ولكن مستوى الوظيفة العملية لماذا يجب
+
+340
+00:24:38,870 --> 00:24:41,950
+أن نعمل على مستوى مستوى الوظيفة العملية؟ نعم؟ لأنه
+
+341
+00:24:41,950 --> 00:24:45,810
+يجب أن نعمل مع الوظيفة العملية ونقوم بعمل عمل أفضل
+
+342
+00:24:50,650 --> 00:24:53,110
+بعمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+343
+00:24:53,110 --> 00:24:57,250
+عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+344
+00:24:57,250 --> 00:24:57,690
+عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+345
+00:24:57,690 --> 00:24:57,750
+عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+346
+00:24:57,750 --> 00:24:57,930
+عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+347
+00:24:57,930 --> 00:25:01,330
+عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+348
+00:25:01,330 --> 00:25:04,550
+عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل عمل
+
+349
+00:25:04,550 --> 00:25:11,770
+عمل عمل
+
+350
+00:25:11,770 --> 00:25:17,820
+عمل عالمزيد من ما يوجد فيه إيجابية، يوجد إيجابية،
+
+351
+00:25:17,820 --> 00:25:22,260
+فإن المؤسسة تستطيع تدفع إيجارات لعملوك، تستطيع
+
+352
+00:25:22,260 --> 00:25:26,900
+تحسين حالة العمل، وهذا يجب أن يؤدي إلى إتفاق أفضل،
+
+353
+00:25:26,900 --> 00:25:30,800
+وإذا كان هناك إتفاق أفضل، فإن الـ turnover أقل،
+
+354
+00:25:30,800 --> 00:25:34,280
+فإن عملية الابسينتزم أقل، فإن الوظائف في المجال
+
+355
+00:25:34,280 --> 00:25:36,500
+العمل أيضًا أقل،
+
+356
+00:25:44,330 --> 00:25:48,650
+لأ، هناك أيضًا علاقة بين كل .. نستطيع أن نفكر
+
+357
+00:25:48,650 --> 00:25:51,290
+بطريقة أخرى، نستطيع أن نفكر في دائمًا مؤسسة
+
+358
+00:25:51,290 --> 00:25:56,110
+متعاملة، حسنًا؟ حيث كل المصادر متعلقة مع بعضها
+
+359
+00:25:56,110 --> 00:25:59,170
+البعض، حسنًا؟ عندما نتحدث عن إهتمام العمل لاحقًا،
+
+360
+00:25:59,170 --> 00:26:03,390
+سنتحدث عن ما هي الواردات التي ستؤثر على الإهتمام
+
+361
+00:26:03,390 --> 00:26:08,200
+بشكل نقلي ومناسب، حسنًا؟ولكن مرة أخرى، إنه نفس
+
+362
+00:26:08,200 --> 00:26:12,200
+الطريقة إذا كنت تفكر في إنتجام وإنجاز العمل من
+
+363
+00:26:12,200 --> 00:26:16,000
+نقطة مختلفة، فستحصل على نتيجة مشابقة ولكن من نقطة
+
+364
+00:26:16,000 --> 00:26:20,920
+مختلفة من النظر، حسنًا؟ لكن جميع هذه العلاقات ليست
+
+365
+00:26:20,920 --> 00:26:24,200
+كاملة أيضًا، يعني على سبيل المثال، أحيانًا أنا
+
+366
+00:26:24,200 --> 00:26:29,080
+أتكلم عنفي حالة معينة لتفهم ما أحاول أن أقوله هنا
+
+367
+00:26:29,080 --> 00:26:34,540
+بعض المؤسسات لديها إيجارات جيدة جيدة وإيجارات جيدة
+
+368
+00:26:34,540 --> 00:26:35,780
+أو إيجارات جيدة أو إيجارات جيدة أو إيجارات جيدة أو
+
+369
+00:26:35,780 --> 00:26:36,360
+إيجارات جيدة أو إيجارات جيدة أو إيجارات جيدة أو
+
+370
+00:26:36,360 --> 00:26:36,400
+إيجارات جيدة أو إيجارات جيدة أو إيجارات جيدة أو
+
+371
+00:26:36,400 --> 00:26:36,620
+إيجارات جيدة أو إيجارات جيدة أو إيجارات جيدة أو
+
+372
+00:26:36,620 --> 00:26:42,120
+إيجارات جيدة أو إيجارات جيدة أو إيجارات جيدة أو
+
+373
+00:26:42,120 --> 00:26:46,780
+إيجارات
+
+374
+00:26:46,780 --> 00:26:51,740
+جيدة أو
+
+375
+00:26:51,740 --> 00:26:58,220
+إوهذا مرة أخرى سنتحدث عنه لاحقًا إذا كانت المعجزة
+
+376
+00:26:58,220 --> 00:27:02,200
+مفيدة، ليس بالطبع أنها ستتحسن التجارب، يعني لا
+
+377
+00:27:02,200 --> 00:27:07,180
+يوجد علاقة абсолютية بين المعجزة والتجارب، لكن
+
+378
+00:27:07,180 --> 00:27:11,100
+هناك علاقة абсолютية بين المعجزة والتغلب، بين
+
+379
+00:27:11,100 --> 00:27:15,790
+المعجزة والتغلبAbsentism يعني أحيانًا الناس مستمرة
+
+380
+00:27:15,790 --> 00:27:20,610
+ولكن تجاربها سيئة لماذا؟ لأنهم ربما لايوجدوا
+
+381
+00:27:20,610 --> 00:27:24,890
+مهاراتهم على سبيل المثال أو أحيانًا ربما السيطرة
+
+382
+00:27:24,890 --> 00:27:28,490
+التي تم تحكيها الوظيفة ليست مفهومة بطريقة صحيحة
+
+383
+00:27:28,490 --> 00:27:32,550
+على سبيل المثال، فالتجارب ستكون مفارقة أو ربما
+
+384
+00:27:32,550 --> 00:27:35,850
+الأدوات والأسلحة والسيستم والميكانيزم وما إلى وما
+
+385
+00:27:35,850 --> 00:27:41,330
+إلى ليسوا مشروعي، فالتجارب ستكون مفارقة، لكن على
+
+386
+00:27:41,330 --> 00:27:47,970
+الأقلالإيجابية ستساعد المؤسسة في تحقيق نتائج أخرى
+
+387
+00:27:47,970 --> 00:27:54,590
+التي مرتبطة بالإنجاز ولكنها ليست مرتبطة بالإنجاز
+
+388
+00:27:54,590 --> 00:27:58,750
+فهذا السبب يقولنا دائما أنه لا يوجد علاقة مباشرة
+
+389
+00:27:58,750 --> 00:28:04,170
+بين الإنجاز والإيجاب ولكن هذا لا يعني أيضا أن
+
+390
+00:28:04,170 --> 00:28:10,360
+الإنجاز لن يساعد الناسبإدعائهم لتحسين مهارتهم
+
+391
+00:28:10,360 --> 00:28:11,900
+لتحسين مهارتهم لتحسين مهارتهم لتحسين مهارتهم
+
+392
+00:28:11,900 --> 00:28:12,540
+لتحسين مهارتهم لتحسين مهارتهم لتحسين مهارتهم
+
+393
+00:28:12,540 --> 00:28:12,560
+لتحسين مهارتهم لتحسين مهارتهم لتحسين مهارتهم
+
+394
+00:28:12,560 --> 00:28:15,540
+لتحسين مهارتهم لتحسين مهارتهم لتحسين مهارتهم
+
+395
+00:28:15,540 --> 00:28:16,000
+لتحسين مهارتهم لتحسين مهارتهم لتحسين مهارتهم
+
+396
+00:28:16,000 --> 00:28:19,240
+لتحسين مهارتهم لتحسين مهارتهم لتحسين مهارتهم
+
+397
+00:28:19,240 --> 00:28:28,630
+لتحسين مهارتهم لتحسين مهارتهم لتحسين مهارهي مستوى
+
+398
+00:28:28,630 --> 00:28:34,030
+للدراسة في مجموعات ومجموعات
+
+399
+00:28:34,030 --> 00:28:38,310
+ومجموعات ومجموعات ومجموعات ومجموعات ومجموعات
+
+400
+00:28:38,310 --> 00:28:38,850
+ومجموعات ومجموعات ومجموعات ومجموعات ومجموعات
+
+401
+00:28:38,850 --> 00:28:41,890
+ومجموعات ومجموعات ومجموعات ومجموعات ومجموعات
+
+402
+00:28:41,890 --> 00:28:42,070
+ومجموعات ومجموعات ومجموعات ومجموعات ومجموعات
+
+403
+00:28:42,070 --> 00:28:44,130
+ومجموعات ومجموعات ومجموعات ومجموعات ومجموعات
+
+404
+00:28:44,130 --> 00:28:51,510
+ومجموعات ومجموعات ومجموعات ومج
+
+405
+00:28:51,540 --> 00:28:57,480
+الذي يجب أن نحكم عليه مثلًا هذا سيساعدنا أكتر في
+
+406
+00:28:57,480 --> 00:29:03,520
+فهم العلاقات لدينا المدخل الإنساني ويجب أن نحصل
+
+407
+00:29:03,520 --> 00:29:07,920
+على نتيجة الخروج من هنا نحن نتكلم عن الاختلافات
+
+408
+00:29:07,920 --> 00:29:12,560
+الاختلافات، الابسنطيزم، الانتقال، العمل، عمل
+
+409
+00:29:12,560 --> 00:29:14,660
+مخاطر، عمل مكان، عمل مخاطر، عمل مخاطر، عمل مخاطر،
+
+410
+00:29:14,660 --> 00:29:15,800
+مخاطر، عمل مخاطر، عمل مخاطر، عمل مخاطر، عمل مخاطر،
+
+411
+00:29:15,800 --> 00:29:17,170
+عمل مخاطر، عمل مخاطر، عمل مخاطر، عمل مخاطلذلك يجب
+
+412
+00:29:17,170 --> 00:29:20,790
+أن نصل إلى نتيجة إيجابية لكي نصل إلى نتيجة إيجابية
+
+413
+00:29:20,790 --> 00:29:21,850
+لكي نصل إلى نتيجة إيجابية لكي نصل إلى نتيجة
+
+414
+00:29:21,850 --> 00:29:25,350
+إيجابية لكي نصل إلى نتيجة إيجابية لكي نصل إلى
+
+415
+00:29:25,350 --> 00:29:26,570
+نتيجة إيجابية لكي نصل إلى نتيجة إيجابية لكي نصل
+
+416
+00:29:26,570 --> 00:29:26,710
+إلى نتيجة إيجابية لكي نصل إلى نتيجة إيجابية لكي
+
+417
+00:29:26,710 --> 00:29:29,950
+إيجابية لكي نصل إلى نتيجة إيجابية لكي نصل إلى
+
+418
+00:29:29,950 --> 00:29:37,570
+نتيجةهذا ما سنكتشفه على مستوى الشخصي نحتاج أن
+
+419
+00:29:37,570 --> 00:29:42,350
+نتعامل مع شخصية الموظفين نحتاج أن نتعامل مع قيم
+
+420
+00:29:42,350 --> 00:29:45,930
+الموظفين نحتاج أن نشجع الموظفين نحتاج على سبيل
+
+421
+00:29:45,930 --> 00:29:52,210
+المثال أن نعمل على أهداف شخصية الموظفين نحتاج أن
+
+422
+00:29:52,210 --> 00:29:54,930
+نعمل على أهداف شخصية الموظفين نحتاج أن نعمل على
+
+423
+00:29:54,930 --> 00:29:56,870
+أهداف شخصية الموظفين نحتاج أن نعمل على أهداف شخصية
+
+424
+00:29:56,870 --> 00:29:57,730
+الموظفين نحتاج أن نعمل على أهداف شخصية الموظفين
+
+425
+00:29:57,730 --> 00:29:59,270
+نحتاج أن نعمل على أهداف شخصية الموظفين نحتاج أن
+
+426
+00:29:59,270 --> 00:30:02,220
+نعمل على أهداف شخصية الموظفين نحتنحن نسميها
+
+427
+00:30:02,220 --> 00:30:07,420
+الانتجارات الانتجارات هذه يجب أن تساعدنا إذا كنا
+
+428
+00:30:07,420 --> 00:30:12,000
+نتحكم بطريقة مهمة للغاية لتحسين النتائج اللي
+
+429
+00:30:12,000 --> 00:30:14,980
+نحتاجها لتحقيقها وهي الانتجارات الانتجارية
+
+430
+00:30:14,980 --> 00:30:17,220
+الانتجارية الانتجارية الانتجارية الانتجارية
+
+431
+00:30:17,220 --> 00:30:18,800
+الانتجارية الانتجارية الانتجارية الانتجارية
+
+432
+00:30:18,800 --> 00:30:19,020
+الانتجارية الانتجارية الانتجارية الانتجارية
+
+433
+00:30:19,020 --> 00:30:22,720
+الانتجارية الانتجارية الانتجارية الانتميكانيزم
+
+434
+00:30:22,720 --> 00:30:26,960
+الوطن، رئيسية، التواصل، إدارة التغيير، قوة، كيفية
+
+435
+00:30:26,960 --> 00:30:30,960
+التعامل مع المشاكل ومعالجة المشاكل داخل المؤسسة
+
+436
+00:30:30,960 --> 00:30:36,360
+ومعالجة المشاكل داخل المؤسسة ومعالجة المشاكل
+
+437
+00:30:36,360 --> 00:30:37,360
+ومعالجة المشاكل ومعالجة المشاكل ومعالجة المشاكل
+
+438
+00:30:37,360 --> 00:30:37,460
+ومعالجة المشاكل ومعالجة المشاكل ومعالجة المشاكل
+
+439
+00:30:37,460 --> 00:30:39,590
+ومعالجة المشاكلعندما نتحدث عن مستوى الانجلاز نحن
+
+440
+00:30:39,590 --> 00:30:42,750
+نتحدث عن الانجلاز الانجلاز الانجلاز الانجلاز
+
+441
+00:30:42,750 --> 00:30:44,130
+الانجلاز الانجلاز الانجلاز الانجلاز الانجلاز
+
+442
+00:30:44,130 --> 00:30:44,710
+الانجلاز الانجلاز الانجلاز الانجلاز الانجلاز
+
+443
+00:30:44,710 --> 00:30:44,730
+الانجلاز الانجلاز الانجلاز الانجلاز الانجلاز
+
+444
+00:30:44,730 --> 00:30:45,730
+الانجلاز الانجلاز الانجلاز الانجلاز الانجلاز
+
+445
+00:30:45,730 --> 00:30:46,250
+الانجلاز الانجلاز الانجلاز الانجلاز الانجلاز
+
+446
+00:30:46,250 --> 00:30:47,370
+الانجلاز الانجلاز الانجلاز الانجلاز الانجلاز
+
+447
+00:30:47,370 --> 00:30:56,450
+الانجلاز الانجلاز الانجلاز الانجلاز الانجلاز
+
+448
+00:30:56,450 --> 00:31:04,090
+الانجلا
+
+449
+00:31:04,130 --> 00:31:11,130
+وإذا قمنا بإدارة تلك التغييرات بإمكاننا إدارة
+
+450
+00:31:11,130 --> 00:31:14,010
+تغييرات مستمرة بإمكاننا إدارة تغييرات مستمرة
+
+451
+00:31:14,010 --> 00:31:14,430
+بإمكاننا إدارة تغييرات مستمرة بإمكاننا إدارة
+
+452
+00:31:14,430 --> 00:31:15,590
+تغييرات مستمرة بإمكاننا إدارة تغييرات مستمرة
+
+453
+00:31:15,590 --> 00:31:16,090
+بإمكاننا إدارة تغييرات مستمرة بإمكاننا إدارة
+
+454
+00:31:16,090 --> 00:31:16,210
+تغييرات مستمرة بإمكاننا إدارة تغييرات مستمرة
+
+455
+00:31:16,210 --> 00:31:17,810
+بإمكاننا إدارة تغييرات مستمرة بإمكاننا إدارة
+
+456
+00:31:17,810 --> 00:31:21,050
+تغييرات مستمرة بإمكاننا إدارة تغييرات مستمرة
+
+457
+00:31:21,050 --> 00:31:25,350
+بإمكاننا
+
+458
+00:31:25,350 --> 00:31:32,190
+إدار
+
+459
+00:31:40,060 --> 00:31:45,440
+Okay. This is also يعني another topic which we are
+
+460
+00:31:45,440 --> 00:31:48,580
+going to discuss later. But it is like when you
+
+461
+00:31:48,580 --> 00:31:50,900
+talk about the community, but in different way.
+
+462
+00:31:51,000 --> 00:31:55,520
+When you talk about ideal citizen and another or
+
+463
+00:31:55,520 --> 00:31:59,320
+other citizens who are not committed to laws,
+
+464
+00:31:59,520 --> 00:32:05,080
+regulations, etc. Okay. When you talk aboutعندما
+
+465
+00:32:05,080 --> 00:32:13,360
+نتكلم عن مجتمع، نتكلم عن موظفين لديهم مرتبط عالي و
+
+466
+00:32:13,360 --> 00:32:18,860
+عادةً يشعرون بطريقة ما أنهم يعملون داخل المنزل
+
+467
+00:32:23,140 --> 00:32:29,400
+على مستوى اعتبار الشركة، وهذا يجب أن يؤثر على
+
+468
+00:32:29,400 --> 00:32:30,460
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+469
+00:32:30,460 --> 00:32:33,140
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+470
+00:32:33,140 --> 00:32:36,740
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+471
+00:32:36,740 --> 00:32:37,380
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+472
+00:32:37,380 --> 00:32:40,000
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+473
+00:32:40,000 --> 00:32:40,580
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+474
+00:32:40,580 --> 00:32:41,100
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+475
+00:32:41,100 --> 00:32:41,660
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+476
+00:32:41,660 --> 00:32:43,200
+عملية عملية
+
+477
+00:32:45,950 --> 00:32:51,610
+هذا ما يسمى بـ Citizenship إنه نوع من الشعور اللي
+
+478
+00:32:51,610 --> 00:32:56,110
+يكون للموظفين اللي يكون للموظفين اللي يكون
+
+479
+00:32:56,110 --> 00:32:56,130
+للموظفين اللي يكون للموظفين اللي يكون للموظفين
+
+480
+00:32:56,130 --> 00:32:57,090
+اللي يكون للموظفين اللي يكون للموظفين اللي يكون
+
+481
+00:32:57,090 --> 00:32:57,950
+للموظفين اللي يكون للموظفين اللي يكون للموظفين
+
+482
+00:32:57,950 --> 00:32:58,590
+اللي يكون للموظفين اللي يكون للموظفين اللي يكون
+
+483
+00:32:58,590 --> 00:32:59,810
+للموظفين اللي يكون للموظفين اللي يكون للموظفين
+
+484
+00:32:59,810 --> 00:33:01,630
+اللي يكون للموظفين اللي يكون للموظفين اللي يكون
+
+485
+00:33:01,630 --> 00:33:05,490
+للموظفين اللي يكون للموظفين اللي يكون للموظفين
+
+486
+00:33:05,490 --> 00:33:12,630
+اللي
+
+487
+00:33:12,630 --> 00:33:14,750
+يكون للم
+
diff --git a/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/2BApdALeEyM.srt b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/2BApdALeEyM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..35f904f7c87293e1fdfc0358157b1b59b5910775
--- /dev/null
+++ b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/2BApdALeEyM.srt
@@ -0,0 +1,2099 @@
+1
+00:00:20,790 --> 00:00:23,750
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:23,750 --> 00:00:28,370
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى 
+
+3
+00:00:28,370 --> 00:00:32,910
+آله وصحبه وسلم إن شاء الله يا إخواننا يا إخوة سوف
+
+4
+00:00:32,910 --> 00:00:37,170
+نكون معكم في هذا الفصل مع متطلب من متطلبات الجامعة 
+
+5
+00:00:37,170 --> 00:00:41,770
+الإسلامية اللي هو القرآن الكريم جزء الأحقاف سوف
+
+6
+00:00:41,770 --> 00:00:46,980
+يكون معكم الدكتور زهدي أبو نعمة المقرر الموجود معنا 
+
+7
+00:00:46,980 --> 00:00:51,980
+في هذا المساق هو جزء الأحقاف أو نصف الجزء الأحقاف 
+
+8
+00:00:51,980 --> 00:00:56,160
+يعني سورة الأحقاف وسورة محمد و17 آية من سورة الفتح 
+
+9
+00:00:56,160 --> 00:01:01,340
+هذه حفظًا بالإضافة لمعاني الكلمات الغريبة في هذا 
+
+10
+00:01:01,340 --> 00:01:06,480
+الجزء المقرر يعني سورة الأحقاف وسورة محمد 17 آية من 
+
+11
+00:01:06,480 --> 00:01:09,840
+سورة الفتح معاني الكلمات الغريبة في هذه الصور 
+
+12
+00:01:09,840 --> 00:01:16,360
+الثلاثة 17 آية من سورة الفتح اللي هو الحزب الأول من 
+
+13
+00:01:16,360 --> 00:01:21,180
+الجزء السادس والعشرين سورة الأحقاف وسورة محمد 17
+
+14
+00:01:21,180 --> 00:01:25,180
+آية من سورة الفتح معانا الكلمات الغريبة ومقاصد 
+
+15
+00:01:25,180 --> 00:01:28,600
+وأهداف سورة الأحزاب هناخدها إن شاء الله في نهاية 
+
+16
+00:01:28,600 --> 00:01:33,420
+الفصل بالإضافة إلى أحكام التجويد المقرر معنا في 
+
+17
+00:01:33,420 --> 00:01:37,570
+هذا الفصل الكتاب المقرر معناه هو هذا الكتاب هو 
+
+18
+00:01:37,570 --> 00:01:43,370
+مختصر المغني في علم التجويد أو كذلك الشرائح 
+
+19
+00:01:43,370 --> 00:01:47,030
+الموجودة عند الكمبيوتر أو في الكمبيوتر اللي سوف
+
+20
+00:01:47,030 --> 00:01:51,110
+نشرح منها إن شاء الله في هذا الفصل موجودة في صفحة 
+
+21
+00:01:51,110 --> 00:01:54,450
+الدكتور زهدي لو فتحت على ال google  دكتور أو زهدي 
+
+22
+00:01:54,450 --> 00:01:58,410
+أبو نعمة هتجد صفحته في الجامعة بإمكانك أن تأخذ
+
+23
+00:01:58,410 --> 00:02:03,210
+المقرر المطلوب جزء الأحقاف  وتستفيد من الشروحات
+
+24
+00:02:03,210 --> 00:02:09,400
+الموجودة في هذا الفصل إن شاء الله أول موضوع معانا
+
+25
+00:02:09,400 --> 00:02:13,800
+هو موضوع الوقف والابتداء الأحكام الموجودة معانا 
+
+26
+00:02:13,800 --> 00:02:19,060
+الوقف والابتداء بالإضافة إلى القطع والسكت وهمزة
+
+27
+00:02:19,060 --> 00:02:22,980
+الوصل أو الابتداء بهمزة الوصل نبدأ في هذه المحاضرة 
+
+28
+00:02:22,980 --> 00:02:28,060
+أيها الأخوة مع تعريفات عامة بجزء الأحقاف اللي هو
+
+29
+00:02:28,060 --> 00:02:33,550
+بداية وأهمية الوقف الوقف يعد من الموضوعات المهمة
+
+30
+00:02:33,550 --> 00:02:38,790
+والتي ينبغي على الإنسان المسلم أن يقف عند الأماكن
+
+31
+00:02:38,790 --> 00:02:43,030
+التي يوقف عندها لأن لو وقف على موضع لا يوقف عنده
+
+32
+00:02:43,030 --> 00:02:48,110
+ممكن تؤدي لمعنى غير المعنى المراد أو يعني تخلو
+
+33
+00:02:48,110 --> 00:02:51,890
+بالمعنى لذلك يعد الوقف من الموضوعات المهمة
+
+34
+00:02:51,890 --> 00:02:56,580
+والمسائل الهامة في علم التجويد وقد سئل الإمام علي
+
+35
+00:02:56,580 --> 00:03:01,740
+رضي الله عنه عن قوله تعالى ورتل القرآن ترتيله قال
+
+36
+00:03:01,740 --> 00:03:06,560
+الترتيل هو تجويد الحروف ومعرفة الوقوف ما معنى تجويد
+
+37
+00:03:06,560 --> 00:03:12,060
+الحروف؟ ما معنى تجويد الحروف؟ يعني أن نخرج الحرف من
+
+38
+00:03:12,060 --> 00:03:16,730
+مخرجه ونؤتيه حقه ومستحقه من الصفات أن نخرجها لأن
+
+39
+00:03:16,730 --> 00:03:20,170
+هناك كثير من الحروف قد يخرجها بعض الناس من غير
+
+40
+00:03:20,170 --> 00:03:25,430
+مخرجها مثل حرف الذال يلفظه is  ذلك الكتاب وهذا خطأ 
+
+41
+00:03:25,430 --> 00:03:31,630
+أو ثمة يقول سمة أو غير ذلك من بعض الحروف فالذي لا
+
+42
+00:03:31,630 --> 00:03:37,330
+يجود الحروف ولا يتقن الحروف أو يعطي الحروف حقها
+
+43
+00:03:37,330 --> 00:03:43,070
+هذا يخلو بالتجويد وكذلك معرفة الوقوف لابد أن يقف
+
+44
+00:03:43,070 --> 00:03:48,070
+عند موضع مناسب والوقف هو يتبع المعنى فإذا اكتمل
+
+45
+00:03:48,070 --> 00:03:52,130
+المعنى يقف القارئ فإذا وقف القارئ على كلمة لم يتم 
+
+46
+00:03:52,130 --> 00:03:56,130
+المعنى عندها أو توهم معنى غير المعنى المراد يختل
+
+47
+00:03:56,130 --> 00:04:02,430
+المعنى وأصل الوقف مأخوذ من حديث أم سلمة رواية عن 
+
+48
+00:04:02,430 --> 00:04:05,990
+أم سلمة رضي الله عنها قالت كان رسول الله صلى الله
+
+49
+00:04:05,990 --> 00:04:11,830
+عليه وسلم يقطع قراءته يقرأ الحمد لله رب العالمين
+
+50
+00:04:11,830 --> 00:04:19,470
+ثم يقف الرحمن الرحيم ثم يقف مالك يوم الدين ثم يقف 
+
+51
+00:04:19,470 --> 00:04:24,290
+وهكذا كان يقطع قراءته وبعد ذلك الصحابة تعلموا من
+
+52
+00:04:24,290 --> 00:04:27,550
+النبي عليه الصلاة والسلام فعرفوا أن هذا المكان 
+
+53
+00:04:27,550 --> 00:04:31,070
+الذي كان الرسول صلى الله عليه وسلم يكثر من الوقف 
+
+54
+00:04:31,070 --> 00:04:36,670
+عليه هو رأس آية فسميت هذه الآيات إذن الوقف مهم لأنه
+
+55
+00:04:36,670 --> 00:04:42,050
+يترتب عليه أن يفهم الإنسان المعنى فما هو تعريف
+
+56
+00:04:42,050 --> 00:04:47,430
+الوقف؟ ما هو تعريف الوقف يا إخواننا؟ الوقف من حيث
+
+57
+00:04:47,430 --> 00:04:52,730
+اللغة اللي هو الكف والحبس يقال أوقفت الدابة بمعنى
+
+58
+00:04:52,730 --> 00:04:57,310
+حبستها فلان موقوف على ذمة التحقيق بمعنى محبوس 
+
+59
+00:04:57,310 --> 00:05:02,570
+وتعريف الوقف في الاصطلاح هو قطع الصوت على آخر
+
+60
+00:05:02,570 --> 00:05:07,370
+الكلمة القرآنية زمنا يسيرا يتنفس فيه القارئ عادة
+
+61
+00:05:07,370 --> 00:05:11,970
+بنية استئناف التلاوة لا بنية الإعراض عنها ما معنى
+
+62
+00:05:11,970 --> 00:05:16,620
+هذا التعريف؟ يعني يقطع الإنسان قراءته ويقطع صوته
+
+63
+00:05:16,620 --> 00:05:21,540
+عند آخر كلمة قرآنية زمنًا عشان يتنفس حتى يتنفس
+
+64
+00:05:21,540 --> 00:05:29,180
+يعني يقول الحمد لله رب العالمين يقف يقف حتى يتنفس
+
+65
+00:05:29,180 --> 00:05:33,040
+عادة لكن لو لم يتنفس ممكن يستمر في القراءة لكن
+
+66
+00:05:33,040 --> 00:05:37,780
+عادة يتنفس القارئ ما بين الآية والآية الرحمن
+
+67
+00:05:37,780 --> 00:05:46,030
+الرحيم مالك يوم الدين وهكذا يسمى هذا الوقف قطع
+
+68
+00:05:46,030 --> 00:05:50,630
+الصوت على آخر الكلمة القرآنية زمنا يسيرا يتنفس فيه
+
+69
+00:05:50,630 --> 00:05:54,670
+القارئ عادة بنية استئناف التلاوة لا بنية الإعراض
+
+70
+00:05:54,670 --> 00:05:59,380
+عنها أين يكون الوقف يا إخواننا؟ يكون الوقف على رؤوس
+
+71
+00:05:59,380 --> 00:06:03,880
+الآيات ويجب أن يقف القارئ في وسط الآية يعني ممكن 
+
+72
+00:06:03,880 --> 00:06:07,440
+أن يقف في وسط الآية لو كانت الآية طويلة وأما الوقف
+
+73
+00:06:07,440 --> 00:06:12,280
+على رؤوس الآيات فهو سنة ولا يمكن أن يقف القارئ في
+
+74
+00:06:12,280 --> 00:06:19,460
+منتصف الكلمة حتى لو كانت متصلة في الكتابة يعني أو
+
+75
+00:06:19,460 --> 00:06:24,740
+متصلة رسمًا يعني الوقف أين يكون على رؤوس الآيات وكذلك
+
+76
+00:06:24,740 --> 00:06:29,140
+يكون في منتصف الآية ولكنه لا يمكن أن يقف 
+
+77
+00:06:29,140 --> 00:06:33,540
+القارئ أو يقطع صوته في منتصف الكلمة حتى في الكلمات
+
+78
+00:06:33,540 --> 00:06:39,080
+المتصلة رسمًا مثل ذلك أَيَحْسَبُ الإِنسَانُ أَن 
+
+79
+00:06:39,080 --> 00:06:43,780
+لَن نَجْمَعَ عِظَامَهُ لو واحد وقف مثلًا أَيَحْسَبُ 
+
+80
+00:06:43,780 --> 00:06:49,900
+الإِنسَانُ أَن وبعدين لن نجمع عظامه لا يصح مع أن
+
+81
+00:06:49,900 --> 00:06:56,720
+أن لن هي مضمرة فصارت ألا نجمع عظامه إذا هنا لا يصح
+
+82
+00:06:56,720 --> 00:07:02,320
+لنا أن نقف على كلمة أن من قوله ألا وكذلك في قول
+
+83
+00:07:02,320 --> 00:07:07,720
+تعالى قال يا ابن أم لا تأخذ بلحيتي ولا برأسي لا 
+
+84
+00:07:07,720 --> 00:07:12,140
+يصح للقارئ أن يقف على الكلمة قال يا ابن أم أو يا
+
+85
+00:07:12,140 --> 00:07:18,390
+ابن قال يا ابن من يا ابن أم فهذا متصل بحيث الرسم في 
+
+86
+00:07:18,390 --> 00:07:25,530
+المصحف الشريف طيب إذا هذا هو تعريف الوقف قطع الصوت 
+
+87
+00:07:25,530 --> 00:07:28,770
+على الكلمة القرآنية زمنًا يسيرًا يتنفس فيه القارئ
+
+88
+00:07:28,770 --> 00:07:33,310
+عادة بنية استئناف التلاوة لا بنية الإعراض عنها فما
+
+89
+00:07:33,310 --> 00:07:38,940
+هو حكم الوقف؟ الوقف طبعًا جائز يجب على القارئ أن يقف
+
+90
+00:07:38,940 --> 00:07:44,400
+عند أي مكان ما لم يوجد ما يوجبه أو يمنعه ما دام ما 
+
+91
+00:07:44,400 --> 00:07:50,600
+لم يوجد ما يوجب الوقف يسمى الوقف اللازم فبإمكانه 
+
+92
+00:07:50,600 --> 00:07:54,800
+أن يقف أو يصل ما لم يوجد ما يوجب الوقف كالوقف 
+
+93
+00:07:54,800 --> 00:07:59,530
+اللازم أو يمنع الوقف كالوقف الممنوع فيلزم القارئ
+
+94
+00:07:59,530 --> 00:08:04,630
+بالوقف أو الواصل باعتبار ما يترتب عليه من المعنى 
+
+95
+00:08:04,630 --> 00:08:09,370
+فالوقف يترتب على المعنى إذا اكتمل المعنى أصل وإذا 
+
+96
+00:08:09,370 --> 00:08:13,890
+لم يكتمل إذا اكتمل المعنى بإمكاني أن أقف وإذا لم 
+
+97
+00:08:13,890 --> 00:08:18,570
+يكتمل بإمكاني أن أتواصل في القراءة مثلًا فإن كان 
+
+98
+00:08:18,570 --> 00:08:23,780
+الوقف يوهم معنى غير المعنى المراد أو لا يفهمه معناه 
+
+99
+00:08:23,780 --> 00:08:28,660
+فلا يصح لنا أن نقف على هذا المكان مثال ذلك لو وقف 
+
+100
+00:08:28,660 --> 00:08:33,620
+القارئ على كلمة والظالمين في قول تعالى يدخل من
+
+101
+00:08:33,620 --> 00:08:39,660
+يشاء في رحمته والظالمين أعد لهم عذابًا أليمة الأصل
+
+102
+00:08:39,660 --> 00:08:47,320
+أين يقف يدخل من يشاء في رحمته والظالمين أعد لهم 
+
+103
+00:08:47,320 --> 00:08:52,310
+عذابًا أليمة لو وقف القارئ عند قوله والظالمين 
+
+104
+00:08:52,310 --> 00:08:58,430
+يدخلوا من يشاء في رحمته والظالمين بتكون داخلة 
+
+105
+00:08:58,430 --> 00:09:02,370
+الظالمين مع الذين يرحمهم الله سبحانه وتعالى وهذا 
+
+106
+00:09:02,370 --> 00:09:06,210
+بتكون أوهمة معنى غير المعنى المراد لذلك لا نقف على 
+
+107
+00:09:06,210 --> 00:09:10,530
+هذا الكلام والوقف عليه يسمى وقفًا خبيثًا لأنها أوهمت
+
+108
+00:09:10,530 --> 00:09:15,650
+معنى غير المعنى المراد والأصل أن يقف عندما يتم 
+
+109
+00:09:15,650 --> 00:09:23,100
+المعنى يدخل من يشاء في رحمته والظالمين أعد لهم عذابًا
+
+110
+00:09:23,100 --> 00:09:28,300
+أليمة وكذلك إذا كان الوصل يغير المعنى ممكن لو وصلنا 
+
+111
+00:09:28,300 --> 00:09:32,800
+بيتغير المعنى يعني وقفنا على كلمة تم المانع عندها
+
+112
+00:09:32,800 --> 00:09:38,620
+لا تتعلق بما بعدها لفظًا ولا معنى وإذا وصلت اختل 
+
+113
+00:09:38,620 --> 00:09:42,840
+المعنى فلا يجب علينا أن نصل ويجب علينا أن نقطع إذا 
+
+114
+00:09:42,840 --> 00:09:47,600
+الوقف أو عدم الوقف على إيه بيرتب؟ على المعنى إذا 
+
+115
+00:09:47,600 --> 00:09:51,340
+كان الوقف ممكن يوهم معنى غير معنى المراد فيجب أن 
+
+116
+00:09:51,340 --> 00:09:55,540
+نصل وإذا كان الوصل يوهم معنى غير معنى المراد يجب
+
+117
+00:09:55,540 --> 00:10:00,180
+علينا أن نقطع مثلًا هنا في قول تعالى وَلَا يَحْزُنْ
+
+118
+00:10:00,180 --> 00:10:06,900
+كَقَوْلُهُمْ إِنَّ الْعِزَّةَ لِلّهِ جَمِيعًا الوقف 
+
+119
+00:10:06,900 --> 00:10:12,300
+على ولا يحزن كقولهم ماذا نسميه؟ وقفًا لازمًا لذلك 
+
+120
+00:10:12,300 --> 00:10:17,840
+يوضع عليه الميم الوقفيّة علامة على الوقف اللازم ولا
+
+121
+00:10:17,840 --> 00:10:25,220
+يحزن كقولهم نقف إن العزة لله جميع فإذا وصلنا 
+
+122
+00:10:25,220 --> 00:10:30,460
+الكلام اختل المعنى مثل ذلك لو قلنا مثلًا ولا
+
+123
+00:10:30,460 --> 00:10:34,020
+يَحْزُنْكَ قَوْلُهُمْ إِنَّ الْعِزَّةَ لِلّهِ 
+
+124
+00:10:34,020 --> 00:10:40,400
+جَمِيعًا أين الخلل هنا؟ من يقول؟ ما رأيكم؟ لو
+
+125
+00:10:40,400 --> 00:10:43,760
+وصلنا قلنا .. وَلَا يَحْزُنْكَ قَوْلُهُمْ إِنَّ
+
+126
+00:10:43,760 --> 00:10:46,080
+الْعِزَّةَ لِلّهِ جَمِيعًا أتفضل 
+
+127
+00:10:49,720 --> 00:10:53,600
+من باقي كلام الكفار هنا إرادتنا سبحانه وتعالى يقول
+
+128
+00:10:53,600 --> 00:10:57,560
+ولا يحزنك قولهم يا محمد يعني الكلام أن الله 
+
+129
+00:10:57,560 --> 00:11:01,520
+سبحانه وتعالى ذكر صفات المؤمنين أو صفات الكافرين 
+
+130
+00:11:01,520 --> 00:11:05,720
+قبل ذلك وأن الكفار قد شتموا الرسول وسبوا الرسول
+
+131
+00:11:05,720 --> 00:11:09,560
+وأذوا الرسول وقالوا عنه ساحر وشاعر وكاهن و
+
+132
+00:11:09,560 --> 00:11:13,870
+مجنون وغير ذلك من هذه الشبهات أو هذه التشكيكات ضد
+
+133
+00:11:13,870 --> 00:11:17,130
+محمد عليه الصلاة والسلام وهذا ما أحزن الرسول فالرب
+
+134
+00:11:17,130 --> 00:11:22,070
+العزيزي يقول له ولا يحزنك قولهم تحزنش يا محمد على 
+
+135
+00:11:22,070 --> 00:11:26,090
+ما يقولونه بعدين كلام جديد مستأنف يقول الله سبحانه 
+
+136
+00:11:26,090 --> 00:11:31,390
+وتعالى فيه إن العزة لله جميع لكن لو وصلنا وصلنا 
+
+137
+00:11:31,390 --> 00:11:34,550
+لكلام باختلال المعنى وتوهم معنى غير المعنى المراد 
+
+138
+00:11:34,550 --> 00:11:39,550
+فلو قلنا ولا يهزنك قولهم إن العزة لله جميع بتسير 
+
+139
+00:11:39,550 --> 00:11:43,670
+الكلام إن العزة لله جميع من كلام مين؟ من كلام
+
+140
+00:11:43,670 --> 00:11:47,990
+الكفار وهذا هو غير المراد وإنما المراد أن قوله إن
+
+141
+00:11:47,990 --> 00:11:51,630
+العزة لله جميعًا هو كلام مستنفد جديد الله سبحانه
+
+142
+00:11:51,630 --> 00:11:55,450
+وتعالى هو الذي ذكره من باب المواساة والتسلية 
+
+143
+00:11:55,450 --> 00:12:00,640
+والتخفيف عن الرسول محمد عليه الصلاة والسلام. طيب ما 
+
+144
+00:12:00,640 --> 00:12:05,900
+هو حكم أو أقسام الوقف؟ يقول لنا الوقف جائز مادام يوجد
+
+145
+00:12:05,900 --> 00:12:11,660
+ما يوجبه أو يمنعه. ينقسم الوقف إلى عدة أقسام وهي
+
+146
+00:12:11,660 --> 00:12:18,900
+أربع أقسام: الوقف الإضطراري، والوقف الاختباري، والوقف 
+
+147
+00:12:18,900 --> 00:12:23,820
+الانتظاري، والوقف الاختياري. هذه هي أقسام الوقف التي
+
+148
+00:12:23,820 --> 00:12:29,980
+تعدّ بشكل عام. من قولنا الوقف الإضطراري، ماذا نفهم؟
+
+149
+00:12:30,720 --> 00:12:35,260
+أن القارئ يضطر أن يقف. ما هي الأمور التي تجعل
+
+150
+00:12:35,260 --> 00:12:40,280
+القارئ يجب عليه أن يقف أو يضطر أن يقف؟ هو انقطاع 
+
+151
+00:12:40,280 --> 00:12:45,020
+النفس. لو كانت الآية طويلة فلم يستطع أن يتمها 
+
+152
+00:12:45,020 --> 00:12:50,360
+فبينقطع نفسه فيقف. اسمه الوقف الإضطراري، يضطر أن يقف، أو 
+
+153
+00:12:50,360 --> 00:12:57,210
+واحد أثناء القراءة سعل أو عطس أو نسي أو بكى أو 
+
+154
+00:12:57,210 --> 00:13:02,390
+تعثر، يعني هذا الشيء بتجبر الإنسان إلى أن يقف. فاسمه 
+
+155
+00:13:02,390 --> 00:13:06,710
+وقف اضطراري. إذا، ما هو الوقف الإضطراري؟ الوقف
+
+156
+00:13:06,710 --> 00:13:10,590
+الإضطراري هذا تعريفه هو الوقوف على كلمة قرآنية 
+
+157
+00:13:10,590 --> 00:13:16,660
+ليست محلًا للوقف غالبًا بسبب ضرورة ألجأته لذلك، كضيق
+
+158
+00:13:16,660 --> 00:13:21,920
+نفس أو عطاس أو سعال أو بكاء أو نسيان أو عاجز عن 
+
+159
+00:13:21,920 --> 00:13:26,520
+الخرقة أو غير ذلك من الأمور التي يضطر فيها القارئ 
+
+160
+00:13:26,520 --> 00:13:31,580
+إلى أن يقف. ويسمى هذا الوقف الإضطراري. فما هو حكم
+
+161
+00:13:31,580 --> 00:13:37,470
+الوقف الإضطراري؟ جائز. يجب للقارئ أن يقف على أي موضع 
+
+162
+00:13:37,470 --> 00:13:41,470
+في القرآن الكريم حتى لو كان هذا الموضع موضع وقف 
+
+163
+00:13:41,470 --> 00:13:47,810
+قبيح، اضطراريا. يعني بيقرأ فعطس، مرغم على العطس أو 
+
+164
+00:13:47,810 --> 00:13:51,510
+مثلا اضطر إلى أن يسعل، اضطر إلى أن يبكي، اضطر إلى أن 
+
+165
+00:13:51,510 --> 00:13:57,720
+يعني نسيها فوقف. فالوقف الإضطراري جائز. يجب للقارئ أن 
+
+166
+00:13:57,720 --> 00:14:01,380
+يقف على أي موضع من القرآن الكريم وقفا اضطراريا
+
+167
+00:14:01,380 --> 00:14:05,140
+بسبب الضرورة. ولكن إذا أراد أن يستأنف التلاوة ماذا 
+
+168
+00:14:05,140 --> 00:14:10,880
+يفعل؟ يعيد الكلمة التي وقف عندها أو على بعد منها 
+
+169
+00:14:10,880 --> 00:14:15,580
+يعني يرجع كلمتين أو أكثر حتى يستقيم المعنى ويستأنف
+
+170
+00:14:15,580 --> 00:14:20,570
+التلاوة. وهذا بيحصل كثير عند القراء. ممكن بيقرأ و
+
+171
+00:14:20,570 --> 00:14:24,430
+بيقف عند كلمة نتيجة ضيق النفس أو سعال. إذا أراد أن
+
+172
+00:14:24,430 --> 00:14:28,750
+يستأنف في التلاوة، يعيد الكلمة إذا كان سطع أن يعيدها 
+
+173
+00:14:28,750 --> 00:14:32,650
+يعيدها إذا كانت تؤدي معنى أو أكثر من كلمة، كلمتين
+
+174
+00:14:32,650 --> 00:14:36,190
+ثلاثة، حتى يستقيم المعنى ثم يستمر في التلاوة. إذا 
+
+175
+00:14:36,190 --> 00:14:40,170
+حكم الوقف الإضطراري يجب للقارئ أن يقف على أي موضع
+
+176
+00:14:40,170 --> 00:14:45,080
+للضرورة، ثم يبدأ من الكلمة التي وقف عليها إن كانت
+
+177
+00:14:45,080 --> 00:14:47,720
+تفيد معناها. إذا كان معناها مفيد، ممكن أن يعيدها
+
+178
+00:14:47,720 --> 00:14:53,820
+مع ما بعدها، أو وإلا فليبدأ بما قبلها مما يصلح 
+
+179
+00:14:53,820 --> 00:14:56,800
+الابتداء به. إذا كان، والله لو قعدنا الكلمة أيضا 
+
+180
+00:14:56,800 --> 00:14:59,960
+تبقى الكلمة، المعنى اللي غير مفهوم، لأ يرجع كمان حتى
+
+181
+00:14:59,960 --> 00:15:04,260
+أكثر من كلمة حتى يستقيم المعنى. هذا هو القسم الأول
+
+182
+00:15:04,260 --> 00:15:07,120
+أو النوع الأول من الوقف اللي هو بشكل عام اللي هو 
+
+183
+00:15:07,120 --> 00:15:10,700
+الوقف الإضطراب، هو أن يقف القارئ على كلمة قرآنية
+
+184
+00:15:11,350 --> 00:15:14,310
+هو الوقوف على كلمة قرآنية ليست محلًا للوقف
+
+185
+00:15:14,310 --> 00:15:19,930
+غالبًا بسبب ضرورة الجأتِ ولذلك. هذا الرقم واحد أو 
+
+186
+00:15:19,930 --> 00:15:22,950
+أولًا اللي هو الوقف الإضطراري أو القسم الأول من 
+
+187
+00:15:22,950 --> 00:15:30,290
+أقسام الوقف اللي بشكل عام. الوقف الثاني هو الوقف 
+
+188
+00:15:30,290 --> 00:15:35,590
+الاختباري. من كلمة اختباري، ماذا نفهم؟ أن هناك في 
+
+189
+00:15:35,590 --> 00:15:42,150
+اختبار. من الذي يختبر الآخر؟ الشيخ أم التلميذ؟ الشيخ
+
+190
+00:15:42,150 --> 00:15:46,830
+يختبر التلميذ، يوقفه عند أي موضع يريد أن يوقفه عنده
+
+191
+00:15:46,830 --> 00:15:51,450
+ويسأله عن أحكام التجويذ، صل هذه الكلمة، قف هنا، عيد 
+
+192
+00:15:51,450 --> 00:15:55,390
+هذه الكلمة، بين الحكم، طبق الحكم الفلاني، هذه يسمى
+
+193
+00:15:55,390 --> 00:16:00,710
+وقف اختباري. يجب للشيخ أن يوقف التلميذ عند أي موضع
+
+194
+00:16:00,710 --> 00:16:05,570
+يريد أن يوقفه عنده بقصد الاختبار، يختبره. إذا لو
+
+195
+00:16:05,570 --> 00:16:11,290
+قلنا ما هو تعليل الوقف الاختباري؟ هو الوقوف على كلمة 
+
+196
+00:16:11,290 --> 00:16:16,890
+قرآنية ليست محلًا للوقف غالبًا، يعني غالبًا ليست محلًا 
+
+197
+00:16:16,890 --> 00:16:22,210
+للوقف، و ذلك في مقام التعليم والاختبار، 
+
+198
+00:16:22,210 --> 00:16:26,050
+لبيان حكم الكلمة الموقوف عليها من حيث الحذف
+
+199
+00:16:26,050 --> 00:16:30,690
+والإثبات أو القاطع والوصل وغير ذلك. والأمثلة على 
+
+200
+00:16:30,690 --> 00:16:36,910
+ذلك كثيرة، نذكر مثلًا مثالًا للاختبار، مثلًا عندما يقرأ
+
+201
+00:16:36,910 --> 00:16:43,710
+القارئ فيقول: أم لهم شرك في السماوات؟ ائتوني بكتاب
+
+202
+00:16:43,710 --> 00:16:51,970
+من قبل هذا أو أئتوني بعلم إن كنتم صادقين. لو قال 
+
+203
+00:16:51,970 --> 00:16:59,600
+القارئ: أم لهم شرك في السماوات؟ وقف عندها، و أراد أن يبدأ 
+
+204
+00:16:59,600 --> 00:17:05,460
+بـ "ائتني"، كيف يقرأها؟ يقول: "ائتني بكتاب من قبل هذا".
+
+205
+00:17:05,460 --> 00:17:11,240
+طيب ممكن الشيخ لأن هنا يحتاج أيضًا لو قرأها بالوصل
+
+206
+00:17:11,240 --> 00:17:15,800
+لها قراءة خاصة. يقول: "طيب ارجع مع واصلة كلمة 
+
+207
+00:17:15,800 --> 00:17:19,520
+السماوات" بقوله: "ائتني"، كيف تقرأها من يقرأها منكم؟
+
+208
+00:17:19,520 --> 00:17:36,410
+من يقرأها أو لو مش عارفين. في السماوات، إيش؟ أما إذا 
+
+209
+00:17:36,410 --> 00:17:41,210
+وقفنا عند "السماوات"
+
+210
+00:17:41,210 --> 00:17:47,310
+"ائتني بكتاب" نقرأها بمدّ البدل. حكم الوقف الاختباري
+
+211
+00:17:47,310 --> 00:17:53,110
+نفس حكم الوقف الإضطراري. ماذا قلنا أثناء بيان حكم
+
+212
+00:17:53,110 --> 00:17:58,450
+الوقف الإضطراري؟ يجوز الوقف عليه. يعني أن يقف القارئ
+
+213
+00:17:58,450 --> 00:18:04,170
+وقفا اختباريا جائز. ولكن إذا أراد القارئ أن يستأنف
+
+214
+00:18:04,170 --> 00:18:09,810
+التلاوة ماذا يفعل؟ يعيد الكلمة التي وقف عندها إن
+
+215
+00:18:09,810 --> 00:18:14,310
+كانت تؤدي معنى أو أن يرجع أكثر من كلمة حتى يستقيم
+
+216
+00:18:14,310 --> 00:18:18,910
+المعنى. نفس حكم الوقف الإضطراري. كان حكم الوقف
+
+217
+00:18:18,910 --> 00:18:25,550
+الاختباري كذلك. القسم الثالث يا إخواننا يا كرام هو 
+
+218
+00:18:25,550 --> 00:18:31,750
+الوقف الانتظاري. ما المقصود بالوقف الانتظاري؟ هنا هو 
+
+219
+00:18:31,750 --> 00:18:35,770
+الوقوف على الكلمة القرآنية بقصد استيفاء أو إظهار
+
+220
+00:18:35,770 --> 00:18:39,470
+الاختلاف في القراءات الأخرى. إذا بتكون في بعض
+
+221
+00:18:39,470 --> 00:18:43,850
+الكلمات أحيانًا بعض الاختلاف، يعني أكثر من قراءة
+
+222
+00:18:44,290 --> 00:18:48,590
+قراءة حافظ عن عاصم، ورش عن نافع، قالون عن نافع، أدول
+
+223
+00:18:48,590 --> 00:18:52,950
+عن أبي عمرو البصري. هذا يكون في مقام التعليم وليس
+
+224
+00:18:52,950 --> 00:18:56,870
+يعني في مقام الصلاة مثلًا أو أي مكان لأنه يريد أن
+
+225
+00:18:56,870 --> 00:19:01,710
+يقرأ القرآن في مقام التعليم ليعلم الناس. يجوز له أن
+
+226
+00:19:01,710 --> 00:19:05,430
+يقف على الكلمة ليعلم الطلاب بأن هذه الكلمة فيها
+
+227
+00:19:05,430 --> 00:19:09,090
+أكثر من وجه في القراءة، في عندك قراءتين أو ثلاثة
+
+228
+00:19:09,090 --> 00:19:16,700
+مثال ذلك لو قال مثلًا: "مالك يوم الدين"، مالك يوم الدين.
+
+229
+00:19:16,700 --> 00:19:24,840
+مالك يوم الدين، مالك يوم الدين. الآن كلمة مالك عندنا
+
+230
+00:19:24,840 --> 00:19:30,070
+في قراءة حافظ عن عاصم: "مالك يوم الدين"، في قراءة ورش عن
+
+231
+00:19:30,070 --> 00:19:36,590
+النافع: "مالك يوم الدين". أما قراءة "مالكَ" و"مالكي" فهما
+
+232
+00:19:36,590 --> 00:19:40,430
+قراءتان شاذتان لا يأخذ بهما، إنما هي يعني هي نقض
+
+233
+00:19:40,430 --> 00:19:44,930
+القراءتين المتواترتين "مالك" و"مالك". وهذا جائز لأن
+
+234
+00:19:44,930 --> 00:19:51,130
+"مالك" يكون ليس كل مالك مالك، ولكن "مالك" هو المالك.
+
+235
+00:19:51,130 --> 00:19:55,390
+فالله عز وجل مالك يوم الدين، وهو المالك في يوم
+
+236
+00:19:55,390 --> 00:20:00,170
+الدين. يعني يجب للقارئ أن يستعرض أوجه الاختلاف، يقول
+
+237
+00:20:00,170 --> 00:20:04,350
+هنا عدة قراءات فيقف عندها. وهذا يسمى الوقف 
+
+238
+00:20:04,350 --> 00:20:08,850
+الانتظاري. فما هو حكم الوقف الانتظاري؟ الوقف 
+
+239
+00:20:08,850 --> 00:20:13,650
+الانتظاري حكمه جائز مثل حكم الوقف الإضطراري والوقف 
+
+240
+00:20:13,650 --> 00:20:17,610
+الاختباري، يجب له أن يقف، ولكن إذا أراد أن يستأنف في
+
+241
+00:20:17,610 --> 00:20:22,760
+التلاوة ماذا يفعل؟ يعيد الكلمة التي وقف عندها إن
+
+242
+00:20:22,760 --> 00:20:27,200
+كانت تؤدي معناها، أو يرجع أكثر من كلمة حتى يستقيم
+
+243
+00:20:27,200 --> 00:20:32,880
+المعنى. إذا كان قسم حتى الآن صدر، ماخدين الوقف الإيه
+
+244
+00:20:32,880 --> 00:20:37,760
+الإضطراري، اثنين الوقف الاختباري، ثلاثة الوقف
+
+245
+00:20:37,760 --> 00:20:42,220
+الانتظاري. في عندنا القسم الرابع والأخير هو الوقف 
+
+246
+00:20:42,220 --> 00:20:47,760
+الإيه، الوقف الاختياري. وهذا الذي نعتمد عليه. من كلمة
+
+247
+00:20:47,760 --> 00:20:52,550
+اختياري، ماذا نفهم؟ هو أن يقف القارئ على الكلمة
+
+248
+00:20:52,550 --> 00:20:57,110
+القرآنية بإرادته أو بمحض إرادته واختياره باعتباره 
+
+249
+00:20:57,110 --> 00:21:01,490
+أنها أدت معنى أو استقام المعنى، وقف عندها بإرادته
+
+250
+00:21:01,490 --> 00:21:06,990
+وهذا يسمى الوقف الاختياري. والوقف الاختياري ينقسم
+
+251
+00:21:06,990 --> 00:21:14,130
+إلى أربعة أقسام، هو الوقف التام، والوقف الكافي
+
+252
+00:21:14,130 --> 00:21:20,050
+والوقف الحسن، والوقف القبيح. إذا لابد أن نفرق ما بين
+
+253
+00:21:20,050 --> 00:21:26,110
+الوقف اللي بشكل عام والوقف الاختياري. لو سألنا سؤال 
+
+254
+00:21:26,110 --> 00:21:31,290
+ما هي أنواع الوقف اللي بشكل عام؟ هنقول الإضطراري 
+
+255
+00:21:31,290 --> 00:21:37,360
+والاختباري والانتظاري والاختياري. أربعة أقسام. الوقف
+
+256
+00:21:37,360 --> 00:21:40,800
+الاختياري ينقسم إلى أربعة أقسام أيضًا، هو الوقف
+
+257
+00:21:40,800 --> 00:21:45,060
+التام، والوقف الكافي، والوقف الحسن، والوقف القبيح.
+
+258
+00:21:45,060 --> 00:21:50,380
+وهذا هو الذي نريد أن نركز عليه. أول قسم من أقسام
+
+259
+00:21:50,380 --> 00:21:56,380
+الوقف الاختياري هو وقف التام. فما معنى الوقف التام؟ 
+
+260
+00:21:56,380 --> 00:22:00,960
+معنى الوقف التام من يعرف لنا إياه؟ من يقرأها؟ هو 
+
+261
+00:22:00,960 --> 00:22:05,280
+أن يقف القارئ على إيه؟ برضه؟ هو أن يقف القارئ على
+
+262
+00:22:08,430 --> 00:22:11,310
+تمّ المعنى عندها. تتم المعنى عندها، و لا تتعلق بما
+
+263
+00:22:11,310 --> 00:22:14,630
+بعدها لفظًا ولا معنى. صحيح في عيننا الوقف التام
+
+264
+00:22:14,630 --> 00:22:18,970
+والوقف الكافي والوقف الحسن والوقف القبيح وكلهم
+
+265
+00:22:18,970 --> 00:22:23,370
+تقريبًا كل واحد له تعريف، لابد أن نفرق ما بين كل
+
+266
+00:22:23,370 --> 00:22:27,150
+نوع من هذه الأنواع الأربعة. الوقف التام هو أن يقف
+
+267
+00:22:27,150 --> 00:22:31,830
+القارئ على كلمة قرآنية، تم المعنى عندها لا تتعلق
+
+268
+00:22:31,830 --> 00:22:36,230
+بما بعدها لفظًا ولا معنى. إذا، أن يقف على مكان تم
+
+269
+00:22:36,230 --> 00:22:41,300
+المعنى واجتمل وصار المعنى مفهوم، ليس له تعلق بالذي
+
+270
+00:22:41,300 --> 00:22:45,560
+بعده لا من حيث اللفظ ولا من حيث المعنى. فما المقصود 
+
+271
+00:22:45,560 --> 00:22:49,980
+بالتعلق اللفظي أو التعلق المعنوي؟ ما هو التعلق 
+
+272
+00:22:49,980 --> 00:22:54,080
+اللفظي؟ التعلق اللفظي هنا هو أن يتعلق الكلام 
+
+273
+00:22:54,080 --> 00:22:59,200
+الموقوف عليه بالكلام الذي بعده من حيث الإعراب. بمعنى
+
+274
+00:22:59,200 --> 00:23:05,560
+إن الكلمة التي بعد ما وقفنا عليها ليست صفة للكلمة 
+
+275
+00:23:05,560 --> 00:23:10,780
+التي وقفنا عليها، وليست حال، وليست تمييز، وليست مثلًا
+
+276
+00:23:10,780 --> 00:23:16,800
+مفعول به أو مضاف إليه، انتهى الكلام وتم المعنى، وما
+
+277
+00:23:16,800 --> 00:23:20,400
+لهاش علاقة باللي بعده لا من حيث اللفظ، يعني الإعراب
+
+278
+00:23:20,400 --> 00:23:25,260
+ولا من حيث المعنى اللي هو موضوع الآيات. لأن في عندنا 
+
+279
+00:23:25,260 --> 00:23:30,660
+مثلًا عشر آيات مثلًا عشرين آية أو صورة أو أقل، كلها
+
+280
+00:23:30,660 --> 00:23:34,660
+تتكلم على موضوع واحد. اسمه التعلق المعنوي. إذا في 
+
+281
+00:23:34,660 --> 00:23:38,520
+عندنا تعلق لفظي وتعلق معنوي، التعلق اللفظي هو 
+
+282
+00:23:38,520 --> 00:23:42,520
+الكلام الذي يتعلق بالكلام الذي بعده من حيث الإعراب
+
+283
+00:23:42,520 --> 00:23:48,580
+صفة حال، تمييز، أفعل به، مضاف إليه، من هذه الكلمات ليس 
+
+284
+00:23:48,580 --> 00:23:51,380
+له علاقة مع اللي بعده، اسمه لم يتعلق باللي بعده من
+
+285
+00:23:51,380 --> 00:23:55,350
+حيث اللفظ، وكذلك من حيث المعنى بيكون المعنى الذي
+
+286
+00:23:55,350 --> 00:23:59,350
+وقفنا عليه تم، المعنى عنده ليس له علاقة معنوية
+
+287
+00:23:59,350 --> 00:24:02,930
+بالذي بعدها، يعني انتهت قصة النبي، وبعدين قصة نبي 
+
+288
+00:24:02,930 --> 00:24:08,070
+آخر، أو انتهى حكم من الأحكام الإسلامية، وبعدين بحكم 
+
+289
+00:24:08,070 --> 00:24:14,990
+آخر، اسم هذا ليس له باللي بعده تعلق معنوي، وسمي 
+
+290
+00:24:14,990 --> 00:24:20,480
+بالوقف التام، لماذا؟ لأن المعنى تم، بسبب تسمية الوقف 
+
+291
+00:24:20,480 --> 00:24:24,720
+التام بهذا الاسم، احنا سميناه وقف تام، لماذا سمي هذا 
+
+292
+00:24:24,720 --> 00:24:29,260
+الوقف بالوقف التام؟ لتمام الكلام به وانقطاع ما بعده 
+
+293
+00:24:29,260 --> 00:24:32,820
+عنه في اللفظ والمعنى، لأنه تم المعنى ليس له علاقة 
+
+294
+00:24:32,820 --> 00:24:37,760
+باللي بعده، لا لفظ ولا معنى، فلأنه تم المعنى من جميع 
+
+295
+00:24:37,760 --> 00:24:41,620
+النواحي وليس له علاقة باللي بعده، لا لفظ ولا معنى، يسمى
+
+296
+00:24:41,620 --> 00:24:49,920
+هذا النوع الوقف التام، ما هو حكم الوقف التام؟ جائز،
+
+297
+00:24:49,920 --> 00:24:54,520
+يجوز أن أو يحصل الوقوف عليه ويحصل الابتداء بما 
+
+298
+00:24:54,520 --> 00:24:59,140
+بعده، إذا يجوز الوقف عليه ويجوز الابتداء بما بعده 
+
+299
+00:24:59,140 --> 00:25:03,800
+بل الوقف عليه أولى من الابتداء بما بعده مع الوصل
+
+300
+00:25:03,800 --> 00:25:09,320
+لذلك الرمز الذي يرمز لهذا النوع من الوقف، ما هو يا 
+
+301
+00:25:09,320 --> 00:25:17,100
+أخواننا؟ قلة، ما معنى قلة؟ قلة عبارة عن كلمة مشتقة من
+
+302
+00:25:17,100 --> 00:25:24,150
+الوقف، أولى، يعني الوقف أولى، الوقف ق أولى أ، فبيحطوله 
+
+303
+00:25:24,150 --> 00:25:30,370
+قلة، القلة، القاف أولى، ألف، كوفية توضع في هذا الموضع 
+
+304
+00:25:30,370 --> 00:25:35,610
+معناته تعني هذه الكلمة التي وضع عليها قلة ماذا 
+
+305
+00:25:35,610 --> 00:25:40,330
+تعني أن هذا الوقف وقف تم، ولكن الوقف التام هذا 
+
+306
+00:25:40,330 --> 00:25:43,850
+القلة لا يوضع على رأس الآية، أحيانا بيكون الوقف على 
+
+307
+00:25:43,850 --> 00:25:49,900
+رأس الآية، لا نضع قلة على رأس الآية، وإنما قلب، توضع 
+
+308
+00:25:49,900 --> 00:25:53,380
+عندما يكون الوقف التام في منتصف الآية، لماذا يا 
+
+309
+00:25:53,380 --> 00:25:57,660
+أخواننا يا كرام؟ لأن الوقف على رأس الآية سنة 
+
+310
+00:25:57,660 --> 00:26:01,220
+فلأن الوقف على رأس الآية سنة فنكتفي بالوقف 
+
+311
+00:26:01,220 --> 00:26:06,560
+بالسنة، أما إذا كان في وسط الآية فيجب أن نقف عليها 
+
+312
+00:26:06,560 --> 00:26:11,680
+وقفا تاما، والوقف التام رمزه قلة، ومعنى قلة يعني 
+
+313
+00:26:11,680 --> 00:26:17,140
+الوقف أولى، مثال، وذلك أو عندنا العديد من الأمثلة
+
+314
+00:26:17,830 --> 00:26:22,270
+المثال الذي نذكره أولا، مثال سهل بإمكان كل واحد أن 
+
+315
+00:26:22,270 --> 00:26:25,930
+يحفظه حتى يعني يستقر، لأن الفاتحة كل المسلمين
+
+316
+00:26:25,930 --> 00:26:29,910
+يحفظها، الفاتحة عندما نقول مثلا الحمد لله رب 
+
+317
+00:26:29,910 --> 00:26:38,690
+العالمين، الرحمن الرحيم، مالك يوم الدين، وقفت عند 
+
+318
+00:26:38,690 --> 00:26:43,050
+مالك يوم الدين، الآيات الثلاثة هذه كلها ثناء على
+
+319
+00:26:43,050 --> 00:26:48,040
+الله، تفني على الله، نحمد الله، الحمد لله رب العالمين
+
+320
+00:26:48,040 --> 00:26:53,580
+أنا هو رب العالمين، ومن صفاتي أنه رحمن رحيم، وأنه 
+
+321
+00:26:53,580 --> 00:26:58,260
+كذلك مالك يوم الدين، كلها هذه الآيات الثلاثة عبارة 
+
+322
+00:26:58,260 --> 00:27:02,840
+عن ثناء على الله عز وجل، بعد ذلك بيأتي موضوع آخر 
+
+323
+00:27:03,630 --> 00:27:08,770
+كلام مستأنف، دعاء، إياك نعبد وإياك نستعين، إهدنا 
+
+324
+00:27:08,770 --> 00:27:13,330
+الصراط المستقيم، صراط الذين أنعمت عليهم غير المغضوب
+
+325
+00:27:13,330 --> 00:27:18,230
+عليهم ولا الظالين، إذا الوقف على الدي مالك يوم الدين 
+
+326
+00:27:18,230 --> 00:27:25,930
+اسمه وقف إيش؟ وقف تم، تم المعنى عنده، لا يتعلق مع ما 
+
+327
+00:27:25,930 --> 00:27:30,490
+بعده لا من حيث الإعراب اللي هو اللفظ ولا من حيث
+
+328
+00:27:30,490 --> 00:27:34,470
+المعنى، من حيث الإعراب إياك نعبد وإياك نستعين كلام
+
+329
+00:27:34,470 --> 00:27:38,630
+جديد، يعني نعبدك يا الله ونستعينك كلام جديد ما لوش
+
+330
+00:27:38,630 --> 00:27:44,300
+علاقة مع صفات الله عز وجل، ومالك يوم الدين من حيث 
+
+331
+00:27:44,300 --> 00:27:50,180
+المعنى، خلصنا الثناء على الله وبدأنا بالطلب من الله
+
+332
+00:27:50,180 --> 00:27:53,900
+وهذا ربنا سبحانه وتعالى بعلمنا التأدب، إذا أردنا أن 
+
+333
+00:27:53,900 --> 00:27:58,760
+نطلب من الله شيئا لابد أن نثني عليه أولا ثم ندعو 
+
+334
+00:27:58,760 --> 00:28:02,260
+الله سبحانه وتعالى بما نريد، وذلك تأدبا مع الله 
+
+335
+00:28:02,260 --> 00:28:07,300
+سبحانه وتعالى حتى يستجيب لنا الدعاء، مثل كذلك في 
+
+336
+00:28:07,300 --> 00:28:11,060
+الأمور العادية، يعني أي واحد يريد أن يطلب طلب من
+
+337
+00:28:11,060 --> 00:28:19,120
+إنسان ملك ووزير ورئيس يعني ممكن يعني يقدم مقدمة طلب
+
+338
+00:28:19,120 --> 00:28:24,680
+فيه ثناء على هذا الفاعل الخير الذي يقف مع 
+
+339
+00:28:24,680 --> 00:28:27,160
+المساكين ومع الفقراء ومع المحتاجين ويفعل كده وكده 
+
+340
+00:28:27,160 --> 00:28:30,680
+وكده وكده وعليه فإني أطلب منك كده وكده، يعني أول شيء
+
+341
+00:28:30,680 --> 00:28:33,880
+ثناء وبعدين الطلب، وربنا سبحانه وتعالى يعلمنا في
+
+342
+00:28:33,880 --> 00:28:38,540
+هذه الآية الأدب، نثني على الله وبعدين نطلب من الله
+
+343
+00:28:38,540 --> 00:28:42,040
+سبحانه وتعالى، فالوقف على مالك يوم الدين يسمى وقف
+
+344
+00:28:42,040 --> 00:28:46,420
+إيه يا أخواننا؟ وقف تم.. تم المعنى عنده لا يتعلق
+
+345
+00:28:46,420 --> 00:28:52,240
+بما بعده، لا لفظ ولا معنى، وكذلك ليس لها علاقة لا 
+
+346
+00:28:52,240 --> 00:28:55,340
+لفظ من حيث اللفظ الإعرابي ولا من حيث المعنى، لأن 
+
+347
+00:28:55,340 --> 00:28:59,090
+هذا كلام وهذا كلام.. هذا المثال الأول، نشوف مثال 
+
+348
+00:28:59,090 --> 00:29:05,190
+آخر أيضًا فيه الوقف التام في أول صورة البقرة طبعًا 
+
+349
+00:29:05,190 --> 00:29:09,770
+الآيات أو أول عدة آيات من صورة البقرة تقسم الناس
+
+350
+00:29:09,770 --> 00:29:14,610
+إلى ثلاث أقسام، القسم الأول هو المتقين وصفاتهم 
+
+351
+00:29:14,610 --> 00:29:20,470
+القسم الثاني الكافرين وماذا يحصل معهم، القسم الثالث
+
+352
+00:29:20,470 --> 00:29:24,790
+المنافقين، أما القسم الأول فربنا سبحانه وتعالى يقول
+
+353
+00:29:24,790 --> 00:29:31,960
+خذ للمتقين، الذين يؤمنون بالغيب ويقيمون الصلاة ومما 
+
+354
+00:29:31,960 --> 00:29:38,640
+رزقناهم ينفقون والذين يؤمنون بما أنزل إليك وما 
+
+355
+00:29:38,640 --> 00:29:45,080
+أنزل من قبلك وبالآخرة هم يوقنون، أولئك على هدى من 
+
+356
+00:29:45,080 --> 00:29:51,120
+ربهم، وأولئك هم المفلحون، انتهت صفات المتقين، أولئك
+
+357
+00:29:51,120 --> 00:29:54,960
+على هدى من ربهم وأولئك هم المفلحون، خلصنا صفات 
+
+358
+00:29:54,960 --> 00:30:02,680
+المتقين، فالوقف على كلمة المفلحون هو وقف تم، تم
+
+359
+00:30:02,680 --> 00:30:07,360
+المعنى عنده، لا يتعلق بما بعده، لا لفظة يعني
+
+360
+00:30:07,360 --> 00:30:12,440
+إعرابه، ولا معنى، لأن الآيات التي جاءت بعدها هو 
+
+361
+00:30:12,440 --> 00:30:19,340
+قوله تعالى: إن الذين كفروا سواء عليهم أنذرتهم أم لم 
+
+362
+00:30:19,340 --> 00:30:23,800
+تنذرهم لا يؤمنون، إذا الكلام هنا كلام عن الكفار 
+
+363
+00:30:24,490 --> 00:30:29,830
+وانتهينا كلام عن المتقين، فالوقف على المفلحون هنا 
+
+364
+00:30:29,830 --> 00:30:35,230
+يسمى وقف تام، تم المعنى عنده لا يتعلق بما بعده لا 
+
+365
+00:30:35,230 --> 00:30:42,090
+لفظ ولا معنى، يسمى وقف تام، كذلك في قوله تعالى أيضًا
+
+366
+00:30:42,090 --> 00:30:46,290
+هنا ختم الله هو آية الرقم سبع من صوت البقرة وهي 
+
+367
+00:30:46,290 --> 00:30:52,270
+إكمال لصفات الكافرين، إن الذين كفروا سواء عليهم 
+
+368
+00:30:52,270 --> 00:30:58,310
+أن أنذرتهم أم لم تنذرهم لا يؤمنون، ختم الله على 
+
+369
+00:30:58,310 --> 00:31:04,370
+قلوبهم وعلى سمعهم وعلى أبصارهم غشاوة ولهم عذاب 
+
+370
+00:31:04,370 --> 00:31:10,360
+عظيم، أيضًا على عذاب عظيم، انتهت صفات الكافرين وبدأنا
+
+371
+00:31:10,360 --> 00:31:16,960
+بعدها بصفات، ومن الناس من يقول آمنا بالله وباليوم 
+
+372
+00:31:16,960 --> 00:31:23,920
+الآخر وما هم بمؤمنين، بدأنا بصفات مين؟ المنافقين، إذا 
+
+373
+00:31:23,920 --> 00:31:28,340
+القسم الأول قسم المتقين، وقفنا عليها تم المعنى 
+
+374
+00:31:28,340 --> 00:31:32,960
+عندها لا تتعلق بما بعدها لا لفظ ولا معنى، بدأت 
+
+375
+00:31:32,960 --> 00:31:37,710
+بصفات الكافرين إن الذين كفروا، واختمات بقوله ولهم 
+
+376
+00:31:37,710 --> 00:31:43,870
+عذاب عظيم، انتهت صفات الكافرين فالوقف عليها وقف تم
+
+377
+00:31:43,870 --> 00:31:48,230
+تم المعنى عندها لا تتعلق بما بعدها لا لفظ ولا معنى
+
+378
+00:31:48,230 --> 00:31:53,510
+لأنه لبعدها ومن الناس من يقول آمنا بالله وباليوم 
+
+379
+00:31:53,510 --> 00:31:59,110
+الآخر وما هم بمؤمنين، ومن الناس منهم تبعيضية يعني
+
+380
+00:31:59,110 --> 00:32:03,490
+بعض الناس، مش كل الناس، بعض يعني حتى لا يعمم الإنسان
+
+381
+00:32:03,490 --> 00:32:06,670
+فربنا بعلمنا أنه لا تعميم يعني بعض الناس يقولوا
+
+382
+00:32:06,670 --> 00:32:12,590
+البلد الفلانية كلهم حرمية، العيلة الفلانية كلهم كده 
+
+383
+00:32:12,590 --> 00:32:16,530
+وكده، لأ في وفي يعني الواحد بيكون عنده أولاد 
+
+384
+00:32:16,530 --> 00:32:20,250
+أولاد كلهم، ليس كل ولاده مثلا كلهم أربع خمسة، ليس
+
+385
+00:32:20,250 --> 00:32:23,930
+كلهم بصفة واحدة، بعضهم مؤدب بعضهم أقل أدب بعضهم
+
+386
+00:32:23,930 --> 00:32:28,580
+مشاكس بعضهم مؤدب وهكذا، فهنا ومن الناس بيقولنا بعض 
+
+387
+00:32:28,580 --> 00:32:33,160
+الناس، هؤلاء الناس، ومن الناس من يقولوا آمنا بالله
+
+388
+00:32:33,160 --> 00:32:37,420
+وباليوم الآخر بأفواههم وما هم بمؤمنين، يعني حقيقة
+
+389
+00:32:37,420 --> 00:32:41,540
+الأمر أنهم ليسوا بمؤمنين، فهنا الوقف عليه اسمه وقف
+
+390
+00:32:41,540 --> 00:32:47,040
+تام، هل يوضع على الآية هنا قلة وهي علامة للوقف 
+
+391
+00:32:47,040 --> 00:32:52,880
+التام ولا لا يوضع؟ لا يوضع، لماذا؟ لأن الوقف على رأس
+
+392
+00:32:52,880 --> 00:32:59,580
+الآية يعد سنة، أما آيات متعددة والأمثلة كثيرة، شوف 
+
+393
+00:32:59,580 --> 00:33:04,740
+مثلا، مثال على الوقف التام اللي في وسط الآية، ممكن 
+
+394
+00:33:04,740 --> 00:33:07,840
+يكون وقف تام على رأس الآية وهذا كثير أو نهاية 
+
+395
+00:33:07,840 --> 00:33:11,700
+القصص أو نهاية الصور، الوقف عليها وقف تام، تم المعنى 
+
+396
+00:33:11,700 --> 00:33:15,560
+عندها لا تتعلق بما بعدها لفظ ولا معنى، لكن ممكن
+
+397
+00:33:15,560 --> 00:33:20,660
+يكون عندنا وقف تام في منتصف الآية، والوقف التام اللي 
+
+398
+00:33:20,660 --> 00:33:25,780
+في منتصف الآية، هذا الذي نضع عليه رمز قلة، ومعنى قلة
+
+399
+00:33:25,780 --> 00:33:30,740
+الوقف أولى من الواصل، يعني يجب الوقف ويجب الواصل
+
+400
+00:33:30,740 --> 00:33:36,600
+ولكن الوقف أولى، نشوف هنا مثلا لقد أضلني عن الذكر 
+
+401
+00:33:36,600 --> 00:33:43,930
+بعد إذ جاءني، وكان الشيطان للإنسان خذولا، إذا هنا 
+
+402
+00:33:43,930 --> 00:33:50,370
+الكافر الذي صاحب أناسا قد أضله على الطريق، هو نفسه
+
+403
+00:33:50,370 --> 00:33:56,030
+يقول لقد أضلني عن الذكري بعد إذ جاءني، على كلمة 
+
+404
+00:33:56,030 --> 00:34:01,710
+جاءني وقف تم، تم المعنى عنده لا يتعلق بما بعده لا 
+
+405
+00:34:01,710 --> 00:34:05,610
+لفظة ولا معنى، لأنه وكان الشيطان للإنسان اللي خد 
+
+406
+00:34:05,610 --> 00:34:09,990
+قولها ليس من كلام الكافر، الكافر بيقول أنه يا ليتني
+
+407
+00:34:09,990 --> 00:34:13,570
+لم أتخذ فلانا خليلا، صاحب الذي أظله الطريق، لقد
+
+408
+00:34:13,570 --> 00:34:17,390
+أظلني عن الذكر بعد إذا جاءني، وكان الشيطان الإنسان
+
+409
+00:34:17,390 --> 00:34:19,830
+يخذوله، الكلام وكان الشيطان الإنسان يخذوله الكلام
+
+410
+00:34:19,830 --> 00:34:25,250
+جديد ليس من باقي كلام الكافر، لذلك الوقف على جاءني 
+
+411
+00:34:25,250 --> 00:34:30,910
+يسمى وقف تم، تم المعنى عنده ولا يتعلق بما بعده لا 
+
+412
+00:34:30,910 --> 00:34:37,240
+لفظ ولا معنى، هذه الكلمة جاءني، ويضع عليها رمز قلة 
+
+413
+00:34:37,240 --> 00:34:42,280
+الوقف أولى لأنه في وسط الآية، كذلك في قول تعالى
+
+414
+00:34:42,280 --> 00:34:47,230
+وَإِنَّكُمْ لَتَمُرُّونَ عَلَيْهِمْ مُصْبِحِينَ 
+
+415
+00:34:47,230 --> 00:34:53,230
+وَبالليل أفلا تعقلون، كلمة وبالليل أيضًا الوقف عليها
+
+416
+00:34:53,230 --> 00:34:59,250
+وقف يعني تم المعنى عنده لا يتعلق بما بعده أفلا 
+
+417
+00:34:59,250 --> 00:35:03,290
+تعقلون لا يتعلق بما بعده لا لفظ ولا معنى وبالتالي 
+
+418
+00:35:03,290 --> 00:35:09,690
+ما نسميها ده وقف تم في منتصف الآية، وما يعلم تأويله 
+
+419
+00:35:09,690 --> 00:35:14,630
+إلا الله والراسخون في العلم يقولون آمن به كل من 
+
+420
+00:35:14,630 --> 00:35:19,900
+عند ربنا، في قوله وما يعلم تأويله إلا الله كلام لا 
+
+421
+00:35:19,900 --> 00:35:23,940
+يعلم تأويل هذه الكلمات أو هذه الأحوال إلا الله
+
+422
+00:35:23,940 --> 00:35:28,180
+سبحانه وتعالى ثم كلام جديد نقول والراسخون في العلم 
+
+423
+00:35:28,180 --> 00:35:33,660
+يقولون آمنا لأنه لو قلنا وما يعلم تأويله إلا الله
+
+424
+00:35:33,660 --> 00:35:38,160
+وما يعلم تأويله إلا الله والراسخون في العلم يصير
+
+425
+00:35:38,160 --> 00:35:42,520
+الله والراسخون يعلمون تأويل هذه الكلمات وهذا هو
+
+426
+00:35:42,520 --> 00:35:48,130
+غير مطلوب لذلك نقف على كلمة الله من سمي وقف تام في
+
+427
+00:35:48,130 --> 00:35:52,310
+وسط الكلمة تم المعنى عندها لا تتعلق بما بعدها لا 
+
+428
+00:35:52,310 --> 00:35:58,810
+لفظة ولا معنى في عندنا يا إخواننا يتبع الوقف التام 
+
+429
+00:35:58,810 --> 00:36:03,310
+نوع من أنواع الوقف وبعض العلماء اعتبروا يعني نوع
+
+430
+00:36:03,310 --> 00:36:08,890
+مستقل هذا النوع هو الوقف اللازم عندنا يعني العلماء
+
+431
+00:36:08,890 --> 00:36:13,370
+أدخله ضمن الوقف التام لأنه نفس موضوع الوقف التام
+
+432
+00:36:13,370 --> 00:36:18,410
+لكن منزيد عليه فإذا وصلت الكلام اختل المعنى وهو ما
+
+433
+00:36:18,410 --> 00:36:23,130
+يسمى بالوقف اللازم ما هو تعريف الوقف اللازم؟ من 
+
+434
+00:36:23,130 --> 00:36:26,850
+يعرف لنا الوقف اللازم هو نفس تعريف الوقف التام أن 
+
+435
+00:36:26,850 --> 00:36:31,350
+يقف القارئ على كلمة قرآنية تم المعنى عندها لا 
+
+436
+00:36:31,350 --> 00:36:36,970
+تتعلق بما بعدها لفظا ولا معناه حتى هنا اسم تعريف
+
+437
+00:36:36,970 --> 00:36:42,360
+الوقف التام فإذا وصلت الكلام اختل المعنى أو أوخمة
+
+438
+00:36:42,360 --> 00:36:46,540
+معنى غير المعنى المراد يسمى هذا وقف إيه؟ وقف لازم
+
+439
+00:36:46,540 --> 00:36:52,080
+إذا هو الوقف اللازم يتبع الوقف التام ولكن بدأ نزيد
+
+440
+00:36:52,080 --> 00:36:56,280
+عليه فإذا وصلت الكلام اختل المعنى لأنه عندما نقف
+
+441
+00:36:56,280 --> 00:36:59,060
+عليه بكون تم المعنى لا يتعلق بالبعد ولا لفظ ولا
+
+442
+00:36:59,060 --> 00:37:02,260
+معنى ولكن هذه الكلمة لو وصلتها هيؤد معنى غير
+
+443
+00:37:02,260 --> 00:37:06,100
+المعنى المراد والأمثل على ذلك متعددة نشوف هنا ما
+
+444
+00:37:06,100 --> 00:37:11,650
+يرمز الوقف اللازم رمز الوقف اللازم اللي هي الياء ميم 
+
+445
+00:37:11,650 --> 00:37:16,870
+الأفقية اللي هي هذه إذا وضعت على المكان على هذه
+
+446
+00:37:16,870 --> 00:37:21,350
+الكلمة معناته أنه يجب أن تقف وقفا لازما على هذا
+
+447
+00:37:21,350 --> 00:37:29,530
+الموضع مثال ذلك الأمثلة هنا ولا يحزن كقولهم إن
+
+448
+00:37:29,530 --> 00:37:35,010
+العزة لله جميعا هنا في قوله ولا يحزنك قولهم يعني
+
+449
+00:37:35,010 --> 00:37:39,930
+لا تحزن يا محمد على ما قاله الكفار من أنك ساحر و
+
+450
+00:37:39,930 --> 00:37:44,830
+شاعر وكاهن ومجنون إن العزة لله جميعا الله عز وجل
+
+451
+00:37:44,830 --> 00:37:50,070
+هو الذي يعزه وهو الذي يذله وهو سوف يعزك ويذلهم
+
+452
+00:37:50,070 --> 00:37:54,910
+وهذا الذي وقع فقد عز الله عز وجل رسوله محمد فهو
+
+453
+00:37:54,910 --> 00:37:59,850
+العزيز وأذل الكافرين في بعد ذلك في حياة النبي عليه
+
+454
+00:37:59,850 --> 00:38:04,210
+الصلاة والسلام إذا ولا يحزنك قولهم لعن لا تحزن يا 
+
+455
+00:38:04,210 --> 00:38:08,190
+محمد على ما قاله الكفار من أنك ساحر وشاعر فهنا
+
+456
+00:38:08,190 --> 00:38:13,010
+بحط وقف لازم يجب أن تقف وقفا لازما إن العزة لله
+
+457
+00:38:13,010 --> 00:38:17,670
+جميعه كلام جديد ولو وصلناها هتوهم معنى غير المعنى
+
+458
+00:38:17,670 --> 00:38:22,990
+المراد ممن الإخوة الكرام اللي يوصل هذه الآية نشوف كيف
+
+459
+00:38:22,990 --> 00:38:31,350
+تؤدي المعنى مين عارف؟ ولا يعرف متقبيله إلا الله و
+
+460
+00:38:31,350 --> 00:38:35,410
+راصخونا من المهاجمة ووقف لازم هو نفس الوقف اللازم 
+
+461
+00:38:35,410 --> 00:38:39,350
+وهو نوع من أنواع الوقف التام يعني بعض المصاحف
+
+462
+00:38:39,350 --> 00:38:43,350
+اعتبروا قلة وحطت عليها قلة يعني وقف تام وبعضهم 
+
+463
+00:38:43,350 --> 00:38:48,630
+اعتبروا وقف لازم وعالوقف اللازم له معنى وعالوقف
+
+464
+00:38:48,630 --> 00:38:54,510
+التام له معنى إنما المراد هنا ولا يحزنك قولهم في
+
+465
+00:38:54,510 --> 00:38:59,550
+ميم بعدين إن العزة لله جميع اسم واقف لازم لو وصلت 
+
+466
+00:38:59,550 --> 00:39:02,670
+بدأ أوصل أنا وبدأ منكم واحد يقول إيش معناها في 
+
+467
+00:39:02,670 --> 00:39:07,770
+حالة الواصل لو قلنا مثلا ولا يحزنك قولهم إن العزة
+
+468
+00:39:07,770 --> 00:39:11,830
+لله جميع إيش بيصير المعنى؟ فضل 
+
+469
+00:39:15,080 --> 00:39:19,840
+لو وصلناها بتصير كلام إن العزة لله جماعة هو من
+
+470
+00:39:19,840 --> 00:39:24,340
+كلام الكفار وإنهم
+
+471
+00:39:24,340 --> 00:39:28,060
+قالوا إن العزة لله جماعة لذلك حزن الرسول ولكن هذا
+
+472
+00:39:28,060 --> 00:39:32,220
+ليس هو المراد إن الله سبحانه وتعالى يواسي رسوله
+
+473
+00:39:32,220 --> 00:39:35,850
+يقول له يا محمد لا تحزن على ما قالوه الله هو 
+
+474
+00:39:35,850 --> 00:39:39,430
+العزيز، والله هو الذي يعز ما يشاء ويذل ما يشاء، إن 
+
+475
+00:39:39,430 --> 00:39:42,850
+العزة لله جميعها كلام جديد وكلام مستنف، وهو كلام
+
+476
+00:39:42,850 --> 00:39:45,870
+الله سبحانه وتعالى، لو وصله، بيصير هو كلام
+
+477
+00:39:45,870 --> 00:39:48,730
+الكافرين، ولو وقفنا عليه وقفا لازما، بيصير هذا
+
+478
+00:39:48,730 --> 00:39:52,050
+كلام الله سبحانه وتعالى، وهذا هو المعنى المراد 
+
+479
+00:39:52,050 --> 00:39:59,030
+وليس الواصل نشوف مثال آخر قوله تعالى مثلا فلا يحزن
+
+480
+00:39:59,030 --> 00:40:03,630
+كقولهم إنا نعلم ما يسرون وما
+
+481
+00:40:03,630 --> 00:40:09,270
+يعلنون الآن فلا يحزن كقولهم برضه نفس الكلام
+
+482
+00:40:09,270 --> 00:40:13,090
+الكفار سبوا الرسول وأذوه فربنا بيواصل الرسول محمد 
+
+483
+00:40:13,090 --> 00:40:16,830
+عليه الصلاة والسلام يقول لهم يعني لا تحزن يا محمد
+
+484
+00:40:16,830 --> 00:40:22,390
+على ما يقولونه فلا يحزن كقولهم الله بيعلم إننا نعلم 
+
+485
+00:40:22,390 --> 00:40:25,670
+ما يسرون وما يعلنون كلام الله لو وصلناها إيش
+
+486
+00:40:25,670 --> 00:40:29,630
+بيصير كلا إننا نعلم ما يسرون وما يعلنون هو كلام 
+
+487
+00:40:29,630 --> 00:40:34,610
+الكافرين يعني لو وصلها فلا يحزن كقولهم إننا نعلم 
+
+488
+00:40:34,610 --> 00:40:38,410
+ما يسرون وما يعلنون بيصير أنه اللي أحزن الرسول أن
+
+489
+00:40:38,410 --> 00:40:41,770
+الكفار قالوا إننا نعلم ما يسرون وما يعلنون و
+
+490
+00:40:41,770 --> 00:40:45,150
+بيصير الكلام هو كلام الكفار وهذا ليس هو المراد، 
+
+491
+00:40:45,150 --> 00:40:49,960
+مفهوم يا إخواننا؟ فلا يحزنوا كقولهم الآن تم المعنى 
+
+492
+00:40:49,960 --> 00:40:54,860
+عنده لا يتعلق بمبادئه لا لفظ ولا معنى وفي عنا وقف 
+
+493
+00:40:54,860 --> 00:41:01,220
+لازم عليه ونبدأ بقوله إنا نعلم ما يسرون وما يعلنون 
+
+494
+00:41:01,220 --> 00:41:06,280
+آخر مثال عندنا في الوقف اللازم في قول تعالى ولا
+
+495
+00:41:06,280 --> 00:41:11,760
+خوف عليهم ولا هم يحزنون من هؤلاء الناس الذين لا
+
+496
+00:41:11,760 --> 00:41:18,520
+خوف عليهم ولا هم يحزنون الذين يؤمنوا المؤمنون 
+
+497
+00:41:18,520 --> 00:41:22,900
+الصادقون الصالحون هم الذين ولا خوف عليهم يعني لا
+
+498
+00:41:22,900 --> 00:41:27,400
+.. لا خوف عليهم لأن الإنسان بيخاف من المستقبل لا 
+
+499
+00:41:27,400 --> 00:41:32,320
+خوف عليهم لأن مستقبلهم الجنة ولا هم يحزنون عما عما 
+
+500
+00:41:32,320 --> 00:41:35,000
+تركوه في الدنيا من ال .. تركوا الأموال وتركوا
+
+501
+00:41:35,000 --> 00:41:39,140
+الدنيا فالدنيا بتحزنش لا تحزن على الدنيا ولا تخاف
+
+502
+00:41:39,140 --> 00:41:42,560
+على المستقبل مستقبلك في الجنة وبعد تحزن فالمؤمنون 
+
+503
+00:41:42,560 --> 00:41:48,130
+ولا خوف عليهم ولا هم يحزنون وبعدين كلام جديد بقصة
+
+504
+00:41:48,130 --> 00:41:53,250
+جديدة بحكم جديد هو حكم الربا الذين يأكلون الربا لا
+
+505
+00:41:53,250 --> 00:41:58,530
+يقومون إلا كما يقوم الذي يتخبطه الشيطان من المسطيب
+
+506
+00:41:58,530 --> 00:42:03,250
+يبقى هذا كلام جديد إذا الوقف على ولا خوف عليهم ولا
+
+507
+00:42:03,250 --> 00:42:08,830
+هم يحزنون اسم وقف لازم تم المعنى عندهم لا يتعلق
+
+508
+00:42:08,830 --> 00:42:13,390
+بما بعدهم لا لفظ ولا معنى فإذا وصلت الكلام اختل
+
+509
+00:42:13,390 --> 00:42:17,810
+المعنى لو تشوف كيف أوصل الكلام الآن ونشوف كيف
+
+510
+00:42:17,810 --> 00:42:23,090
+بتغير المعنى لو واحد قال ولا خوف عليهم ولا هم
+
+511
+00:42:23,090 --> 00:42:27,640
+يحزنون الذين يأكلون الربا تصير الذين يأكلون الربح 
+
+512
+00:42:27,640 --> 00:42:29,960
+دولة هم الذين لا خوفوا عليه ولا هم يحزنوا عليه
+
+513
+00:42:29,960 --> 00:42:34,020
+اتغير المعنى ولا ما اتغير؟ اتغير المعنى وتغيره 
+
+514
+00:42:34,020 --> 00:42:38,440
+تغير غير صحيح وبالتالي لابد إنسان مسلم أن يقرأ
+
+515
+00:42:38,440 --> 00:42:42,220
+القرآن ويقف عند المواضع التي يوقف عندها فإذا وقف 
+
+516
+00:42:42,220 --> 00:42:46,180
+على موضع لا يدفده معنى أو يوهم معنى غير المعنى
+
+517
+00:42:46,180 --> 00:42:50,530
+المراد فهذا يعد وقفا قبيحا ولا يصح له أن يقف أما إذا
+
+518
+00:42:50,530 --> 00:42:53,870
+أردت أن يقف وقفا صحيحا يقف على الكلمة التي تم
+
+519
+00:42:53,870 --> 00:42:58,010
+المعنى عندها ولا تتعلق بما بعدها لا لفظ ولا معنى
+
+520
+00:42:58,010 --> 00:43:01,530
+الآن ذكرنا النوع الأول أو القسم الأول من أقسام
+
+521
+00:43:01,530 --> 00:43:04,550
+الوقف وسوف نكمل إن شاء الله في المحاضرة القادمة 
+
+522
+00:43:04,550 --> 00:43:08,990
+باقي الأنواع عندنا القسم الثاني الوقف الكافي ثم
+
+523
+00:43:08,990 --> 00:43:12,150
+الوقف الحسن ثم الوقف القبيح إن شاء الله نذكره في
+
+524
+00:43:12,150 --> 00:43:15,170
+المحاضرة القادمة بارك الله فيكم والسلام عليكم ورحمة
+
+525
+00:43:15,170 --> 00:43:16,110
+الله وبركاته
diff --git a/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/CgqSGjePIaw_raw.srt b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/CgqSGjePIaw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a03b6d6af888f1ccaa1f51905821622ff20e65a4
--- /dev/null
+++ b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/CgqSGjePIaw_raw.srt
@@ -0,0 +1,1192 @@
+1
+00:00:20,940 --> 00:00:23,400
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:23,400 --> 00:00:27,260
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى
+
+3
+00:00:27,260 --> 00:00:30,460
+آله وصحابه وسلم أن هنا يا أخواننا يا كرام في
+
+4
+00:00:30,460 --> 00:00:33,800
+المحاضرة الماضية يعني يزم من أحكام الوقف والابتداء
+
+5
+00:00:33,800 --> 00:00:39,580
+وخدنا بعدها مباشرة موضوع السكت والقطع والابتداء
+
+6
+00:00:39,580 --> 00:00:44,740
+وهمزة الوصل الابتداء بهمزة الوصل وقلنا أن همزة
+
+7
+00:00:44,740 --> 00:00:47,840
+الوصل هي همزة زائدة عن بنية الكلمة تلحق أول
+
+8
+00:00:47,840 --> 00:00:51,510
+الأسماء والأفعال والحروفلو سألنا سؤال ما هي
+
+9
+00:00:51,510 --> 00:00:57,510
+الأفعال التي تلحقها همزة الوصل؟ من يقبلنا؟ همزة
+
+10
+00:00:57,510 --> 00:01:00,450
+الوصل بالنسبة للأفعال اللي هو ماضي الخماسي
+
+11
+00:01:00,450 --> 00:01:07,280
+والسادسي كذلك أمر الثلاثي والخماسي والسادسيو كذلك
+
+12
+00:01:07,280 --> 00:01:11,860
+تلحق الأسماء و تلحق الحروف أما بالنسبة لحركة
+
+13
+00:01:11,860 --> 00:01:14,260
+hamster whistle أيضا أخدناها يا إخواننا يا إكرام
+
+14
+00:01:14,260 --> 00:01:18,180
+في المحاضرة الماضية ف hamster whistle إما أن تكون
+
+15
+00:01:18,180 --> 00:01:22,360
+عند إتداء بيها مضمومة إذا كان الحرف التالت للفعل
+
+16
+00:01:22,360 --> 00:01:28,820
+مضموممثل كلمة انظر او ادعو هنا الحرف الثالث مضموم
+
+17
+00:01:28,820 --> 00:01:34,100
+هذا طبعا ادعو و انظر و اتلو كله يعني أمر الثلاثي
+
+18
+00:01:34,100 --> 00:01:38,220
+فهمس و همس و اتواصل حركته حركة همس و اتواصل عند
+
+19
+00:01:38,220 --> 00:01:41,380
+الابتداء بها ادعو مضموم لماذا ضمة همس و اتواصل هنا
+
+20
+00:01:41,380 --> 00:01:46,660
+لأن الحرف التالت مضمونكذلك يبدأ بهمس الوصل في
+
+21
+00:01:46,660 --> 00:01:51,780
+الأفعال بالكسري إذا كان ثالث الحرف مفتوح مثل وإذا
+
+22
+00:01:51,780 --> 00:01:56,640
+قلبوا أو عند الإبتداء بيها ان قلبوا تكسر لأن الحرف
+
+23
+00:01:56,640 --> 00:02:02,640
+التالت مفتوح أو الحرف التالت مكسور مثل اصبر اصبر
+
+24
+00:02:02,640 --> 00:02:06,860
+حرف الهمس الوصل نبدأ بيها مكسورة لأن الحرف التالت
+
+25
+00:02:06,860 --> 00:02:13,260
+اصبر او اضرب ارا ارا مكسورة ان هو الحرف الثالثأو
+
+26
+00:02:13,260 --> 00:02:18,240
+إذا كان ثالث الفعل مضمون ضمن عارضا وهو لا يقع إلا
+
+27
+00:02:18,240 --> 00:02:25,000
+في خمس كلمات اقضوا امشوا اقتوا ابنوا اقتوا يعني
+
+28
+00:02:25,000 --> 00:02:30,420
+اقضوا ابنوا امضوا امشوا اقتوا هذه خمس كلمات هتكسر
+
+29
+00:02:30,420 --> 00:02:34,120
+همس الواصل عند ابتدائها لأن الحرف الثالث من هذا
+
+30
+00:02:34,120 --> 00:02:38,360
+الفعل مضمون ضمن عارضا مامعنى ضمن عارضا يعني هو ليس
+
+31
+00:02:38,360 --> 00:02:43,850
+أصليوإنما استبدلت الكسرة بضمة عارضة لتتناسب مع
+
+32
+00:02:43,850 --> 00:02:49,250
+الواو هنا اقضو أصل الضمة اللي هنا بتاعة اقضو أصلها
+
+33
+00:02:49,250 --> 00:02:55,550
+كسرة اللي هي اقضي مكسورة لكن وضعنا ضمة عارضة بدلا
+
+34
+00:02:55,550 --> 00:02:59,730
+من الكسرة لتتناسب مع الواو الجماعة وكذلك ابن
+
+35
+00:02:59,730 --> 00:03:04,990
+الجماعة منها ابنو فوضعت الضمة على النون لتتناسب مع
+
+36
+00:03:04,990 --> 00:03:09,500
+الواوو هذه في ال .. و هذا .. هكذا كان في الكلمات
+
+37
+00:03:09,500 --> 00:03:14,900
+الخامسةكذلك أخدنا يا أخواننا يا كرام همزة الوصل
+
+38
+00:03:14,900 --> 00:03:18,260
+اللي في الأسماء ما هي الأسماء اللي همزتها همزة وصل
+
+39
+00:03:18,260 --> 00:03:25,000
+فيها سماعي أسماء سماعية وفي أسماء قياسية أما
+
+40
+00:03:25,000 --> 00:03:29,000
+بالنسبة للقياسية يعني لها ميئزان معين وهي مصدر
+
+41
+00:03:29,000 --> 00:03:33,620
+الخماسي والسداسي مصدر الفعل الخماسي والسداسي مثل
+
+42
+00:03:33,620 --> 00:03:37,680
+ابتغاء ابتغاء مثلا ابتغاء عبارة عن المفروض المطلق
+
+43
+00:03:37,680 --> 00:03:43,050
+يعني مصدرابتغاء يعني ابتغاء ابتغاء اختلف اختلاف
+
+44
+00:03:43,050 --> 00:03:48,110
+اختلاف استغفر استغفر فالاستغفار والابتغاء
+
+45
+00:03:48,110 --> 00:03:54,590
+والاستنثار والاستنشاق والاستكبار كل هذه عبارة عن
+
+46
+00:03:54,590 --> 00:03:59,370
+مصادر مصدر الخماسي والسداسي حمزة حمزة واصل طيب عند
+
+47
+00:03:59,370 --> 00:04:04,130
+الابتداء بحمزة الواصل عند الابتداء بالكلمة اللي هي
+
+48
+00:04:04,130 --> 00:04:07,470
+الكلمة التي حمزة حمزة واصل ما هي حركة حمزة واصل في
+
+49
+00:04:07,470 --> 00:04:14,070
+الأسماء؟الكسر يبقى تكسر همثل واصل في الأسماء سواء
+
+50
+00:04:14,070 --> 00:04:21,260
+كانت سماعية أو قياسية مثل استغفاراستكبار استنشاق
+
+51
+00:04:21,260 --> 00:04:26,880
+استنثار كل هذه همزة مكسورة أو بالنسبة للخماسي مصدر
+
+52
+00:04:26,880 --> 00:04:32,700
+الخماسي ابتغاء اختلاف انتقاء برضه همزة همزة ايش
+
+53
+00:04:32,700 --> 00:04:36,500
+همزة وصل مكسور بتكون همزة الوصل في الأسماء مكسورة
+
+54
+00:04:36,500 --> 00:04:41,060
+سواء كانت قياسية مثل هذه الأسماء اللي احنا رأيناها
+
+55
+00:04:41,060 --> 00:04:45,100
+او حتى سماعية ما هي الأسماء السماعية يا اخوانا يا
+
+56
+00:04:45,100 --> 00:04:50,240
+كرام الأسماء السماعية اللي همزة همزة وصلهي حوارق
+
+57
+00:04:50,240 --> 00:04:56,380
+سبعة كلمات اللي هي ابن و ابنة اثنان اثنتان امرأ و
+
+58
+00:04:56,380 --> 00:05:00,200
+امرأة و اسم هذه كلها عند الابتداء بيها نقول ابن
+
+59
+00:05:00,200 --> 00:05:04,220
+ابنة اثنان نبتدأ بها الكلام ولكن عندما توصل بما
+
+60
+00:05:04,220 --> 00:05:08,580
+قبلها تحذف همزة الوصل لان همزة الوصل تثبتوا اذا
+
+61
+00:05:08,580 --> 00:05:12,860
+ابتدأنا بها الكلام وتحذفوا او تسقطوا اذا وصلت بما
+
+62
+00:05:12,860 --> 00:05:19,000
+قبلهامثال ذلك إن ابني من أهله ابني عندما أقول ابني
+
+63
+00:05:19,000 --> 00:05:24,620
+هي ذكرت الهمزة ألفظها بالهمزة لكن ان ابني تسقط
+
+64
+00:05:24,620 --> 00:05:29,000
+همزة الواصل في حالة واصل الكلمة بالتي قبلها إذا في
+
+65
+00:05:29,000 --> 00:05:32,840
+عندنا سبع كلمات همزة همزة واصل وهذه أسماء سماعية
+
+66
+00:05:32,840 --> 00:05:36,200
+أما بالنسبة لحركة همزة الواصل في الأسماء يا أخوان
+
+67
+00:05:36,200 --> 00:05:40,360
+ما هيالكسر دائما همزة الوصل في الأسماء بتكون
+
+68
+00:05:40,360 --> 00:05:44,280
+maximum أخدنا ذلك في عندنا همزة الوصل اللي في
+
+69
+00:05:44,280 --> 00:05:49,540
+الحروف لأن همزة الوصل تلحق الأفعال وتلحق الأسماء
+
+70
+00:05:49,540 --> 00:05:53,540
+وتلحق الحروف عرفنا الأفعال وعرفنا الأسماء وعرفنا
+
+71
+00:05:53,540 --> 00:05:57,480
+بالنسبة للحروف ما هي الحروف اللتي همزتها همزة وصل
+
+72
+00:05:58,760 --> 00:06:03,840
+نعم بس حرف واحد وهو قلة تعريف لكن اللتي و اللذي لا
+
+73
+00:06:03,840 --> 00:06:11,080
+تعدوا من حروف التي همزت و همزت واصل هنا يا إخواننا
+
+74
+00:06:11,080 --> 00:06:16,340
+يا كرام طبعا حركة همزة الواصل في قلة تعريف الفتح
+
+75
+00:06:17,070 --> 00:06:21,010
+يبقى همسة الواصل في قلة تعريف ما هو حركتها الفتح،
+
+76
+00:06:21,010 --> 00:06:24,630
+همسة الواصل اللي في الأسماء حركتها الكسر، همسة
+
+77
+00:06:24,630 --> 00:06:28,390
+الواصل اللي في الأفعال إما أن تكون مضمومة لو كان
+
+78
+00:06:28,390 --> 00:06:33,650
+الحرف التالت مضموم مثل اطلو ادعو أو يكون مكسول لو
+
+79
+00:06:33,650 --> 00:06:36,750
+كان حرف التالت مفتوح مثل انطلقوا
+
+80
+00:06:38,910 --> 00:06:46,070
+انطلقوا او مكسور لو كان حرف التالت مفتوح او مكسور
+
+81
+00:06:46,070 --> 00:06:52,210
+مثل اصبر او مضمون ضمن عرض مثل ابنه واخده هذا
+
+82
+00:06:52,210 --> 00:06:57,710
+بالنسبة لهمزة الوصل في عندنا يا اخوان فوائد مهمة
+
+83
+00:06:57,710 --> 00:07:02,150
+لو بدنا نتعرف عليها بالنسبة لهمزة الوصل اللي في
+
+84
+00:07:02,150 --> 00:07:05,510
+قلة تعريف او فيهمزة الوصل بشكل اهم الفوائد الاولى
+
+85
+00:07:06,560 --> 00:07:11,360
+عندنا تُحذف همسة الوصل لفظا وخطا من قل التعريف إذا
+
+86
+00:07:11,360 --> 00:07:17,000
+دخلت عليها لام الجار يعني أي كلمة فيها قل التعريف
+
+87
+00:07:17,000 --> 00:07:24,620
+يعني المدرسة المتقين الطيبات الجنة لو دخلت عليها
+
+88
+00:07:24,620 --> 00:07:29,720
+حرف جار اللام تُحذف
+
+89
+00:07:29,720 --> 00:07:34,820
+همسة الوصل لفظا وخطا تُحذف همسة الوصل لفظا وخطا
+
+90
+00:07:34,820 --> 00:07:40,450
+يعني لا تُكتبكتابة ولا .. ولا نلفظها إذا دخلت
+
+91
+00:07:40,450 --> 00:07:45,810
+عليها لام الجار لو قلنا مثلا المدرسة لو دخلنا
+
+92
+00:07:45,810 --> 00:07:53,610
+عليها لام نقول للمدرسة مثلا المتقينللمتقين الجنة
+
+93
+00:07:53,610 --> 00:08:00,270
+للجنة تسقط همس الوصل لفظا وخطا لنكتبها لكن إذا
+
+94
+00:08:00,270 --> 00:08:04,310
+وضعنا حرف جار أي حرف من حروف الجار غير اللام نقول
+
+95
+00:08:04,310 --> 00:08:10,630
+من المدرسة من الجنة من المتقين أو إلى المتقين عن
+
+96
+00:08:10,630 --> 00:08:15,390
+المتقين بالمتقين أي حرف من حروف الجار دخلت عليها
+
+97
+00:08:17,170 --> 00:08:21,790
+دخلت على الإسم المعرف بقال عند إذن يبقى همزة ..
+
+98
+00:08:21,790 --> 00:08:27,990
+يبقى همزة الوصل خطا ويحذف لفظا يعني لا نلفظه أنا
+
+99
+00:08:27,990 --> 00:08:34,470
+أقول بالمتقين بالجنة بالطيبات مثلا لفظا لا يلفظ
+
+100
+00:08:34,470 --> 00:08:38,930
+لأن همزة الوصل بتسقط لكن تكتب كتابة إلا حرف الجر
+
+101
+00:08:38,930 --> 00:08:42,870
+اللام إذا دخل على الإسم المعرف بقال بيسقط همزة
+
+102
+00:08:42,870 --> 00:08:50,110
+الوصل تسقط لفظا وخطاالمثال هو ذلك إن للمتقين مفازة
+
+103
+00:08:50,110 --> 00:08:55,390
+للمتقين هكذا يعني نشوف نرى إنه هي أصلا المتقين
+
+104
+00:08:55,390 --> 00:08:59,450
+دخلت عليها اللام فكتبت للمتقين ثقت همست الوصل لفظا
+
+105
+00:08:59,450 --> 00:09:05,730
+وخطا كذلك للذين أحسنوا الحسن وزيادة للذين هي أصلا
+
+106
+00:09:05,730 --> 00:09:10,750
+الذين دخلت عليها اللام فصارت للذين حُذفت همست
+
+107
+00:09:10,750 --> 00:09:16,740
+الوصل لفظا وخطاأما إذا تدخل عليها أي حرف من حروف
+
+108
+00:09:16,740 --> 00:09:24,040
+الجر يحدث بس لفظا و يبقى خطا مثال ذلك الذين يؤمنون
+
+109
+00:09:24,040 --> 00:09:29,560
+بالغيب بالغيب دخلت البا على الإسم المعرف بل زي
+
+110
+00:09:29,560 --> 00:09:34,080
+الغيب فسارت بالغيب تبقى همس الوصل خطا و تسقطه لفظا
+
+111
+00:09:34,080 --> 00:09:39,500
+كذلك و بالآخرة هم يوقنونبالآخر ادخلت حرف الجر
+
+112
+00:09:39,500 --> 00:09:44,160
+اللام على الاسم المعرف ب L فبقيت همسة الوصل خطا و
+
+113
+00:09:44,160 --> 00:09:48,180
+حوتفات وصل و هكذا في جميع الكلمات هذه هي الفائدة
+
+114
+00:09:48,180 --> 00:09:51,520
+الأولى و هي دخول حرف الجر اللام على الاسم المعرف ب
+
+115
+00:09:51,520 --> 00:09:56,560
+L بيسقط همسة الوصل لفظا و خطاالفادة الثانية يا
+
+116
+00:09:56,560 --> 00:10:00,200
+إخواننا يا كرام، وهو إذا دخلت همزة الاستفهام على
+
+117
+00:10:00,200 --> 00:10:04,080
+الإسم المعرف بـL، تبقى همزة الواصل ولا تُحذف لألا
+
+118
+00:10:04,080 --> 00:10:09,240
+يلتبس الاستفهام بالخبر، فيتغير المعنى، وهذا لا يقع
+
+119
+00:10:09,240 --> 00:10:13,710
+إلا في تلت كلمات، يعني همزة الاستفهام القاعدةإذا
+
+120
+00:10:13,710 --> 00:10:18,690
+دخلت همس الاستفهام على الاسم المعرف بال همس الواصل
+
+121
+00:10:18,690 --> 00:10:24,790
+لا نحذفها بل تبقى وتبدأ إلى حرف مد ونمده ست حركات
+
+122
+00:10:24,790 --> 00:10:32,560
+وهذا لا يقع إلا في تلت كلمات اللي هيالذكرين او
+
+123
+00:10:32,560 --> 00:10:42,000
+الله اذن لكم او انا وقد كنتم به تستعجلون تلت كلمات
+
+124
+00:10:42,000 --> 00:10:46,830
+في القرآن هذه الكلمات الثلاثةهمزة الاستفهام دخلت
+
+125
+00:10:46,830 --> 00:10:51,310
+على الاسم المعرف بإن هذا الأصل في الهمزة قلت عليه
+
+126
+00:10:51,310 --> 00:10:56,170
+تسقط لكنها حتى يصير .. يعني لأنه بيحدث لبس لو سقطت
+
+127
+00:10:56,170 --> 00:11:00,110
+تبقى همزة الواصل وتبدأ بحرف مد ونمدة وست حركات
+
+128
+00:11:00,110 --> 00:11:05,450
+ويسمى أيضا مد الفرقيسمى مد الفرق ليش الفرق؟ لأن
+
+129
+00:11:05,450 --> 00:11:09,990
+هذا الحرف المد اللي هي ال a تفرق ما بين همزة
+
+130
+00:11:09,990 --> 00:11:14,550
+الاستفام و همزة الخبر وهو لا يقع إلا في تلت كلمات
+
+131
+00:11:14,550 --> 00:11:21,910
+في قول تعالى قل ا الذكرين يحرم أم الأنثيين ا
+
+132
+00:11:21,910 --> 00:11:26,250
+الذكرين تمدوا ست حركات كذلك الكلمة الثانية
+
+133
+00:11:28,980 --> 00:11:34,040
+الان وقد كنتم به تستعجلون هذا أخذناه سابقا يا
+
+134
+00:11:34,040 --> 00:11:37,000
+أخواننا زمان أنه نوع من أنواع المادة ما هو نوع
+
+135
+00:11:37,000 --> 00:11:43,440
+المادة اللي في قوله الان وقد عصيت قبل وكنت من
+
+136
+00:11:43,440 --> 00:11:49,590
+المفسدين الان نسميه مادة الفرق وله اسم آخراللي هو
+
+137
+00:11:49,590 --> 00:11:54,790
+مد لازم مخفف فى مد لازم مخفف و مد لازم كلمه مخفف و
+
+138
+00:11:54,790 --> 00:11:59,690
+مد لازم كلمه مثقل هنا فى قوله أ الآن مد لازم كلمه
+
+139
+00:11:59,690 --> 00:12:05,170
+مخفف لأنه جاء حرف المد وجاء وراه حرف ساكن اللام و
+
+140
+00:12:05,170 --> 00:12:09,730
+كذلك فى قوله أ الذكرين هذا هي ايضا جاء حرف المد
+
+141
+00:12:09,730 --> 00:12:13,590
+وجاء بعده حرف مشدد ماهو الحرف المشدد اللى فى قوله
+
+142
+00:12:13,590 --> 00:12:19,200
+أ الذكرينالذال المشددة لماذا؟ لأن اللام بتاعة ال
+
+143
+00:12:19,200 --> 00:12:23,840
+تضغم .. لام شمسية تضغم مع الذال .. تضغم مع الذال
+
+144
+00:12:23,840 --> 00:12:28,620
+فنقول الذكرين فالذي بعد حرف المد فيه حرف الذال
+
+145
+00:12:28,620 --> 00:12:33,040
+المشدد المضغم مع اللام وعند إذن بنسميه مد لازم
+
+146
+00:12:33,040 --> 00:12:39,010
+كلمة مثقلفي هذه الكلمة ويسمى كذلك مد الفرق وكمان
+
+147
+00:12:39,010 --> 00:12:42,930
+الحكم آخر اللي هو القاعدة اللي عندنا إذا دخلت همسة
+
+148
+00:12:42,930 --> 00:12:46,990
+الاستفام على الإسم المعرف بال لا يسقط همسة الواصل
+
+149
+00:12:46,990 --> 00:12:51,250
+بل تبدأ بحرف مد ومن مده ست حركات ومن سمي مد الفرق
+
+150
+00:12:51,250 --> 00:12:57,370
+وكذلك يسمى مد اللازم كلام متقل مثل ا الذكرين او مد
+
+151
+00:12:57,370 --> 00:13:03,670
+لازم كلام مخفف مثل الان ونقرأها الان
+
+152
+00:13:04,180 --> 00:13:09,820
+كذلك الكلمة الثالثة يا أخواننا اللي هي قل أ الله
+
+153
+00:13:09,820 --> 00:13:16,900
+أذن لكم أ الله هي أصلا الله قال للتعريف الله ذكرت
+
+154
+00:13:16,900 --> 00:13:22,060
+عليها همس الاستفهام فلا نقرأها أ الله بل همس
+
+155
+00:13:22,060 --> 00:13:27,780
+الواصل تبدأ إلى حرف مد وتمد تحركات فنقرأها قل أ
+
+156
+00:13:27,780 --> 00:13:34,180
+الله أذن لكموهي نفسها مادة الفرق وكمان نسمى مادة
+
+157
+00:13:34,180 --> 00:13:39,620
+لازم كلمة مثقل لأنه لو قلنا اللام مع اللام مضغمة و
+
+158
+00:13:39,620 --> 00:13:44,060
+بعد حرف المادة في عنا حرف مشددة في كلمة واحدة يسمى
+
+159
+00:13:44,060 --> 00:13:48,560
+مادة لازم كلمة مثقل هذا هو الفائدة الثانية الفائدة
+
+160
+00:13:48,560 --> 00:13:53,200
+الأولى حرف اللام دخلت على اسم المعرف بال إبتسفط
+
+161
+00:13:53,200 --> 00:13:58,020
+خمس الوصل لفظا وخطاالفايدة الثانية لو دخلت همزة
+
+162
+00:13:58,020 --> 00:14:02,140
+الاستفهام على الاسم المعرف بأل همزة الواصل في أل
+
+163
+00:14:02,140 --> 00:14:06,040
+التعريف لا تسقط بل تبدأ بحرف مد ومن مده ست حركات
+
+164
+00:14:06,040 --> 00:14:09,320
+ومن سميه مد الفرح أو مد اللي نازم الكلام المثقل أو
+
+165
+00:14:09,320 --> 00:14:14,740
+المخفف على حسب التشديدو هنا طبعا في عنا وجهين من
+
+166
+00:14:14,740 --> 00:14:19,200
+أوجه القراءة تقرأ زي ما قلت مثلا بالست حركات نمدة
+
+167
+00:14:19,200 --> 00:14:22,960
+ست حركات و نسميها مادة لازم كلام مثقل أو مادة
+
+168
+00:14:22,960 --> 00:14:26,900
+الفرق و يجب علينا أن نقرأها مع تسهيل همزة الوصل
+
+169
+00:14:27,250 --> 00:14:31,050
+يعني تاعة .. ال .. الهمزة تاعة الذكرين أو الله أو
+
+170
+00:14:31,050 --> 00:14:34,830
+الآن لا تبدأ إلى حرف ماده من مدسة حركات بالقراءة
+
+171
+00:14:34,830 --> 00:14:39,450
+ثانية بل تقرأ بالتسهيل لهمزة الوصل و هي قراءة همزة
+
+172
+00:14:39,450 --> 00:14:43,890
+الوصل أو النطق بيها ما بين الهمزة والألف فنقول
+
+173
+00:14:43,890 --> 00:14:48,570
+مثلا هنا الذكرين حرم .. الذكرين حرم أم الأنف
+
+174
+00:14:48,570 --> 00:14:52,930
+نقرأها بتسهيل الهمزة الثانية ما بين همزة الوصل و
+
+175
+00:14:52,930 --> 00:14:55,450
+همزة ال .. الاستفهام
+
+176
+00:14:58,220 --> 00:15:00,820
+طيب عندنا الفائدة الثالثة يا أخواننا يا كرام و هي
+
+177
+00:15:00,820 --> 00:15:05,300
+إذا دخلت همزة الاستفهام على الأفعال المبدوعة بهمزة
+
+178
+00:15:05,300 --> 00:15:09,200
+وصل مكسورة يعني دخلت همزة الاستفهام على الأفعال مش
+
+179
+00:15:09,200 --> 00:15:13,960
+على التعريف على الفعل المبدوع بهمزة وصل مكسورة عند
+
+180
+00:15:13,960 --> 00:15:19,120
+إذن تحذف همزة الوصل لأنه مأمون اللفس وتقرأ بهمزة
+
+181
+00:15:19,120 --> 00:15:23,520
+الاستفهام المفتوحة وهذا طبعا موجودة في كام كلمة في
+
+182
+00:15:23,520 --> 00:15:30,160
+سبع مواضع الموضع الأول وهوقل اتخذتم عند الله عهده
+
+183
+00:15:30,160 --> 00:15:36,460
+اتخذتم هي اصلا ايش اخواننا اتخذتم فالهمزة مكسورة
+
+184
+00:15:36,460 --> 00:15:41,040
+اتخذتم على اساس ان الهمزة تواصل لان هو ماضي
+
+185
+00:15:41,040 --> 00:15:46,970
+الخماسيفدخلت عليه همزة الاستفهام فصارت ا اتخذتم
+
+186
+00:15:46,970 --> 00:15:51,270
+لكن همزة الوصل تسقط في حالة الوصل وعساس ان هي
+
+187
+00:15:51,270 --> 00:15:55,590
+مكسورة و همزة الاستفهام مفتوحة لا حاجة لنا او تسقط
+
+188
+00:15:55,590 --> 00:16:01,210
+همزة الوصل ومأمون اللبس فتقرأ اتخذتم وتفهم ضمن ان
+
+189
+00:16:01,210 --> 00:16:05,570
+الهمزة اللي هنا ليست همزة اتخذتم وانما همزة
+
+190
+00:16:05,570 --> 00:16:10,800
+الاستفهام اتخذتم عند الله عهديعني مفهومة أنها قُل
+
+191
+00:16:10,800 --> 00:16:15,240
+أتخذتُ معينا نضال الله عهدة فهمزتها همزة وصل
+
+192
+00:16:15,240 --> 00:16:20,140
+فالقاعدة إذا دخلت همزة الاستفهام على الفعل المبدو
+
+193
+00:16:20,140 --> 00:16:24,420
+بهمزة وصل مكسورة تُحدث همزة الوصل المكسورة لأنها
+
+194
+00:16:24,420 --> 00:16:29,000
+مأمون اللبس وتبقى همزة الاستفهام فنقرأها أتخذتُه
+
+195
+00:16:29,000 --> 00:16:33,260
+في كام كلمة كرت هذه أو وجدت في القرآن الكريم بس في
+
+196
+00:16:33,260 --> 00:16:38,060
+سبع مواضع الموضع الأول هو قل أتخذتُ معينا نضال
+
+197
+00:16:38,060 --> 00:16:44,130
+الله عهدةهذه الموضوع الثمانية اقرأها اتطلع الغيب
+
+198
+00:16:44,130 --> 00:16:50,170
+اتطلع
+
+199
+00:16:50,170 --> 00:16:56,330
+هي ماضي الخماسي اتطلع اتطلع الهمزة مكسورة فلما
+
+200
+00:16:56,330 --> 00:17:01,770
+دخلت عليه همزة ال sfm لنقرأها اتطلع لأن مأمون
+
+201
+00:17:01,770 --> 00:17:06,880
+النفس فتحدث همزة الوصلوتبقى همست الاستثمام فتقرأ
+
+202
+00:17:06,880 --> 00:17:12,240
+اتطلع الغيب ام اتخذ عنه انظر الله عهده اتطلع يعني
+
+203
+00:17:12,240 --> 00:17:19,080
+اتطلع الغيب كذلك افترى افترى ايضا اللي هو مبدوعة
+
+204
+00:17:19,080 --> 00:17:24,440
+بهمست وصل مكسورةدخلت عليها همزة الاستفام فلا
+
+205
+00:17:24,440 --> 00:17:30,320
+نقرأها أفترى بل تحدث همزة الواصل لأنه طبيعي أنه في
+
+206
+00:17:30,320 --> 00:17:34,620
+حالة الواصل تسقط همزة الاستفام فيبقى عندنا همزة
+
+207
+00:17:34,620 --> 00:17:39,240
+الاستفام ويبقى عندنا همزة الاستفام فنقرأها أفترى
+
+208
+00:17:39,240 --> 00:17:46,170
+على الله كذبا أم به جنة أفترىالموضوع الرابع اصطفى
+
+209
+00:17:46,170 --> 00:17:51,270
+البنات اصطفى هي فعل ماضي يعني ماضي الخماسي دخلت
+
+210
+00:17:51,270 --> 00:17:57,790
+عليه همزة الاستفام ا اصطفى فتسقط همزة الوصل وتبقى
+
+211
+00:17:57,790 --> 00:18:02,350
+اصطفى البنات على البنين اصطفى فمعروف ان هذه همزة
+
+212
+00:18:02,350 --> 00:18:09,320
+الوصل كذلك اتخذناهم اتخذناهم برضه ماضيلكن إذا دخلت
+
+213
+00:18:09,320 --> 00:18:14,100
+عليه همزة الاستفام فصارت ا اتخذناهم فتسقط همزة
+
+214
+00:18:14,100 --> 00:18:19,960
+الوصل اللي اتعت اتخذناهم وتبقى همزة الاستفام فتقرأ
+
+215
+00:18:19,960 --> 00:18:26,280
+اتخذناهم سخرية كذلك استكبرت هي أصلا استكبرة
+
+216
+00:18:26,280 --> 00:18:31,060
+سوداسية ماضي السوداسي همزة همزة وصل مكسورة دخلت
+
+217
+00:18:31,060 --> 00:18:36,190
+عليه همزة الاستفام فصارتأستكبرت فتحذف همس الوصل
+
+218
+00:18:36,190 --> 00:18:40,410
+لأنه وصل في تحذف رسمي وتبقى همس الاستفان فتقرأ
+
+219
+00:18:40,410 --> 00:18:45,850
+أستكبرت أم كنت من العالين أستكبرت مش استكبرت
+
+220
+00:18:45,850 --> 00:18:52,510
+أستكبرت كذلك كلمة أستغفرت لهم أم لم تستغفر لهم هنا
+
+221
+00:18:52,510 --> 00:18:59,540
+أستغفرت نفس الموضوع الفائدة الرابعة يا إخوانناوهي
+
+222
+00:18:59,540 --> 00:19:03,360
+إذا تقدمت همزة الوصل على همزة القطع الساكنة في
+
+223
+00:19:03,360 --> 00:19:08,160
+الكلمة يعني في عندنا تلت كلمات موجودة اللي هي
+
+224
+00:19:08,160 --> 00:19:14,840
+أؤتمنا أو أئذن أو أئتوني القاعدة اللي عندنا إذا
+
+225
+00:19:14,840 --> 00:19:21,680
+دخلت أو تقدمت همزتين همزة الوصلالأولى وبعدها همزة
+
+226
+00:19:21,680 --> 00:19:26,240
+قطع ساكنة همزة الواصل طبعا بتكون مكسورة أو مضمومة
+
+227
+00:19:26,240 --> 00:19:30,460
+حسب وضعها مكسورة أو مضمومة لكن همزة الثانية في
+
+228
+00:19:30,460 --> 00:19:33,940
+الكلمة همزة الأصلية اللي في الكلمة اللي هي الساكنة
+
+229
+00:19:33,940 --> 00:19:37,380
+يبقى فيها أن همزة واصل في أول كلمة وهي همزة زائدة
+
+230
+00:19:37,380 --> 00:19:41,650
+عن بنية الكلمة لحقت بالأفعالوالهمزة الثانية همزة
+
+231
+00:19:41,650 --> 00:19:46,930
+أصلية في قوله أؤتمنا أؤتمنا في عندنا همزتين الهمزة
+
+232
+00:19:46,930 --> 00:19:51,450
+الأولى همزة الأو الأولى مضمومة والتانية أؤتمنا
+
+233
+00:19:51,450 --> 00:19:57,530
+الساكنة ولماذا قرأناها احنا بضم الهمزة همزة الأولى
+
+234
+00:19:57,530 --> 00:20:00,590
+اللي هي همزة الواصل لأن الحرف التالت مضمومها
+
+235
+00:20:00,590 --> 00:20:06,280
+أؤتمنا فلأن الحرف التالت مضمومعند النطق بهمزة
+
+236
+00:20:06,280 --> 00:20:11,100
+الوصل نقول أؤتمنا، يعني لا نقرأها أأتمنا ولا
+
+237
+00:20:11,100 --> 00:20:15,480
+ائتمنا، نقرأها بالضمن لأن الحرف التالت مضموم، يعني
+
+238
+00:20:15,480 --> 00:20:19,700
+في عندنا همزتين، همزة الأولى همزة وصل مضمومة لأن
+
+239
+00:20:19,700 --> 00:20:24,050
+حرف التالت مضموموالهمزة الثانية ساكنة فالقاعدة
+
+240
+00:20:24,050 --> 00:20:29,550
+اللى عندنا إذا وصلناها إذا وصلت تسقط همزة الوصل
+
+241
+00:20:29,550 --> 00:20:34,590
+فتقرأ فليؤدى الذي أتمنى أمانته فتسقط همزة الوصل
+
+242
+00:20:34,590 --> 00:20:39,330
+يعني في حالة الوصل عند أن توصل هذه الكلمة تسقط
+
+243
+00:20:39,330 --> 00:20:43,250
+همزة الوصل وتظهر الهمزة الثانية اللى هى همزة
+
+244
+00:20:43,250 --> 00:20:47,710
+الكلمة اللى هى الأصلية اللى هى همزة القطعفليؤد
+
+245
+00:20:47,710 --> 00:20:52,210
+اللذي اقتمن أمانته هنا ومنهم يقول ائذن ليه يقول
+
+246
+00:20:52,210 --> 00:20:57,190
+ائذن ليه يبقى مش يقول ا ائذن ليه انما يقول ومنهم
+
+247
+00:20:57,190 --> 00:21:01,010
+يقول ائذن ليه تسقط همزة الوصل و تلفظ الهمزة
+
+248
+00:21:01,010 --> 00:21:06,530
+الثانية كذلك هنا املهم شركم في السماوات اقتوني في
+
+249
+00:21:06,530 --> 00:21:10,870
+حالة الوصل السماوات اقتوني تسقط همزة الوصل و تلفظ
+
+250
+00:21:10,870 --> 00:21:14,670
+الهمزة الثانيةلكن إذا بدأنا بها الكلام في حالة
+
+251
+00:21:14,670 --> 00:21:19,310
+الاختبار، يعني مثلا قلت كمدرس للطالب اللي بدأ
+
+252
+00:21:19,310 --> 00:21:23,130
+اختبره فأقول له مثلا قف لو سمحت عند قوله في
+
+253
+00:21:23,130 --> 00:21:26,990
+السماوات وابدأ الكلام من قوله اقتوني كيف تقراها؟
+
+254
+00:21:26,990 --> 00:21:32,850
+من يقراها منكم؟ فضل اعمل له مشركه في السماوات،
+
+255
+00:21:32,850 --> 00:21:38,970
+مجراها؟ ايتوني بكتابي من قبل هذاكذلك هنا و منهم
+
+256
+00:21:38,970 --> 00:21:46,150
+يقول في حالة اختبار ابدأ من قول اذنلينقول إي ذن لي
+
+257
+00:21:46,150 --> 00:21:51,630
+إي ذن لي لكن في حالة الواصل ومنهم يقول إي ذن لي
+
+258
+00:21:51,630 --> 00:21:56,730
+يقول إي ذن لي فليؤد الذي أؤت من أمانته طب لو وقفنا
+
+259
+00:21:56,730 --> 00:21:59,430
+في حالة الاختبار طبعا لا يوقف عليه هنا لأن الوقف
+
+260
+00:21:59,430 --> 00:22:04,130
+طبيعي لكن في حالة الاختبار المدرس يقول له قف عند
+
+261
+00:22:04,130 --> 00:22:08,330
+الذي فليؤد الذي وابدأ الكلام من قوله أؤت منك كيف
+
+262
+00:22:08,330 --> 00:22:12,890
+نقرأها نقرأ أيش يا أخواننا أؤت منك وهذا ما يسمى
+
+263
+00:22:12,890 --> 00:22:19,430
+مادة البدلمد البدل إذا وقعت همزتين في كلمة واحدة
+
+264
+00:22:19,430 --> 00:22:23,410
+وكانت الهمزة الأولى متحركة والهمزة الثانية ساكنة
+
+265
+00:22:23,410 --> 00:22:30,090
+مثل هذه اقتوني او اقتن او اقتمنة تبدل الهمزة
+
+266
+00:22:30,090 --> 00:22:34,650
+الثانية الساكنة سواء كان و او ي بحرف مد من جنس
+
+267
+00:22:34,650 --> 00:22:38,170
+حركة الهمزة الأولى فإذا كانت الهمزة الأولى مفتوحة
+
+268
+00:22:38,890 --> 00:22:44,750
+أه فتبدأ الحمزة الثانية تفتق بحرف الألف مثل آمن و
+
+269
+00:22:44,750 --> 00:22:50,870
+آذر و آدم إذا كانت الحمزة الأولى مكسورة مثل اقتوني
+
+270
+00:22:50,870 --> 00:22:54,710
+تبدأ الحمزة الثانية بيها فنقول ايتوني وإذا كانت
+
+271
+00:22:54,710 --> 00:23:00,630
+الحمزة الأولى مضمومة مثل اقتومنة تبدأ الحمزة
+
+272
+00:23:00,630 --> 00:23:05,130
+الثانية اللي هي الساكنةبحرف مد الواو فنقول أُتمنى
+
+273
+00:23:05,130 --> 00:23:08,430
+وهذا ما يسمى يا أخوان يا كلام بمد البذل وهو من
+
+274
+00:23:08,430 --> 00:23:12,690
+حقات المد الطبيعي ومن مده بمقدار إيش حركتين هنا
+
+275
+00:23:12,690 --> 00:23:16,550
+طبعا في حال الواصل نقراها بدون همزة باصل نقراها
+
+276
+00:23:16,550 --> 00:23:23,070
+كذا الذي أُتمنى يقول إذنلي في السماوات إتوني لكن
+
+277
+00:23:23,070 --> 00:23:29,010
+في حالة الإبتداء منها نقول أُتمنى إيذنلي إيتوني
+
+278
+00:23:29,010 --> 00:23:34,660
+بكتاب فهيكون بمد البذلالفائدة الخامسة يا إخواننا
+
+279
+00:23:34,660 --> 00:23:39,240
+يا كرام، و هو إذا وقف القارئ على كلمة اسم أو بأسة
+
+280
+00:23:39,240 --> 00:23:44,000
+و أراد أن يبدأ بكلمة اسم، طبعا من قول تعالى بأسة
+
+281
+00:23:44,000 --> 00:23:48,600
+اسم الفسوق بعد الإيمان، بأس الاسم إذا وصلها مع
+
+282
+00:23:48,600 --> 00:23:52,020
+بعض، بأس الاسم، طبيعي، ماعندي مشكلة عندهم أنه همس
+
+283
+00:23:52,020 --> 00:23:57,870
+الوصل، ابتسقط، فتقرأ بأس الاسملكن في حال اختبار
+
+284
+00:23:57,870 --> 00:24:03,950
+البدء من قوله اسم لو قال المدرسة الطالب قف عند
+
+285
+00:24:03,950 --> 00:24:09,490
+كلمة بئسة و ابدا بقوله الاسم كيف تقراها تقرا
+
+286
+00:24:09,490 --> 00:24:16,810
+بحلتين سياغتين طبعا تقرا اما ان اقراها بقوله الاسم
+
+287
+00:24:16,810 --> 00:24:21,270
+يعني وقفنا عند كلمة بئس طبعا اختبارا و بدنا ابدا
+
+288
+00:24:22,220 --> 00:24:26,780
+الاسم الفسوق بعد الإيمان هذه حالة تقرأ الاسم
+
+289
+00:24:26,780 --> 00:24:31,840
+الفسوق بعد الإيمان وممكن أن تقرأ أيضا لحالها الاسم
+
+290
+00:24:31,840 --> 00:24:35,820
+الفسوق بعد الإيمان حالتين وكلهما وجهان صحيحان
+
+291
+00:24:35,820 --> 00:24:39,280
+وقرؤن بيهم ولكن الوجه الأول مقدم في الأداء على
+
+292
+00:24:39,280 --> 00:24:43,040
+الوجه التاني وذلك لرسم المصحف والكلمة ليست موضع
+
+293
+00:24:43,040 --> 00:24:48,180
+ابتداء إذا تقرأ إما نقراها الاسمالاسم الفسوق بعد
+
+294
+00:24:48,180 --> 00:24:52,060
+الإيمان على أساس أنه ابتدأنا بها الكلام و فتسقط
+
+295
+00:24:52,060 --> 00:24:55,920
+همزة الواصل أو ممكن نقرأها اسم الفسوق بعد الإيمان
+
+296
+00:24:55,920 --> 00:25:00,620
+و قراءة ثانية و كذا هما صحيحة ولكن القراءة الأولى
+
+297
+00:25:00,620 --> 00:25:07,920
+قراءة هي المقدمة في الأداء هذه هي ملاحظات همزة
+
+298
+00:25:07,920 --> 00:25:09,940
+الواصل نكتفي بهذا القدر
+
diff --git a/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/XL5r64Rtb6Y.srt b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/XL5r64Rtb6Y.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bb600a601a6628778ca1101918b2a2b2a56dbbec
--- /dev/null
+++ b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/XL5r64Rtb6Y.srt
@@ -0,0 +1,2179 @@
+1
+00:00:20,790 --> 00:00:23,350
+السلام عليكم ورحمة الله وبركاته بسم الله الرحمن
+
+2
+00:00:23,350 --> 00:00:27,370
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى 
+
+3
+00:00:27,370 --> 00:00:32,170
+آله وصحبه وسلم أخذنا يا إخواننا يا كرام في اللقاء 
+
+4
+00:00:32,170 --> 00:00:36,730
+الماضي المحاضرة الماضية الوقف بدأنا بالوقف والوقف 
+
+5
+00:00:36,730 --> 00:00:41,150
+بشكل عام هو قطع الصوت على الكلمة القرآنية زمنا 
+
+6
+00:00:41,150 --> 00:00:45,450
+يسيرا يتنفس فيه القارئ وعادة بنية استئناف التلاوة 
+
+7
+00:00:45,450 --> 00:00:50,370
+لا بنية الإعراض عنها وينقسم إلى أربعة أقسام من يقول 
+
+8
+00:00:50,370 --> 00:00:54,490
+ما هي الأقسام الأربعة التي ينقسم منها الـ الـ 
+
+9
+00:00:54,490 --> 00:00:59,710
+الوقف اللي بشكل عام الوقف الـ الوقف الإضطراري 
+
+10
+00:00:59,710 --> 00:01:06,590
+أولا ثم الوقف الاختياري ثم الوقف الانتظاري ثم 
+
+11
+00:01:06,590 --> 00:01:09,850
+الوقف الإختياري أربع أنواع من أنواع الوقف اللي 
+
+12
+00:01:09,850 --> 00:01:13,910
+بشكل عام الوقف الإختياري أيضا ينقسم إلى أربعة 
+
+13
+00:01:13,910 --> 00:01:20,210
+أقسام وهو الوقف التام والوقف الكافي والوقف الحسن 
+
+14
+00:01:20,210 --> 00:01:24,730
+والوقف القبيح تحدثنا في اللقاء الماضي عن شيء من 
+
+15
+00:01:24,730 --> 00:01:29,570
+الوقف التام والوقف التام هو هو لو أن يقف القارئ 
+
+16
+00:01:29,570 --> 00:01:34,310
+على كلمة قرآنية تم المعنى عندها لا تتعلق بما بعدها 
+
+17
+00:01:34,310 --> 00:01:39,810
+لا لفظ ولا معنى على 
+
+18
+00:01:39,810 --> 00:01:47,140
+حسب المعنى ستأخذ إن شاء الله هنطبق على نحن الآن في 
+
+19
+00:01:47,140 --> 00:01:52,040
+طور الدراسة النظرية بعد محاضرته إن شاء الله سوف 
+
+20
+00:01:52,040 --> 00:01:55,780
+يعني يكون أمامنا القرآن الكريم برضه على الـ 
+
+21
+00:01:55,780 --> 00:02:01,020
+powerpoint ونقرأ آية آية ونتعرف كيف نقف طبعا 
+
+22
+00:02:01,020 --> 00:02:05,870
+الوقف حسب المعنى لأن الإنسان قد يقف على كلام لم يتم 
+
+23
+00:02:05,870 --> 00:02:10,390
+المعنى عنده فيكون الوقف اسمه وقف قبيح فالوقف يجب 
+
+24
+00:02:10,390 --> 00:02:14,390
+أن يكون قد اكتمل المعنى وليس له تعلق بما بعده لا 
+
+25
+00:02:14,390 --> 00:02:18,630
+لفظ ولا معنى لذلك الوقف التام ما هو الوقف التام أو 
+
+26
+00:02:18,630 --> 00:02:22,410
+تعريف الوقف التام كما هو واضح هنا أن يقف القارئ 
+
+27
+00:02:22,410 --> 00:02:27,990
+على كلمة قرآنية تم المعنى عندها لا تتعلق بما بعدها 
+
+28
+00:02:27,990 --> 00:02:32,490
+لفظ ولا معنى يعني يكون قد اكتمل المعنى تم المعنى 
+
+29
+00:02:32,490 --> 00:02:37,150
+عنده ليس لها علاقة لا علاقة إعرابية مع الكلمة التي 
+
+30
+00:02:37,150 --> 00:02:42,490
+تليها ولا علاقة معنوية فمعنى التعلق اللفظي هو 
+
+31
+00:02:42,490 --> 00:02:46,050
+التعلق بالإعراب فلا يوجد أي علاقة يعني الكلمة التي 
+
+32
+00:02:46,050 --> 00:02:51,910
+تليها ليست هي عبارة عن مثلا حال أو تمييز أو صفة أو 
+
+33
+00:02:51,910 --> 00:02:56,530
+أي شيء ليس لها أي علاقة مع الكلمة التي قبلها إذا 
+
+34
+00:02:56,530 --> 00:03:00,510
+الوقف التام هو أن يقف القارئ على كلمة القرآنية تم 
+
+35
+00:03:00,510 --> 00:03:05,610
+المانع عندها، لا تتعلق بما بعدها لفظا ولا معنى، مش 
+
+36
+00:03:05,610 --> 00:03:08,990
+لا تعلق لفظي ولا تعلق معنوي، ما المراد يا إخواننا 
+
+37
+00:03:08,990 --> 00:03:13,050
+يا كرام بالتعلق اللفظي؟ هو الإعرابي، وما المراد 
+
+38
+00:03:13,050 --> 00:03:17,370
+بالتعلق المعنوي؟ ما هو المعنى؟ أحيانا تدفع من 
+
+39
+00:03:17,370 --> 00:03:22,930
+الآيات، مجموع عشر آيات، خمسة، سبع آيات، وهكذا، 
+
+40
+00:03:22,930 --> 00:03:26,630
+تتحدث عن موضوع واحد، مثلا سبع آيات أو خمس آيات 
+
+41
+00:03:26,630 --> 00:03:30,790
+تتحدث عن قصة نوح، فإذا انتهت قصة نوح، إذا انتهت 
+
+42
+00:03:30,790 --> 00:03:34,590
+العلاقة المعنوية اللي بينها هنا لو كان فيه لا 
+
+43
+00:03:34,590 --> 00:03:38,370
+علاقة أيضا لفظية مع التي بعدها بيكون هنا وقف تم 
+
+44
+00:03:38,370 --> 00:03:42,290
+إذا الوقف التام أن يقف القارئ على كلمة القرآنية تم 
+
+45
+00:03:42,290 --> 00:03:46,370
+المعنى عندها لا تتعلق بما بعدها لا لفظ ولا معنى 
+
+46
+00:03:46,370 --> 00:03:50,630
+التعلق اللفظي هو التعلق الإعرابي والتعلق المعنى هو 
+
+47
+00:03:50,630 --> 00:03:56,140
+التعلق بالمعنى فتكون القصة قد انتهت أين يكون عادة 
+
+48
+00:03:56,140 --> 00:04:01,100
+الوقف التام؟ عادة يكون في نهاية القصص وعلى نهاية 
+
+49
+00:04:01,100 --> 00:04:06,880
+الآيات وقد يكون الوقف التام في منتصف الآية للوقف 
+
+50
+00:04:06,880 --> 00:04:10,340
+التام يا إخواننا يا كرام رمز ما هو رمز الوقف 
+
+51
+00:04:10,340 --> 00:04:17,500
+التام؟ قلا ما معنى القلاقلة منحوطة يعني الرمز هذا 
+
+52
+00:04:17,500 --> 00:04:23,740
+منحوط من جملة الوقف أولى ق الوقف أ أولى قلة الوقف 
+
+53
+00:04:23,740 --> 00:04:28,000
+أولى يعني أولى من الوصل يعني تقف هنا لأن المعنى تم 
+
+54
+00:04:28,000 --> 00:04:31,560
+ليس له علاقة بما بعده للفظ ولا معنى بكون تم 
+
+55
+00:04:31,560 --> 00:04:36,660
+المعنى إذا هنا اسمه اللي هو قلة يعني الوقف أولى 
+
+56
+00:04:36,660 --> 00:04:45,800
+مثال ذلك مثلا في قوله تعالى مالك يوم الدين عندما 
+
+57
+00:04:45,800 --> 00:04:51,880
+وقفت على مالك يوم الدين إذا هنا تم المعنى وكذلك 
+
+58
+00:04:51,880 --> 00:04:55,740
+ليس لها علاقة عربية مع الكلمة التي بعدها التي 
+
+59
+00:04:55,740 --> 00:05:01,340
+بعدها إياك نعبد وإياك نستعين إذا الآيات الأولى من 
+
+60
+00:05:01,340 --> 00:05:05,980
+حيث المعنى فيها ثناء على الله الحمد لله رب 
+
+61
+00:05:05,980 --> 00:05:09,080
+العالمين يعني أنا أشكر الله اللي هو رب العالمين 
+
+62
+00:05:09,650 --> 00:05:12,930
+يعني الرحمن الرحيم من صفات أنه رحمان رحيم ففيه 
+
+63
+00:05:12,930 --> 00:05:16,670
+ثناء على الله عز وجل مالك يوم الدين أن الله اللي 
+
+64
+00:05:16,670 --> 00:05:19,870
+هو الرحمن الرحيم اللي هو مالك يوم الدين وقف عند 
+
+65
+00:05:19,870 --> 00:05:24,250
+مالك يوم الدين بعدها بيأتي الدعاء مباشرة إذا هنا 
+
+66
+00:05:24,250 --> 00:05:29,070
+تم المعنى ليس لها علاقة مع ما بعدها في الإعراب ولا 
+
+67
+00:05:29,070 --> 00:05:35,210
+حتى في المعنى إذا هنا يسمى وقف تام رمز الوقف التام 
+
+68
+00:05:35,210 --> 00:05:41,850
+قلنا ما هو يا إخواننا هل يوضع رمز قلة على رأس الآية؟ 
+
+69
+00:05:41,850 --> 00:05:47,030
+لا يوضع رمز قلة على رأس الآية، لماذا؟ لأن أصلا 
+
+70
+00:05:47,030 --> 00:05:52,130
+الوقف على رأس الآية سنة فمعنى رقم رأس الآية اللي 
+
+71
+00:05:52,130 --> 00:05:55,790
+عند الرقم هذا أقوى من قلة أو صلة أو أي واحدة ثانية 
+
+72
+00:05:55,790 --> 00:06:00,420
+لأن الوقف على رأس الآية سنة مثال آخر أيضًا فيه 
+
+73
+00:06:00,420 --> 00:06:06,860
+الوقف التام قوله تعالى مثلا من أوائل سورة البقرة 
+
+74
+00:06:06,860 --> 00:06:09,980
+ألف لامين ذلك الكتاب الذي فيه هدى للمتقين 
+
+75
+00:06:09,980 --> 00:06:14,220
+الذين يؤمنون بالغيب ويقيمون الصلاة ومما رزقناهم 
+
+76
+00:06:14,220 --> 00:06:19,580
+ينفقون والذين يؤمنون بما أنزل إليك وما أنزل من 
+
+77
+00:06:19,580 --> 00:06:25,660
+قبلك وبالآخرة هم يقنون هنا أولئك على هدى من ربهم 
+
+78
+00:06:25,660 --> 00:06:31,630
+وأولئك هم المفلحون الوقف على المفلحون هنا اسمه وقف 
+
+79
+00:06:31,630 --> 00:06:36,330
+تام تم المانع عنده لا يتعلق بما بعده لا لفظ ولا 
+
+80
+00:06:36,330 --> 00:06:41,010
+معنى لأن الذي بعده في عندك إن الذين كفروا سواء 
+
+81
+00:06:41,010 --> 00:06:45,710
+عليهم أأنذرتهم أم لم تنذرهم لا يؤمنون الكلام فيها 
+
+82
+00:06:45,710 --> 00:06:51,270
+عن الكفار إذن هنا في الآيات السابقة كلها تتكلم على 
+
+83
+00:06:51,270 --> 00:06:55,350
+المتقين صفات المتقين هدى للمتقين الذين يؤمنون 
+
+84
+00:06:55,350 --> 00:06:58,360
+بالغيب إلى نهاية الآيات ثم يقول الله سبحانه وتعالى 
+
+85
+00:06:58,360 --> 00:07:04,660
+بعد ذلك أولئك على هدى من ربهم وأولئك هم المفلحون 
+
+86
+00:07:04,660 --> 00:07:10,520
+من هؤلاء اللي هم المتقين المؤمنين أما بالنسبة للذي 
+
+87
+00:07:10,520 --> 00:07:14,060
+بعدها إن الذين كفروا الآن تبدأ آيات بالذين كفروا 
+
+88
+00:07:14,060 --> 00:07:18,420
+لذلك الوقف على آية رقم خمسة من سورة البقرة أولئك 
+
+89
+00:07:18,420 --> 00:07:22,720
+على هدى من ربهم وأولئك هم المفلحون هنا في عندنا 
+
+90
+00:07:22,720 --> 00:07:29,090
+الوقف هذا اسمه وقف تام ويجب علينا أن نقف عنده ونبدأ 
+
+91
+00:07:29,090 --> 00:07:35,950
+بالذي بعده وهو إن الذين كفروا سواء عليهم أنذرتهم 
+
+92
+00:07:35,950 --> 00:07:41,790
+أم لم تنذرهم لا يؤمنون الآن الكلام بتكلم على مين؟ 
+
+93
+00:07:41,790 --> 00:07:47,270
+على الكافرين خاصة بداية سورة البقرة في بدايتها قسمت 
+
+94
+00:07:47,270 --> 00:07:53,440
+الناس إلى فئة مؤمنة وفئة كافرة إن الذين كفروا سواء 
+
+95
+00:07:53,440 --> 00:07:57,740
+عليهم وفئة منافقة ومن الناس من يقول آمنا بالله 
+
+96
+00:07:57,740 --> 00:08:00,060
+باليوم الآخر وما هم بالمؤمنين 
+
+97
+00:08:03,430 --> 00:08:09,510
+المفلحون يقولون إنه وقف تام المانع عندهم ثم تبدأ 
+
+98
+00:08:09,510 --> 00:08:13,290
+الآيات إن الذين كفروا سواء عليهم أنذرتهم أم لم 
+
+99
+00:08:13,290 --> 00:08:18,150
+تنذرهم لا يؤمنون ختم الله على قلوبهم وعلى سمعهم 
+
+100
+00:08:18,150 --> 00:08:24,760
+وعلى أبصارهم غشاوة ولهم عذاب عظيم الوقف على ولهم 
+
+101
+00:08:24,760 --> 00:08:30,400
+عذاب عظيم أيضا يسمى وقف تام تم المعنى عنده لا تعلق 
+
+102
+00:08:30,400 --> 00:08:35,140
+بما بعده ولا لفظ ولا معنى لأن ما بعده هي صفات 
+
+103
+00:08:35,140 --> 00:08:42,040
+للمنافقين هذا هي ومن الناس من يقول آمنا بالله و 
+
+104
+00:08:42,040 --> 00:08:46,920
+باليوم الآخر وما هم بمؤمنين الآن بدأ صفات 
+
+105
+00:08:47,260 --> 00:08:52,800
+المنافقين إذا الوقف التام تعريفه هو أن يقف القارئ 
+
+106
+00:08:52,800 --> 00:08:58,060
+على كلام تم المعنى عنده لا يتعلق بما بعده لا لفظ 
+
+107
+00:08:58,060 --> 00:09:02,220
+ولا معنى الوقف التام يكون على رؤوس الآيات وبينفع 
+
+108
+00:09:02,220 --> 00:09:06,640
+يكون أيضا في منتصف الآية يعني عندنا عدة أمثلة على 
+
+109
+00:09:06,640 --> 00:09:11,280
+رؤوس الآيات وكذلك في منتصف الآية مثلا قوله تعالى 
+
+110
+00:09:11,280 --> 00:09:18,750
+لقد أضلني عن الذكر بعد إذ جاءني بعدين وكان الشيطان 
+
+111
+00:09:18,750 --> 00:09:24,490
+للإنسان خذولا هنا على جاءني اسم الوقف اللي هنا وقف 
+
+112
+00:09:24,490 --> 00:09:28,670
+تام تم المانع عنده لا يتعلق باللي بعده لا لفظ ولا 
+
+113
+00:09:28,670 --> 00:09:32,950
+معنى وهنا الوقف التام في .. على رأس الآية ولا في 
+
+114
+00:09:32,950 --> 00:09:37,270
+منتصف الآية؟ في منتصف الآية إذا هنا نجد رمز قلا 
+
+115
+00:09:37,270 --> 00:09:42,290
+بمعنى الوقف إيش الوقف أولى في عندنا كذلك يا 
+
+116
+00:09:42,290 --> 00:09:46,030
+إخواننا يا كرام اللي هو الوقف اللازم الوقف اللازم 
+
+117
+00:09:46,030 --> 00:09:52,310
+يتبع الوقف التام والوقف اللازم قد قعده بعض العلماء 
+
+118
+00:09:52,310 --> 00:09:57,470
+بأنه يعني مستقل وبعض العلماء أتبعه للوقف اللازم 
+
+119
+00:09:57,470 --> 00:10:01,330
+لأنه حقيقة هو تابع للوقف اللازم وبعض العلماء 
+
+120
+00:10:01,330 --> 00:10:07,530
+يسمونه وقف البيان التام هو وقف اللازم فما هو تعريف 
+
+121
+00:10:07,530 --> 00:10:13,640
+الوقف اللازم؟ نفس تعريف الوقف التام هو أن يقف 
+
+122
+00:10:13,640 --> 00:10:17,400
+القارئ على كلمة القرآنية تم المانع عندها لا تتعلق 
+
+123
+00:10:17,400 --> 00:10:22,280
+بما بعدها لفظا ولا معنى هنا هو تعريف الوقف التام 
+
+124
+00:10:23,240 --> 00:10:28,580
+سنضع جملة أخرى بصير عنها تعريف للوقف اللازم وهو 
+
+125
+00:10:28,580 --> 00:10:33,220
+فإذا وصلت الكلام اختل المعنى أو أوهمت معنى غير 
+
+126
+00:10:33,220 --> 00:10:36,900
+المعنى المراد لو وصلت بما بعدها بصير معنى آخر 
+
+127
+00:10:36,900 --> 00:10:41,680
+عندنا العديد من الأمثلة نشوف مثلا هنا المثال في 
+
+128
+00:10:41,680 --> 00:10:50,010
+قوله تعالى ولا يحزنك قولهم إن العزة لله جميع .. هنا 
+
+129
+00:10:50,010 --> 00:10:56,510
+عند قولهم اسم وقف إيه؟ وقف اللازم ما هو رمز الوقف 
+
+130
+00:10:56,510 --> 00:11:02,680
+اللازم؟ الميم الوقفية اسمه وقف لازم عند قولهم نجد 
+
+131
+00:11:02,680 --> 00:11:08,440
+أن هنا وقف لازم تقف عنده لو وصلت سيختل المعنى نشوف 
+
+132
+00:11:08,440 --> 00:11:12,520
+مثلا اقرأها أنا ونشوف كيف سيختل المعنى عند وصلها 
+
+133
+00:11:12,520 --> 00:11:19,020
+عندما نقول مثلا ولا يحزن كقولهم إن العزة لله جميع 
+
+134
+00:11:19,020 --> 00:11:24,330
+تصير كلمة إن العزة لله جميع من قول من من قول 
+
+135
+00:11:24,330 --> 00:11:28,950
+الكفار لكن الحقيقة أنه ليس من قول الكفار هو من 
+
+136
+00:11:28,950 --> 00:11:32,430
+كلام من؟ من كلام الله سبحانه وتعالى كلام مستقل 
+
+137
+00:11:32,430 --> 00:11:38,310
+الله سبحانه وتعالى يقول فلا ولا يحزنك قولهم بعدين 
+
+138
+00:11:38,310 --> 00:11:44,210
+كلام جديد إن العزة لله جميع يعني لا تحزن يا محمد 
+
+139
+00:11:44,210 --> 00:11:49,270
+على أن الكفار قد وصفوك بصفات سيئة قالوا عنك شاعر 
+
+140
+00:11:49,270 --> 00:11:53,810
+أو ساحر أو كاهن أو مجنون أو هذه الأوصاف من الحرب 
+
+141
+00:11:53,810 --> 00:11:57,670
+الإعلامية التي يشنها الكفار على أصحاب الحق وعلى
+
+142
+00:11:57,670 --> 00:12:01,410
+رأسهم الأنبياء فما من نبي أرسل إلى قومه إلا وقال 
+
+143
+00:12:01,410 --> 00:12:04,970
+لقومه يا قوم اعبدوا الله ما لكم من إله غيره ونجد
+
+144
+00:12:04,970 --> 00:12:09,690
+أن الملأ أو الأعداء أو أصحاب الشأن والسلطان يتعارض
+
+145
+00:12:09,690 --> 00:12:13,570
+تتعارض مصلحتهم مع مصلحة النبي أو مع مصلحة الدعوة
+
+146
+00:12:13,570 --> 00:12:17,740
+فيشنون حرب تشويهية على الدعوة وعلى المسلمين حتى
+
+147
+00:12:17,740 --> 00:12:22,100
+يعني يبطلوا أعمالهم لكن بينقلب الأمر عليهم فينتصر
+
+148
+00:12:22,100 --> 00:12:26,640
+الحق في نهاية المطاف ويهزم الباطل فربنا بيقولوا  و
+
+149
+00:12:26,640 --> 00:12:33,460
+لا يحزنوا  كقولهم بعدين كلام جديد من مستنث إن العزة 
+
+150
+00:12:33,460 --> 00:12:39,760
+لله جامعة كذلك مثال آخر في قوله مثلًا نأت للمثال
+
+151
+00:12:39,760 --> 00:12:46,360
+اللي فيه ليه هنا و لا خوف عليهم ولا هم يحزنون بعدين
+
+152
+00:12:46,360 --> 00:12:50,540
+كلام جديد الذين يأكلون الربا لا يقومون إلا كما
+
+153
+00:12:50,540 --> 00:12:56,520
+يقوم الذي يتخبطه الشيطان من المس  إذا هذه نهاية
+
+154
+00:12:56,520 --> 00:13:01,460
+الآية التي تتكلم في سورة البقرة آية رقم مائتين
+
+155
+00:13:01,460 --> 00:13:07,000
+وأربعة وسبعين نهاية الآية هذه انتهت قصة المؤمنين
+
+156
+00:13:07,000 --> 00:13:12,200
+الذين يقولوا الله عز وجل عنهم ولا خوف عليهم ولا
+
+157
+00:13:12,200 --> 00:13:16,870
+يحزنون ولا خوف عليهم في المستقبل لأن الإنسان يخاف
+
+158
+00:13:16,870 --> 00:13:19,950
+من أيه يا إخواننا؟ من المستقبل يعني لا خوف عليهم
+
+159
+00:13:19,950 --> 00:13:24,350
+من المستقبل فالمستقبل مأمون فهم أهل الجنة ولا هم 
+
+160
+00:13:24,350 --> 00:13:28,150
+يحزنون على ما مضى مما تركه في الدنيا تركوا الأموال
+
+161
+00:13:28,150 --> 00:13:33,290
+تركوا الديار تركوا الأبناء فالماضي لا تحزن عليه
+
+162
+00:13:33,290 --> 00:13:37,030
+والخوف مأمون بالنسبة لك فلا خوف عليهم ولا هم
+
+163
+00:13:37,030 --> 00:13:41,160
+يحزنون إذا آيات تتكلم على مين؟ على المؤمنين انتهت 
+
+164
+00:13:41,160 --> 00:13:45,400
+صفات المؤمنين و أحوال المؤمنين بعد ذلك تتكلم عن
+
+165
+00:13:45,400 --> 00:13:51,040
+حكم جديد وهو الذين يأكلون الربا لا يقومون إلا كما
+
+166
+00:13:51,040 --> 00:13:56,400
+يقوموا الذين يتخبطه الشيطان من المصر طبعًا نقف
+
+167
+00:13:56,400 --> 00:14:01,300
+عليها وقف لازِم تقضى عليها علامة الـ Meme الميم
+
+168
+00:14:01,300 --> 00:14:06,600
+الأفقية معناه أن هنا وقف لازم لكن لو وصلنا سيختل
+
+169
+00:14:06,600 --> 00:14:12,920
+المعنى الآن لو قلنا مثلًا هنا ولا خوف عليهم ولا
+
+170
+00:14:12,920 --> 00:14:17,720
+هم يحزنون الذين يأكلون الربا تصير الآية فيها خلل
+
+171
+00:14:18,400 --> 00:14:22,940
+وهو أن الذين يأكلون الربا هم الذين لا يخافون عليهم
+
+172
+00:14:22,940 --> 00:14:30,240
+ولا يحزنون لذلك هنا الرمز ميم وهو وقف لازم يجب أن
+
+173
+00:14:30,240 --> 00:14:34,900
+تقف عليه لأن لو وصلت سيختل المعنى أو تؤدي معنى غير 
+
+174
+00:14:34,900 --> 00:14:40,560
+المعنى المراد هذا هو الوقف التام وهو القسم الأول
+
+175
+00:14:40,560 --> 00:14:44,540
+من أقسام الوقف الاختياري القسم الثاني يا إخواننا يا 
+
+176
+00:14:44,540 --> 00:14:49,680
+كرام هو الوقف الكافي الوقف الكافي نسير على نفس
+
+177
+00:14:49,680 --> 00:14:54,440
+التعريف هو أن يقف القارئ أو نقف على كلام أفاد معنى
+
+178
+00:14:54,440 --> 00:14:59,460
+في ذاته ولكنه يتعلق بما بعده في المعنى دون اللفظ
+
+179
+00:14:59,460 --> 00:15:04,860
+يعني في تعلق معنوي وليس في تعلق لفظي قلنا التعلق
+
+180
+00:15:04,860 --> 00:15:09,400
+المعنوي إن الكلام بتتكلم عن قصة واحدة أو عن آيات
+
+181
+00:15:09,400 --> 00:15:13,680
+تتحدث عن حكم واحد أو عن موضوع واحد لكن بالنسبة
+
+182
+00:15:13,680 --> 00:15:18,020
+للتعلق اللفظي يعني التعلق الإعرابي فهنا بيكون قصة عن
+
+183
+00:15:18,020 --> 00:15:22,560
+كلام بتتكلم على موضوع واحد لكن الموقف الذي وقفنا
+
+184
+00:15:22,560 --> 00:15:27,380
+عليه لا يوجد هناك علاقة إعرابية مع الآية التي 
+
+185
+00:15:27,380 --> 00:15:31,890
+تتليها والأمثل على ذلك متعددة ما هو رمز أو لماذا
+
+186
+00:15:31,890 --> 00:15:36,650
+السمية الوقف التام أو الكافي لأنه مكتف به يعني 
+
+187
+00:15:36,650 --> 00:15:40,910
+ممكن اكتفاء به لأنه تم المعنى ولا يتعلق بالبعد من
+
+188
+00:15:40,910 --> 00:15:46,010
+حيث الإعراب لكن يتعلق بالبعد من حيث المعنى إذا هو
+
+189
+00:15:46,010 --> 00:15:53,510
+كافي لذلك السمية كافي ما هو رمزه؟ رمزه صلاة أو جيم
+
+190
+00:15:53,510 --> 00:15:58,870
+على حسب المعنى ما معناه الصلاة؟ صلى يعني الوصل 
+
+191
+00:15:58,870 --> 00:16:03,650
+أولى، صلى بمعنى الوصل أولى، يعني يجوز الوقف ويجوز
+
+192
+00:16:03,650 --> 00:16:09,390
+الوصل ولكن الوصل أولى وهناك رمز آخر له أيضًا الوقف
+
+193
+00:16:09,390 --> 00:16:16,570
+الكافي وهو جيم وجيم بمعنى الوقف جائز يعني يجوز
+
+194
+00:16:16,570 --> 00:16:21,190
+الوقف ويجوز الوصل وكلاهما بمرتبة واحدة ومستوى
+
+195
+00:16:21,190 --> 00:16:26,630
+واحدة من أراد أن يقف فليقف ومن أراد أن يصل مع
+
+196
+00:16:26,630 --> 00:16:31,850
+الآية التي تليها فليصل فالمعنى أخذ اكتمل والجيم
+
+197
+00:16:31,850 --> 00:16:36,510
+أشد كفاية من صلى يعني الصلاة لسه فيه شوية علاقة
+
+198
+00:16:36,510 --> 00:16:41,490
+في المعنى ممكن لم تتم بشكل واضح لكن الجيم قد اكتمل
+
+199
+00:16:41,490 --> 00:16:47,050
+المعنى لذلك يقولون أن جيم أشد كفاية من صلى نشوف 
+
+200
+00:16:47,050 --> 00:16:53,490
+هنا الأمثلة على الوقف الكافي يعني هيكتم المعنى
+
+201
+00:16:53,490 --> 00:16:58,650
+لكنه يتعلق بما بعده في المعنى دون اللفظ نشوف الآية 
+
+202
+00:16:58,650 --> 00:17:04,800
+هذه مثلًا في سورة البقرة أيضًا طبعًا احنا قلنا أولئك
+
+203
+00:17:04,800 --> 00:17:08,160
+على هدى من ربهم وأولئك هم الذين فلحوا هنا وقف 
+
+204
+00:17:08,160 --> 00:17:12,180
+إيش؟ وقف تام لكن الآيات اللي قبلها أنها موضوعها
+
+205
+00:17:12,180 --> 00:17:17,680
+واحد تتكلم عن صفات المؤمنين صفات المتقين كلها تم
+
+206
+00:17:17,680 --> 00:17:21,820
+المعنى عندها تتعلق بما بعدها في المعنى اللي هي
+
+207
+00:17:21,820 --> 00:17:25,920
+صفات المتقين ولكن لا تتعلق بما بعدها في اللفظ يعني 
+
+208
+00:17:25,920 --> 00:17:31,430
+في الإعراب نشوف  حُدى للمتقين الذين يؤمنون بالغيب و
+
+209
+00:17:31,430 --> 00:17:37,790
+يقيمون الصلاة ومما رزقناهم ينفقون كلمة ينفقون تم 
+
+210
+00:17:37,790 --> 00:17:42,890
+المعنى عندها لا تتعلق بما بعدها في الإعراب ولكنه
+
+211
+00:17:42,890 --> 00:17:46,090
+يتعلق بما بعده في إيش؟ في المعنى لأن الكلام لسه
+
+212
+00:17:46,090 --> 00:17:51,480
+بتتكلم على صفات المتقين أه فهنا ما نسميها على
+
+213
+00:17:51,480 --> 00:17:57,900
+ينفقون يسمى الوقف وقف كافي تم المعنى عندها يتعلق
+
+214
+00:17:57,900 --> 00:18:02,720
+بما بعده في المعنى دون الإعراب أو اللفظ فلو بدأنا
+
+215
+00:18:02,720 --> 00:18:09,000
+والذين يؤمنون بما أنزل إليك وما أنزل من قبلك
+
+216
+00:18:09,000 --> 00:18:14,820
+وبالآخرة هم يوقنون برضه على يوقنون يسمى وقف إيش؟
+
+217
+00:18:15,120 --> 00:18:20,060
+وقف كافي تم المعنى عنده لكنه يتعلق بما بعده في 
+
+218
+00:18:20,060 --> 00:18:24,820
+المعنى دون اللفظ لذلك الآية التي بعدها أولئك على
+
+219
+00:18:24,820 --> 00:18:29,560
+هدى من ربهم وأولئك هم المفلحون هنا انتهت قصة
+
+220
+00:18:29,560 --> 00:18:34,640
+المتقين وبعدين بقصة الذين كفروا فيسمى وقف تام لكن
+
+221
+00:18:34,640 --> 00:18:42,880
+الوقفين السابقين يسمى وقف كافي مثل آخر مثلًا في قول
+
+222
+00:18:42,880 --> 00:18:47,400
+تعالى الوقف على يعمهون من قول تعالى الله يستهزئ 
+
+223
+00:18:47,400 --> 00:18:53,440
+بهم ويمدهم في طغيانهم يعمهون أولئك الذين اشتروا
+
+224
+00:18:53,440 --> 00:18:58,000
+الضلالة بالهدى فما ربحوا تجارتهم وما كانوا مهتدين 
+
+225
+00:18:58,000 --> 00:19:03,560
+هذه الآية تتكلم على من؟ على المنافقين كانوا 
+
+226
+00:19:03,560 --> 00:19:08,550
+يستهزئوا من المسلمين؟ فالرب يقول الله يستهزئ بهم 
+
+227
+00:19:08,550 --> 00:19:13,850
+ويمدهم في طغيانهم يعمهون اللي هم المنافقين والآية
+
+228
+00:19:13,850 --> 00:19:18,990
+التي بعدها ليس لها علاقة من حيث اللفظ لكن لها
+
+229
+00:19:18,990 --> 00:19:24,950
+علاقة من حيث المعنى لذلك الوقف على يعمهون وقف كافي
+
+230
+00:19:24,950 --> 00:19:29,430
+لأن الوقف يعني عندما سئل علي بن أبي طالب عن قول 
+
+231
+00:19:29,430 --> 00:19:33,910
+تعالى ورتل القرآن ترتيلًا قال هو تجويد الحروف
+
+232
+00:19:33,910 --> 00:19:41,160
+ومعرفة الوقوف لأننا نقف على المعنى فالوقف تبع للمعنى
+
+233
+00:19:41,160 --> 00:19:46,280
+إذا تم المعنى نقف لم يتم المعنى لا نقف إلا إذا كان 
+
+234
+00:19:46,280 --> 00:19:52,860
+حصل هناك أمر يوجب الوقف ونسميه وقف لازم أو أحيانًا
+
+235
+00:19:52,860 --> 00:20:00,980
+يمنع الوقف ويسمى وقف قبل الوقف الكافي قد يكون على 
+
+236
+00:20:00,980 --> 00:20:06,310
+رؤوس الآيات وقد يكون في منتصف يعني الآية مثال قوله 
+
+237
+00:20:06,310 --> 00:20:11,230
+تعالى أشهدوا يعني هنا وجعلوا الملائكة الذين هم
+
+238
+00:20:11,230 --> 00:20:16,790
+عباد الرحمن إناثًا أشهدوا خلقهم ستكتبوا شهادتهم
+
+239
+00:20:16,790 --> 00:20:23,250
+ويسألون الوقف على كلمة أشهدوا خلقهم اسمه وقف كافي
+
+240
+00:20:23,250 --> 00:20:28,560
+تم المعنى عنده ليس هناك علاقة إعرابية مع بعضه يعني 
+
+241
+00:20:28,560 --> 00:20:32,100
+ستكتبوا شهادتهم ويسألون كلام مستقل وليس له علاقة 
+
+242
+00:20:32,100 --> 00:20:37,080
+إعرابية مع السابق له لكن المعنى كله بتتكلم عن نفس 
+
+243
+00:20:37,080 --> 00:20:40,920
+الموضوع للملائكة وجعل الملائكة الذين هم عباده
+
+244
+00:20:40,920 --> 00:20:45,140
+الرحمن إناثًا من الذي قال هذا الكلام؟ من الذي جعل
+
+245
+00:20:45,140 --> 00:20:49,640
+الملائكة إناثًا؟ اللي هو الكفار قالوا أن الملائكة 
+
+246
+00:20:49,640 --> 00:20:54,800
+بنات الله فربنا بيقول أشهدوا خلقهم استفهام إنكاري
+
+247
+00:20:54,800 --> 00:20:58,700
+بيستنكر على الملائكة أشهدتم خلق الملائكة حتى
+
+248
+00:20:58,700 --> 00:21:02,960
+تحكموا بأن الملائكة هم إناث هل رأيتم الملائكة من
+
+249
+00:21:02,960 --> 00:21:07,610
+باب الاستفهام الاستنكاري بيستنكر على الكفار فربنا 
+
+250
+00:21:07,610 --> 00:21:12,730
+بيقول ستكتبوا شهادتهم ويسألون كلام مستقل جديد لكن 
+
+251
+00:21:12,730 --> 00:21:17,890
+الوقف هنا وقف بنسميه وقف كافي ما هو رمز الوقف
+
+252
+00:21:17,890 --> 00:21:22,910
+الكافي اللي هو الgym أو الصلاة الصلاة يعني الوقف
+
+253
+00:21:22,910 --> 00:21:29,210
+الأولى وgym يعني يجوز الوجهين والوقف الجيم أشد 
+
+254
+00:21:29,210 --> 00:21:36,620
+كفاية من الصلاة طيب في عندنا كذلك النوع الثالث وهو
+
+255
+00:21:36,620 --> 00:21:42,240
+الوقف الحسن احنا قلنا إن الوقف الاختياري ينقسم إلى
+
+256
+00:21:42,240 --> 00:21:48,520
+كم قسم؟ إلى أربعة أقسام وقف تام ووقف كافِ هنا هم
+
+257
+00:21:48,520 --> 00:21:52,600
+الآن الوقف الحسن وبقي علينا الوقف القبيح ما هو
+
+258
+00:21:52,600 --> 00:21:57,540
+الوقف الحسن؟ نشوف نفس التعريف هو أن يقف القارئ على 
+
+259
+00:21:57,540 --> 00:22:04,640
+كلام أفاد معنى في ذاته لكنه يتعلق بما بعده لفظًا
+
+260
+00:22:04,640 --> 00:22:10,520
+ومعنى يعني هو لحد ذاته تم المعنى عنده لكنه يتعلق
+
+261
+00:22:10,520 --> 00:22:14,860
+بما بعده في اللفظ يعني في الإعرابي وفي المعنى
+
+262
+00:22:14,860 --> 00:22:22,840
+وحكمه فيه تفصيل لأن ممكن الوقف الحسن يقف على منتصف 
+
+263
+00:22:22,840 --> 00:22:29,120
+الآية يكون وقف حسن وممكن يكون وقف حسن في آخر الآية 
+
+264
+00:22:29,910 --> 00:22:35,090
+إذا كان الوقف الحسن في منتصف الآية له حكم وإذا كان 
+
+265
+00:22:35,090 --> 00:22:39,830
+على رأس الآية له حكم نشوف هنا النوع الأول الوقف 
+
+266
+00:22:39,830 --> 00:22:45,690
+الحسن في وسط الآية ما هو حكمه ما حكم الوقف الحسن
+
+267
+00:22:45,690 --> 00:22:49,510
+عندما يكون في منتصف الآية احنا قلنا الوقف الحسن هو
+
+268
+00:22:49,510 --> 00:22:52,770
+أن يقف القارئ على كلمة قرآنية تم المعنى عندها أو
+
+269
+00:22:52,770 --> 00:22:58,690
+أفادت معنى ولكنها تتعلق بما بعدها لفظًا ومعنى الوقف 
+
+270
+00:22:58,690 --> 00:23:02,990
+التام إيش كان؟ لا تتعلق لا لفظ ولا معنى، الوقف 
+
+271
+00:23:02,990 --> 00:23:07,470
+الكافي تتعلق بما بعده في المعنى دون اللفظ، الوقف 
+
+272
+00:23:07,470 --> 00:23:11,830
+الحسن تم المعنى لا تتعلق بما بعده لا لفظ ولا معنى،
+
+273
+00:23:11,830 --> 00:23:17,550
+فلابد أن نحدد التام والكافي والحسن والقبيح بعد ذلك 
+
+274
+00:23:18,190 --> 00:23:23,090
+هنا الوقف الحسن عندما يقع في منتصف الآية له حكم و
+
+275
+00:23:23,090 --> 00:23:27,510
+هو يجوز الوقف عليه ولا يجوز الابتداء بما بعده
+
+276
+00:23:27,510 --> 00:23:32,970
+لتعلقه به لفظًا ومعنى، إذا حكم الوقف الحسن عندما 
+
+277
+00:23:32,970 --> 00:23:37,280
+يكون في منتصف الآية يجوز أن تقف عنده لكن لا يجوز
+
+278
+00:23:37,280 --> 00:23:42,660
+الابتداء بما بعده بل يجب وصله بما قبله يعني تجف 
+
+279
+00:23:42,660 --> 00:23:48,120
+عنده يجوز لكن اللي بعده لو وصلته مش ستفهم أي شيء
+
+280
+00:23:48,120 --> 00:23:52,380
+لأنه متعلق بما قبله في اللفظ والمعنى تم المعنى
+
+281
+00:23:52,380 --> 00:23:55,940
+عنده يتعلق بما بعده لفظا ومعنى اسم واقف حسن عشان
+
+282
+00:23:55,940 --> 00:24:00,500
+في نص الآية يجوز حكمه يجوز الوقف عليه ولا يجوز
+
+283
+00:24:00,500 --> 00:24:05,650
+الابتداء بما بعده بل يجب أن ترجع كلمة أو كلمتين حتى 
+
+284
+00:24:05,650 --> 00:24:09,790
+يستقيم المعنى وتستمر في التلاوة هذا إذا أراد
+
+285
+00:24:09,790 --> 00:24:14,050
+القارئ أن يقف على الوقف الحسن اللي في منتصف الآية
+
+286
+00:24:14,050 --> 00:24:20,830
+أمثل على ذلك هنا مثلا الحمد لله أيش نوع الوقف اللي
+
+287
+00:24:20,830 --> 00:24:25,590
+هنا؟ كلمة الحمد لله يا إخواننا يا كرام يعني أفادت
+
+288
+00:24:25,590 --> 00:24:30,020
+معنى الحمد لله يعني الشكر والثناء على الله لكن رب
+
+289
+00:24:30,020 --> 00:24:33,680
+العالمين، هذا ما الحمد لله في منتصف الآية رب
+
+290
+00:24:33,680 --> 00:24:39,940
+العالمين في علاقة معنوية وعلاقة إعرابية العلاقة
+
+291
+00:24:39,940 --> 00:24:44,840
+المعنوية أن الحمد لله رب العالمين فيها ثناء على
+
+292
+00:24:44,840 --> 00:24:50,270
+الله يعني أنا أشكر الله الذي هو رب العالمين و من
+
+293
+00:24:50,270 --> 00:24:55,410
+حيث الإعراب فإعراب رب العالمين لها علاقة لله فهي
+
+294
+00:24:55,410 --> 00:24:59,890
+بدل من لله الحمد لله رب العالمين بدل إذا في علاقة
+
+295
+00:24:59,890 --> 00:25:05,050
+إعرابية وعلاقة معنوية وهي في منتصف الآية إيش
+
+296
+00:25:05,050 --> 00:25:11,230
+حكمها بيكون الآن يجوز الوقف عليها على الحمد لله ولا
+
+297
+00:25:11,230 --> 00:25:14,070
+يجوز الابتداء بما بعدها يعني لا يجوز أن نقول
+
+298
+00:25:14,070 --> 00:25:22,300
+مثلا الحمد لله بعدين نقول رب العالمين طبعا خطأ إذا
+
+299
+00:25:22,300 --> 00:25:26,460
+أردت أن تقف على الحمد لله لا تقف عليها إلا يعني
+
+300
+00:25:26,460 --> 00:25:29,920
+يجب أن تقف لكن إذا أردت أن تبدأ بدك ترجع فتقول
+
+301
+00:25:29,920 --> 00:25:37,600
+الحمد لله الحمد لله بعدين الحمد لله رب العالمين
+
+302
+00:25:37,600 --> 00:25:42,340
+على أساس أنه لابد أن يكون الواصل مع الـ .. مع الآية
+
+303
+00:25:42,340 --> 00:25:46,410
+التي أو مع الكلام الذي قبلها في هذا الموضوع نفس
+
+304
+00:25:46,410 --> 00:25:50,570
+الشيء، من يشرح ليها نفس المعنى، هنا الحمد لله فاطر
+
+305
+00:25:50,570 --> 00:25:54,330
+السماوات والأرض، من يبين أين الوقف الحسن؟ فضل يا
+
+306
+00:25:54,330 --> 00:25:57,410
+أخي طبعا الوقف الحسن يكون على كلمة الله
+
+307
+00:26:05,390 --> 00:26:10,910
+أحسن ممتاز يبقى تقول الحمد لله يعني واحد يريد أن
+
+308
+00:26:10,910 --> 00:26:18,000
+يستمتع بالثناء على الله يكررها الحمد لله الحمد لله
+
+309
+00:26:18,000 --> 00:26:23,860
+الحمد لله فاطر السماوات والأرض يعني يجوز أن يقف
+
+310
+00:26:23,860 --> 00:26:28,840
+عليها لكن لا يجوز أن يقول الحمد لله بعدين فاطر
+
+311
+00:26:28,840 --> 00:26:33,100
+السماوات والأرض أيش نوع الوقف؟ وقف حسن تم المعنى
+
+312
+00:26:33,100 --> 00:26:39,560
+عنده يتعلق بما بعده لفظا ومعنى وهو في منتصف الآية
+
+313
+00:26:39,560 --> 00:26:45,230
+كذلك مثلا كلمة بسم الله الرحمن الرحيم برضه نفس
+
+314
+00:26:45,230 --> 00:26:48,710
+الموضوع، من يبين لنا أين الوقف الحسن على بسم الله
+
+315
+00:26:48,710 --> 00:26:52,610
+الرحمن الرحيم نفس الكلام، فضل يا أخي الوقف الحسن
+
+316
+00:26:52,610 --> 00:26:57,830
+على كلمة الله، يجوز أن نقف .. مش الله، بسم الله
+
+317
+00:26:57,830 --> 00:27:01,430
+على لفظ الجلالة نقف على لفظ الجلالة يجوز أن نقف 
+
+318
+00:27:01,430 --> 00:27:04,790
+لكن لا يجوز أن نبتدأ الرحمن الرحيم، لأن الرحمن
+
+319
+00:27:04,790 --> 00:27:08,850
+الرحيم تتعلق بما قبلها من حيث المعنى واللفظ أحسن
+
+320
+00:27:08,850 --> 00:27:12,610
+طيب هذا يا إخواني يا كرام اللي هو الوقف الحسن في
+
+321
+00:27:12,610 --> 00:27:17,330
+منتصف الآية هذا حكمه عندما ياتيكم سؤال بين حكم
+
+322
+00:27:17,330 --> 00:27:21,330
+الوقف الحسن هتقول أنه ينقسم إلى قسمين وقف حسن في
+
+323
+00:27:21,330 --> 00:27:25,670
+منتصف الآية ووقف حسن على رأس الآية الوقف الحسن
+
+324
+00:27:25,670 --> 00:27:29,010
+اللي في منتصف الآية يجوز الوقف عليه ولا يجوز
+
+325
+00:27:29,010 --> 00:27:33,230
+الابتداء بما بعده أما الوقف الحسن اللي على رأس
+
+326
+00:27:33,230 --> 00:27:36,950
+الآية عند رقم الآية عند بداية الآية يعني فيجوز
+
+327
+00:27:36,950 --> 00:27:42,210
+الوقف عليه ويجوز الابتداء بما بعده هنا مثلا يجوز
+
+328
+00:27:42,210 --> 00:27:46,310
+الوقف على رأس الآية ويجوز الابتداء بما بعده لأن
+
+329
+00:27:46,310 --> 00:27:51,480
+الوقف على رأس الآية سنة نشوف مثلا المثال أيضا نأتي
+
+330
+00:27:51,480 --> 00:27:58,360
+لكم بمثال سهل الحمد لله رب العالمين الحمد لله رب
+
+331
+00:27:58,360 --> 00:28:05,020
+العالمين اسمه واقف حسن لأنه تم المعنى عنده يتعلق
+
+332
+00:28:05,020 --> 00:28:08,720
+بما بعده في المعنى لأنه لسه الكلام بيتكلم عن ثناء
+
+333
+00:28:08,720 --> 00:28:11,780
+على الله الحمد لله رب العالمين الرحمن الرحيم
+
+334
+00:28:11,780 --> 00:28:18,240
+الكلام فيه ثناء على الله فالمعنى لسه لم ينتهي و رب
+
+335
+00:28:18,240 --> 00:28:23,800
+العالمين عبارة عن صفة لـ .. الرحمن الرحيم صفة لرب
+
+336
+00:28:23,800 --> 00:28:28,200
+العالمين يعني الحمد لله اللي من صفاته أنه رحمن
+
+337
+00:28:28,200 --> 00:28:33,980
+رحيم إذا في علاقة إعرابية وفي علاقة معنوية فالوقف
+
+338
+00:28:33,980 --> 00:28:39,720
+على الحمد لله رب العالمين اسمه وقف حسن على أيّه؟
+
+339
+00:28:39,720 --> 00:28:44,260
+على رأس الآية يجوز الوقف عليه ويجوز الابتداء بما
+
+340
+00:28:44,260 --> 00:28:49,430
+بعده لأن الوقف عليه رأس الآية سنة كذلك هنا في آية
+
+341
+00:28:49,430 --> 00:28:55,230
+سورة البقرة في قول تعالى كذلك يبين الله لكم الآيات
+
+342
+00:28:55,230 --> 00:29:02,950
+لعلكم تتفكرون في الدنيا والآخرة هنا تتفكرون تم
+
+343
+00:29:02,950 --> 00:29:07,150
+المانع عندها لكنها في علاقة معنوية تتفكرون في
+
+344
+00:29:07,150 --> 00:29:11,150
+الدنيا والآخرة وفي علاقة كذلك إعرابية في الدنيا
+
+345
+00:29:11,150 --> 00:29:14,730
+والأخرى جار ومجرور ومتعلق بالكلمة التي قبلها يعني
+
+346
+00:29:14,730 --> 00:29:19,030
+تتفكرون في الدنيا والأخرى إذا علاقة إعرابية وعلاقة
+
+347
+00:29:19,030 --> 00:29:24,530
+معنوية فالوقف عليها يسمى وقف حسن على رأس الآية تم
+
+348
+00:29:24,530 --> 00:29:29,230
+المانع عندها تتعلق بعدها لفظا ومعنى وهذا المعنى
+
+349
+00:29:29,230 --> 00:29:36,900
+موجود في عدة أمثلة لكن في عندنا حكم آخر وهو الوقف
+
+350
+00:29:36,900 --> 00:29:41,340
+الحسن على رأس الآية لكنه يوهم معنى غير المعنى
+
+351
+00:29:41,340 --> 00:29:46,320
+المراد إذا كان في عندنا وقف حسن على رأس الآية يوهم
+
+352
+00:29:46,320 --> 00:29:49,920
+معنى غير المعنى المراد فيه حكم خاص وهو موجود في
+
+353
+00:29:49,920 --> 00:29:54,980
+عدة آيات من القرآن مثل ذلك في سورة المعونة فوين
+
+354
+00:29:54,980 --> 00:30:03,410
+للمصلين الذين هم عن صلاتهم ساهون هنا الوقف على
+
+355
+00:30:03,410 --> 00:30:10,160
+المصلين ما هو حكمه؟ يعني وقف حسن تم المانع عنده
+
+356
+00:30:10,160 --> 00:30:14,340
+يتعلق بما بعده في اللفظ والمعنى يعني هو صلة
+
+357
+00:30:14,340 --> 00:30:18,600
+الموصول فوين المصلين؟ من هم المصلين الذين لهم
+
+358
+00:30:18,600 --> 00:30:23,700
+الويل؟ هم الذين هم عن صلاتهم ساهون فهو صلة الموصول
+
+359
+00:30:23,700 --> 00:30:29,080
+علاقة إعرابية علاقة يعني إعرابية وفي عندنا المعنى
+
+360
+00:30:29,080 --> 00:30:33,280
+كله بتتكلم على المصلين الذين يسفون عن الصلاة
+
+361
+00:30:33,280 --> 00:30:40,120
+ولأنها هي رأس آية الأصل أنه يجوز الوقف عليه ويجوز
+
+362
+00:30:40,120 --> 00:30:44,820
+الابتداء بما بعده رأس آية ويجوز الوقف عليها ويجوز
+
+363
+00:30:44,820 --> 00:30:50,120
+الابتداء من رأس الآية لكن هذا الموضع لأنه يتحدث عن
+
+364
+00:30:50,120 --> 00:30:55,920
+حكم قد يؤدي معنى غير المعنى المراد ذكر العلماء في
+
+365
+00:30:55,920 --> 00:31:00,180
+تفصيل هذا الكلام ثلاث أقوال يعني في عندنا اختلاف بين
+
+366
+00:31:00,180 --> 00:31:03,540
+العلماء، هل يجوز الوقف عليه والابتداء بما بعده؟
+
+367
+00:31:03,540 --> 00:31:06,680
+ولا لا يجوز الوقف عليه والابتداء بما بعده؟ لأنه
+
+368
+00:31:06,680 --> 00:31:11,100
+عندما نقول فويل للمصلين، كلام يعني الويل، ما هو
+
+369
+00:31:11,100 --> 00:31:15,650
+الويل يا إخواننا؟ الويل هو بدء فيه جهنم تستعيذ منه
+
+370
+00:31:15,650 --> 00:31:22,090
+جهنم كل يوم يعني سبعين أو مائة مرة يعني تهديد فليس
+
+371
+00:31:22,090 --> 00:31:26,970
+من الحكمة أن أقول فويل للمصلين فهذا يعني خطأ لذلك
+
+372
+00:31:26,970 --> 00:31:31,810
+هنا لأنها قد توهم معنى غير المعنى المراد اختلف
+
+373
+00:31:31,810 --> 00:31:36,530
+العلماء إلى ثلاث أقوال نشوف الأقوال التي ذهب إليها
+
+374
+00:31:36,530 --> 00:31:40,330
+العلماء القول الأول يا إخواننا يا كرام لا يجوز
+
+375
+00:31:40,330 --> 00:31:45,250
+الوقف عليه إلا مضطرا ويجب وصله بما بعده وهذا هو
+
+376
+00:31:45,250 --> 00:31:51,430
+مذهب ابن الجزري يعني مثلا يعني يقول فوين للمصلين
+
+377
+00:31:51,430 --> 00:31:56,910
+ومضطر أن يقف ما هي الأمور التي تجعل الإنسان يضطر
+
+378
+00:31:56,910 --> 00:32:03,410
+أن يقف يعني كسعال أو عطاس أو ضيق نفس أو تعثر أو
+
+379
+00:32:03,410 --> 00:32:07,470
+نسيان أو بكاء أو أي يعني من الأمور اللي تجبره أن
+
+380
+00:32:07,470 --> 00:32:13,440
+يقف فبقوله يجب لك أن تقف وقفا اضطراريا أو لا يجب
+
+381
+00:32:13,440 --> 00:32:17,540
+عليك أن تقف إلا وقفا اضطراريا وإذا وقفت اضطراريا
+
+382
+00:32:17,540 --> 00:32:22,860
+يجب أن توصلوا بالبعد يعني تقول مثلا فوين للمصلين
+
+383
+00:32:22,860 --> 00:32:29,580
+سعلت مثلا وترجع فوين للمصلين الذين هم عن صلاتهم
+
+384
+00:32:29,580 --> 00:32:35,360
+ساهون على أساس أنه يتم المعنى هذا هو موقف ابن
+
+385
+00:32:35,360 --> 00:32:42,090
+الجزري أو رأي ابن الجزري كأنه وقف حسن في منتصف الآية
+
+386
+00:32:42,090 --> 00:32:47,230
+طبعا هنا فوين للمصلين من هم المصلين اللي وين
+
+387
+00:32:47,230 --> 00:32:51,250
+لهم هم الذين هم عن صلاتهم ساهون لا يجوز الوقف عليه
+
+388
+00:32:51,250 --> 00:32:57,790
+إلا مضطرا ويجب وصله بما بعدهم هذا القول القول
+
+389
+00:32:57,790 --> 00:33:02,730
+الثاني قالوا يجوز الوقف عليه اختياريا ولكن لا
+
+390
+00:33:02,730 --> 00:33:09,520
+يجوزه ويجب وصله بما قبله يعني يجب عليك أن تقف عليه
+
+391
+00:33:09,520 --> 00:33:13,820
+وقفا .. يعني مش اضطراريا اختياريا ولكن إذا وقفت
+
+392
+00:33:13,820 --> 00:33:16,660
+عليه باختيارك ما ينفعش تقول الذين هم عن صلاتهم
+
+393
+00:33:16,660 --> 00:33:21,740
+ساهون يجب أن تقول .. ترجع وتقول فوين للمصلين الذين
+
+394
+00:33:21,740 --> 00:33:26,580
+هم عن صلاتهم ساهون إذا ما الفرق بين الرأي الأول
+
+395
+00:33:26,580 --> 00:33:32,870
+والرأي الثاني؟ فضل أخي الوقف الاضطراري عن الرأي 
+
+396
+00:33:32,870 --> 00:33:37,590
+الثاني صحيح لكن نفس الحكم الرأي الأول يقول لا يجوز
+
+397
+00:33:37,590 --> 00:33:42,010
+الوقف على المصلين إلا مضطرا ويجب وصله بما بعدهم
+
+398
+00:33:42,010 --> 00:33:45,450
+الرأي الثاني يقول يجوز الوقف عليه اختياريا لأنه
+
+399
+00:33:45,450 --> 00:33:49,590
+رأس آية ولكن يجب وصله بما بعدها هذا الرأي الثاني
+
+400
+00:33:49,590 --> 00:33:55,130
+الرأي الثالث يجوز الوقف عليه اختياريا لأنه رأس آية
+
+401
+00:33:55,130 --> 00:34:01,170
+ويجوز الابتداء بما بعده ولكن لا يجوز قطع القراءة
+
+402
+00:34:01,170 --> 00:34:08,670
+يعني يجوز أن تقول فويل للمصلين الذين هم عن صلاتهم
+
+403
+00:34:08,670 --> 00:34:14,610
+ساهون وتكمل القراءة يجوز ولكن الذي لا يجوز قطع
+
+404
+00:34:14,610 --> 00:34:19,570
+القراءة كيف قطع القراءة؟ أن تنهي القراءة على قوله
+
+405
+00:34:19,570 --> 00:34:22,110
+فويل للمصلين وتركع
+
+406
+00:34:28,890 --> 00:34:33,730
+فَوَيْنٌ لِلْمُصَلِّينَ الله أكبر ويركع بيكون إيش
+
+407
+00:34:33,730 --> 00:34:38,350
+أوهمت معنى أن الـ ويل لكم يا مصلين وهذا كلام يعني
+
+408
+00:34:38,350 --> 00:34:42,010
+غير لائق لا يجوز قطع القراءة وانشغال عن القراءة
+
+409
+00:34:42,010 --> 00:34:47,650
+بأمر آخر وهو الركوع أو السجود أو مثلا أو مثلا
+
+410
+00:34:47,650 --> 00:34:51,470
+تنهي القراءة وتقول صداقة الله العظيم وتمشي هذا
+
+411
+00:34:51,470 --> 00:34:58,610
+بيكون تؤدي معنى غير المعنى المراد أي رأي أرجح الرأي
+
+412
+00:34:58,610 --> 00:35:05,010
+الثالث هو الرأي الذي يقول يجوز الوقف عليه لأنه رأس
+
+413
+00:35:05,010 --> 00:35:10,650
+آية ويجوز الابتداء بما بعده ولكن الذي لا يجوز هو
+
+414
+00:35:10,650 --> 00:35:16,410
+أن تقطع القراءة وتنشغل عنها بأمر يعني خارجي آخر
+
+415
+00:35:16,410 --> 00:35:22,920
+بقي علينا الوقف القبيح يعني نذكر وقف القبيح لأنه
+
+416
+00:35:22,920 --> 00:35:27,200
+أيضا نتابع للموضوع الأقسام الأربعة ما هو الوقف
+
+417
+00:35:27,200 --> 00:35:32,080
+القبيح يا إخواننا الوقف القبيح هو الوقوف على كلام
+
+418
+00:35:32,080 --> 00:35:38,510
+لم يفد معنى لشدة تعلقه بما بعده لفظا ومعنى أو هو
+
+419
+00:35:38,510 --> 00:35:41,950
+الوقوف على كلام يوهم معنى غير المعنى المراد يبقى
+
+420
+00:35:41,950 --> 00:35:47,190
+أن يقف القارئ على كلام لم يفد معنى لشدة تعلقه بما 
+
+421
+00:35:47,190 --> 00:35:52,210
+بعده لفظا ومعنى أو لأنه يوهم معنى غير المعنى
+
+422
+00:35:52,210 --> 00:35:57,130
+المراد يسمى هذا الوقف وقف قبيح إحنا قلنا أقسام
+
+423
+00:35:57,130 --> 00:36:05,080
+الوقف الاختياري وقف تم وقف كافٍ حسن وهذا القبيح
+
+424
+00:36:05,080 --> 00:36:09,680
+القبيح أن يقف القارئ على كلام لم يفد معنى لشدة
+
+425
+00:36:09,680 --> 00:36:14,860
+تعلقه بما بعده لفظا ومعنى أو لأنه يوهم معنى غير 
+
+426
+00:36:14,860 --> 00:36:20,660
+المعنى المراد لذلك نسمي هذا الوقف وقف قبيح القسم 
+
+427
+00:36:20,660 --> 00:36:24,720
+الأول يقسم إلى قسمين واحد يقول لأنه يوهم هنا مثلا 
+
+428
+00:36:24,720 --> 00:36:28,080
+هو الوقف على كلام لم يفد معنى لشدة تعلقه بما بعده
+
+429
+00:36:28,080 --> 00:36:33,460
+لفظا ومعنى هذا نوع وقف على كلام متعلق بالذي بعده
+
+430
+00:36:33,460 --> 00:36:37,240
+لفظا ومعنى اسمه النوع الثاني يوهم معنى غير المعنى 
+
+431
+00:36:37,240 --> 00:36:41,100
+المراد نشوف النوع الأول مثلا النوع الأول هو الوقف
+
+432
+00:36:41,100 --> 00:36:44,880
+على كلام لم يفد معنى لشدة تعلقه بما بعده لفظا
+
+433
+00:36:44,880 --> 00:36:49,740
+ومعنى مثل إيش مثلا كأن يقف القارئ على كلمة الحمد
+
+434
+00:36:49,740 --> 00:36:54,580
+من قوله الحمد لله رب العالمين عندما وقفت أنا مثلا
+
+435
+00:36:54,580 --> 00:37:00,620
+عند كلمة الحمد فهمت إيش مفهوم يبقى وقفت على كلمة
+
+436
+00:37:00,620 --> 00:37:04,640
+لم تفد معنى لأنها تتعلق بما بعدها لفظا ومعنى لابد
+
+437
+00:37:04,640 --> 00:37:07,700
+أن أقول الحمد لله أو الحمد لله رب العالمين فأنا 
+
+438
+00:37:07,700 --> 00:37:11,400
+وقفت على كلام لم يفد معنى لشدة تعلقه بما بعده لفظا
+
+439
+00:37:11,400 --> 00:37:15,860
+ومعنى اسم الوقف اللي هنا وقف قوي لا يجوز الوقف
+
+440
+00:37:15,860 --> 00:37:20,160
+عليه إلا مضطرا وإذا أردت أن تبدأ الكلام ترجع كلمة 
+
+441
+00:37:20,160 --> 00:37:25,040
+أو كلمتين حتى يصدق المعنى موضوع آخر عندما لو وقف 
+
+442
+00:37:25,040 --> 00:37:29,920
+القارئ على كلمة الناس من قوله تعالى كان الناس أمة 
+
+443
+00:37:29,920 --> 00:37:38,690
+واحدة لو واحد قال كان الناس إيش استفاد؟ يعني كان ..
+
+444
+00:37:38,690 --> 00:37:42,190
+إيش كان الناس؟ كلام لم يفد معنى، لأنها متعلقة
+
+445
+00:37:42,190 --> 00:37:45,610
+بالبعدها، يعني في عيننا كان الناس و الناس اسم كان،
+
+446
+00:37:45,610 --> 00:37:49,290
+أين خبرها، أين باقي الكلام، فلما قفت على كلمة كان
+
+447
+00:37:49,290 --> 00:37:54,410
+الناس مش مفهوم أو مثلا لو واحد وقف عند كلمة كان، 
+
+448
+00:37:54,410 --> 00:37:59,640
+إيش كان؟ كان الناس أمة لحالها يعني ضابط أن يكون 
+
+449
+00:37:59,640 --> 00:38:04,860
+الكلام يفيد معنى لذلك الوقف على كان الناس الناس
+
+450
+00:38:04,860 --> 00:38:09,880
+اسمه وقف قبيح لأنه وقفنا على كلام لم يفد معنى 
+
+451
+00:38:09,880 --> 00:38:15,140
+لأنه يتعلق باللي بعده لفظا ومعنى موضوع آخر أو مثال 
+
+452
+00:38:15,140 --> 00:38:22,440
+آخر على الوقف القبيح مثلا ألا يظن أولئك أنهم 
+
+453
+00:38:22,440 --> 00:38:29,040
+مبعوثون؟ لو واحد وقف عند كلمة ألا فهمت إشي؟ لأ مش 
+
+454
+00:38:29,040 --> 00:38:33,480
+مفهوم، إذا لم تفد معنى، ألا يظنوا .. لو قفت عنده 
+
+455
+00:38:33,480 --> 00:38:38,700
+يظنوا، برضه وقف قبيح، مش مفهوم، ألا يظن أولئك ..
+
+456
+00:38:38,700 --> 00:38:43,440
+برضه نفس الموضوع، لم يفد معنى، لذلك الوقف القبيح 
+
+457
+00:38:43,440 --> 00:38:48,160
+لو قلنا مثلا، من يأتي بمثال أي آية أجف على مكان 
+
+458
+00:38:48,160 --> 00:38:52,330
+فيها يعني لم تفد معنى، يكون هو الوقف إيه؟ وقف قبيح 
+
+459
+00:38:52,330 --> 00:38:56,450
+لو غمطت عينك وحطيت يدك على المصحف أو أصبعك وقلت من 
+
+460
+00:38:56,450 --> 00:38:59,850
+هنا وقفت عنها غالب ما تكون الوقف إيه الوقف قبيح
+
+461
+00:38:59,850 --> 00:39:05,510
+لأنه لابد أن يكون المعنى قد تمل إذا هنا ألا يظن 
+
+462
+00:39:05,510 --> 00:39:11,290
+أولئك اسم وقف قبيح لأنه وقفنا على كلام لم يفد معنى
+
+463
+00:39:11,290 --> 00:39:16,470
+لشدة تعلقه بما بعده لفظا ومعنى إيش حكمه لا يجوز 
+
+464
+00:39:16,470 --> 00:39:21,730
+الوقف عليه إلا مضطرا وإذا وقفت عليه بتعيد الكلمة
+
+465
+00:39:21,730 --> 00:39:25,330
+اللي وقفت عندها أو أكثر كلمة أو كلمتين حتى يستقيم
+
+466
+00:39:25,330 --> 00:39:30,730
+المعنى وتستمر في التلاوة مثال آخر إن هذا أخي له 
+
+467
+00:39:30,730 --> 00:39:36,070
+تسع وتسعون نعجته ولي نعجته واحدة لو واحد وقف عند 
+
+468
+00:39:36,070 --> 00:39:38,810
+كلمة إن هذا أخي له تسع وتسعون
+
+469
+00:39:41,300 --> 00:39:47,300
+مش مفهومة لذلك اسم الوقف يسمى وقف قبيح لأنه أفاد 
+
+470
+00:39:47,300 --> 00:39:52,840
+معنى غير المعنى أنه أقفنا على كلام قبيح لشدة تعليقه 
+
+471
+00:39:52,840 --> 00:39:57,120
+بما بعده لفظا ومعنى القسم الثاني يوهم معنى غير 
+
+472
+00:39:57,120 --> 00:40:01,300
+المعنى المراد يعني بيؤدي إلى معنى ثاني مثل ذلك إن 
+
+473
+00:40:01,300 --> 00:40:08,890
+الله لا يستحي أي ضربة مثلا مابعودة فما فوقها لو
+
+474
+00:40:08,890 --> 00:40:14,650
+وقف القارئ عند كلمة إن الله لا يستحي يعني هذا يعني
+
+475
+00:40:14,650 --> 00:40:17,750
+سوء أدب مع الله سبحانه وتعالى أوهمت معنى غير
+
+476
+00:40:17,750 --> 00:40:21,310
+المعنى المراد الذي هو مطلوب إن الله لا يستحي أي 
+
+477
+00:40:21,310 --> 00:40:25,470
+ضربة مثلا مابعودة فما فوقها أو مثلا قوله تعالى يا
+
+478
+00:40:25,470 --> 00:40:30,790
+أيها الذين آمنوا لا تقربوا الصلاة وأنتم سكارى لو
+
+479
+00:40:30,790 --> 00:40:36,090
+وقف على كلمة لا تقربوا الصلاة يعني فيه نهي عن 
+
+480
+00:40:36,090 --> 00:40:39,090
+الاقتراب من الصلاة يبقى يوهم معنى غير المعنى 
+
+481
+00:40:39,090 --> 00:40:44,470
+المراد كذلك وما أرسلنا من رسول إلا ليطهر بإذن الله
+
+482
+00:40:44,970 --> 00:40:50,190
+لو وقف القارئ عند كلمة وما أرسلنا من رسول يعني أن 
+
+483
+00:40:50,190 --> 00:40:54,590
+الله لم يرسل أي رسول وبالتالي تؤدي إلى إيش؟ إلى خلل 
+
+484
+00:40:54,590 --> 00:40:59,830
+فلابد أن يكون الـ الـ يكون الكلام له معنى يؤدي
+
+485
+00:40:59,830 --> 00:41:03,350
+معنى المراد حكم الوقف القبيح لا يجوز الوقف عليه
+
+486
+00:41:03,350 --> 00:41:07,270
+إلا مضطرا وإذا أراد القارئ أن يستأنف يعيد الكلام
+
+487
+00:41:07,270 --> 00:41:11,990
+ويرجع كلمة أو كلمتين حتى يستفيد ما هو رمز الوقف 
+
+488
+00:41:11,990 --> 00:41:17,850
+القبيح؟ رمزه يعني هو أصلا لا يوضع له رمز ولكن في
+
+489
+00:41:17,850 --> 00:41:23,810
+المواضع التي تؤدي إلى معنى غير يعني معنى آخر أو 
+
+490
+00:41:23,810 --> 00:41:27,190
+توفر معنى غير المعنى المراد يوضع عليها كلمة لا
+
+491
+00:41:27,190 --> 00:41:31,850
+يعني لا تقف يعني الوقف في هذا الموضع ممنوع تستخدم
+
+492
+00:41:31,850 --> 00:41:36,770
+لا للوقف القبيح إذا أفادت معنى غير المعنى المراد أو 
+
+493
+00:41:36,770 --> 00:41:41,770
+مثلا تستخدم كذلك لا عند الوقف الحسن إذا كان ممنوع
+
+494
+00:41:41,770 --> 00:41:46,450
+القطع القراءة على هذا المكان مثل فوين المصليين 
+
+495
+00:41:46,450 --> 00:41:50,270
+الذين هم عن صلاتهم سهون بنجد أن وين المصليين مكتوب 
+
+496
+00:41:50,270 --> 00:41:54,050
+لا يعني لا تقطع القراءة على هذا الموضع لأنه يؤدي 
+
+497
+00:41:54,050 --> 00:41:58,130
+إلى خلل معين قد يكون رمز لا على رأس الآية على
+
+498
+00:41:58,130 --> 00:42:01,530
+الوقف الحسن وهنا وقف قبيح ومعناه لا تقطع القراءة 
+
+499
+00:42:01,530 --> 00:42:05,720
+وتنشغل عنها بأمر خارجي آخر عرفنا يا إخواننا يا كرام 
+
+500
+00:42:05,720 --> 00:42:09,880
+آخر نقطة عندي اللي هي بعض الرموز ال meme الأفقية
+
+501
+00:42:09,880 --> 00:42:16,760
+هو رمز لإيش؟ للوقف اللازم القلة وقف تام الصلاة وقف 
+
+502
+00:42:16,760 --> 00:42:22,740
+كافٍ gym يجوز الوقف والواصل وهو رمز للوقف 
+
+503
+00:42:22,740 --> 00:42:24,400
+الكافي الليلة
+
+504
+00:42:26,660 --> 00:42:30,840
+للوقف القبيح والوقف الحسن وطبعا في عندنا الوقف 
+
+505
+00:42:30,840 --> 00:42:36,100
+التعانق اللي هو الثلاث نقاط فوق بعض معناه أنه إذا 
+
+506
+00:42:36,100 --> 00:42:39,800
+وقفت على الأولى لا تقف على الثانية لأنها .. يعني
+
+507
+00:42:39,800 --> 00:42:48,260
+كل واحدة لها معنى مثال ذلك مثلا ذلك هنا مثلا كمثال
+
+508
+00:42:48,260 --> 00:42:53,900
+ذلك الكتاب لا ريب فيه هدا للمتقين فوق كلمة ريب 
+
+509
+00:42:53,900 --> 00:42:58,960
+هنلاقي ثلاث نقاط وفوق كلمة فيه ثلاث نقاط إما أن تقف
+
+510
+00:42:58,960 --> 00:43:02,520
+على الأولى أو تقف على الثانية لو أقفت على الأولى
+
+511
+00:43:02,520 --> 00:43:07,420
+ذلك الكتاب لا ريب بتكون لا نافية للجنس وريب اسمها 
+
+512
+00:43:07,420 --> 00:43:14,050
+وخبر ريب محذوف تقديره فيه وكلمة فيه هدى للمتقين
+
+513
+00:43:14,050 --> 00:43:19,590
+بتكون فيه شبه جملة بما في حال رافع خبر مقدم وهدى
+
+514
+00:43:19,590 --> 00:43:23,650
+بيكون اسمها يعني بتكون إعرابين وتؤدي إلى معنى آخر 
+
+515
+00:43:23,650 --> 00:43:29,040
+يعني يا إما تكف على كلمة ذلك الكتاب لا ريب فيه هدا
+
+516
+00:43:29,040 --> 00:43:35,760
+للمتقين أو تقول ذلك الكتاب لا ريب فيه هدا للمتقين 
+
+517
+00:43:35,760 --> 00:43:39,540
+أو ما تكفّش على أي واحدة منهم فتقول ذلك الكتاب لا 
+
+518
+00:43:39,540 --> 00:43:44,280
+ريب فيه هدا للمتقين يجوز الحلقات الثلاث كذلك آخر
+
+519
+00:43:44,280 --> 00:43:51,700
+نقطة وهي قال فإنها محرمة عليهم أربعين سنة يتيهون 
+
+520
+00:43:51,700 --> 00:43:56,160
+في الأرض الآية تتكلم على مين؟ على بني إسرائيل الذين
+
+521
+00:43:56,160 --> 00:43:59,780
+قالوا لسيدنا موسى اذهب أنت وربك فقاتلها إنها هنا
+
+522
+00:43:59,780 --> 00:44:03,300
+قاعدون وقالوا إن فيها قوما جبارين وإننا لن ندخلها 
+
+523
+00:44:03,300 --> 00:44:08,180
+ما داموا فيها يعني هم اعترضوا على أمر الله لما قال 
+
+524
+00:44:08,180 --> 00:44:12,280
+موسى ادخلوا الأرض المقدسة فهم اعترضوا وقالوا إن 
+
+525
+00:44:12,280 --> 00:44:15,800
+فيها قوما جبارين واذهب أنت وربك فقاتلها فربنا
+
+526
+00:44:15,800 --> 00:44:19,640
+سبحانه وتعالى عاقبهم إيش العقوبة؟ قال له سيدنا 
+
+527
+00:44:19,640 --> 00:44:25,240
+موسى فإنها محرمة عليهم إذا وقفنا عليهم عن وقف 
+
+528
+00:44:25,240 --> 00:44:29,120
+التعانق الأول، بتأدي معنى أن الأرض محرمة عليهم 
+
+529
+00:44:29,120 --> 00:44:34,420
+أبدا، وبعدين عقوبة لقولهم أربعين سنة يتيهون في
+
+530
+00:44:34,420 --> 00:44:38,900
+الأرض، يعني لما نجف على محرمة عليهم بكلها معنى، 
+
+531
+00:44:38,900 --> 00:44:42,440
+بتكون محرمة عليهم أبدا، وأربعين سنة عقوبة لقولكم
+
+532
+00:44:42,440 --> 00:44:47,260
+هذا. لكن لو قلنا مثلا إن في عندنا نقف على كلمة
+
+533
+00:44:47,260 --> 00:44:53,320
+أربعين سنة فنقول مثلا قال فإنها محرمة عليهم أربعين
+
+534
+00:44:53,320 --> 00:44:57,850
+سنة يتيهون في الأرض فلا تأسى على القوم الفاسقين
+
+535
+00:44:57,850 --> 00:45:02,890
+بتكون مدة التحريم مش أبدي بل هي أربعين سنة إيه 
+
+536
+00:45:02,890 --> 00:45:07,050
+الموضعين كان تطبيقا وموجود اللي هو الآية المعنى 
+
+537
+00:45:07,050 --> 00:45:10,710
+الثاني اللي هو قال فإنها محرمة عليهم أربعين سنة
+
+538
+00:45:10,710 --> 00:45:14,010
+لأن الأربعين سنة حرمت هذه الأرض على بني إسرائيل 
+
+539
+00:45:14,010 --> 00:45:17,990
+وفي هذه الفترة توفي موسى عليه الصلاة والسلام و
+
+540
+00:45:17,990 --> 00:45:22,850
+هارون وأرسل الله نبيه آخر وكان معهم داود وحصلت
+
+541
+00:45:22,850 --> 00:45:28,510
+المعركة بينهم وبين جالوت وانتصر بنو إسرائيل على
+
+542
+00:45:28,510 --> 00:45:34,650
+العمالقة الآن هنا موضوع الوقف كله وهنبدأ إن شاء 
+
+543
+00:45:34,650 --> 00:45:37,430
+الله في الموضوع الآخر وهو الموضوع في المحاضرة
+
+544
+00:45:37,430 --> 00:45:40,170
+القادمة بارك الله فيكم جميعا وجزاكم الله خير و
+
+545
+00:45:40,170 --> 00:45:41,990
+السلام عليكم ورحمة الله وبركاته 
diff --git a/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/bfhcVHk-Rjk.srt b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/bfhcVHk-Rjk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..943a770ade5d76768441ef1ca9e2acf227382daa
--- /dev/null
+++ b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/bfhcVHk-Rjk.srt
@@ -0,0 +1,1479 @@
+1
+00:00:20,640 --> 00:00:23,500
+السلام عليكم ورحمة الله وبركاته بسم الله الرحمن
+
+2
+00:00:23,500 --> 00:00:27,460
+الرحيم الحمد لله الصلاة والسلام على رسول الله وعلى 
+
+3
+00:00:27,460 --> 00:00:32,200
+آله وصحبه وسلم أخذنا سابقا في المحاضرات السابقة
+
+4
+00:00:32,200 --> 00:00:36,620
+أحكام الوقف بشكل عام وهي تنقسم إلى أربع أقسام يعني
+
+5
+00:00:36,620 --> 00:00:40,600
+الوقف الإضطراري والاختباري والاختياري والانتظاري
+
+6
+00:00:41,070 --> 00:00:44,230
+أحكام اللي الاختيار يتنقسم أو الوقف الاختياري
+
+7
+00:00:44,230 --> 00:00:48,270
+يتنقسم أيضًا إلى أربع أقسام الوقف التام والكافي 
+
+8
+00:00:48,270 --> 00:00:52,010
+والحسن والقبيح كل هذا أخدناه سابقًا ثم أخذنا
+
+9
+00:00:52,010 --> 00:00:57,230
+الإبتداء وأخدنا كذلك القطع وأخدنا كذلك السكت
+
+10
+00:00:57,230 --> 00:01:02,630
+وأخدنا كذلك حمزة الوصل وإلى هنا وسنطبق إن شاء الله
+
+11
+00:01:02,630 --> 00:01:06,190
+في هذه المحاضرة أحكام التجويد التي أخذناها سابقًا
+
+12
+00:01:06,190 --> 00:01:11,910
+على آيات من صورة الأحقاف من يقرأ فضل اقرأ الآية هذه
+
+13
+00:01:11,910 --> 00:01:19,070
+اللي تقصد ورا اعوذ بالله من الشيطان الرجيم بسم
+
+14
+00:01:19,070 --> 00:01:27,350
+الله الرحمن الرحيم قل أرأيتم أن .. أرأ .. قل 
+
+15
+00:01:27,350 --> 00:01:35,810
+أرأيتم أن كان من عند الله وكفرتم به وشهد شهد من
+
+16
+00:01:35,810 --> 00:01:38,410
+بني إسرائيل
+
+17
+00:01:56,390 --> 00:02:02,050
+أحسن بارك الله فيك طبعًا في هذه الآية الله سبحانه
+
+18
+00:02:02,050 --> 00:02:06,310
+وتعالى يعني قال قل أرأيتم إن كان من عند الله
+
+19
+00:02:06,310 --> 00:02:13,350
+وقفرتم به وشهد شاهدهم من بني إسرائيل أنت وقفت على
+
+20
+00:02:13,350 --> 00:02:18,330
+بني إسرائيل ما هو نوع الوقف اللي هنا وقفته على هذا
+
+21
+00:02:18,330 --> 00:02:22,990
+المكان اسمه الوقف اللي إيه الاضطرار الإضطراري يعني
+
+22
+00:02:22,990 --> 00:02:27,130
+الإنسان قاعد بيقرأ انتهى النفس صار عندك ضيق نفس
+
+23
+00:02:27,130 --> 00:02:30,910
+وقفت عند إسرائيل فإذا عرضت أن تستأنف القراءة فأعدّ 
+
+24
+00:02:30,910 --> 00:02:35,130
+الكلام يعني ابدأ من حيث الكلمة التي وقفت عندها أو 
+
+25
+00:02:35,130 --> 00:02:39,150
+ارجع كلمة أو كلمتين حتى يستقيم المعنى أنت رجعت قلت 
+
+26
+00:02:39,150 --> 00:02:46,250
+من بني إسرائيل على مثله فآمنوا واستكبرتمو استكبرتم
+
+27
+00:02:46,250 --> 00:02:55,290
+هنا الوقف الموجود على قوله واستكبرتم بعدين الوقف 
+
+28
+00:02:55,290 --> 00:03:00,590
+اللي هنا تمّ المعنى عنده يتعلق بما بعده يعني في
+
+29
+00:03:00,590 --> 00:03:06,080
+المعنى واللفظ في المعنى دون اللفظ لأن الكلام كله
+
+30
+00:03:06,080 --> 00:03:10,280
+يتكلم على الكفار وبالتالي هنا الوقف يسمى الوقف
+
+31
+00:03:10,280 --> 00:03:14,480
+الكافي إذا تمّ المعنى عنده إذا تمّ المعنى عنده لا
+
+32
+00:03:14,480 --> 00:03:19,520
+يتعلق بما بعده لفظًا وإنما يتعلق بالمعنى يسمى الوقف
+
+33
+00:03:19,520 --> 00:03:23,440
+الكافي أما إذا كان وقفنا على كلمة تمّ المعنى عندها 
+
+34
+00:03:23,440 --> 00:03:28,320
+لا تتعلق بما بعدها لا لفظًا ولا معنى يسمى إيش الوقف
+
+35
+00:03:28,320 --> 00:03:31,990
+التام وإذا كان الكلام الذي وقفنا عليه يتعلق بما
+
+36
+00:03:31,990 --> 00:03:36,650
+بعده لفظًا ومعنى يسمى وقف إيه؟ وقف حسن فإذا وقف 
+
+37
+00:03:36,650 --> 00:03:40,350
+القارئ على كلمة قرأنية لم يتمّ المعنى عندها لشدة
+
+38
+00:03:40,350 --> 00:03:45,030
+تعلقها بما بعدها يسمى وقف قبيح مثلًا لو قرأ القارئ
+
+39
+00:03:45,030 --> 00:03:52,270
+مثلًا قال قل أرأيتم إن كان منس على يسمى وقف إضطراري
+
+40
+00:03:52,270 --> 00:03:58,170
+أو قال قل أرأيتم أن وقف عندها يسمى وقف إيه وقف
+
+41
+00:03:58,170 --> 00:04:02,950
+قبيح لأنه وقف على كلمة لم يتمّ المعنى عندها لشدة 
+
+42
+00:04:02,950 --> 00:04:07,470
+تعلقها بما بعدها لفظًا ومعنى فيسمى هذا الوقف وقف
+
+43
+00:04:07,470 --> 00:04:13,480
+قبيح وقفنا عند كلمة فآمنوا واستكبرتم يسمى هذا الوقف
+
+44
+00:04:13,480 --> 00:04:18,020
+وقف كافي تمّ المعنى عنده يتعلق بما بعده في المعنى 
+
+45
+00:04:18,020 --> 00:04:23,680
+دون اللفظ ولكن أخذنا احنا همزة الوصل واستكبرتم هي 
+
+46
+00:04:23,680 --> 00:04:28,460
+همزة .. همزة إيه؟ همزة همزة وصل لماذا؟ لأنها ماضي
+
+47
+00:04:28,460 --> 00:04:34,680
+.. ماضي السداسي ماضي الفعل السداسي همزة الوصل تقع
+
+48
+00:04:34,680 --> 00:04:39,560
+طبعًا في الأفعال وتقع في الأسماء وتقع في الحروف
+
+49
+00:04:39,560 --> 00:04:43,680
+وتعريف همزة الوصل هي همزة زائدة عن بنية الكلمة 
+
+50
+00:04:43,680 --> 00:04:48,980
+تلحق أول أسماء أو الأفعال أو الحروف تثبت إذا بدأنا
+
+51
+00:04:48,980 --> 00:04:54,620
+بها الكلام وتسقط إذا وصلت بما قبلها فهنا يعني لو
+
+52
+00:04:54,620 --> 00:05:00,040
+بدأنا بها الكلام قلنا استكبرتم نلفظ الهمزة وبتكون 
+
+53
+00:05:00,040 --> 00:05:03,820
+طبعًا استكبرتم مكسورة لأن الحرف الثالث .. الحرف 
+
+54
+00:05:03,820 --> 00:05:09,980
+الثالث هذا مفتوح أما لو قلنا مثلًا واستكبرتم تسقط
+
+55
+00:05:09,980 --> 00:05:15,100
+همزة الوصل إذا لماذا هذه همزة وصل؟ لأنها ماضي
+
+56
+00:05:15,100 --> 00:05:19,940
+السداسي وفي كذلك عندنا ماضي الخماسي ماذا يعني ماضي
+
+57
+00:05:19,940 --> 00:05:26,310
+الخماسي؟ مثل مثلًا انطلاقة أو مثلًا ابتغى همزة وهمزة
+
+58
+00:05:26,310 --> 00:05:31,610
+وصل وأمر الثلاثي والخماسي والسداسي همزة وهمزة 
+
+59
+00:05:31,610 --> 00:05:37,650
+وصل مثل اضرب نقرأها واضرب لهم مثلًا كذلك انطلقوا
+
+60
+00:05:37,650 --> 00:05:42,890
+همزة وهمزة وصل لأنه يعني أمر الخماسي استغفر لهم 
+
+61
+00:05:42,890 --> 00:05:47,750
+الهمزة وهمزة وصل لأنها يعني أمر السداسي أما 
+
+62
+00:05:47,750 --> 00:05:50,470
+بالنسبة للأسماء فهمزة والوصل الموجودة في الأسماء
+
+63
+00:05:50,850 --> 00:05:55,230
+أما أن تكون قياسية أو تكون سماعية القياسية مثل
+
+64
+00:05:55,230 --> 00:05:58,470
+يعني اللي هو مصدر الخماسي والسداسي وهو المفعول
+
+65
+00:05:58,470 --> 00:06:04,810
+المطلق استغفار انطلاق ابتغاء هذه كلها همزة همزة
+
+66
+00:06:04,810 --> 00:06:09,650
+وصل لأنها أسماء وهمزة تكون مكسورة وكذلك في عندنا
+
+67
+00:06:09,650 --> 00:06:15,450
+الأسماء السماعية سبع كلمات ابن ابن اثنان اثنتان 
+
+68
+00:06:15,450 --> 00:06:22,430
+امرأ امرأة واسمهنا كمان إن الله لا يهدي القوم
+
+69
+00:06:22,430 --> 00:06:29,590
+الظالمين وقفنا عندها يسمى أيضًا وقف تام أو لا هنا
+
+70
+00:06:29,590 --> 00:06:34,710
+وقف كافي كافي لأن تمّ المعنى عنده لكنه يتعلق بما 
+
+71
+00:06:34,710 --> 00:06:39,070
+بعده في المعنى دون اللفظ الآن المعنى كله هنا لم
+
+72
+00:06:39,070 --> 00:06:43,400
+ينتهي اتكلم عن الكفار وقال الذين كفر .. إذا كل
+
+73
+00:06:43,400 --> 00:06:48,360
+الكلام متواصل في المعنى لكننا وقفنا على الكلمة تمّ
+
+74
+00:06:48,360 --> 00:06:52,820
+المعنى عندها تتعلق بالمعنى دون اللفظ لو قلنا هنا
+
+75
+00:06:52,820 --> 00:06:58,920
+مثلًا ما معنى التعلق اللفظي التعلق اللفظي هو التعلق
+
+76
+00:06:58,920 --> 00:07:03,460
+الإعرابي في الإعراب لأنه وقال الذين كفروا ليس لها
+
+77
+00:07:03,460 --> 00:07:07,520
+علاقة إعرابية مع قوله إن الله لا يهدي القوم
+
+78
+00:07:07,520 --> 00:07:10,940
+الظالمين يعني ليست صفة ولا حال ولا تمييز ولا معطوف
+
+79
+00:07:10,940 --> 00:07:15,040
+عليها لا شيء إذا العلاقة هنا فيش علاقة إعرابية
+
+80
+00:07:15,040 --> 00:07:21,860
+الآية الثانية تفضل اقرأ وقال الذين كفروا للذين
+
+81
+00:07:21,860 --> 00:07:24,860
+آمنوا لو كان خيرًا
+
+82
+00:07:38,210 --> 00:07:44,210
+أحسن هنا وقال الذين كفروا للذين آمنوا لو كان خيرًا
+
+83
+00:07:44,210 --> 00:07:50,790
+ما سبقونا إليه هنا الوقف على إليه يسمى أيضًا وقف 
+
+84
+00:07:50,790 --> 00:07:54,170
+كافي وحلاظ أنه كثير جدًا الوقف الكافي موجود في
+
+85
+00:07:54,170 --> 00:07:59,110
+القرآن لأنه يعني الآيات القرانية لما نزلت نزلت 
+
+86
+00:07:59,110 --> 00:08:02,550
+دفعات دفعات يعني مجموعة من الآيات أو فيها قصص يعني 
+
+87
+00:08:02,550 --> 00:08:07,090
+لو كانت القصة واحدة موجودة في العشر آيات كلهم دفعة
+
+88
+00:08:07,090 --> 00:08:10,950
+واحدة تتكلم على موضوع معين هذا في المعنى واحد لكن
+
+89
+00:08:10,950 --> 00:08:16,320
+ممكن مافيش علاقة عربية بينها هنا لو قلنا الوقف عليه
+
+90
+00:08:16,320 --> 00:08:22,220
+يسمى وقف كافي وقال الذين كفروا للذين للذين أخذنا
+
+91
+00:08:22,220 --> 00:08:27,160
+أيضًا الذين الذين نفسها همزة الوصل في قلة التعريف
+
+92
+00:08:27,160 --> 00:08:31,380
+يعني يسمى هذا أن همزة الوصل في الحروف أخذناها سابقًا
+
+93
+00:08:31,940 --> 00:08:36,160
+ما هي الحروف التي همزتها همزة وصل بس قلة التعريف
+
+94
+00:08:36,160 --> 00:08:42,240
+أما إليه إلى أ ليست همزة همزة وصل بل هي قطعة أما
+
+95
+00:08:42,240 --> 00:08:49,180
+بالنسبة للذين فهمزة همزة وصل فإذا دخلت لام الجر
+
+96
+00:08:49,180 --> 00:08:56,340
+على الاسم المعرف بال تُسقط همزة الوصل لفظًا لفظًا و
+
+97
+00:08:56,340 --> 00:09:03,110
+كتابة وخطًّا هذه ننظر هنا مثلًا قوله وقال الذين
+
+98
+00:09:03,110 --> 00:09:08,530
+كفروا للذين هي أصلًا الذين فإذا دخلت عليها همزة أو
+
+99
+00:09:08,530 --> 00:09:14,050
+لامَة لام الجار بتصير للذين سقطت الهمزة الواصل خطًّا
+
+100
+00:09:14,050 --> 00:09:20,230
+وسقطت لفظًا لكن الذين التي عندها وقال الذين هي 
+
+101
+00:09:20,230 --> 00:09:28,160
+كما موجودة لو وصلت وقلنا وقال الذين وقال الذين لا
+
+102
+00:09:28,160 --> 00:09:33,260
+نقول وقال الذين إذا نقول وقال الذين همزة الوصل 
+
+103
+00:09:33,260 --> 00:09:39,200
+هنا تسقط ونقول وقال الذين كفروا للذين دخلت اللام
+
+104
+00:09:39,200 --> 00:09:43,660
+الجار على الاسم المعرف بال تُسقط همزة الوصل لفظًا
+
+105
+00:09:43,660 --> 00:09:49,280
+وخطًّا وقال الذين كفروا للذين آمنوا لو كان خيرًا ما 
+
+106
+00:09:49,280 --> 00:09:56,220
+سبقونا إليه هنا إليه من الحروف حرف لكنه همزة و
+
+107
+00:09:56,220 --> 00:10:00,930
+همزة قطع لأنه ليس التعريف ولكن الوقف اللي علق إليه
+
+108
+00:10:00,930 --> 00:10:06,750
+يسمى وقف كافٍ تمّ المعنى عندها تتعلق بما بعدها في 
+
+109
+00:10:06,750 --> 00:10:12,650
+المعنى دون اللفظ وإذ لم يهتدوا به فسيقولون هذا إفك 
+
+110
+00:10:12,650 --> 00:10:17,870
+قديم ما معنى إفك قديم الإفك الكذب المفترق يعني
+
+111
+00:10:17,870 --> 00:10:22,630
+افترق قديم وسابق وهكذا طيب واقرأ الآية اللي
+
+112
+00:10:22,630 --> 00:10:22,930
+بعدها
+
+113
+00:10:42,000 --> 00:10:49,100
+أحسن هنا في قوله ومن قبله الآن بدأنا بدأنا اسم 
+
+114
+00:10:49,100 --> 00:10:53,200
+الابتداء الابتداء هو الشروع في القراءة هل بدأنا
+
+115
+00:10:53,200 --> 00:10:59,490
+بعد قطع أم بعد وقف بعد قطع .. بعد قطع أم بعد وقف؟ 
+
+116
+00:10:59,490 --> 00:11:03,970
+هو بعد وقف لأ بعد وقف لأننا وقفنا عليها إفك قديم
+
+117
+00:11:03,970 --> 00:11:08,590
+وقفنا حتى أخذ نفس ثم بدأنا ومن قبله كتاب موسى إذا
+
+118
+00:11:08,590 --> 00:11:13,150
+ابتداء بعد وقف ما هو حكم البسملة إذا ابتدأنا بعد
+
+119
+00:11:13,150 --> 00:11:17,750
+وقف البسملة والاستعاذة لا يؤتى بالبسملة ولا
+
+120
+00:11:17,750 --> 00:11:21,670
+بالاستعاذة إذا كانت الابتداء بعد وقف أما إذا كان
+
+121
+00:11:21,670 --> 00:11:26,780
+الابتداء بعد قطع فتستحب الاستعادة والبسملة إلا إذا 
+
+122
+00:11:26,780 --> 00:11:31,720
+كان من أول صورة جديدة فتستحب الاستعاذة وتُجيب
+
+123
+00:11:31,720 --> 00:11:39,120
+البسملة إذا قرأناها من صورة جديدة نعم ومن قبله كتاب
+
+124
+00:11:39,120 --> 00:11:45,380
+موسى إمامًا ورحمة هنا الوقف اللي على قوله ورحمة
+
+125
+00:11:45,380 --> 00:11:48,940
+أيضًا وقف كافي لأن الكلام كله بتتعلق على موسى 
+
+126
+00:11:48,940 --> 00:11:54,600
+والكتاب اللي معه سيدنا موسى وهذا كتاب مصدق لسانًا
+
+127
+00:11:54,600 --> 00:11:59,670
+عربيًا لينذر الذين ظلموا وبشرى للمحسنين كذلك
+
+128
+00:11:59,670 --> 00:12:05,010
+المحسنين هي أصلها بشرى للمحسنين لام مجرورة دخلت على 
+
+129
+00:12:05,010 --> 00:12:09,830
+الاسم المعرف بال فصارت للمحسنين سقطت همزة الوصل
+
+130
+00:12:09,830 --> 00:12:16,170
+لفظًا وخطًّا اقرأ أولئك 
+
+131
+00:12:29,080 --> 00:12:38,840
+أولئك أصحاب الجنة خالدين فيها جزاء
+
+132
+00:12:38,840 --> 00:12:44,560
+بما كانوا  أحسن طبعًا أنت وقفت على خالدين فيها ليست 
+
+133
+00:12:44,560 --> 00:12:49,960
+محلًّا للوقف لكن وقفت وقفًا إضطراريًا ويحسن بك أنك 
+
+134
+00:12:49,960 --> 00:12:54,460
+أعدت الكلمة التي وقفت عندها فقلت خالدين فيها 
+
+135
+00:12:54,460 --> 00:13:02,060
+جزاء بما كانوا يعملون الوقف على أو البداية في هنا
+
+136
+00:13:02,060 --> 00:13:06,260
+إن الذين قالوا ربنا الله ثم استقاموا كلام جديد يعني 
+
+137
+00:13:06,260 --> 00:13:11,960
+ليس من السابق كلام جديد جدًا وبالتالي بدأنا بكلام
+
+138
+00:13:11,960 --> 00:13:19,500
+جديد بعد وقف ويسمى الوقف اللي علاق للمحسنين وقف
+
+139
+00:13:19,500 --> 00:13:24,660
+تام تمّ المعنى عنده لا يتعلق بما بعده لا لفظة ولا
+
+140
+00:13:24,660 --> 00:13:31,120
+معنى، إذا هناك وقف تام ما هو رمز الوقف التام؟
+
+141
+00:13:31,120 --> 00:13:38,050
+الوقف التام رمزه قلقلق و الوقف الكافي رمزه صلاة
+
+142
+00:13:38,050 --> 00:13:42,650
+أو جيم و جيم أشد كفاية من صلاة لكنها لا توضع على
+
+143
+00:13:42,650 --> 00:13:46,470
+رؤوس الآيات يعني هنا للمحسنين الوقف الذي عليها
+
+144
+00:13:46,470 --> 00:13:53,610
+يسمى وقف تام الأصل أن نضع عليه قلق لكنها لأنها رأس
+
+145
+00:13:53,610 --> 00:13:57,390
+آية لا نضع عليها قلق لأن الوقف على رأس الآية سنة
+
+146
+00:13:57,390 --> 00:14:03,430
+أين توضع هذه الرموز قلق و صلاة و جيم و لا توضع إذا
+
+147
+00:14:03,430 --> 00:14:07,970
+كانت في أثناء الآية توضع هذه العلامات صلى معناها 
+
+148
+00:14:07,970 --> 00:14:12,670
+الوصل أولى وقلى الوقف أولى يعني يجب الوقف و الوصل
+
+149
+00:14:12,670 --> 00:14:17,550
+و الوصل أولى في صلى أو يجب الوقف و الوصل و الوقف 
+
+150
+00:14:17,550 --> 00:14:22,910
+أولى في قلى قلى وقف أو رمز الوقف التام و صلى رمز
+
+151
+00:14:22,910 --> 00:14:27,290
+الوقف الكافي و كذلك جيم جواز الوجهين الوقف و الوصل
+
+152
+00:14:27,290 --> 00:14:33,480
+في رمز الوقف الكافي في قول هنا مثلا يحزنون أيضا
+
+153
+00:14:33,480 --> 00:14:39,720
+يسمى وقف كافي تم المعنى عنده يتعلق بما بعده في
+
+154
+00:14:39,720 --> 00:14:44,000
+المعنى دون اللفظ أولئك أصحاب الجنة خالدين فيها
+
+155
+00:14:44,000 --> 00:14:50,940
+جزاء بما كانوا يعملون وقفنا على كلمة يعملون الوقف
+
+156
+00:14:50,940 --> 00:14:56,400
+اللي هنا يسمى وقف تم لماذا؟ لأن تم المعنى عنده لا
+
+157
+00:14:56,400 --> 00:15:00,960
+يتعلق بما بعده لا لفظ ولا معنى لأن الكلام الذي
+
+158
+00:15:00,960 --> 00:15:06,420
+بعده هو ووصينا الإنسان بوالديه إحسانا يعني كلام
+
+159
+00:15:06,420 --> 00:15:11,060
+جديد يتكلم على بر الوالدين الآن الآيات كلها التي
+
+160
+00:15:11,060 --> 00:15:14,840
+سوف تأتي فيها تتكلم عن الوالدين إذا هي معناها كل
+
+161
+00:15:14,840 --> 00:15:22,340
+واحد اقرأ الآية دي ووصينا الإنسان بوالديه إحسانا
+
+162
+00:15:22,340 --> 00:15:33,250
+حملته أمه كرها ووضعته كرها وحمله وفصاله ثلاثون شهرا 
+
+163
+00:15:33,250 --> 00:15:38,410
+لو وقفت على كلمة إحسانة اسمه وقف كافي نقول مثلا وصينا
+
+164
+00:15:38,410 --> 00:15:46,050
+الإنسان بوالديه إحسانا حملته أمه كرها ووضعته كرها
+
+165
+00:15:46,050 --> 00:15:50,470
+هنا وقف يعني يسمى وقف كافي تم المعنى عنده يتعلق
+
+166
+00:15:50,470 --> 00:15:56,670
+بعده في المعنى دون اللفظ وحمله وفصاله ثلاثون شهرا
+
+167
+00:15:56,670 --> 00:16:00,290
+أيضا وقف كافي ما معنى حمله وفصاله
+
+168
+00:16:02,940 --> 00:16:08,020
+يعني مدة الحمل والفصال معناه الرضاعة ثلاثون شهرا
+
+169
+00:16:08,540 --> 00:16:13,100
+والثلاثون ربنا سبحانه وتعالى يقول وفصاله في عامين
+
+170
+00:16:13,100 --> 00:16:18,420
+يعني أربع وعشرين شهرا اللي هو فترة الرضاعة ويستدل
+
+171
+00:16:18,420 --> 00:16:22,820
+العلماء بهذه الآية على أن مدة أقصر مدة للحمل اللي
+
+172
+00:16:22,820 --> 00:16:27,560
+هو ستة أشهر فأربع وعشرين شهرا زائد ستة أشهر يكون
+
+173
+00:16:27,560 --> 00:16:31,720
+ثلاثون شهرا كما قال الله سبحانه وتعالى أكمل وحمله
+
+174
+00:16:31,720 --> 00:16:38,810
+وفصاله لأنه .. حتى يستقيم المعنى ثلاثون شهرا حتى
+
+175
+00:16:38,810 --> 00:16:46,430
+إذا بلغ أشدّه وبلغ أربعين سنة وقفت وقفا اضطراريا
+
+176
+00:16:46,430 --> 00:16:53,410
+أضيق النفس وبلغ أربعين سنة قال ربي أوزعني أن أشكر
+
+177
+00:16:53,410 --> 00:17:02,190
+ نعمتك التي أنعمت علي وعلى والدي وعلى والدي وأن
+
+178
+00:17:02,190 --> 00:17:13,420
+أعمل صالحا ترضاه وأصلحني في جُرَيِّتي إني توت إليك وإني
+
+179
+00:17:13,420 --> 00:17:19,370
+من المسلمين مساك الله خير في قوله أيضا آيات الـ أو
+
+180
+00:17:19,370 --> 00:17:23,090
+الوقف الذي وقفته سابقا إما أن يكون وقفا اضطراريا
+
+181
+00:17:23,090 --> 00:17:26,790
+بسبب ضيقة النفس وإما أن يكون وقفا كافيا لأنه يتكلم
+
+182
+00:17:26,790 --> 00:17:30,070
+على نفس الموضوع وهو بر الوالدين حتى الوقف الذي
+
+183
+00:17:30,070 --> 00:17:35,030
+وقفت عليه وإني من المسلمين يسمى وقف كافي تم المعنى
+
+184
+00:17:35,030 --> 00:17:38,850
+عنده يتعلق بالذي بعده في المعنى don't laugh لأنه
+
+185
+00:17:38,850 --> 00:17:44,570
+أولئك الذين نتقبلُ عنهم كلام يعني المتواصل مع
+
+186
+00:17:44,570 --> 00:18:03,620
+السابق اقرأ الآية التي تليها وعلى
+
+187
+00:18:03,620 --> 00:18:05,880
+الصدق الذين كانوا يوعدون
+
+188
+00:18:09,360 --> 00:18:14,060
+أحسن أولئك يعني عن الآيات السابقة تتكلم على بر
+
+189
+00:18:14,060 --> 00:18:19,740
+الوالدين أولئك الذين نتقبلُ عنهم أحسن ما عملوا
+
+190
+00:18:19,740 --> 00:18:26,920
+أحسن ما عملوا هنا الفعل أمر أو فعل أحسن رباعي
+
+191
+00:18:26,920 --> 00:18:32,820
+وبالتالي همزة و همزة قطع ولا همزة و همزة وصل همزة
+
+192
+00:18:32,820 --> 00:18:38,310
+و همزة قطع أحسن لأنه يعني أحسن أفعيل ماضي أو ماضي
+
+193
+00:18:38,310 --> 00:18:42,730
+الرباعي ماضي الرباعي وماضي الثلاثي همزة و همزة
+
+194
+00:18:42,730 --> 00:18:47,990
+قطع لكن أمر الثلاثي والخماسي والسلاسي همزة و
+
+195
+00:18:47,990 --> 00:18:51,990
+همزة وصل ماضي الخماسي والسلاسي همزة و همزة وصل
+
+196
+00:18:52,340 --> 00:18:58,600
+كلمة أحسنة ماضي رباعي لذلك همزته و همزة قطع أحسن
+
+197
+00:18:58,600 --> 00:19:04,440
+ما نعمل هو نتجاوز عن سيئاتهم في أصحاب الجنة أصحاب
+
+198
+00:19:04,440 --> 00:19:09,280
+الجنة يسمى الوقف وقف كافي تم المعنى عنده يتعلق
+
+199
+00:19:09,280 --> 00:19:12,120
+بالبعد في المعنى دون اللفظ لأن المعنى الذي بعده
+
+200
+00:19:12,120 --> 00:19:17,840
+وعد الصدق الذين كانوا يوعدون هنا أيضا كلمة الصدق
+
+201
+00:19:19,510 --> 00:19:24,750
+التعريف في الصدق هي همزة و همزة وصل نقول الصدق
+
+202
+00:19:24,750 --> 00:19:28,890
+ وعدة الصدق همزة و همزة وصل تثبت إذا بدأنا بها
+
+203
+00:19:28,890 --> 00:19:33,970
+الكلام يعني لو قلنا الصدق الحمزة تلفظ مفتوحة وإذا
+
+204
+00:19:33,970 --> 00:19:39,590
+وصلت نقول وعدة الصدق تسقط همزة الوصل طيب الذين
+
+205
+00:19:39,590 --> 00:19:44,570
+كانوا يوعدون الذي هو الذي قل التعريف التي فيها
+
+206
+00:19:44,570 --> 00:19:49,370
+أصلية في الكلمة يعني لا يصح هنا أن نقول D أو T
+
+207
+00:19:49,370 --> 00:19:54,220
+يعني نرفع قل التعريف زي مثلا صدق الصدق لا نقول دي
+
+208
+00:19:54,220 --> 00:19:59,200
+وتي والـذي والـذي بل هي في نفس الكلمة وتعامل معاملة
+
+209
+00:19:59,200 --> 00:20:03,760
+قل التعريف الحقيقية اقرأ طبعا الوقف هنا الوقف
+
+210
+00:20:03,760 --> 00:20:10,160
+عليه إما أن نعتبرها أو هنعتبرها وقف تم لأن تم 
+
+211
+00:20:10,160 --> 00:20:14,040
+المعنى عنده لا يتعلق بالذي بعده لا لفظ ولا معنى لأن
+
+212
+00:20:14,040 --> 00:20:18,320
+الكلام الذي بعده يتكلم على عقوق الوالدين الأول
+
+213
+00:20:18,320 --> 00:20:20,960
+بر الوالدين هنا عقوق الوالدين اقرأ والذي قال
+
+214
+00:20:20,960 --> 00:20:21,400
+لوالدين
+
+215
+00:20:25,630 --> 00:20:39,470
+أتعدّاني أن أخرج وقد خلت القرون من قبلي وهم 
+
+216
+00:20:39,470 --> 00:20:43,650
+يستغيثان بالله ويلك آمن 
+
+217
+00:20:46,860 --> 00:20:52,720
+إن وعد الله حق لو وصلتها .. لو وصلتها لأن المعنى
+
+218
+00:20:52,720 --> 00:20:57,200
+متواصلة في المعنى واللفظ وبالتالي بتكون .. يعني هو
+
+219
+00:20:57,200 --> 00:21:00,520
+أنت وقفت على وقف الحسن دلوقتي الوقف الحسن طبعا أن
+
+220
+00:21:00,520 --> 00:21:04,620
+يقف القارئ على كلمة قرآنية تم المعنى عندها تتعلق
+
+221
+00:21:04,620 --> 00:21:08,710
+بما بعدها في اللفظ والمعنى ويلك آمن إن وعد الله حق
+
+222
+00:21:08,710 --> 00:21:14,730
+ويلك
+
+223
+00:21:14,730 --> 00:21:24,130
+آمن إن وعد الله حق ويلك آمن إن وعد الله حق ويلك
+
+224
+00:21:24,130 --> 00:21:34,420
+آمن إن وعد الله حق ويلك آمن إن وعد الله حق أحسنتوا 
+
+225
+00:21:34,420 --> 00:21:38,580
+هنا أيضا أساطير الأولين وقفنا عليها وقف يسمى أيضا
+
+226
+00:21:38,580 --> 00:21:41,960
+وقف كافي تم المعنى عنده يتعلق بالذي بعده في المعنى
+
+227
+00:21:41,960 --> 00:21:45,980
+دون اللفظ لأن الذي بعده أولئك الذين حق عليهم الخول
+
+228
+00:21:45,980 --> 00:21:53,320
+هم السابقون لكن ما معنى أساطير الأولين؟ يعني هل هي 
+
+229
+00:21:53,320 --> 00:21:59,020
+بمعنى القصص؟ أساطير ليس بمعنى القصص القصة ممكن
+
+230
+00:21:59,020 --> 00:22:04,820
+تكون واقعية لكن الأساطير هي كلام خيالي مثل الخرافات
+
+231
+00:22:04,820 --> 00:22:09,560
+السابقة، خرافات السابقين، كان يقول مثلا أن الله في
+
+232
+00:22:09,560 --> 00:22:14,860
+واحد كذا، يعني أمور خيالية، فبالتالي هم يقولون أن
+
+233
+00:22:14,860 --> 00:22:19,080
+هذه أساطير الأولين بمعنى خرافات الأولين، خرافات
+
+234
+00:22:19,080 --> 00:22:22,580
+الناس السابقين، لأن الرسول عليه الصلاة والسلام لما
+
+235
+00:22:22,580 --> 00:22:26,010
+كان يتلو عليهم القرآن، فيها قصص قصص سيدنا موسى
+
+236
+00:22:26,010 --> 00:22:30,970
+وعيسى وآدم من هذه القصص القرآنية فهم يعني كانوا
+
+237
+00:22:30,970 --> 00:22:35,390
+يقولوا هذه القصص وخرافات أساطير السابقين فكانوا
+
+238
+00:22:35,390 --> 00:22:38,890
+يقولونها أساطير الأولين لكن القصة القرآنية لها
+
+239
+00:22:38,890 --> 00:22:43,670
+ميزة مميزات فهي قصص واقعية حدثت وليست خرافات سابقة
+
+240
+00:22:43,670 --> 00:22:46,390
+كما يتخيلها الكفار أكمل
+
+241
+00:22:49,170 --> 00:22:57,590
+أحق عليهم القور في أمم قد خلق من قبلهم من الجن
+
+242
+00:22:57,590 --> 00:23:06,210
+والإنس من الجن والإنس من الجن والإنس بس هنا وقف
+
+243
+00:23:06,210 --> 00:23:10,690
+يسمى .. يسمى وقف كافي تم المعنى عنده يتعلق بيوم
+
+244
+00:23:10,690 --> 00:23:16,510
+بعده في المعنى دون اللفظ وبعدين إنهم كانوا خاسرين
+
+245
+00:23:17,250 --> 00:23:22,090
+باقي الكلام اللي بيسموها الفاصلة ما معنى الفاصلة؟
+
+246
+00:23:22,090 --> 00:23:26,910
+هي ذيل الآية أو خاتمة الآية إنهم كانوا خاسرين مثلا
+
+247
+00:23:26,910 --> 00:23:30,950
+وكان الله غفور ورحيم إن الله عليهم الحكيم هذه تسمى
+
+248
+00:23:30,950 --> 00:23:36,410
+في القرآن التي هي فاصلة الآية هي ملخص الآية ولها
+
+249
+00:23:36,410 --> 00:23:41,620
+علاقة معنوية في الآية فهي يعني توجد إن الله غفور
+
+250
+00:23:41,620 --> 00:23:44,620
+ورحيم مثلا لأن الآيات تتكلم عن الرحمة إن الله
+
+251
+00:23:44,620 --> 00:23:48,520
+عزيز الحكيم لأن الآيات تتكلم عن العزة وعزة الله
+
+252
+00:23:48,520 --> 00:23:53,720
+سبحانه وتعالى إن الله لطيف بعباده لطيف التي هي من
+
+253
+00:23:53,720 --> 00:23:59,600
+الدقة وهي أنه يعني يلطف بهم وها كده أكمل
+
+254
+00:24:03,650 --> 00:24:12,970
+و لكل درجات مما عملوا و
+
+255
+00:24:12,970 --> 00:24:18,750
+ليوفيهم أعمالهم وهم لا يظلمون الوقف الذي مما
+
+256
+00:24:18,750 --> 00:24:23,290
+عملوا يسمى أيضا وقف كافي تم المعنى عنده اتعلق في
+
+257
+00:24:23,290 --> 00:24:28,170
+المعنى دون اللفظ ولا يظلمون أيضا يسمى وقف كافي
+
+258
+00:24:28,170 --> 00:24:30,090
+أكمل
+
+259
+00:24:37,350 --> 00:24:47,190
+لأ في حياتكم الدنيا واستمتعتم بها
+
+260
+00:24:47,190 --> 00:24:51,710
+فاليوم تجزون عذابا لهوني بما كنتم تستكبرون في
+
+261
+00:24:51,710 --> 00:24:58,170
+الأرض أنا الآن ضاقت نفسي نفسي ضاقت اه انتهى لكن يسمى
+
+262
+00:24:58,170 --> 00:25:03,630
+وقف إيش؟ وقف إقتراري ماذا أفعل؟ أرجع كلمة أو
+
+263
+00:25:03,630 --> 00:25:08,990
+كلمتين يعني أقول مثلا بما كنتم تستكبرون في الأرض
+
+264
+00:25:08,990 --> 00:25:14,810
+بغير الحق وبما كنتم تفسقون وقفنا على كلمة إيش؟
+
+265
+00:25:14,810 --> 00:25:20,910
+تفسقون لو نظرنا إلى كلمة واستمتعتم بها هذه
+
+266
+00:25:20,910 --> 00:25:25,370
+استمتعتم بها ما هي همزة الوصل هنا؟ همزة الوصل في
+
+267
+00:25:25,370 --> 00:25:30,930
+أي فعل؟ اه واستمتعتم استمتع فعل ماضي سلاسي
+
+268
+00:25:30,930 --> 00:25:35,250
+فهمزته همزة وصل ماضي السلاسي وماضي الخماسي همزة و
+
+269
+00:25:35,250 --> 00:25:40,000
+همزة وصل أمر الثلاثي والخماسي والسداسي همزة وهمزة
+
+270
+00:25:40,000 --> 00:25:46,800
+وصل ماضي الرباعي والثلاثي زي أقبل مثلا أحسنة أقطع
+
+271
+00:25:46,800 --> 00:25:53,960
+لكن ماضي الخماسي والسداسي وصل أمر الثلاثي 
+
+272
+00:25:53,960 --> 00:25:59,100
+والخماسي والسداسي الثلاثي مثل ضربوا ضرب لهم مثلا 
+
+273
+00:25:59,100 --> 00:26:04,680
+الخماسي مثل انطلقوا السداسي مثل استغفر لهم فهذه
+
+274
+00:26:04,680 --> 00:26:10,640
+همزته همزة وصل هذه ماضي السداسي واستمتعتم بها
+
+275
+00:26:10,640 --> 00:26:16,200
+همزتها همزة وصل الهوني عذاب الهوني اللام أو الهمزة
+
+276
+00:26:16,200 --> 00:26:20,860
+في الهوني همزته همزة .. وصل لأنه في قلّة تعريف
+
+277
+00:26:20,860 --> 00:26:28,440
+الوقف الآن على قوله وبما كنتم تفسقون بعدها واذكر
+
+278
+00:26:28,440 --> 00:26:33,140
+أخاعد إذ أنظر قومه بالأحقاف كلام جديد إذا مدام
+
+279
+00:26:33,140 --> 00:26:37,020
+كلام جديد إذا انتهى المعنى السابق وبدأنا بمعنى 
+
+280
+00:26:37,020 --> 00:26:41,700
+جديد إذا الوقف الذي على تفسقون هو وقف تم .. تم 
+
+281
+00:26:41,700 --> 00:26:46,890
+المعنى عنده لا يتعلق بما بعده لا لفظًا ولا معنى الآن
+
+282
+00:26:46,890 --> 00:26:53,430
+الآيات تتحدث عن قصة قبيلة عاد الذين أرسل الله عز و 
+
+283
+00:26:53,430 --> 00:26:58,290
+جل إليهم سيدنا هود فيقول تعالى اقرأ واذكر آخر عاد
+
+284
+00:26:58,290 --> 00:27:06,750
+إذ أنذر قومه بالأحقاف وقد خلت النذرون بين يديه 
+
+285
+00:27:06,750 --> 00:27:14,390
+ومن خلفه من بين يديه ومن خلفه أن لا تعبدوا
+
+286
+00:27:26,100 --> 00:27:33,320
+أحسن هنا كلمة وذكر همزتها وهمزتها إيش هنا؟ وصل لأنها
+
+287
+00:27:33,320 --> 00:27:40,100
+أمر الثلاث مثل وضرب وذكر وذكر أخي عاد أخي عاد من
+
+288
+00:27:40,100 --> 00:27:46,810
+هو أخي عاد؟ الذي هو سيدنا هود سيدنا هود يعني النبي
+
+289
+00:27:46,810 --> 00:27:51,450
+الذي أرسله إلى عاد عاد قبيلة يعني نسبة .. نسبة إلى
+
+290
+00:27:51,450 --> 00:27:56,750
+عاد الجد أحد أجدادهم عاد الأولى اسم القبيلة فصار
+
+291
+00:27:56,750 --> 00:28:04,610
+يعني اذكر يا محمد لقومك قصة أخي عاد وهو سيدنا هود
+
+292
+00:28:04,610 --> 00:28:09,170
+عليه الصلاة والسلام إذ أنذر قومه بالأحقاف ما معنى 
+
+293
+00:28:09,170 --> 00:28:15,320
+الأحقاف هنا؟ الأحقاف هي صحراء الأحقاف وهي في اللغة
+
+294
+00:28:15,320 --> 00:28:20,000
+هي الأرض المتموجة بفعل الريح يعني هناك في الأرض في
+
+295
+00:28:20,000 --> 00:28:24,520
+الصحراء بفعل الرياح تضرب التراب والرمال الخفيفة
+
+296
+00:28:24,520 --> 00:28:29,460
+فتجعلها متموجة فهذه اسمها الأحقاف فأطلقت يعني أرض
+
+297
+00:28:29,460 --> 00:28:35,540
+الرمال المتموجة فصارت الأحقاف فهي قوم قبيلة عاد
+
+298
+00:28:35,870 --> 00:28:40,650
+كانوا يسكنون في صحراء الأحقاف الموجودة في منطقة
+
+299
+00:28:40,650 --> 00:28:45,490
+حضرموت في جنوب الجزيرة العربية وقد خلت النذر من
+
+300
+00:28:45,490 --> 00:28:52,770
+بين يديه ومن خلفه أن لا تعبدوا إلا الله إني أخاف 
+
+301
+00:28:52,770 --> 00:28:59,700
+عليكم عذاب يوم عظيم أيضًا على عظيم يسمى وقف أيضًا
+
+302
+00:28:59,700 --> 00:29:05,460
+كافي لأن القصة قالوا أجيئتنا إذا القصة لم تنتهي
+
+303
+00:29:05,460 --> 00:29:09,880
+وقف تم المعنى عندها يتعلق بما بعدها في المعنى لأن
+
+304
+00:29:09,880 --> 00:29:15,410
+المعنى لم ينتهي قصة سيدنا هود لكنها ليس لها علاقة
+
+305
+00:29:15,410 --> 00:29:18,730
+إعرابية مع ما بعدها إذا إن تتعلق بالمعنى دون
+
+306
+00:29:18,730 --> 00:29:25,310
+اللفظ لأن قوله قالوا أجيئتنا لتأفكنا ليست حال ولا
+
+307
+00:29:25,310 --> 00:29:30,270
+تمييز ولا صفة لما سبقت فهي كلام جديد اقرأ قالوا
+
+308
+00:29:30,270 --> 00:29:37,800
+قالوا أجيئتنا لتأفكنا عن آلهتنا عَنْ آلِهَتِنَا
+
+309
+00:29:37,800 --> 00:29:42,460
+فاتنا بما جعلنا إن كنت من 
+
+310
+00:29:42,460 --> 00:29:48,180
+الصَّادِقِينَ أحسن أيضًا الصادقين يسمى وقف كافي تم
+
+311
+00:29:48,180 --> 00:29:52,520
+المعنى عنده لأنه بتعلق باللي بعده في المعنى قال
+
+312
+00:29:52,520 --> 00:29:56,440
+إنما العلم عند الله إذا الكلام متواصل قالوا أجيئتنا
+
+313
+00:29:56,440 --> 00:30:00,480
+لتأفكنا .. ما معنى لتأفكنا؟ من الإفك والافتراض،
+
+314
+00:30:00,480 --> 00:30:04,500
+يعني تفتري علينا وتخرجنا عن آلهتنا، وتضحك علينا
+
+315
+00:30:04,500 --> 00:30:08,260
+وتقول أن هناك آلهة لتأفكنا عن آلهتنا وتصرفنا عن 
+
+316
+00:30:08,260 --> 00:30:13,540
+آلهتنا فاتنا بما تعيدنا إن كنت من الصادقين طبعًا
+
+317
+00:30:13,540 --> 00:30:18,600
+تهدده هو هذا مجادلة ما بين سيدنا هود وما بين قومه
+
+318
+00:30:18,600 --> 00:30:23,360
+يعني ما من رسول أرسل إلى قومه إلا وقال لقومه يا
+
+319
+00:30:23,360 --> 00:30:28,540
+قوم اعبدوا الله ما لكم من إله غيره لكن القوم قسموا
+
+320
+00:30:28,540 --> 00:30:32,960
+إلى قسمين في كل الأنبياء منهم من يؤمن وهم قلة وقليل
+
+321
+00:30:32,960 --> 00:30:37,180
+من عباده الشكور والكثير يبقى على كفره فالله سبحانه
+
+322
+00:30:37,180 --> 00:30:42,100
+وتعالى يختم القصص بأن يهلك الكافرين وينجي المؤمنين
+
+323
+00:30:42,100 --> 00:30:45,980
+وينصر المؤمنين في نهاية المطاف لكن الإبتلاءات التي
+
+324
+00:30:45,980 --> 00:30:50,920
+يبتلى بها الأنبياء لأن الرسول يقول لنا أشد الناس
+
+325
+00:30:50,920 --> 00:30:56,020
+بلاء الأنبياء ثم الأمثل فالأمثل حتى لا يقول إن
+
+326
+00:30:56,020 --> 00:31:01,560
+النبي لم يُبتلى  لأ الإبتلاء يصيب الأنبياء ويصيب
+
+327
+00:31:01,560 --> 00:31:05,440
+الدعاء إلى الله سبحانه وتعالى ولكن في نهاية المطاف
+
+328
+00:31:05,440 --> 00:31:09,780
+يعزوا الله عز وجل أهل الحق وينصروا الحق ويهزم
+
+329
+00:31:09,780 --> 00:31:15,040
+الباطل لكن أهل الحق عليهم أن يثبتوا ويصبروا
+
+330
+00:31:15,040 --> 00:31:20,620
+ويستمروا على جهادهم إلى أن ينصرهم الله عز وجل ها
+
+331
+00:31:20,620 --> 00:31:24,830
+هو النبي عليه الصلاة والسلام مكث عشر سنة .. ثلاث
+
+332
+00:31:24,830 --> 00:31:29,430
+عشر سنة في مكة المكرمة يدعو إلى الله وأخرج وأوذى
+
+333
+00:31:29,430 --> 00:31:33,630
+من .. أخرج من برنامج ذاته بعد الإيذاء له ولأتباعه
+
+334
+00:31:33,630 --> 00:31:37,450
+ثم مكة في الجزيرة العربية أو في المدينة .. في
+
+335
+00:31:37,450 --> 00:31:41,410
+المدينة المنورة بعد الهجرة يعني سبع أو ثمان سنوات
+
+336
+00:31:41,410 --> 00:31:48,230
+كله لم ينتصرمتى النصر؟ نصل خلال نصر واحد أو انتصار
+
+337
+00:31:48,230 --> 00:31:51,630
+سريعًا عندما فتحت مكة بدأت النصر ودخلت 
+
+338
+00:31:51,630 --> 00:31:54,990
+الجزيرة العربية في الإسلام إذا في نهاية الوقت
+
+339
+00:31:54,990 --> 00:31:58,150
+اكتمل النصر والنصر السهل الله عز وجل يسخره
+
+340
+00:31:58,150 --> 00:32:02,410
+للمؤمنين لكن لابد أن يكون هناك ابتلاء الابتلاءات
+
+341
+00:32:02,410 --> 00:32:07,730
+سنة من سنة الله عز وجل يبتلى به الصادق ويبتلى به
+
+342
+00:32:07,730 --> 00:32:12,530
+الصالح حتى يثبت على إيمانه ليقيم الحجة عليه هل ثبتت
+
+343
+00:32:12,530 --> 00:32:22,410
+أم لم تثبت أكمل قال إنما العلم عند الله وأبلغكم ما
+
+344
+00:32:22,410 --> 00:32:31,040
+أرسلت به ولكني أراكم قومًا تجهلون أيضًا الوقف على 
+
+345
+00:32:31,040 --> 00:32:36,860
+تجهلون يسمى أيضًا وقف كافي لأن تم المعنى عنده يتعلق
+
+346
+00:32:36,860 --> 00:32:41,900
+بما بعده في المعنى دون اللفظ هنا نقرأ الآية 
+
+347
+00:32:41,900 --> 00:32:46,840
+الأخيرة دي فلما رأوه عارضًا
+
+348
+00:32:46,840 --> 00:32:55,200
+مستقبل أوديتهم قالوا هذا عارض منطرنا بل هو ما
+
+349
+00:32:55,200 --> 00:33:07,090
+استعجلتم به بل هو مستأجل به ريح فيها عذاب أليم طبعًا
+
+350
+00:33:07,090 --> 00:33:11,850
+استعجلتم ما استعجلتم به .. استعجلتم يعني همزة همزة 
+
+351
+00:33:11,850 --> 00:33:17,870
+بصل لأنه ماضي السلازي استعجلتم همزة همزة بصل ريحهم
+
+352
+00:33:17,870 --> 00:33:23,430
+فيها عذاب أليم هنا أيضًا الوقف يسمى وقف كافي لأن
+
+353
+00:33:23,430 --> 00:33:27,410
+الكلام اللي بعده تدمر كل شيء إذا الريح تدمر إذا
+
+354
+00:33:27,410 --> 00:33:36,970
+المعنى متواصل أكمل تدمر كل شيء تدمر كل شيء بأمر
+
+355
+00:33:36,970 --> 00:33:43,470
+ربها، فأصبحوا لا يُرى إلا مساكن كذلك 
+
+356
+00:33:45,250 --> 00:33:52,970
+إلا مساكنهم كذلك نجزل قوم المجرمين هنا أيضًا يعني
+
+357
+00:33:52,970 --> 00:33:55,830
+كذلك نجزل .. لو بدأت من .. لأن أنا وقفت عدة إلا
+
+358
+00:33:55,830 --> 00:34:01,110
+مساكنهم كذلك .. كذلك نجزل .. نجزل قوم المجرمين
+
+359
+00:34:01,110 --> 00:34:05,430
+يعني بيكون أعادت الكلمة اللي وقفت عليها بعد ذلك
+
+360
+00:34:05,430 --> 00:34:08,190
+بيأتي كلام ولا قد مكنناهم أيضًا أكمل
+
+361
+00:34:29,540 --> 00:34:39,420
+فما أغنى عنهم سمعهم ولا أبصارهم ولا أفئدتهم
+
+362
+00:34:40,970 --> 00:34:52,310
+فما أغنى عنهم سمعهم ولا أبصارهم ولا أفئدتهم شيء إذ
+
+363
+00:34:52,310 --> 00:35:02,290
+كانوا يجحدون بآيات الله كانوا يجحدون بآيات الله
+
+364
+00:35:02,290 --> 00:35:09,430
+وحاق بهم ما كانوا به يستهزئون أيضًا الوقف هنا وقف 
+
+365
+00:35:09,430 --> 00:35:16,910
+إيه؟ وقف كافي و لقد أهلكنا ما حولكم من القرون
+
+366
+00:35:16,910 --> 00:35:23,450
+صرفنا الآيات لعلهم يرجعوا الله خير نكتفي بهذا 
+
+367
+00:35:23,450 --> 00:35:27,250
+القدر الآيات طبعًا نرى أن هناك كثير من الآيات الوقف
+
+368
+00:35:27,250 --> 00:35:31,850
+عليها وقف كافي لأن الآيات تأتي بمعنى دفعات من 
+
+369
+00:35:31,850 --> 00:35:34,210
+الآيات نكتفي بهذا القدر ونكمل إن شاء الله في 
+
+370
+00:35:34,210 --> 00:35:36,490
+اللقاء القادم بارك الله فيكم والسلام عليكم
diff --git a/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/uzGYZDqNdoY_raw.json b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/uzGYZDqNdoY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..74111f0239ab4fe3efe3be145b8ab936d6067ac7
--- /dev/null
+++ b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/uzGYZDqNdoY_raw.json
@@ -0,0 +1 @@
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{"start": 2329.88, "end": 2330.6, "word": " الإقتداء", "probability": 0.70947265625}, {"start": 2330.6, "end": 2331.02, "word": " برسول", "probability": 0.8726806640625}, {"start": 2331.02, "end": 2331.26, "word": " الله", "probability": 0.9248046875}, {"start": 2331.26, "end": 2331.56, "word": " صلى", "probability": 0.875244140625}, {"start": 2331.56, "end": 2331.66, "word": " الله", "probability": 0.96240234375}, {"start": 2331.66, "end": 2331.86, "word": " عليه", "probability": 0.76806640625}, {"start": 2331.86, "end": 2331.92, "word": " وسلم", "probability": 0.7435302734375}, {"start": 2331.92, "end": 2332.64, "word": " كدهوم", "probability": 0.73004150390625}, {"start": 2332.64, "end": 2333.22, "word": " بمحاضرة", "probability": 0.91875}, {"start": 2333.22, "end": 2333.8, "word": " واحدة", "probability": 0.9881184895833334}, {"start": 2333.8, "end": 2334.44, "word": " ناخدهم", "probability": 0.8018798828125}, {"start": 2334.44, "end": 2334.74, "word": " ونكون", "probability": 0.8642578125}, {"start": 2334.74, "end": 2335.0, "word": " بهذا", "probability": 0.955078125}, {"start": 2335.0, "end": 2335.28, "word": " الأمر", "probability": 0.962646484375}, {"start": 2335.28, "end": 2335.52, "word": " قد", "probability": 0.9638671875}, {"start": 2335.52, "end": 2335.96, "word": " أنهينا", "probability": 0.9149169921875}, {"start": 2335.96, "end": 2336.64, "word": " المنهج", "probability": 0.932373046875}, {"start": 2336.64, "end": 2337.0, "word": " بإذن", "probability": 0.9830322265625}, {"start": 2337.0, "end": 2337.2, "word": " الله", "probability": 0.96630859375}, {"start": 2337.2, "end": 2337.64, "word": " سبحانه", "probability": 0.9320068359375}, {"start": 2337.64, "end": 2337.92, "word": " وتعالى", "probability": 0.9534912109375}, {"start": 2337.92, "end": 2338.56, "word": " بارك", "probability": 0.8795572916666666}, {"start": 2338.56, "end": 2338.68, "word": " الله", "probability": 0.8486328125}, {"start": 2338.68, "end": 2338.92, "word": " فيكم", "probability": 0.96630859375}, {"start": 2338.92, "end": 2339.48, "word": " جميعا", "probability": 0.98193359375}, {"start": 2339.48, "end": 2339.86, "word": " وجزاكم", "probability": 0.773779296875}, {"start": 2339.86, "end": 2340.0, "word": " الله", "probability": 0.9755859375}, {"start": 2340.0, "end": 2340.32, "word": " خير", "probability": 0.989501953125}, {"start": 2340.32, "end": 2340.72, "word": " والسلام", "probability": 0.8186848958333334}, {"start": 2340.72, "end": 2341.06, "word": " عليكم", "probability": 0.923828125}, {"start": 2341.06, "end": 2341.42, "word": " ورحمة", "probability": 0.984619140625}, {"start": 2341.42, "end": 2341.72, "word": " الله", "probability": 0.9638671875}, {"start": 2341.72, "end": 2342.52, "word": " وبركاته", "probability": 0.97880859375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2343.59, "duration_after_vad": 2295.492499999998}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/xj9zkUePRdY.srt b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/xj9zkUePRdY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..87480a5c8c46988592ed35bfbc4784a268da76cd
--- /dev/null
+++ b/PL9fwy3NUQKwaIvb3amW8pzhbBL_vlNZyl/xj9zkUePRdY.srt
@@ -0,0 +1,1375 @@
+1
+00:00:20,160 --> 00:00:22,820
+السلام عليكم ورحمة الله وبركاته باسم الله الرحمن
+
+2
+00:00:22,820 --> 00:00:27,480
+الرحيم الحمد لله وصلاة والسلام على رسول الله وعلى 
+
+3
+00:00:27,480 --> 00:00:31,110
+آله وصحبه وسلم. أخذنا يا إخواننا الكرام في 
+
+4
+00:00:31,110 --> 00:00:35,330
+المحاضرات الماضية الوقف الاختياري، نقسمه إلى أربع
+
+5
+00:00:35,330 --> 00:00:39,070
+أقسام: الوقف التام، والوقف الكافي، والوقف الحسن، و
+
+6
+00:00:39,070 --> 00:00:43,450
+الوقف القبيح. ثم أخذنا موضوع القطع والإبتداء، ثم 
+
+7
+00:00:43,450 --> 00:00:48,270
+أخذنا السكت وقلنا أن هناك أربع سكتات واجبة عند الحفظ
+
+8
+00:00:48,270 --> 00:00:53,870
+وسكتتان جائزتان عنده أيضًا. اليوم إن شاء الله هناخد
+
+9
+00:00:53,870 --> 00:00:59,520
+موضوع اللي هو همزة الوصل وكيفية الإبتداء بها. معروف
+
+10
+00:00:59,520 --> 00:01:02,660
+يا إخواننا الكرام أن العرب لا تبدأ الكلام بساكن
+
+11
+00:01:02,660 --> 00:01:07,300
+ولا تقف على متحرك. هذه قاعدة عندهم معروفة أن لا 
+
+12
+00:01:07,300 --> 00:01:11,880
+يمكن أن تكون هناك كلمة ساكنة نبدأ بها ساكنة، ولا نقف 
+
+13
+00:01:11,880 --> 00:01:15,880
+على متحرك. ولكن أحيانًا بعض تصريفات الكلمة سواء كانت
+
+14
+00:01:15,880 --> 00:01:20,800
+الأمر أو المصدر، تحتاج إلى أن نبدأ بساكن. فعندئذٍ 
+
+15
+00:01:20,800 --> 00:01:26,540
+يؤتى بهمزة الوصل لكي نتوصل للابتداء بها بالساكن.
+
+16
+00:01:27,170 --> 00:01:33,750
+مثال ذلك كلمة ضربة. ضربة فعل ماضي ثلاثي ليس له همزة
+
+17
+00:01:33,750 --> 00:01:40,590
+وصل. الأمر منه اضرب، فاحتجنا إلى أن يكون هناك ساكن
+
+18
+00:01:40,590 --> 00:01:44,830
+اللي هو حرف الضاد ساكن في الأمر، لكن العرب لا تبدأ 
+
+19
+00:01:44,830 --> 00:01:48,990
+الكلام بساكن. عندئذٍ جيئة بالنسبة لتصريفات الكلمة 
+
+20
+00:01:48,990 --> 00:01:54,090
+بهمزة الوصل حتى نتوصل بها للابتداء بالسّاكن. إذا سبب 
+
+21
+00:01:54,090 --> 00:01:58,230
+تسمية همزة الوصل، بهمزة الوصل، لأنه يتوصل بها
+
+22
+00:01:58,230 --> 00:02:03,490
+للابتداء بالحرف الساكن، مثل كلمة ضربة. تصريف الأمر 
+
+23
+00:02:03,490 --> 00:02:09,150
+من ضربة اضرب، عشان نبدأ الكلمة بحرف ساكن. جيئة بهمزة 
+
+24
+00:02:09,150 --> 00:02:13,410
+الوصل عشان نقدر نقول اضرب لهم أو اضرب لهم مثلًا.
+
+25
+00:02:13,410 --> 00:02:18,670
+طبعًا إذا ابتدأنا بها الكلام نلفظ حرف الضاد ونعرف
+
+26
+00:02:18,670 --> 00:02:22,790
+أن همزة الوصل أصلاً هي زائدة عن بنية الكلمة. يُعطى 
+
+27
+00:02:22,790 --> 00:02:28,430
+بها عشان توصل للحرف أو للابتداء بالحرف الساكن. فنقول
+
+28
+00:02:28,430 --> 00:02:32,250
+اضرب، هي زائدة عن بنية الكلمة. بتلحق الأسماء والأفعال
+
+29
+00:02:32,250 --> 00:02:37,050
+والحروف. إذا ابتدأنا بها الكلام بنلفظها وتثبت
+
+30
+00:02:37,050 --> 00:02:43,110
+فنقول اضرب، لكن إذا وصلت هذه الكلمة بما قبلها عندئذٍ
+
+31
+00:02:43,110 --> 00:02:50,010
+تسقط همزة الوصل، مثل كلمة واضرب. واضرب همزة الوصل
+
+32
+00:02:50,010 --> 00:02:54,230
+بتاعة اضرب وصلت بالتي قبلها، اللي هو حرف الواو أو
+
+33
+00:02:54,230 --> 00:02:59,030
+مثلًا، فقول: نضرب عصاك اللحظة. نشوف هنا مثلًا تعريف 
+
+34
+00:02:59,030 --> 00:03:05,650
+لهمزة الوصل. من يعرف لنا همزة الوصل؟ هي همزة زائدة
+
+35
+00:03:05,650 --> 00:03:09,170
+عن بنية الكلمة، تلحق أول الأسماء والأفعال والحروف. 
+
+36
+00:03:09,170 --> 00:03:15,610
+تثبت عند الابتداء بها وتسقط عند الوصل. يا علي، احسن. يبقى 
+
+37
+00:03:15,610 --> 00:03:18,850
+هي همزة زائدة عن بنية الكلمة، تلحق الأسماء يعني
+
+38
+00:03:18,850 --> 00:03:22,870
+ممكن تكون في الأسماء والأفعال والحروف. تثبت وإذا 
+
+39
+00:03:22,870 --> 00:03:29,020
+ابتدأنا بها الكلام، مثل اضرب، استغفر، انطلق نلفظها 
+
+40
+00:03:29,020 --> 00:03:35,900
+وتسقط إذا وصلت بما قبلها، مثل واضرب، واستغفر، وانطلق. 
+
+41
+00:03:36,830 --> 00:03:41,050
+إذا هذه تعريفها. ما هو سبب سقوطها؟ يعني أحيانًا بيأتي 
+
+42
+00:03:41,050 --> 00:03:45,270
+سؤال: ما هو سبب سقوط همزة الوصل؟ سبب سقوطها لأن 
+
+43
+00:03:45,270 --> 00:03:49,630
+الحرف الساكن، مثل حرف الضاد في اضرب، الحرف الساكن
+
+44
+00:03:49,630 --> 00:03:56,050
+الذي في أول الكلمة قد اعتمد على حرف قبل، أو غير 
+
+45
+00:03:56,050 --> 00:04:01,450
+همزة الوصل، وهي حرف أصلي، مثل كلمة اضرب. اضرب هنا 
+
+46
+00:04:03,720 --> 00:04:07,300
+طبعًا جئنا بحرف الضاد الساكن عشان أو جئنا بالهمزة
+
+47
+00:04:07,300 --> 00:04:12,820
+الساكنة عشان نتوصل بها للإبتداء بالحرف الساكن تبع
+
+48
+00:04:12,820 --> 00:04:17,080
+اضرب. أما وقد اعتمد حرف الضاد الساكن على حرف أصلي 
+
+49
+00:04:17,080 --> 00:04:21,300
+قبل حرف الهمزة همزة الوصل، عندئذٍ لا حاجة بهمزة 
+
+50
+00:04:21,300 --> 00:04:25,420
+الوصل، فَتَسْقُطُ همزة الوصل. فبدل من أن نقول واضرب لهم 
+
+51
+00:04:25,420 --> 00:04:30,000
+نقول ايش؟ واضرب لهم. فتسقط همزة الوصل لأن حرف الضاد
+
+52
+00:04:30,000 --> 00:04:36,470
+الساكن قد اعتمد على حرف قبله. كذلك استغفر. استغفر 
+
+53
+00:04:36,470 --> 00:04:42,270
+يعني الهمزة همزة الوصل ساكنة. جئنا بهمزة 
+
+54
+00:04:42,270 --> 00:04:47,950
+الوصل حتى نتمكن من الابتداء بالحرف الساكن. إذا 
+
+55
+00:04:47,950 --> 00:04:53,710
+اعتمد الحرف الساكن على حرف أصلي، أثرنا الأصل وسقطت
+
+56
+00:04:53,710 --> 00:04:58,510
+الزائد. مثلًا لو قلنا واستغفر لهم أو قلنا استغفر
+
+57
+00:04:58,510 --> 00:05:02,110
+لهم. عندئذٍ تسقط الهمزة ويكون الحرف السين الساكن
+
+58
+00:05:02,110 --> 00:05:06,810
+قد يعتمد على الحرف الذي قبله. يعني لماذا أو ما هو
+
+59
+00:05:06,810 --> 00:05:11,470
+سبب سقوط همزة الوصل؟ سبب سقوطها أن الحرف الساكن قد 
+
+60
+00:05:11,470 --> 00:05:16,010
+اعتمد على حرف أصلي قبله، فلا حاجة لنا بهمزة الوصل 
+
+61
+00:05:16,010 --> 00:05:23,170
+فتسقط همزة الوصل. مثل وضرب، واستغفر، وانطلق، وامضو 
+
+62
+00:05:23,170 --> 00:05:28,330
+وهكذا. طيب سؤال ثاني: سمت همزة الوصل بهذا الاسم
+
+63
+00:05:28,330 --> 00:05:33,410
+لماذا؟ سمت همزة الوصل بهذا الاسم لأنه يتوصل بها 
+
+64
+00:05:33,410 --> 00:05:36,710
+للابتداء بالساكن. يعني حتى أن التوصل للابتداء 
+
+65
+00:05:36,710 --> 00:05:37,210
+بالساكن.
+
+66
+00:05:47,950 --> 00:05:52,470
+ما الفرق بين همزة الوصل وهمزة القطع؟ هناك 
+
+67
+00:05:52,470 --> 00:05:56,830
+فرق. الفرق الأول ما هو يا إخواننا؟ من نفس التعريف 
+
+68
+00:05:56,830 --> 00:06:00,990
+تبع همزة الوصل نستطيع أن نستخرج الفروق. طبعًا تعريف
+
+69
+00:06:00,990 --> 00:06:05,570
+همزة الوصل هي همزة زائدة عن بنية الكلمة، تلحق 
+
+70
+00:06:05,570 --> 00:06:08,690
+الأسماء والأفعال والحروف، تثبت إذا ابتدأنا بها
+
+71
+00:06:08,690 --> 00:06:13,290
+الكلام وتسقط إذا وصلت بما قبلها. من نفس التعريف 
+
+72
+00:06:13,290 --> 00:06:17,690
+نستطيع أن نستخلص الفرق ما بين همزة الوصل وهمزة
+
+73
+00:06:17,690 --> 00:06:21,930
+القطع. طبعًا همزة الوصل تكتب ألفًا بدون همزة، وفي 
+
+74
+00:06:21,930 --> 00:06:25,910
+المصحف يوضع لها رمز. ما هو الرمز الذي يوضع فوق 
+
+75
+00:06:25,910 --> 00:06:31,300
+همزة الوصل؟ صاد صغيرة. يعني رأس صاد يوضع فوق همزة
+
+76
+00:06:31,300 --> 00:06:35,600
+الوصل دلالة على أن هذا الحرف حرف وصل، بيسقط إذا 
+
+77
+00:06:35,600 --> 00:06:40,860
+بوصل بما قبله وبيثبت إذا ابتدأنا به الكلام. إذا ما 
+
+78
+00:06:40,860 --> 00:06:44,880
+الفرق بين همزة الوصل وهمزة القطع؟ النقطة الأولى
+
+79
+00:06:44,880 --> 00:06:51,210
+همزة الوصل زائدة عن بنية الكلمة، مثل اضرب. أصل الكلمة
+
+80
+00:06:51,210 --> 00:06:55,950
+ضربة. الأمر منها اضرب، فهي زائدة عن بنية الكلمة. 
+
+81
+00:06:55,950 --> 00:07:01,290
+انطلق أيضًا، الحرف همزة الوصل همزة زائدة عن بنية 
+
+82
+00:07:01,290 --> 00:07:06,120
+الكلمة. لذلك همزة الوصل زائدة. أما بالنسبة لهمزة
+
+83
+00:07:06,120 --> 00:07:10,040
+القطع فهي همزة أصلية. هذا النقطة الأولى. يعني واحدة
+
+84
+00:07:10,040 --> 00:07:15,260
+زائدة. همزة الوصل زائدة وهمزة القطع أصلية، مثل كلمة 
+
+85
+00:07:15,260 --> 00:07:21,860
+أكرمة وأحسنة. هذه ماضي الرباعي. وماضي الرباعي وكذلك
+
+86
+00:07:21,860 --> 00:07:28,870
+أمل، رباعي همزة وهمزة قطع. أكرم الماضي أكرم، الأمر 
+
+87
+00:07:28,870 --> 00:07:34,410
+أحسن ماضي أحسن بيكون هو أمر الرباعي فيه همزة وهمزة
+
+88
+00:07:34,410 --> 00:07:40,170
+قطع. هذه النقطة الأولى، يعني الوصل زائدة، القطع أصلية. 
+
+89
+00:07:40,170 --> 00:07:44,730
+بعدين النقطة الثانية أن همزة الوصل تثبت عند 
+
+90
+00:07:44,730 --> 00:07:50,710
+الابتداء بها وتسقط إذا وصلت بما قبلها، يعني مثل ما
+
+91
+00:07:50,710 --> 00:07:58,050
+ذكرنا: اضرب لفظها واضرب سقطت الهمزة الواصلة. استغفر
+
+92
+00:07:58,050 --> 00:08:03,890
+وهي لفظة الهمزة، واستغفر سقطت الهمزة. إذا تثبت همزة
+
+93
+00:08:03,890 --> 00:08:08,110
+الواصلة عند الابتداء بها وتسقط إذا وصلت بما قبلها.
+
+94
+00:08:08,110 --> 00:08:13,630
+أما بالنسبة لهمزة القطع فهي ثابتة إذا ابتدأنا بها
+
+95
+00:08:13,630 --> 00:08:18,610
+الكلام وإذا وصلت بما قبلها. مثال ذلك يعني أكره
+
+96
+00:08:18,610 --> 00:08:24,750
+أكرمه. إذا لفظت لوحدها أكرمة هي لفظنا الهمزة، إذا 
+
+97
+00:08:24,750 --> 00:08:29,810
+وصلناها بما قبلها مثلًا، وأكرمه برضه بتلفظ الهمزة، 
+
+98
+00:08:29,810 --> 00:08:36,670
+كذلك أحسن لفظناها وأحسن أيضًا لفظنا الهمزة، إذا هذا
+
+99
+00:08:36,670 --> 00:08:42,130
+هو الفرق ما بين همزة الوصل وهمزة القطع. الآن لننظر
+
+100
+00:08:42,130 --> 00:08:45,970
+إلى حالات همزة الوصل. طبعًا احنا قلنا أن همزة الوصل 
+
+101
+00:08:45,970 --> 00:08:51,690
+همزة زائدة عن بنية الكلمة تلحق الأسماء والأفعال
+
+102
+00:08:51,690 --> 00:08:55,170
+والحروف، يعني ممكن تأتي همزة الوصل في الأسماء وفي 
+
+103
+00:08:55,170 --> 00:08:59,270
+الأفعال وفي الحروف. نشوف هنا في الأفعال أولًا حالات 
+
+104
+00:08:59,270 --> 00:09:03,830
+همزة الوصل في الأفعال. ما هي الأفعال التي تكون فيها
+
+105
+00:09:03,830 --> 00:09:09,510
+همزة الوصل؟ أول شيء رقم واحد: ماضي الخماسي والسداسي.
+
+106
+00:09:10,070 --> 00:09:14,230
+يعني الفعل الماضي الخماسي والفعل السداسي همزة وهمزة 
+
+107
+00:09:14,230 --> 00:09:22,350
+وصل، مثل اقترب، انطلق، ابتغى. همزة وهمزة وصل.
+
+108
+00:09:23,050 --> 00:09:27,830
+مثلًا قوله تعالى: اقترب للناس حسابهم. يعني لو وصلت 
+
+109
+00:09:27,830 --> 00:09:33,730
+بما قبلها، واقترب اقترب اقترب. الهمزة الأولى هي
+
+110
+00:09:33,730 --> 00:09:38,710
+همزة الوصل. لماضي الخماسي ماضي السداسي، مثل
+
+111
+00:09:38,710 --> 00:09:47,070
+استكبر. مثل ذلك: فسجدوا إلا إبليس أبى واستكبر وكان 
+
+112
+00:09:47,070 --> 00:09:53,730
+من الكافرين. أبى واستكبر. استكبر ماضي السداسي. فهمت؟ وهمزة 
+
+113
+00:09:53,730 --> 00:10:02,650
+وصل. اقترب انطلق، ماضي الخماسي همزة وصل. استسقى، مثل 
+
+114
+00:10:02,650 --> 00:10:07,570
+قوله تعالى: وإذا استسقى موسى لقومه. وإذا استسقى
+
+115
+00:10:07,570 --> 00:10:15,290
+استسقى، همزة وهمزة وصل. وهو ماضي السداسي. إذا أول شيء
+
+116
+00:10:15,290 --> 00:10:20,170
+بالنسبة ل همزة الوصل في الأفعال تلحق ماضي الخماسي 
+
+117
+00:10:20,170 --> 00:10:24,970
+والسداسي. أما بالنسبة لماضي الثلاثي والرباعي، فهمزة 
+
+118
+00:10:24,970 --> 00:10:31,830
+وهمزة قطع. من يأتي بكلمة من ماضي الثلاثي؟ مثل ايش؟ حتى 
+
+119
+00:10:31,830 --> 00:10:36,910
+كلمة ماضي ثلاثي أو ماضي رباعي، همزة وهمزة قطع؟ فضل.
+
+120
+00:10:36,910 --> 00:10:47,110
+أخي أخذ، أمر، أذن، طب. ماضي الرباعي: أكرم أحسن. هذه
+
+121
+00:10:47,110 --> 00:10:51,050
+أقبلة، هذه ماضي الرباعي، إذا ماضي الرباعي وماضي 
+
+122
+00:10:51,050 --> 00:10:56,290
+الثلاثي همزة وهمزة قطع، أما ماضي الخماسي والسداسي
+
+123
+00:10:56,290 --> 00:11:00,570
+فهمزة وهمزة وصل، هذه الحالة الأولى، كذلك يا
+
+124
+00:11:00,570 --> 00:11:05,270
+إخواننا الكرام، أمر الثلاثي والخماسي والسداسي
+
+125
+00:11:05,270 --> 00:11:11,910
+همزة وهمزة وصل. أمر الثلاثي مثل ضربة، الأمر منه اضرب 
+
+126
+00:11:11,910 --> 00:11:18,790
+همزة وهمزة وصل. الخماسي انطلق، الأمر منه انطلق 
+
+127
+00:11:18,790 --> 00:11:22,630
+همزة وهمزة وصل. السداسي أمر السداسي، الماضي منه 
+
+128
+00:11:22,630 --> 00:11:27,850
+استغفر، الأمر منه استغفر برضه همزة وهمزة وصل. إذا 
+
+129
+00:11:27,850 --> 00:11:33,910
+همزة الوصل بتلحق أول شيء ماضي الخماسي والسداسي،
+
+130
+00:11:34,620 --> 00:11:42,080
+أمر الثلاثي والخماسي والسداسي. هذه الآيات بتظهر 
+
+131
+00:11:42,080 --> 00:11:46,420
+كيف نلفظ همزة الوصل في الأفعال؟ من يقرأ الآية
+
+132
+00:11:46,420 --> 00:11:53,920
+الأولى؟ فقول: نضرب عصاك الحجار. آه، فقولنا: ضرب بعصاك
+
+133
+00:11:53,920 --> 00:11:59,320
+الحجر. اضرب. عندما نبدأ بها الكلام اضرب نلفظها فهي 
+
+134
+00:11:59,320 --> 00:12:05,580
+ماضي الثلاثي. إذا وصلناها بما قبلها، فقولنا ضرب. أين 
+
+135
+00:12:05,580 --> 00:12:09,700
+ذهبت الهمزة الوصل؟ سقطت. سقطت لأنه لا حاجة لنا بها
+
+136
+00:12:09,700 --> 00:12:14,620
+لأن حرف بعض ساكن قد اعتمد على حرف قبله وهو 
+
+137
+00:12:14,620 --> 00:12:19,920
+فقولنا ضرب بعصاك. كذلك اتلوا. أما نقرأ الآية الثانية
+
+138
+00:12:19,920 --> 00:12:22,020
+القريخة: واتلوا أوحي إليك
+
+139
+00:12:24,790 --> 00:12:31,010
+واطلوا ما أوحي إليك من كتاب ربك. واطلوا هذا أيضًا
+
+140
+00:12:31,010 --> 00:12:36,050
+يعني أمر الثلاثي هي أصلاً اطلوا. إذا قلنا اطلوا هذه 
+
+141
+00:12:36,050 --> 00:12:39,990
+الهمزة لفظناها وإذا وصلت بما قبلها نقول واطلوا
+
+142
+00:12:39,990 --> 00:12:44,310
+سقطت الهمزة لأن هذا أمر الثلاثي وهمزة وصل وهمزة تواصل
+
+143
+00:12:44,310 --> 00:12:48,090
+تثبت إذا ابتدأنا بها الكلام نقول اطلوا وتسقط إذا 
+
+144
+00:12:48,090 --> 00:12:53,400
+وصلت بما قبلها نقول واطلوا أما بالنسبة للخماسي ..
+
+145
+00:12:53,400 --> 00:13:00,420
+من يقرأ اللي بعد ده؟ تفضل يا أخي أحسن
+
+146
+00:13:00,420 --> 00:13:08,060
+انطلقوا إلى ما كنتم به تكذبون انطلقوا .. أمر إيش
+
+147
+00:13:08,060 --> 00:13:15,220
+ده؟ أمر الخماسي انطلقوا الهمزة همزة تواصل إذا 
+
+148
+00:13:15,220 --> 00:13:18,120
+ابتدأنا بها الكلام نثبتها وإذا وصلت بما قبلها
+
+149
+00:13:18,120 --> 00:13:23,340
+تسقط المثال الآخر دخليه بعده واحد منكم اتفضل
+
+150
+00:13:23,340 --> 00:13:28,620
+اقرأ ولا تقولوا
+
+151
+00:13:28,620 --> 00:13:37,110
+انتهوا خيرا لكم انتهوا .. انتهوا أيضا أمر
+
+152
+00:13:37,110 --> 00:13:41,570
+الخماسي همزة وصل وهمزة تواصل أمر الثلاثي
+
+153
+00:13:41,570 --> 00:13:48,150
+فقلنا استهزئوا أو قل استهزئوا إن الله مخرجهم ما
+
+154
+00:13:48,150 --> 00:13:54,490
+تحذرون استهزئوا كذلك استغفر هذا أمر الثلاثي همزة وصل و
+
+155
+00:13:54,490 --> 00:13:58,740
+همزة تواصل نريد أن نفهم أن همزة الوصل تكون في
+
+156
+00:13:58,740 --> 00:14:02,540
+ماضي الخماسي والثلاثي وأمر الثلاثي والخماسي
+
+157
+00:14:02,540 --> 00:14:06,680
+والثلاثي ونظرنا إلى الأمثلة الموجودة أما بالنسبة
+
+158
+00:14:06,680 --> 00:14:13,340
+لأمر الرباعي والمضارع الهمزة في المضارع كل همزة همزة
+
+159
+00:14:13,340 --> 00:14:21,360
+قطع يعني أمر الرباعي مثل أحسن وأصلح أكرم الهمزة
+
+160
+00:14:21,360 --> 00:14:26,860
+همزة وصل أم قطع؟ قطع لو وصلناها بما قبلها ونقول
+
+161
+00:14:26,860 --> 00:14:33,500
+وأكرم وأحسن وأقبل
+
+162
+00:14:33,500 --> 00:14:38,660
+همزة وهمزة قطع نلفظها حالة ابتدائها وحالة وصلها 
+
+163
+00:14:38,660 --> 00:14:43,780
+بما قبلها أما بالنسبة لِهمزة الفعل المضارع أحيانا
+
+164
+00:14:43,780 --> 00:14:50,380
+إذا أراد القارئ أن يقرأ عن نفسه يقول أكلته أذبحه
+
+165
+00:14:50,380 --> 00:14:56,080
+ألعبه أضربه أرى الهمزة هنا همزة المضارع بتكون همزة
+
+166
+00:14:56,080 --> 00:15:02,870
+وصل أم قطع؟ بتكون قطع طيب هذه الهمزات الوصل اللي
+
+167
+00:15:02,870 --> 00:15:06,390
+في الأفعال ماضي الخماسي والسداسي وأمر الثلاثي
+
+168
+00:15:06,390 --> 00:15:10,290
+والخماسي والسداسي طبعا هناك كثير من الناس لا يفرق
+
+169
+00:15:10,290 --> 00:15:14,930
+بين الهمزة، همزة الوصل والقطع فنجد أنه يضع همزة
+
+170
+00:15:14,930 --> 00:15:20,280
+على همزة الوصل وهذا خطأ أو يترك الهمزة عن
+
+171
+00:15:20,280 --> 00:15:25,520
+همزة القطع ويجعلها ألفا خاصة بإدوات الطباعة الحديثة
+
+172
+00:15:25,520 --> 00:15:30,060
+يعني على الكمبيوتر مثلا يضع الألف بدون همزة ويظن
+
+173
+00:15:30,060 --> 00:15:34,960
+أنه قد كتب الكلمة صح طبعا لابد لمن أراد أن يكتب
+
+174
+00:15:34,960 --> 00:15:40,900
+كتابة سليمة إذا كانت الهمزة همزة قطع يضع همزة
+
+175
+00:15:40,900 --> 00:15:45,460
+يعني shift على الألف وإذا أراد أن يكتب همزة وصل
+
+176
+00:15:45,460 --> 00:15:49,700
+لحالها بتكون على حرف الألف في الkeyboard تبع
+
+177
+00:15:49,700 --> 00:15:55,440
+الطباعة الآن ننتقل إلى ما هي حركة همزة الوصل يعني
+
+178
+00:15:55,440 --> 00:16:00,760
+الحركة نفسها نقول مثلا أطلوا هأطلوا هذه الهمزة
+
+179
+00:16:00,760 --> 00:16:05,060
+مضمومة أ أطلوا في حالة الابتداء بها طبعا لو وصلت بما
+
+180
+00:16:05,060 --> 00:16:11,180
+قبلها نقول واطلوا تسقط الهمزة طيب اضرب اضرب هذه
+
+181
+00:16:11,180 --> 00:16:16,500
+الهمزة مكسورة نلفظها ما هي القاعدة في هذا؟ يعني ما
+
+182
+00:16:16,500 --> 00:16:20,620
+هي حركة همزة الوصل في الأفعال؟ إنها قاعدة أول
+
+183
+00:16:20,620 --> 00:16:24,620
+شيء يبتدأ بهمزة الوصل في الأفعال بالضم إذا كان
+
+184
+00:16:24,620 --> 00:16:28,840
+ثالث الفعل مضموما، ضمًّا أصليا طب يا إخوان، يبتدأ
+
+185
+00:16:28,840 --> 00:16:32,300
+بهمزة الوصل في الأفعال بالضم إذا كان ثالث الفعل
+
+186
+00:16:32,300 --> 00:16:36,120
+مضموما ضمًّا لازما، يعني أصليا نشوف مثلا هنا أمثلة
+
+187
+00:16:36,120 --> 00:16:41,240
+ادعوا إلى سبيل ربك بالحكمة والموعظة الحسنة ادعوا
+
+188
+00:16:41,240 --> 00:16:46,860
+الهمزة همزة إيش؟ وصل، مضمومة، ادعوا، لماذا ضمت همزة
+
+189
+00:16:46,860 --> 00:16:52,920
+الوصل هنا؟ لأن الحرف الثالث ادعوا مضموم، كذلك انظر
+
+190
+00:16:53,560 --> 00:16:59,060
+لم نقول انظر ولا أنظر إنما قلنا انظر فالهمزة مضمومة
+
+191
+00:16:59,060 --> 00:17:03,080
+لماذا ضمت همزة الوصل هنا؟ بس حالي الابتداء بها لو 
+
+192
+00:17:03,080 --> 00:17:06,660
+وصلت مما قبلها تسقط يعني لو قلنا وانظر تسقط همزة
+
+193
+00:17:06,660 --> 00:17:10,220
+الوصل لو قلنا وادعوا تسقط همزة الوصل لكن إذا
+
+194
+00:17:10,220 --> 00:17:13,520
+ابتدأنا بها الكلام اللي نلفظها مضمومة إذا كان
+
+195
+00:17:13,520 --> 00:17:18,100
+الحرف الثالث في الفعل مضموم ادعوا هذه الحرف الثالث
+
+196
+00:17:18,100 --> 00:17:24,400
+بالعين مضمومة انظر حرف الظاء مضمومة أُطلوا حرف اللام
+
+197
+00:17:24,400 --> 00:17:33,380
+مضمومة إذا بيكون همزة الوصل مضمومة هذا
+
+198
+00:17:33,380 --> 00:17:37,440
+لو وصلنا أطلوا لحالها أطلوا مضموم لو وصلت نقول
+
+199
+00:17:37,440 --> 00:17:43,300
+واطلوا عندئذٍ تسقط همزة الوصل طيب كذلك استحفظوا 
+
+200
+00:17:43,300 --> 00:17:44,460
+استحفظوا
+
+201
+00:17:46,410 --> 00:17:51,930
+الـ تاء مضمومة فنقول أُسْتَحْفِظُوا كذلك أبطئُوا الـ تاء
+
+202
+00:17:51,930 --> 00:17:55,970
+مضمومة تضمّ
+
+203
+00:17:55,970 --> 00:18:02,410
+همزة الوصل إذا كان الحرف الثالث مضموم نقرأ همزة
+
+204
+00:18:02,410 --> 00:18:08,570
+الوصل مضمومة كذلك يبتدأ بهمزة الوصل بالكسرة إذا كان
+
+205
+00:18:08,570 --> 00:18:14,890
+الحرف الثالث مفتوحًا أو مكسورًا أو مضموما ضمًّا عارضًا نشوف
+
+206
+00:18:14,890 --> 00:18:20,950
+هنا مثلا مفتوح مثل وإذا قلبوا انقلبوا لا نقول
+
+207
+00:18:20,950 --> 00:18:26,830
+انقلبوا ولا أنقلبوا نقول انقلبوا أيه مكسورة كسرة همزة
+
+208
+00:18:26,830 --> 00:18:30,650
+الوصل هنا لأن الحرف الثالث انقلبوا حرف القاف
+
+209
+00:18:30,650 --> 00:18:35,390
+مفتوح فالهمزة بتكون مكسورة أو إذا كان حرف الثالث
+
+210
+00:18:35,390 --> 00:18:42,910
+مكسور مثل اضرب أو اصبر اصبر لحالها بدون فاء اصبر
+
+211
+00:18:42,910 --> 00:18:48,530
+حرف الباء مكسور إذا إذا إذا ابتدأنا باصبر بالكلمة
+
+212
+00:18:48,530 --> 00:18:55,730
+نقول اصبر اصبر كذلك اضرب اضرب هذه الكلمات كسرة
+
+213
+00:18:55,730 --> 00:19:01,510
+همزة الوصل لأن الحرف الثالث مكسور أو كان مفتوح مثل
+
+214
+00:19:01,510 --> 00:19:06,210
+انقلب أو كان مضموما ضمًّا عارضًا هذه هي أو كان الفعل
+
+215
+00:19:06,210 --> 00:19:10,130
+الثالث مضموما ضمًّا عارضًا وهذا لا يكون إلا في خمس
+
+216
+00:19:10,130 --> 00:19:14,910
+كلمات يعني لا يوجد إلا خمس كلمات فيها المضمومة
+
+217
+00:19:14,910 --> 00:19:21,230
+ضمًّا عارضًا اللي هو اقضوا ابنوا امضوا امشوا اقتوا في
+
+218
+00:19:21,230 --> 00:19:24,910
+كل القرآن لا يوجد إلا هذه الكلمات الخمسة اللي
+
+219
+00:19:24,910 --> 00:19:30,980
+مضمومة ضمًّا عارضًا فما معنى الضم العارض؟ يعني احنا
+
+220
+00:19:30,980 --> 00:19:35,440
+نقول لو كان ضمًّا أصليًّا تضمّها مثل وصل مثل اتلُ لكن
+
+221
+00:19:35,440 --> 00:19:41,220
+هذه ضمًّا عارضًا نقول اقضُوا ضمًّا عارضًا ما معنى ضمّ
+
+222
+00:19:41,220 --> 00:19:42,800
+عارضًا يعني ليست أصلية
+
+223
+00:19:46,050 --> 00:19:50,230
+يعني الأمر معين، هنشوف الآن هنا، طبعا في الكلمات
+
+224
+00:19:50,230 --> 00:19:55,210
+الخمس، في عندنا الضامة هنا ليست أصلية، بل هي
+
+225
+00:19:55,210 --> 00:20:00,530
+عارضة بسبب المناسبة وإلا هي في الأساس مكسورة،
+
+226
+00:20:00,530 --> 00:20:04,510
+الأصل مكسور، فجيء بالضامة بدلًا من الكسرة لمناسبة
+
+227
+00:20:04,510 --> 00:20:07,430
+حرف الواو كما سنرى الآن إن شاء الله هذه بعض
+
+228
+00:20:07,430 --> 00:20:12,950
+الكلمات ثم قضوا إلينا ولا تنظرون، فقالوا ابنوا
+
+229
+00:20:12,950 --> 00:20:17,620
+عليهم، ابنوا عليهم كذلك امضوا الهمزة همزة وصل
+
+230
+00:20:17,620 --> 00:20:22,700
+وامضوا حيث تقمرون امضوا لحالها مكسورة انمشوا
+
+231
+00:20:22,700 --> 00:20:26,840
+واصبروا على آلهتكم امشوا مكسورة لكن في حالة الوصل
+
+232
+00:20:26,840 --> 00:20:32,780
+وانمضوا تسقط همزة الوصل فاجمعوا كيدكم ثم اتوا صفا
+
+233
+00:20:32,780 --> 00:20:37,200
+ائتوا لو وصلنا لو ابتدأنا بها الكلام نقول ائتوا
+
+234
+00:20:37,200 --> 00:20:42,320
+مكسورة كذلك ائتوا أو ايتون في هذه الكلمة تحت
+
+235
+00:20:42,320 --> 00:20:47,350
+الأحقاف لكن ما هو السبب؟ يعني ليش الهمزة
+
+236
+00:20:47,350 --> 00:20:53,310
+الوصل أو الضمة ضمة عارضة الضمة في اقضوا وامشوا و
+
+237
+00:20:53,310 --> 00:20:56,130
+اقتوا وامضوا وابنوا هذه .. لنشوف مثلا هنا
+
+238
+00:20:56,130 --> 00:21:02,170
+اقضوا اقضوا أصلها الفعل الأمر من اقضوا اقضِ الفعل
+
+239
+00:21:02,170 --> 00:21:06,330
+الأمر مبني على حرف العلة اقضِ فبتكون الضاد
+
+240
+00:21:06,330 --> 00:21:12,400
+مكسورة يعني أصل الضاد الحرف الثالث مكسور المثنى من
+
+241
+00:21:12,400 --> 00:21:17,620
+أنه أمر المثنى اقضياه وأمر الجامع الأصل أن يكون
+
+242
+00:21:17,620 --> 00:21:24,380
+اقضِيهُ حُذفت الياء تخفيفا والكسرة التي هي على
+
+243
+00:21:24,380 --> 00:21:30,620
+الضاد استبدلت إلى ضمة عارضة بسبب وجود حرف الواو
+
+244
+00:21:30,620 --> 00:21:35,320
+فبتصير اقضوا زي هذه اقضوا يعني في الأساس أن حرف
+
+245
+00:21:35,320 --> 00:21:39,380
+الضاد ليس عليه ضمة حرف الضاد كسرة لأن أصل الكلمة
+
+246
+00:21:39,380 --> 00:21:43,820
+اقضِ مثلًا مثلًا المثنى منه اقضياه الجامع اقضيوا
+
+247
+00:21:43,820 --> 00:21:52,680
+حُذفت الياء والكسرة التي على الضاد تَبدّلت إلى حرف ضمة
+
+248
+00:21:52,680 --> 00:22:00,220
+لمناسبة حرف الواو فنقول اقضوا كذلك كلمة ابنِ يعني
+
+249
+00:22:00,220 --> 00:22:04,320
+ابْنُ .. الو .. الضمة .. ابْنُ .. ابْنُ .. كسرة حملة 
+
+250
+00:22:04,320 --> 00:22:08,080
+الوصل لأن الحرف الثالث مضموم ضمًّا عارضًا. إيش يعني
+
+251
+00:22:08,080 --> 00:22:13,700
+ضمًّا عارضًا؟ الأصل أنه يكون مكسور، لذا وضعنا الضمة
+
+252
+00:22:13,700 --> 00:22:18,560
+بدلًا من الكسرة بسبب حرف الواو مثلا كلمة ابنُ حرف
+
+253
+00:22:18,560 --> 00:22:22,560
+أمر أو كل .. يعني أمر .. فعل أمر مبني على حرف ..
+
+254
+00:22:22,560 --> 00:22:27,210
+حرف العلة، إنه مكسورة المثال منه ابنِ ياء الجامع
+
+255
+00:22:27,210 --> 00:22:32,050
+ابنِيهُ حُذفت الياء لتخفيفا والباء النون المكسورة
+
+256
+00:22:32,050 --> 00:22:38,670
+استبدلت الكسرة إلى ضمة عارضة بسبب مناسبة حرف الواو
+
+257
+00:22:38,670 --> 00:22:43,910
+فصارت ابْنُوا وهكذا باقي الكلمات اللي هي امضوا وامشوا
+
+258
+00:22:43,910 --> 00:22:45,010
+واقتوا
+
+259
+00:22:48,460 --> 00:22:52,160
+طيب الآن انتهينا من همزة الوصل اللي في الأفعال لو سألنا
+
+260
+00:22:52,160 --> 00:23:00,060
+سؤال ما هي الأفعال التي همزتها همزة وصل؟ ماضي
+
+261
+00:23:00,060 --> 00:23:05,000
+الخماسي والثلاثي
+
+262
+00:23:05,000 --> 00:23:07,760
+والخماسي والثلاثي والخماسي والثلاثي يبقى ماضي
+
+263
+00:23:07,760 --> 00:23:15,230
+الخماسي والثلاثي زي انطلقت أو استغفرت وأمر الثلاثي
+
+264
+00:23:15,230 --> 00:23:21,810
+زي اضرب والخماسي مثل انطلق والسداسي استغفر طبعا
+
+265
+00:23:21,810 --> 00:23:25,470
+كل الكلمات السداسية مسبوقة بـ است استغفر أو 
+
+266
+00:23:25,470 --> 00:23:29,930
+استغفرة استنشق استنثر استنثر أي شيء من هذه
+
+267
+00:23:29,930 --> 00:23:35,320
+الكلمات المسبوقة بـ است أما بالنسبة للأسماء، احنا
+
+268
+00:23:35,320 --> 00:23:37,940
+قلنا إن همزة الوصل همزة زائدة عن بنية الكلمة تلحق
+
+269
+00:23:37,940 --> 00:23:41,640
+الأفعال والأسماء، أخذنا الأفعال نشوف ما هي الأسماء
+
+270
+00:23:41,640 --> 00:23:45,820
+اللي همزتها همزة وصل الهمزات في الأسماء تقسم إلى
+
+271
+00:23:45,820 --> 00:23:50,280
+قسمين، فيهمزات قياسية لها قواعد قاعدة معينة
+
+272
+00:23:50,280 --> 00:23:55,280
+وفيهمزات سماعية سمعت هكذا أما بالنسبة للقياسية فهي
+
+273
+00:23:55,280 --> 00:23:58,820
+مصدر الخماسي والثلاثي يعني مصدر الفعل الخماسي
+
+274
+00:23:58,820 --> 00:24:03,520
+والثلاثي انطلق انطلاقا يعني مفعول المطلق منه انطلق
+
+275
+00:24:03,520 --> 00:24:08,820
+انطلاقا استغفر استغفار استكبر استكبار
+
+276
+00:24:11,650 --> 00:24:16,670
+مصدر الخماسي والثلاثي همزة وصل وهمزة تواصل ابتغى
+
+277
+00:24:16,670 --> 00:24:23,810
+ابتغاء ومن الناس من يشتري نفسه ابتغاء مرضات الله
+
+278
+00:24:23,810 --> 00:24:31,600
+ابتغاء همزة وصل وهمزة تواصل يعني وصلناها وابتغاء تسقط
+
+279
+00:24:31,600 --> 00:24:36,400
+همزة الوصل كذلك اختلاف هذه خماسية مصدر الخماسي إذا
+
+280
+00:24:36,400 --> 00:24:42,980
+ابتغاء واختلاف مصدر الخماسي فهمزة وهمزة وصل إن في 
+
+281
+00:24:42,980 --> 00:24:47,580
+اختلاف الليل والنهار اختلاف همزة وهمزة وصل لأنه
+
+282
+00:24:47,580 --> 00:24:54,190
+مصدر الخماسي استعجالهما  استعجال أو استعجالهم حمزته 
+
+283
+00:24:54,190 --> 00:24:59,810
+همزة وصل لأنه ماضي السداسي أو مصدر السداسي استعجلة
+
+284
+00:24:59,810 --> 00:25:03,810
+استعجالا اللي هو المصدر بيكون المفعول المطلق حط
+
+285
+00:25:03,810 --> 00:25:08,730
+قبله استعجلة استعجالا ابتغى ابتغاء انطلق انطلاق
+
+286
+00:25:08,730 --> 00:25:13,990
+اختلف اختلاف استغفر استغفار استكبر استكبار كل
+
+287
+00:25:13,990 --> 00:25:16,730
+المفعول المطلق اسمها مصادر لأنه أصلا المفعول
+
+288
+00:25:16,730 --> 00:25:23,200
+المطلق هو مصدر مصدر الخماسي والسلاسي همزة وصل أما
+
+289
+00:25:23,200 --> 00:25:29,460
+بالنسبة للسماعية سمعت من العرب هكذا وهي عندنا سبع
+
+290
+00:25:29,460 --> 00:25:37,310
+كلمات هي ابن وابنة واثنان واثنتان وامرأ وامرأة
+
+291
+00:25:37,310 --> 00:25:41,610
+واسم هذه الكلمات السبعة أو الأسماء السبعة كلها
+
+292
+00:25:41,610 --> 00:25:47,550
+همزات وصل لأنها سماعية سمعت هكذا مثال ذلك ونادى
+
+293
+00:25:47,550 --> 00:25:53,370
+نوح ربه فقال رب إن ابني من أهلي ما قلناش إن ابني
+
+294
+00:25:53,370 --> 00:25:59,130
+قلنا إن ابني لماذا؟ لأن الهمزة هنا همزة وصل همزة
+
+295
+00:25:59,130 --> 00:26:04,650
+وصل طيب ومريم ابنة عمران  ومريم ابنة عمران
+
+296
+00:26:04,650 --> 00:26:08,450
+ومريم ابنة ابنة مريم ابنة إذا سقطت همزة الوصل
+
+297
+00:26:08,450 --> 00:26:14,170
+فالحمزة في ابن وابن همزة وصل وهمزة وصل كذلك لكل امرئ
+
+298
+00:26:14,170 --> 00:26:21,450
+منهم اكتسب من الأثم امرئ وامرأ وامرأة همزة وصل وهمزة
+
+299
+00:26:21,450 --> 00:26:28,330
+وصل سماعية كذلك امرأة هنا مثلا ضرب الله مثلا للذين 
+
+300
+00:26:28,330 --> 00:26:34,100
+كفروا امرأة نوح  امرأة امرأة همزة وهمزة وصل و
+
+301
+00:26:34,100 --> 00:26:39,600
+كذلك إذا أخرجهم الذين كفروا ثانية اثنين اثنين همزة
+
+302
+00:26:39,600 --> 00:26:45,660
+وهمزة وصل إن عدة شهور عند الله اثنى عشر شهر اثنى 
+
+303
+00:26:45,660 --> 00:26:49,700
+همزة وهمزة وصل واثنتا همزة وهمزة وصل سبح اسم
+
+304
+00:26:49,700 --> 00:26:53,500
+ربك الأعلى اسم أيضا همزة وهمزة وصل هذه الكلمات
+
+305
+00:26:53,500 --> 00:26:57,830
+التي كررت في القرآن الكريم فكانت همزتها همزة وصل.
+
+306
+00:26:57,830 --> 00:27:02,170
+إذا ما هي الأسماء السماعية التي سمعتها كذا؟ كم
+
+307
+00:27:02,170 --> 00:27:08,850
+اسم؟ سبعة، اللي هي ابن وابنة، اثنان اثنتان، امرأ
+
+308
+00:27:08,850 --> 00:27:12,920
+وامرأة واسم يعني احنا نقول بسم الله الرحمن الرحيم
+
+309
+00:27:12,920 --> 00:27:17,560
+لا نقول باسم الله الرحمن الرحيم نقول سبح .. سبح
+
+310
+00:27:17,560 --> 00:27:21,900
+اسم ربك الأعلى ولا نقول سبح اسم ربك الأعلى فالهمزة
+
+311
+00:27:21,900 --> 00:27:25,920
+همزة وصل طيب إذا حركة .. طب ما هي حركة همزة الوصل
+
+312
+00:27:25,920 --> 00:27:29,100
+اللي في الأسماء؟ احنا قلنا فيه سماعية وفيه قياسية
+
+313
+00:27:29,100 --> 00:27:33,190
+القياسية مصدر الخماسي والسلاسي في الأسماء انطلاق أو
+
+314
+00:27:33,190 --> 00:27:37,650
+استغفار وبالنسبة للأسماء السماعية اللي هي ابن و
+
+315
+00:27:37,650 --> 00:27:43,130
+ابنة اثنان اثنتان امرأة اسم سبع كلمات همزة وهمزة
+
+316
+00:27:43,130 --> 00:27:46,950
+وصل ما هي حركة همزة وهمزة واصل؟ هل هي مثل
+
+317
+00:27:46,950 --> 00:27:53,350
+الأفعال إن كان حرف التالت مضموم تضام مثل مثلا ادعو
+
+318
+00:27:53,350 --> 00:27:57,950
+وإذا كان هكذا ولا شيء ثاني له قعد ثاني همزة الوصل
+
+319
+00:27:57,950 --> 00:28:02,270
+في الأسماء فقط مكسورة قولا واحدا يعني ليس هناك 
+
+320
+00:28:02,270 --> 00:28:06,150
+قاعدة لا تضم ولا تفتح همزة الوصل اللي في الأسماء
+
+321
+00:28:06,150 --> 00:28:12,830
+باستمرار مكسورة نقول مثلا امرأة ابن أو مثلا انطلق
+
+322
+00:28:12,830 --> 00:28:18,390
+استغفار همزة الوصل اللي في الأفعال ممكن نقول
+
+323
+00:28:18,390 --> 00:28:23,130
+مفتوحة مضمومة أو مكسورة أو مفتوحة أو مكسورة أما
+
+324
+00:28:23,130 --> 00:28:27,980
+بالأسماء كلها طبعا بتكون مكسورة رقم ثلاثة هو همزة
+
+325
+00:28:27,980 --> 00:28:32,580
+الوصل إلا في الحروف نحن قلنا همزة الوصل في الأفعال
+
+326
+00:28:32,580 --> 00:28:39,200
+وفي الأسماء وفي الحروف ما هي الحروف التي همزتها و
+
+327
+00:28:39,200 --> 00:28:43,520
+همزت وصلها لا يوجد إلا في حرف واحد وهو أل التعريف
+
+328
+00:28:44,450 --> 00:28:49,770
+أل التعريف همزة وصل همزة واصلة مثال ذلك الله الهمزة
+
+329
+00:28:49,770 --> 00:28:56,350
+الله الملك القدوس السلام المؤمن المهيمن العزيز
+
+330
+00:28:56,350 --> 00:29:00,970
+هذا كله همزة وصل همزة واصلة لو قرأت لوحدها الله
+
+331
+00:29:00,970 --> 00:29:08,270
+لفظها الملك القدوس السلام المؤمن المهيمن أنا قاعد
+
+332
+00:29:08,270 --> 00:29:14,010
+بألفظها لكننا قلنا الله الملك القدوس السلام المؤمن
+
+333
+00:29:14,010 --> 00:29:18,070
+المهيمن العزيز الجبار المتكبر وذكرنا أسماء اللي 
+
+334
+00:29:18,070 --> 00:29:22,430
+لها الحسنة ولا واحدة فيها همزة الوصل تسقط همزة
+
+335
+00:29:22,430 --> 00:29:26,470
+الوصل لأن وصلناها إذا همزة الوصل في الحروف فقط في
+
+336
+00:29:26,470 --> 00:29:30,890
+أي حرف في أل التعريف طيب وحركة همزة الوصل في أل
+
+337
+00:29:30,890 --> 00:29:34,710
+التعريف ما هي يا شباب مفتوحة دائما زي ما قلنا همزة
+
+338
+00:29:34,710 --> 00:29:38,050
+الوصل اللي في الأسماء مكسورة، همزة الوصل اللي في
+
+339
+00:29:38,050 --> 00:29:41,610
+الحروف مفتوحة، همزة الوصل اللي في الأفعال إما
+
+340
+00:29:41,610 --> 00:29:44,650
+مضمومة لو كان حرف الثالث مضموم أو مكسورة لو كان
+
+341
+00:29:44,650 --> 00:29:50,290
+حرف الثالث مفتوح أو مضموم أو مضمون ضمان عارضًا أو 
+
+342
+00:29:50,290 --> 00:29:53,550
+مكسور إنك تفهم هذا القدر وإن شاء الله نلقى في
+
+343
+00:29:53,550 --> 00:29:56,410
+اللقاء القادم بارك الله فيكم وجزاكم الله خير و
+
+344
+00:29:56,410 --> 00:29:57,310
+السلام عليكم ورحمة الله
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/2fLs3qcbN4s_postprocess.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/2fLs3qcbN4s_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0ec7b74664906edd9618ea7a5ece6597d8861c83
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/2fLs3qcbN4s_postprocess.srt
@@ -0,0 +1,1504 @@
+1
+00:00:19,490 --> 00:00:24,050
+بسم الله الرحمن الرحيم المحاضرة رقم 16 نظرية
+
+2
+00:00:24,050 --> 00:00:28,490
+الأعداد قسم رياضيات الجامعة الإسلامية كوليوتية
+
+3
+00:00:28,490 --> 00:00:36,580
+العلوم والتربيةهنكمل اليوم الحديث عن ما تبقى من
+
+4
+00:00:36,580 --> 00:00:41,980
+section Chinese remainder theorem and the linear
+
+5
+00:00:41,980 --> 00:00:46,900
+congruences وصلنا لعند نظرية 4.9 عليها the system
+
+6
+00:00:46,900 --> 00:00:54,620
+of linear congruences Ax زي By بسوء R تطابق
+
+7
+00:00:54,620 --> 00:01:06,850
+R modulo andو d abc x زائد dy وطابق s modulo n هذا
+
+8
+00:01:06,850 --> 00:01:17,470
+ال system المعدلتين مع بعض has a unique solution
+
+9
+00:01:17,470 --> 00:01:23,990
+modulo n whenever
+
+10
+00:01:26,400 --> 00:01:36,160
+الـ Greatest Common Divisor بين الـ AD نقص BC و
+
+11
+00:01:36,160 --> 00:01:43,780
+الـ N بساوي 1 الـ proof النظرية
+
+12
+00:01:43,780 --> 00:01:49,110
+كما يلي مرة أخرىالنظرية بتقول إن الـ system of
+
+13
+00:01:49,110 --> 00:01:51,970
+linear congruences اللي أمامي طبعاً عندي ال
+
+14
+00:01:51,970 --> 00:01:55,330
+congruence الأولى فيها مجهولين X و Y و ال
+
+15
+00:01:55,330 --> 00:01:58,530
+congruence التانية برضه فيها مجهولين لأن الحل
+
+16
+00:01:58,530 --> 00:02:04,490
+المشترك لـ two congruences موجود و unique مدلقاً
+
+17
+00:02:04,490 --> 00:02:09,240
+في حال إنه كان العامل المشترك الأعلى بينه لاحظاللي
+
+18
+00:02:09,240 --> 00:02:15,020
+هو AD معامل X في الأولى مضروب معامل Y في التانية
+
+19
+00:02:15,020 --> 00:02:20,800
+ناقص معامل X في التانية مضروب في معامل Y في الأولى
+
+20
+00:02:20,800 --> 00:02:24,180
+المعامل المشترك الأعلى بين هذا الرقم اللي .. اللي
+
+21
+00:02:24,180 --> 00:02:27,240
+.. اللي حكيته وبين الـ N إيش بيساوي؟ بيساوي واحد
+
+22
+00:02:27,240 --> 00:02:29,500
+إذا كان موجود بيساوي واحد هذا العامل المشترك
+
+23
+00:02:29,500 --> 00:02:33,160
+الأعلى معناته اللي هو الـlinear congruences هدولة
+
+24
+00:02:33,160 --> 00:02:41,400
+الهن حل مشترك وحيد Modulo N خلينا نحلبنثبت أن هذا
+
+25
+00:02:41,400 --> 00:02:47,120
+هو الحل الوحيد الآن كما بنعمل بالظبط في المعادلة
+
+26
+00:02:47,120 --> 00:02:50,640
+العاديةاللي هي في المجهولين بنضرب الأولى في رقم
+
+27
+00:02:50,640 --> 00:02:53,940
+والتانية في رقم بحيث أنه بنترحن أو بنجمحن بالطريقة
+
+28
+00:02:53,940 --> 00:02:58,380
+المناسبة بحيث ن cancel أحد اللي هو المجهولين ونوجد
+
+29
+00:02:58,380 --> 00:03:03,820
+من المجهول الآخر عنا طبعا مين المجهيل X وY وX وY
+
+30
+00:03:03,820 --> 00:03:08,720
+هاي المجهيل ومين اللي هي الـA والـB والـC والـD
+
+31
+00:03:08,720 --> 00:03:13,200
+والـR والـS والـN هي عبارة عن ثوابت بين دينا بتكون
+
+32
+00:03:13,200 --> 00:03:18,090
+معطية لناإذاً الغرض أن وجد قيمة X وY هل موجودات و
+
+33
+00:03:18,090 --> 00:03:23,630
+لا مش موجودات نضرب المعادلة الأولى خلّيني أضربها
+
+34
+00:03:23,630 --> 00:03:29,970
+في D هذه بدأت أضربها في D وهذه بدأت أضربها في مين؟
+
+35
+00:03:29,970 --> 00:03:35,090
+في B عرفته ليش؟ عساس أن أضرب هذه في D وهذه في B
+
+36
+00:03:35,090 --> 00:03:39,650
+واترحل من بعض بكون طيارة مين؟ المتغير Y وضل عند
+
+37
+00:03:39,650 --> 00:03:44,130
+المتغير مين؟ X بصير عندي الآن D
+
+38
+00:03:46,840 --> 00:03:54,580
+A و هنا B ناقص B في C الكل في X فاهمين عليها مش ده
+
+39
+00:03:54,580 --> 00:03:59,920
+علي التفصيل موجود التفصيل كله في الكتاب تطابق D في
+
+40
+00:03:59,920 --> 00:04:10,220
+R ناقص B في S كله مضلمين Moduli اذا بضرب طرفي
+
+41
+00:04:10,830 --> 00:04:15,290
+التطابق الأولى في D وطرفي التطابق الثانية في B
+
+42
+00:04:15,290 --> 00:04:21,170
+وطرح اللى هو الأولى ناقص الثانية بطلع عندى اللى هو
+
+43
+00:04:21,170 --> 00:04:27,850
+اللى أمامى Model 1 الان هو معطينى أن العامل
+
+44
+00:04:27,850 --> 00:04:34,150
+المشترك الأعلى ال greatest common divisor since ال
+
+45
+00:04:34,150 --> 00:04:40,520
+greatest common divisor بين الـDA ناقص BCوالـ N
+
+46
+00:04:40,520 --> 00:04:46,960
+بساوي واحد ثم الآن
+
+47
+00:04:46,960 --> 00:04:57,680
+التطابقة اللي هي AD ناقص BC في Z تطابق الواحد
+
+48
+00:04:57,680 --> 00:05:06,140
+Modulo N has a unique solution
+
+49
+00:05:07,650 --> 00:05:12,170
+Modulo N ايش اللي سويته؟ ايش عملت تيك؟ احنا غربنا
+
+50
+00:05:12,170 --> 00:05:18,170
+ايه؟ عشان نوجد قيمة مين؟ قيمة X ماشي؟ الان بدي
+
+51
+00:05:18,170 --> 00:05:22,910
+اعمل اللي هو بدي اواجد قيمة T اللي بتحقق طرفي
+
+52
+00:05:22,910 --> 00:05:29,010
+المعادلة هذه ايش معنى هذه؟ بعد شوية هوصل هذا الطرف
+
+53
+00:05:29,010 --> 00:05:35,150
+للطرف هنا بطريقة معينة ومن خلالها هصل لقيمة X شوف
+
+54
+00:05:35,150 --> 00:05:39,580
+عليها ايش اللي بقولهالان المتطابقة هذه تطابق واحد
+
+55
+00:05:39,580 --> 00:05:43,320
+مضلوان بما ان العام المشترك اللي على بين هذه و هذه
+
+56
+00:05:43,320 --> 00:05:47,260
+بيساوي واحد اذا it has a unique solution هذه
+
+57
+00:05:47,260 --> 00:05:50,560
+بالظبط مشابهة للي كنا نحكي فيه في ال linear
+
+58
+00:05:50,560 --> 00:05:55,300
+congruences لما نوجد قيمة اللي هو ال X في ال
+
+59
+00:05:55,300 --> 00:05:58,540
+linear congruences العادية و في الآخر نعوضها في
+
+60
+00:05:58,540 --> 00:06:03,180
+الحل العام و نوجد قيمة ال X bar نفس المتطابقة لكن
+
+61
+00:06:03,180 --> 00:06:07,710
+اللي هي العام اللي اختلف الاناتفاجرنا ان هذا الوضع
+
+62
+00:06:07,710 --> 00:06:13,230
+لديه حلول إيميجية Say then أو then there exist T
+
+63
+00:06:13,230 --> 00:06:21,470
+element in Z such that AD-BC في T يطابق الواحد
+
+64
+00:06:21,470 --> 00:06:26,850
+مضلومين مضلوا عنه سميلي هذه التي هي اتنين وهذه
+
+65
+00:06:26,850 --> 00:06:33,940
+سميها واحد معايا يا شبابماذا يعني أن هذه المعادلة
+
+66
+00:06:33,940 --> 00:06:38,100
+لديها solution يعني صارت بين إيديا في T في Z
+
+67
+00:06:38,100 --> 00:06:41,880
+بتحقيق الطرفين يعني بمعنى آخر هذه في T تطابق
+
+68
+00:06:41,880 --> 00:06:46,560
+الواحد مدلومين مدلون اضرب لي هذه المعادلة هذه
+
+69
+00:06:46,560 --> 00:06:58,540
+اضربها في X بيصير عندي AD-BC في X في T تطابق ال X
+
+70
+00:06:58,540 --> 00:07:04,220
+مدلومين مدلون واضح أه؟بصيرنا عارفين وحالنا و اين
+
+71
+00:07:04,220 --> 00:07:13,360
+رايحين الان واحد اضربها برضه في مين؟ في T ليش؟ لما
+
+72
+00:07:13,360 --> 00:07:20,200
+اضرب في T بيصير عبارة عن AD ناقص BC في X في T
+
+73
+00:07:20,200 --> 00:07:28,280
+تطابق الـDR ناقص BS في مين؟ في T كله مين؟ Modulo N
+
+74
+00:07:28,280 --> 00:07:33,920
+تنسوش ان الـT صار رقم بين إيدياوهذه كلها المددات
+
+75
+00:07:33,920 --> 00:07:38,520
+بين إيديها لأن من هذه ومن هذه خاصية التعدي معناته
+
+76
+00:07:38,520 --> 00:07:46,180
+صارت X أشمالها X تطابق T في DR ناقص BS كله مدلوا
+
+77
+00:07:46,180 --> 00:07:51,300
+مين والـ T unique وحيدة من الأول مدلوا أن إذا صار
+
+78
+00:07:51,300 --> 00:07:56,200
+عند X has a unique value مدلوا أن اللي هي مين
+
+79
+00:07:56,200 --> 00:08:03,410
+بالظبط الـ T في DR ناقص مينباس هذه الآن قيمة X
+
+80
+00:08:03,410 --> 00:08:09,530
+بدوجن قيمة مين؟ قيمة Y Similarly بالنسبة لقيمة Y
+
+81
+00:08:09,530 --> 00:08:15,150
+بضرب المعادلة الأولى الآن والمعادلة التانية أو
+
+82
+00:08:15,150 --> 00:08:20,330
+التطابق الأولى والتطابق الثانية بضرب الأولى عشان
+
+83
+00:08:20,330 --> 00:08:26,750
+أضيع مين الآن؟اللي هو X بضرب الهدف C وهدف مين في A
+
+84
+00:08:26,750 --> 00:08:34,790
+و بترحل من بعض فبصير عنده C في B C في B ناقص A في
+
+85
+00:08:34,790 --> 00:08:45,270
+D الكل في Y تطابق اللي هو CR ناقص AS كله مضلوا مين
+
+86
+00:08:45,270 --> 00:08:48,070
+مضلوا يعني واضح أه
+
+87
+00:08:51,220 --> 00:09:00,520
+معنى يا عزيزي اه؟ الان
+
+88
+00:09:00,520 --> 00:09:06,880
+هذه الان هي التطابقه اللي بدها توصلي لقيمة اللي هي
+
+89
+00:09:06,880 --> 00:09:11,900
+ل .. اللي هي لما اضربها الان في X الجهتين بعد ما
+
+90
+00:09:11,900 --> 00:09:18,070
+وصلت لجتياللي هي هذه أداء للوصول لربط اللي هي
+
+91
+00:09:18,070 --> 00:09:21,750
+التطابق اللي بتطلع منها بالتطابق الأصلي من أجل
+
+92
+00:09:21,750 --> 00:09:27,060
+الحصول على X كيف وصلنا لجينة T؟طب كيف لجينا الـ T؟
+
+93
+00:09:27,060 --> 00:09:31,440
+قولنا هذا و هذا عاملهم واحد إذا فيه أكيد T و وجدنا
+
+94
+00:09:31,440 --> 00:09:35,740
+الـ T هذا الآن جسر وصلنا من خلاله ضربناه في X
+
+95
+00:09:35,740 --> 00:09:40,620
+حصلنا على هذه و الأولى ضربناها في T و حصلنا على
+
+96
+00:09:40,620 --> 00:09:44,720
+هذا هو نفس الطرف هذا صار عندي هذا بيساوي في T
+
+97
+00:09:44,720 --> 00:09:49,900
+بيساوي مين؟ قيمة X إذا هي عبارة عن مفتاح الأمر
+
+98
+00:09:49,900 --> 00:09:55,660
+للحلأي بني هذي هتكون مفتاح لحل اللي عندي شوف كيف
+
+99
+00:09:55,660 --> 00:10:00,200
+وصلنا لهذه فاهمين كيف وصلنا ضربنا الطرفين هذولة
+
+100
+00:10:00,200 --> 00:10:04,320
+الأول في C والتاني في A وطرحناها من بعض طيبنا قيمة
+
+101
+00:10:04,320 --> 00:10:09,480
+X وطلعت عندي القيمة اللي أمامي الآن بالضبط بهذه
+
+102
+00:10:09,480 --> 00:10:13,080
+المعادلة كلها في مين في T T صرت جيبها أنا وعرفها
+
+103
+00:10:13,080 --> 00:10:21,360
+فبصير عندي الآن CBنقص A في D في Y في T تطابق CR
+
+104
+00:10:21,360 --> 00:10:28,240
+نقص AS في T كله مدلون مين مدلون حصلت على هذه برجع
+
+105
+00:10:28,240 --> 00:10:34,580
+لمين لأكتر طابق اتنين اللي هي مفتاح الحل هذه بدرب
+
+106
+00:10:34,580 --> 00:10:43,720
+في مين الطرفين في Y بيصير عندك الان Y AD نقص BC في
+
+107
+00:10:43,720 --> 00:10:54,110
+Yفى T نضربها فى مين فى سالب تطابق ال AS نقص CR فى
+
+108
+00:10:54,110 --> 00:11:00,950
+مين فاش ضربنا احنا لأ اش ضربنا احنا ضربنا في مين
+
+109
+00:11:00,950 --> 00:11:05,750
+انا اللى برا اتكلم ده ضربنا في Y فبصير عندى تطابق
+
+110
+00:11:05,750 --> 00:11:14,850
+Y مظبوطة Modulo مين Modulo Nواضح؟ الان عندي هذا هو
+
+111
+00:11:14,850 --> 00:11:18,490
+هذا مع هذا سالب إذا من التنتين مع بعض بخاصية
+
+112
+00:11:18,490 --> 00:11:23,390
+التعدي بالسير Y تطابق اللي هو الآن سالب بتاخد هذا
+
+113
+00:11:23,390 --> 00:11:31,350
+بالسير AS نقص CR في T modulo mean مفهوم أه؟ هذا
+
+114
+00:11:31,350 --> 00:11:36,910
+اللي هو قيمة mean قيمة Y إذا صار عندي the unique
+
+115
+00:11:36,910 --> 00:11:47,080
+solution modulo Nاللي هو X بتساوي كده و
+
+116
+00:11:47,080 --> 00:11:55,020
+Y بتساوي كده من هنا مفتاح الأمر إلينا اللي هي
+
+117
+00:11:55,020 --> 00:11:56,500
+التطابق اللي أمامنا
+
+118
+00:12:00,340 --> 00:12:02,920
+والـ T أشمالها واحدة إذاً هي كأثباتنا unique
+
+119
+00:12:02,920 --> 00:12:09,900
+solution مدلوق لاحظ الآن إذا عمليا عشان اللي هو
+
+120
+00:12:09,900 --> 00:12:13,360
+نتذكر إيش اللي بنعمله عشان نحل السؤال من هذا النوع
+
+121
+00:12:14,180 --> 00:12:19,380
+إيش اللي بلزمني؟ بلزمني بس أحل التطابق هذه طبعاً
+
+122
+00:12:19,380 --> 00:12:22,000
+واحد بده يحل بنفس الطريقة اللي حلناها ويمشي نفس
+
+123
+00:12:22,000 --> 00:12:26,980
+الاشي بنفع بس كل مرة إيش ماله بده يطول في الحل لكن
+
+124
+00:12:26,980 --> 00:12:32,460
+أنا الأن فهمت روح البرهان وفهمت روح الحديث لحل
+
+125
+00:12:32,460 --> 00:12:36,780
+التطابق تاني إذا بس خليني أركز على اللي هي كيف
+
+126
+00:12:36,780 --> 00:12:40,640
+اللي هو بحل هذا التطابق ومن ثم أعوض عن X وY ويكون
+
+127
+00:12:40,640 --> 00:12:46,510
+خلصناه شوف عنديوانتبه علي أيش اللي بقوله إذا الأول
+
+128
+00:12:46,510 --> 00:12:49,230
+خطوة أن أنا بفحص
+
+129
+00:12:51,970 --> 00:12:55,690
+A×D مُعامل X في الأولى مضروب في مُعامل Y في
+
+130
+00:12:55,690 --> 00:12:59,990
+الثانية ناقص مُعامل X في الثانية مضروب في مُعامل Y
+
+131
+00:12:59,990 --> 00:13:03,830
+في الأولى إذا كان هذا العدد مع اللي هو الآن الـ
+
+132
+00:13:03,830 --> 00:13:06,090
+Grade-Sum Indivisor بساوي واحد معناته فيه عندي إيش
+
+133
+00:13:06,090 --> 00:13:09,790
+مال و بضمن فيه عندي unique solution مُدرُع ماشي
+
+134
+00:13:09,790 --> 00:13:13,830
+الحالة طيب الآن لجيته اللي هو بساوي بطابق الواحد
+
+135
+00:13:13,830 --> 00:13:18,560
+إيش بسوي الخطوة الثانية باجياللي فحصت فيه ركزوا في
+
+136
+00:13:18,560 --> 00:13:22,020
+اللي بحكي اللي فحصت فيه اللي هو هذا بضربه في T
+
+137
+00:13:22,020 --> 00:13:25,960
+تطابق واحد مضلقا و بوجد ال solution لأنه أنا ضامن
+
+138
+00:13:25,960 --> 00:13:28,640
+ال answer ان هو هذا و هذا واحد معناته في unique
+
+139
+00:13:28,640 --> 00:13:32,660
+solution بوجد قيمة مين الآن قيمة T بصير T بين
+
+140
+00:13:32,660 --> 00:13:36,720
+إيديا بعد ما صير ال T بين إيديا باجي بقول إذا ال
+
+141
+00:13:36,720 --> 00:13:41,920
+solution هو X بتساوي ال T اللي لجيتها مضروبة في D
+
+142
+00:13:41,920 --> 00:13:53,810
+في مين؟ في Rهذا قيمة X باخد معامل Y في الثانية
+
+143
+00:13:53,810 --> 00:13:58,290
+وبضربه في مين في الحد المطلق اللي هو في الأولى
+
+144
+00:14:04,780 --> 00:14:12,440
+في الثانية فاهمين هذا مين اللي هو X و Y بعكس ببدأ
+
+145
+00:14:12,440 --> 00:14:16,300
+بمين بالمعامل X في الأولى و بضربه في الحد المطلق
+
+146
+00:14:16,300 --> 00:14:20,120
+في الثانية و نفس الاشي في الثانية و بضربه في الحد
+
+147
+00:14:20,120 --> 00:14:25,630
+المطلق في الأولى اللي هومعامل X عشان الـ Y وهنا
+
+148
+00:14:25,630 --> 00:14:29,010
+معامل Y عشان الـ X مضروب في الحد المطلق في كل
+
+149
+00:14:29,010 --> 00:14:32,070
+منهما و مرة باخد المعادلة الأولى قبل و مرة باخد
+
+150
+00:14:32,070 --> 00:14:35,030
+المعادلة الثانية قبل عساس إشارة النقص واضح اللي
+
+151
+00:14:35,030 --> 00:14:45,690
+بحكيه طيب نيجي الآن بدنا ناخد مثال example
+
+152
+00:14:45,690 --> 00:14:50,970
+find the solution example
+
+153
+00:14:54,360 --> 00:15:07,260
+Find the solution of the system 7x
+
+154
+00:15:07,260 --> 00:15:11,820
+plus 3y تطابق
+
+155
+00:15:11,820 --> 00:15:24,180
+العشرة modulo 16 2x plus 5yتطابق التسعة modulo 16
+
+156
+00:15:24,180 --> 00:15:30,020
+الآن
+
+157
+00:15:30,020 --> 00:15:35,880
+بدي أحل هذا ال system of two linear congruences of
+
+158
+00:15:35,880 --> 00:15:39,040
+two variables يعني بدي أحل بمعنى أخر بدي أجد قيمة
+
+159
+00:15:39,040 --> 00:15:45,380
+XY اللي بتحقق اللي هو التطابقتين الآن أول شيء بقول
+
+160
+00:15:45,380 --> 00:15:46,540
+solution
+
+161
+00:15:48,420 --> 00:15:51,940
+بقول الـ greatest بما انه الـ greatest common
+
+162
+00:15:51,940 --> 00:15:58,640
+divisor بين سبعة في خمسة خمسة و تلاتين ناقص اتنين
+
+163
+00:15:58,640 --> 00:16:05,260
+في تلاتة بستة مع الست عشر بساوي ال greatest common
+
+164
+00:16:05,260 --> 00:16:10,180
+divisor هذا العدد من هو تسعة و عشرين مع الست عشر
+
+165
+00:16:10,180 --> 00:16:15,540
+ايش هيساوي طبيعي واحد اذا ال system
+
+166
+00:16:18,430 --> 00:16:24,210
+Has a unique solution
+
+167
+00:16:24,210 --> 00:16:30,110
+modulo 16 معاه؟ بدنا نوجد هذا ال solution قولنا
+
+168
+00:16:30,110 --> 00:16:39,250
+مفتاح الحل مين هي؟ الـ هي هذه الآن عندياللي فحصت
+
+169
+00:16:39,250 --> 00:16:44,890
+فيها هي اللي هي الـ 29 بضربها في T اللي فحصت فيها
+
+170
+00:16:44,890 --> 00:16:51,490
+تطابق الواحد modulo 16 معايا وهي اللي بتوجد الـ T
+
+171
+00:16:51,490 --> 00:16:57,630
+فيها او جد الـ T بكون خلصت الان الان 29 بدي أشيل
+
+172
+00:16:57,630 --> 00:17:02,370
+منها 16 أو تنتين يمكن 16 أسهل لي اللي هي بشيل 32
+
+173
+00:17:02,370 --> 00:17:10,420
+يعني بيصير ناقص 3T ناقص 3Tتطابق الـ 1 الـ 1 سأجعل
+
+174
+00:17:10,420 --> 00:17:15,600
+شيء يقبل الجسم على ثلاثة واضح لو أجهزت من الـ 1 16
+
+175
+00:17:15,600 --> 00:17:22,040
+يصبح ناقص 15 ناقص 15 يعني جاي على طول مضله مين
+
+176
+00:17:22,040 --> 00:17:25,600
+مضله 16 بقسم الجهتين على مين على ناقص ثلاثة لو
+
+177
+00:17:25,600 --> 00:17:29,340
+جلسكم الـ divisor مع السلطه عشان يساوي واحد يصبح
+
+178
+00:17:29,340 --> 00:17:36,410
+عند الـ T تطابق الخمسةمعدل مين 16 الان ال
+
+179
+00:17:36,410 --> 00:17:43,410
+solutions او solution the solution is
+
+180
+00:17:43,410 --> 00:17:53,670
+لان كنا وحيد ايش هو X بتساوي الان وين معدلتنا اللي
+
+181
+00:17:53,670 --> 00:18:00,230
+هو الان اباجي لمين لو Y ماشي عندى خمسة في عشرة
+
+182
+00:18:00,230 --> 00:18:13,600
+خمسينناقص 3×9 هو 27 وهو عبارة عن جداش 23 مظبوط
+
+183
+00:18:13,600 --> 00:18:25,820
+مدله 16 الـ 23 جداش بيكون X تطابق 7 مدله 16 هذا
+
+184
+00:18:25,820 --> 00:18:34,020
+اللي هو قيمة X الـ Y Y تساوي الآن أخدتأه في T أسف
+
+185
+00:18:34,020 --> 00:18:40,560
+أسف جدش T خمسة خمسة بتطلع خمسة في تلاتة و عشرين
+
+186
+00:18:40,560 --> 00:18:46,700
+جدش بتطلع عندنا قولوا معنا 115 هي جدش طلعت هنا
+
+187
+00:18:46,700 --> 00:18:51,440
+سبعة خمسة و تلاتين تلاتة يعني عارفين كيف حسبتها
+
+188
+00:18:51,440 --> 00:18:54,940
+طلعت هذه جدش أنا في الأول سبعة في خمسة و خمسة و
+
+189
+00:18:54,940 --> 00:18:57,400
+تلاتين خمسة و تلاتين شيل اتنين اتنين و تلاتين ضال
+
+190
+00:18:57,400 --> 00:18:59,380
+جدش تلاتة فاهمين why
+
+191
+00:19:02,640 --> 00:19:06,860
+الحسابات كلها why نجيب خواي ايش ال why اللي هو
+
+192
+00:19:06,860 --> 00:19:12,380
+سبعة في تسعة عكس تشايفين تلاتة و ستين ناقص اتنين
+
+193
+00:19:12,380 --> 00:19:18,520
+فعشرة بعشرين في ال T جداش ال T خمسة بلاش ننسيها زي
+
+194
+00:19:18,520 --> 00:19:22,660
+قبل شوية تلاتة و أربعين في خمسةاللي هي بتساوي
+
+195
+00:19:22,660 --> 00:19:26,680
+الستة عشر اتنين و تلاتين اتنين و تلاتين بزيد قداش
+
+196
+00:19:26,680 --> 00:19:31,580
+احداش احداش في خمسة خمسة و خمسين خمسة و خمسين شيل
+
+197
+00:19:31,580 --> 00:19:38,300
+منها شيل منها اتنين و تلاتين سبعة سبعة مضله ستة
+
+198
+00:19:38,300 --> 00:19:42,000
+عشر شيل منها اتنين و تلاتين التمانية و اربعين شيل
+
+199
+00:19:42,000 --> 00:19:45,140
+منها تمانية و اربعين من التلاتة من ال .. من ال ..
+
+200
+00:19:45,140 --> 00:19:51,040
+مضال مضال قداش سبعة باضح
+
+201
+00:19:51,040 --> 00:19:51,380
+اه؟
+
+202
+00:19:55,760 --> 00:20:04,320
+هذا اللي هو عندى y تطابق السبعة مدله 16 اتنين هذا
+
+203
+00:20:04,320 --> 00:20:07,840
+اللي هو the unique solution مدله 16 ال X وY هكذا
+
+204
+00:20:07,840 --> 00:20:11,960
+نكون خلصنا شبتر أربعة اللي هو the theory of
+
+205
+00:20:11,960 --> 00:20:17,660
+congruences الآن بدنا ننتقل إلى شبتر خمسة
+
+206
+00:21:24,530 --> 00:21:29,690
+الجزء الثاني من المحاضرة هو عبارة عن .. هندخل في
+
+207
+00:21:29,690 --> 00:21:33,810
+شقطر 5 اللي هو الـ Fermat's theorem أول section
+
+208
+00:21:33,810 --> 00:21:36,250
+هنبدأ فيه اللي هو خمسة اتنين اللي هو Fermat's
+
+209
+00:21:36,250 --> 00:21:41,170
+little theorem and pseudo-primes نحكي عن اللي هو
+
+210
+00:21:41,170 --> 00:21:49,070
+ال Fermat's little theoremالنظرية هي كما يلي بتقول
+
+211
+00:21:49,070 --> 00:21:54,950
+إذا كان عند بي برايم and
+
+212
+00:21:54,950 --> 00:22:03,130
+ال b لا يقسم ال a then ال a to the b minus one
+
+213
+00:22:03,130 --> 00:22:09,410
+تطابق الواحد modulo b a proof برايم number
+
+214
+00:22:15,080 --> 00:22:21,360
+عند بي الزبران معاياis a prime number والـ A is
+
+215
+00:22:21,360 --> 00:22:26,180
+any integer بحقق مالي أن الـ B لا تقسم من الـ A
+
+216
+00:22:26,180 --> 00:22:30,900
+إذا الـ A to the B minus واحد تطابق الواحد أشماله
+
+217
+00:22:30,900 --> 00:22:35,960
+modulo B طبعا هذه النظرية بتسهل علي كتير كتير كتير
+
+218
+00:22:35,960 --> 00:22:42,100
+كتير لعملية إيجاد ال remainder اللي هو عند القسمة
+
+219
+00:22:42,100 --> 00:22:46,260
+على A prime الأعداد اللي هو مرفوعة لقوة عالية جدا
+
+220
+00:22:47,010 --> 00:22:53,550
+خلّيني أبرهن النظرية والاشياء النظرية برهانها
+
+221
+00:22:53,550 --> 00:22:58,750
+يعتمد على الـ 6 التالية بدا أقول لك consider الـ
+
+222
+00:22:58,750 --> 00:23:05,290
+6S إيش الـ 6S هذا اللي بتداخلها؟ هي عبارة عن A و
+
+223
+00:23:05,290 --> 00:23:12,350
+2Aوتلاتة ايه لما أصل بي ماينس واحد في مين فيه ماشي
+
+224
+00:23:12,350 --> 00:23:17,850
+consider us بتساوي زي ما هى أمامى الآن هذه الست
+
+225
+00:23:17,850 --> 00:23:23,130
+بتثبتلك شغلتين فيها بتثبتلك ان ولا واحد من هدولة
+
+226
+00:23:23,130 --> 00:23:29,180
+عبارة عن سفرمدلبي يعني لا يطابق السفر مدلبي ولا
+
+227
+00:23:29,180 --> 00:23:34,240
+واحد منها اي واحد اتنين بدي اثبتلك انه كل العناصر
+
+228
+00:23:34,240 --> 00:23:38,580
+اللي موجودة هنا are incongruent ماشي ولا واحد
+
+229
+00:23:38,580 --> 00:23:42,340
+congruent لمين لا التاني طيب ايش علاقته بموضوعنا
+
+230
+00:23:42,340 --> 00:23:46,880
+هل جيت نشوف ايش علاقته بموضوعنا الان بدي افرض عشان
+
+231
+00:23:46,880 --> 00:23:53,540
+اثبت to prove thatاللي هو S Contains No Element
+
+232
+00:23:53,540 --> 00:23:58,920
+Congruent to Zero Modulo B We Assume Not يعني بدنا
+
+233
+00:23:58,920 --> 00:24:06,130
+نقول صبازبدأ أقول suppose that there exists S A في
+
+234
+00:24:06,130 --> 00:24:13,610
+الـ S S A as small S A المتنقض such that S A يطابق
+
+235
+00:24:13,610 --> 00:24:18,490
+الـ Zero modulo Min modulo B يعني فرضت أنه في يوجد
+
+236
+00:24:18,490 --> 00:24:23,050
+عنصر هنا اللي هو اسمه S A يطابق الـ Zero Min
+
+237
+00:24:23,050 --> 00:24:26,460
+modulo B و أسأل a contradictionمدام الاس ايه في
+
+238
+00:24:26,460 --> 00:24:30,980
+الاس؟ معناته الأصل الصغيرة هذه، يا واحد، يا اتنين،
+
+239
+00:24:30,980 --> 00:24:35,520
+يا تلاتة، يا مين، يعني صارت الاس هذه وين موجودة في
+
+240
+00:24:35,520 --> 00:24:42,130
+الواحد والتنين اللي عند البي ماقص واحدواضح؟ الـ S
+
+241
+00:24:42,130 --> 00:24:45,970
+A هذا اللي موجود في الـ S الكبيرة سيصبح الـ S A يا
+
+242
+00:24:45,970 --> 00:24:49,910
+صورة A يا اتنين A يا تلاتة A يا B minus واحد في A
+
+243
+00:24:49,910 --> 00:24:54,150
+يعني الـ S هذا عامل الـ A هيكون يا واحد يا اتنين
+
+244
+00:24:54,150 --> 00:24:57,810
+يا تلاتة يا B minus واحد يعني عامل الـ A هذا هيكون
+
+245
+00:24:57,810 --> 00:25:03,370
+في الست واحد اتنين عند مين B minus واحد طيب الآن
+
+246
+00:25:04,940 --> 00:25:08,380
+مدام S A تطبق الـ Zero modulo B وانا بعرف ان
+
+247
+00:25:08,380 --> 00:25:12,860
+العامل المشترك الأعلى B لا تقسم الـ A يعني بي مش
+
+248
+00:25:12,860 --> 00:25:17,540
+موجودة من الـ A من أصله إذا أكيد العامل المشترك
+
+249
+00:25:17,540 --> 00:25:20,640
+الأعلى بين الـ B و الـ A مش بساوي واحد مش عامل
+
+250
+00:25:20,640 --> 00:25:23,460
+بينهم لأن بي is a prime إذا صار عند ال greatest
+
+251
+00:25:23,460 --> 00:25:29,200
+common divisor بين الـ B و الـ A بساوي واحد إذا
+
+252
+00:25:29,200 --> 00:25:34,040
+معناته أنه بقدر أختصر الـ A من هنا و بيصير عند S
+
+253
+00:25:35,230 --> 00:25:40,970
+then S تطابق الـ 0 مضنوا مين مضنوا B صارت الـ S
+
+254
+00:25:40,970 --> 00:25:45,990
+small تطابق الـ 0 يعني بمعنى أخر الـ S الـ B بيكسب
+
+255
+00:25:45,990 --> 00:25:50,230
+من الـ S يعني الـ B الـ S من مضاعفات الـ B وهنا
+
+256
+00:25:50,230 --> 00:25:55,230
+أصلا الـ S مستحيل تكون اللي هي من مضاعفات الـ B
+
+257
+00:25:55,230 --> 00:26:00,590
+لأن الـ S عبارة عن واحد أو 2 أو B minus 1واضح وهذا
+
+258
+00:26:00,590 --> 00:26:07,530
+which is a contradiction يدن therefore therefore S
+
+259
+00:26:07,530 --> 00:26:12,930
+A لا تطابق ال zero modulo B for every S A element
+
+260
+00:26:12,930 --> 00:26:17,390
+in me هنا إذا فش ولا واحد فين بطابق ال zero اي
+
+261
+00:26:17,390 --> 00:26:24,810
+واحد اتنين بدي أثبت لك انه فش شيءأي واحد متطابق
+
+262
+00:26:24,810 --> 00:26:29,230
+التاني جوا ماشي الحال بدي أقولك برضه suppose not
+
+263
+00:26:29,230 --> 00:26:34,330
+يعني نفترض أنه في اتنين هنا متطابقين يعني بدي
+
+264
+00:26:34,330 --> 00:26:43,490
+أقولك suppose that there exist sr or sa or ra
+
+265
+00:26:43,490 --> 00:26:51,400
+element in s such that sa يطابق الra مضلمينفرضت
+
+266
+00:26:51,400 --> 00:26:58,040
+إنه فيه اتنين في الـ S متطابقين أكيد الـ S والـ R
+
+267
+00:26:58,040 --> 00:27:02,140
+مدام الـ S أيه هنا والـ R أيه موجودة هنا هيكون الـ
+
+268
+00:27:02,140 --> 00:27:06,280
+S أيه الـ S والـ R موجودات في الواحد والتانية اللي
+
+269
+00:27:06,280 --> 00:27:12,670
+عند مين بـ-1بما أن B لا يقسم الـA وB زبرايما، إذاً
+
+270
+00:27:12,670 --> 00:27:14,850
+العامل المشترك الأعلى بين الـB والـA زي ما قلنا
+
+271
+00:27:14,850 --> 00:27:19,410
+بـS1 إذاً بختصر هذه محادثة تظهر عند الـS تطابق
+
+272
+00:27:19,410 --> 00:27:24,950
+الـR Modulo B لكن هذا أصلاً كل العناصر اللي فيها
+
+273
+00:27:24,950 --> 00:27:28,410
+incomplete .. اللي هو incongruent، ليش؟ لأن أصلاً
+
+274
+00:27:28,410 --> 00:27:31,730
+هذا هو جزء من الـComplete Residue System Modulo B
+
+275
+00:27:31,730 --> 00:27:34,250
+يعني هذا Complete Residue System Modulo B إذا
+
+276
+00:27:34,250 --> 00:27:38,730
+دفنانه بالـ0إذاً أكيد العناصر أشمالهم are
+
+277
+00:27:38,730 --> 00:27:42,510
+incongruent إذاً هذا صار أشماله contradiction
+
+278
+00:27:42,510 --> 00:27:48,430
+Therefore .. Therefore صار S A لايطابق الـ R A في
+
+279
+00:27:48,430 --> 00:27:53,150
+كل العناصر الموجودة في مين فاس إذاً صار عندي اللي
+
+280
+00:27:53,150 --> 00:27:57,450
+صار عندي ما يليه أن الـ S هذه اللي هي عبارة عن الـ
+
+281
+00:27:57,450 --> 00:28:05,940
+A و 2A لعند الـ B-1 في الـ A عبارة عناللي هو
+
+282
+00:28:05,940 --> 00:28:11,800
+مجموعة فيها كم عنصر بي ماينس واحد من العناصر ركز
+
+283
+00:28:11,800 --> 00:28:18,860
+ولا واحد من هدولة بطابق إيش الآخر ولا واحد بطابق
+
+284
+00:28:18,860 --> 00:28:22,820
+الـ Zero إذا يعني لو بتناله الـ Zero هيصير
+
+285
+00:28:22,820 --> 00:28:29,320
+Complete Residue System مضلمين مضلبينبالظبط بالظبط
+
+286
+00:28:29,320 --> 00:28:35,900
+هذا صفر و واحد لعند الـ B- واحد ايش برضه Complete
+
+287
+00:28:35,900 --> 00:28:42,060
+Residue System Modulo B Modulo B نعرف هذا طيب يعني
+
+288
+00:28:42,060 --> 00:28:46,660
+الآن هذا الصفر اللي هنا والصفر اللي هنا لو شلناها
+
+289
+00:28:47,560 --> 00:28:51,480
+بصير هذا هو عبارة عن الـ Complete Residue مع هذا
+
+290
+00:28:51,480 --> 00:28:55,360
+الـ 0 وهذا الـ Complete Residue مع هذا الـ 2 يعني
+
+291
+00:28:55,360 --> 00:29:00,380
+بمعنى أخر كل عصر من هنا is congruent to one and
+
+292
+00:29:00,380 --> 00:29:05,730
+only one element هنايعني كل واحد فيه الواحد و بس
+
+293
+00:29:05,730 --> 00:29:09,490
+واحد عددهم هدولة بيه minus واحد وبعدها عددهم مين
+
+294
+00:29:09,490 --> 00:29:14,570
+بيه minus واحد يعني كل واحد من هان congruent one
+
+295
+00:29:14,570 --> 00:29:19,210
+and only one in this set إذا صار حاصل ضرب هدولة
+
+296
+00:29:19,210 --> 00:29:23,670
+أكيد أشماله يطابق حاصل ضرب هدولة يعني بمعنى أخر
+
+297
+00:29:23,670 --> 00:29:29,100
+صار عندك الفى الاتنين ايه لما أصل لعند الـ B-1 في
+
+298
+00:29:29,100 --> 00:29:35,640
+A يطابق الواحد فى التنين لعند ما أصل لعند مين مضله
+
+299
+00:29:35,640 --> 00:29:42,720
+مين مضله B طيب الان هذولة الآن ال A عدد هنا كم
+
+300
+00:29:42,720 --> 00:29:49,220
+واحدة واحدة تنتين لعند B-1 يعني فى عندك A مضروبة
+
+301
+00:29:49,220 --> 00:29:54,480
+في حالها B-1 من المرات معايا له A بيصير A أقصد B-1
+
+302
+00:29:55,650 --> 00:30:06,150
+مضروبة في 1 في 2 في B-1 تطابق هذه مين هي أصلاً B-1
+
+303
+00:30:06,150 --> 00:30:13,690
+فكتوريال وهذه مين برضه B-1 فكتوريال مضلوا مين
+
+304
+00:30:13,690 --> 00:30:17,650
+مضلوا B لاحظ العامل المشترك الأعلى بين ال B وB-1
+
+305
+00:30:17,650 --> 00:30:21,250
+فكتوريال ليش مثاوى لأن هذي 1 2 3 فاش فيهم B
+
+306
+00:30:21,250 --> 00:30:24,580
+بالمعروف أن ال B أكبر منه برأيإذا صار عند الان
+
+307
+00:30:24,580 --> 00:30:30,440
+اشماله الـ a to the b minus واحد تطابق الواحد
+
+308
+00:30:30,440 --> 00:30:43,260
+modulo b وهو المطلوب أي سؤال؟ طيب نيجي
+
+309
+00:30:43,260 --> 00:30:45,100
+الآن في عندنا corollary
+
+310
+00:30:50,020 --> 00:31:00,100
+بتقول if B is prime then A أُس B تطابق الـ A
+
+311
+00:31:00,100 --> 00:31:08,480
+modulo B الآن بيقول لي بغض النظر عن علاقة ال B و
+
+312
+00:31:08,480 --> 00:31:14,140
+ال A في بعض دايما هتلاقي أن A أُس B تطابق ال A
+
+313
+00:31:14,140 --> 00:31:14,980
+modulo A
+
+314
+00:31:21,340 --> 00:31:28,180
+الان عندى حلتين proof عندى
+
+315
+00:31:28,180 --> 00:31:35,740
+يال بى بتقسمش ال a يال بى بتقسماش ال a فى غير هيك
+
+316
+00:31:35,740 --> 00:31:40,220
+ليش جزأتين هيك لإنه أصلا نظريتي اللى بتعتمد عليها
+
+317
+00:31:40,220 --> 00:31:43,580
+اللى بتدرب الطرفين فيه زى ما قلته بس بتيجينانى لل
+
+318
+00:31:43,580 --> 00:31:49,800
+بى ده تقسم ال a لإن الحلتين هى trivialالأهل جاي
+
+319
+00:31:49,800 --> 00:31:55,280
+بتشوف الآن الـ B لتقسم مين الـ A مدام الـ B لتقسم
+
+320
+00:31:55,280 --> 00:31:58,960
+الـ A إذا by ال theorem اللي قبل بشوية A to the B
+
+321
+00:31:58,960 --> 00:32:03,140
+minus واحد تطابق الواحد مضلوا مين؟ مضلوا B اضرب
+
+322
+00:32:03,140 --> 00:32:10,400
+الجهتين في مين؟ في A فبصير الـ A تطابق الـ A مضلوا
+
+323
+00:32:10,400 --> 00:32:14,520
+مين؟ في A إيش أعمل اضربت الطرفين؟ في A مدن هذه
+
+324
+00:32:14,520 --> 00:32:16,300
+صحيحة
+
+325
+00:32:17,720 --> 00:32:20,580
+الـ B تقسم الـ A مادام الـ B تقسم الـ A أصلا على
+
+326
+00:32:20,580 --> 00:32:28,240
+طول الـ B هتقسم الـ A to the B minus 1 أو A to the
+
+327
+00:32:28,240 --> 00:32:32,740
+B أو A to the أي إشي مظبوط؟ A to the أي positive
+
+328
+00:32:32,740 --> 00:32:37,300
+number فاهمين؟ إذا هتقسم مين أي linear combination
+
+329
+00:32:37,300 --> 00:32:41,700
+بينهم يعني الـ A الـ B هتقسم الـ A to the B نقص
+
+330
+00:32:41,700 --> 00:32:47,720
+الـ A صح؟ يعني معناته أن الـ B الـ A to the Bتطابق
+
+331
+00:32:47,720 --> 00:32:54,280
+الـ A مضله مين؟ مضله B وهو المصطلح إذن أصلاً هذه
+
+332
+00:32:54,280 --> 00:33:00,200
+في حالة الـ B بتقسم الـ A في حالة الـ B اللي هي لا
+
+333
+00:33:00,200 --> 00:33:03,040
+تقسم الـ A الـ A تده B مانس واحد تطابق الواحد مضله
+
+334
+00:33:03,040 --> 00:33:08,260
+B على طول وفي حالة الـ B بتقسم الـ A على طول ما هي
+
+335
+00:33:08,260 --> 00:33:10,780
+الـ B بتقسم الـ B الـ A تده B إذن الـ B بتقسم الـ
+
+336
+00:33:10,780 --> 00:33:14,960
+A تده B نقص A إذن الـ A تده B تطابق الـ A مضله B
+
+337
+00:33:14,960 --> 00:33:19,620
+فاهمين علشان ما أقول؟ طيبيجي ناخد مثالنا الأخير
+
+338
+00:33:19,620 --> 00:33:25,080
+وننهي فيه المحاضرة المثال
+
+339
+00:33:25,080 --> 00:33:35,020
+كما يلي example
+
+340
+00:33:35,020 --> 00:33:38,360
+example
+
+341
+00:33:38,360 --> 00:33:46,340
+find the remainder of
+
+342
+00:33:47,900 --> 00:33:54,060
+خمسة مثلا زي ما هو الكاتب أس سبعة ستة أربعة تلاتة
+
+343
+00:33:54,060 --> 00:34:09,240
+اتنين تلاتة تمانية when it is divided by 11 اه بدي
+
+344
+00:34:09,240 --> 00:34:15,580
+اللي هو ال remainder لهذا العدد لو قسمناه على مين
+
+345
+00:34:15,580 --> 00:34:22,130
+على 11الـ solution أكيد صار بده إيش هو؟ بده إيه؟
+
+346
+00:34:22,130 --> 00:34:26,630
+خمسة لإن سبعة، ستة، أربعة، تلاتة، اتنين، تلاتة،
+
+347
+00:34:26,630 --> 00:34:35,270
+تمانية تطابق ماذا مدلوا مين مدلوا أحداشر الآن أكيد
+
+348
+00:34:35,270 --> 00:34:38,910
+هنحلوا على مين، هنسهل على حالة مش معقول واحد ييجي
+
+349
+00:34:38,910 --> 00:34:55,070
+يحسب هذولةماذا نفعل حسب نظرية الهان ال 11 لا تقسم
+
+350
+00:34:55,070 --> 00:35:02,730
+الخمسة اذا عندي خمسة أس بي ماينس واحد اللي هو عشرة
+
+351
+00:35:02,730 --> 00:35:08,710
+هي بي تطابق الواحد مدله مين مدله 11
+
+352
+00:35:12,310 --> 00:35:20,010
+أس سبعة ستة أربعة تلاتة اتنين تلاتة سفر هي نفسها
+
+353
+00:35:20,010 --> 00:35:25,730
+عبارة عن خمسة أس عشرة أس فاهمين عليها سبعة ستة
+
+354
+00:35:25,730 --> 00:35:32,490
+أربعة تلاتة اتنين تلاتة ماشي
+
+355
+00:35:32,490 --> 00:35:39,430
+سلت التمانية متفقين على هذا احنا اه اه ده ايش ماله
+
+356
+00:35:39,430 --> 00:35:46,710
+هو هذالأن رفعت يعني الواحد لهذا الأُس بيصير هذا
+
+357
+00:35:46,710 --> 00:35:51,250
+بطابق برضه مين مُدُل ومين مُدُل واحد عاشر إذا ان
+
+358
+00:35:51,250 --> 00:35:53,290
+رقمنا هذا بطابق الواحد مُدُل واحد عاشر ضال مين
+
+359
+00:35:53,290 --> 00:35:57,810
+عنده إذا نسأله ضال بس خمسة أُس إيش تمانية لو
+
+360
+00:35:57,810 --> 00:36:02,490
+ضربناها في الطرفين بنحصل اللي بدناها الآن اتطلع
+
+361
+00:36:02,490 --> 00:36:07,260
+على خمساش تمانية اتطلع عليهاحسبة بسيطة خمسة أقصى
+
+362
+00:36:07,260 --> 00:36:10,680
+اتنين اشمالها اللي هي خمسة وعشرين الخمسة وعشرين
+
+363
+00:36:10,680 --> 00:36:16,180
+بالنسبة للأحداش جديش تلاتة تلاتة modulo مين modulo
+
+364
+00:36:16,180 --> 00:36:21,540
+أحداش التلاتة ارفعليها دا أقصى اتنين بصير أقصى
+
+365
+00:36:21,540 --> 00:36:24,400
+اتنين تطابق تلاتة أقصى اتنين اللي هي مين تسعة
+
+366
+00:36:24,400 --> 00:36:31,270
+التسعة اشمالها ناقص اتنين modulo أحداشواضح ها ارفع
+
+367
+00:36:31,270 --> 00:36:34,290
+للتنين طبعا باي طريقة ممكن تحسبها مرة واحدة ارفع
+
+368
+00:36:34,290 --> 00:36:37,650
+للتنين بإيش لو ماعكاش قلب اعمل زي هيك الان ارفع
+
+369
+00:36:37,650 --> 00:36:41,910
+ليها اللي اقص تنين كمان بيصير خمسة اقص ثمانية
+
+370
+00:36:41,910 --> 00:36:47,230
+تطابق نقص اتنين اقص اتنين مظبوط اللي هي جداش اربعة
+
+371
+00:36:47,230 --> 00:36:53,210
+مدلو احداش صار عندي هذه الحسبة اليدوية وهذه الحسبة
+
+372
+00:36:53,210 --> 00:36:58,460
+الوسطى النظريةبصير together اتنتين مع بعض اذا
+
+373
+00:36:58,460 --> 00:37:05,720
+اضربهم في بعض اذا خمسة أس سبعة ستة تلاتة اتنين
+
+374
+00:37:05,720 --> 00:37:11,240
+تلاتة تمانية تطابق أربعة في مين في واحد اللي هي
+
+375
+00:37:11,240 --> 00:37:20,100
+تطابق الأربعة Modulo 11 عشان تشوف كم تسهل علينا
+
+376
+00:37:20,100 --> 00:37:23,100
+نظرية من هذا النوع وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/2fLs3qcbN4s_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/2fLs3qcbN4s_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0ec7b74664906edd9618ea7a5ece6597d8861c83
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/2fLs3qcbN4s_raw.srt
@@ -0,0 +1,1504 @@
+1
+00:00:19,490 --> 00:00:24,050
+بسم الله الرحمن الرحيم المحاضرة رقم 16 نظرية
+
+2
+00:00:24,050 --> 00:00:28,490
+الأعداد قسم رياضيات الجامعة الإسلامية كوليوتية
+
+3
+00:00:28,490 --> 00:00:36,580
+العلوم والتربيةهنكمل اليوم الحديث عن ما تبقى من
+
+4
+00:00:36,580 --> 00:00:41,980
+section Chinese remainder theorem and the linear
+
+5
+00:00:41,980 --> 00:00:46,900
+congruences وصلنا لعند نظرية 4.9 عليها the system
+
+6
+00:00:46,900 --> 00:00:54,620
+of linear congruences Ax زي By بسوء R تطابق
+
+7
+00:00:54,620 --> 00:01:06,850
+R modulo andو d abc x زائد dy وطابق s modulo n هذا
+
+8
+00:01:06,850 --> 00:01:17,470
+ال system المعدلتين مع بعض has a unique solution
+
+9
+00:01:17,470 --> 00:01:23,990
+modulo n whenever
+
+10
+00:01:26,400 --> 00:01:36,160
+الـ Greatest Common Divisor بين الـ AD نقص BC و
+
+11
+00:01:36,160 --> 00:01:43,780
+الـ N بساوي 1 الـ proof النظرية
+
+12
+00:01:43,780 --> 00:01:49,110
+كما يلي مرة أخرىالنظرية بتقول إن الـ system of
+
+13
+00:01:49,110 --> 00:01:51,970
+linear congruences اللي أمامي طبعاً عندي ال
+
+14
+00:01:51,970 --> 00:01:55,330
+congruence الأولى فيها مجهولين X و Y و ال
+
+15
+00:01:55,330 --> 00:01:58,530
+congruence التانية برضه فيها مجهولين لأن الحل
+
+16
+00:01:58,530 --> 00:02:04,490
+المشترك لـ two congruences موجود و unique مدلقاً
+
+17
+00:02:04,490 --> 00:02:09,240
+في حال إنه كان العامل المشترك الأعلى بينه لاحظاللي
+
+18
+00:02:09,240 --> 00:02:15,020
+هو AD معامل X في الأولى مضروب معامل Y في التانية
+
+19
+00:02:15,020 --> 00:02:20,800
+ناقص معامل X في التانية مضروب في معامل Y في الأولى
+
+20
+00:02:20,800 --> 00:02:24,180
+المعامل المشترك الأعلى بين هذا الرقم اللي .. اللي
+
+21
+00:02:24,180 --> 00:02:27,240
+.. اللي حكيته وبين الـ N إيش بيساوي؟ بيساوي واحد
+
+22
+00:02:27,240 --> 00:02:29,500
+إذا كان موجود بيساوي واحد هذا العامل المشترك
+
+23
+00:02:29,500 --> 00:02:33,160
+الأعلى معناته اللي هو الـlinear congruences هدولة
+
+24
+00:02:33,160 --> 00:02:41,400
+الهن حل مشترك وحيد Modulo N خلينا نحلبنثبت أن هذا
+
+25
+00:02:41,400 --> 00:02:47,120
+هو الحل الوحيد الآن كما بنعمل بالظبط في المعادلة
+
+26
+00:02:47,120 --> 00:02:50,640
+العاديةاللي هي في المجهولين بنضرب الأولى في رقم
+
+27
+00:02:50,640 --> 00:02:53,940
+والتانية في رقم بحيث أنه بنترحن أو بنجمحن بالطريقة
+
+28
+00:02:53,940 --> 00:02:58,380
+المناسبة بحيث ن cancel أحد اللي هو المجهولين ونوجد
+
+29
+00:02:58,380 --> 00:03:03,820
+من المجهول الآخر عنا طبعا مين المجهيل X وY وX وY
+
+30
+00:03:03,820 --> 00:03:08,720
+هاي المجهيل ومين اللي هي الـA والـB والـC والـD
+
+31
+00:03:08,720 --> 00:03:13,200
+والـR والـS والـN هي عبارة عن ثوابت بين دينا بتكون
+
+32
+00:03:13,200 --> 00:03:18,090
+معطية لناإذاً الغرض أن وجد قيمة X وY هل موجودات و
+
+33
+00:03:18,090 --> 00:03:23,630
+لا مش موجودات نضرب المعادلة الأولى خلّيني أضربها
+
+34
+00:03:23,630 --> 00:03:29,970
+في D هذه بدأت أضربها في D وهذه بدأت أضربها في مين؟
+
+35
+00:03:29,970 --> 00:03:35,090
+في B عرفته ليش؟ عساس أن أضرب هذه في D وهذه في B
+
+36
+00:03:35,090 --> 00:03:39,650
+واترحل من بعض بكون طيارة مين؟ المتغير Y وضل عند
+
+37
+00:03:39,650 --> 00:03:44,130
+المتغير مين؟ X بصير عندي الآن D
+
+38
+00:03:46,840 --> 00:03:54,580
+A و هنا B ناقص B في C الكل في X فاهمين عليها مش ده
+
+39
+00:03:54,580 --> 00:03:59,920
+علي التفصيل موجود التفصيل كله في الكتاب تطابق D في
+
+40
+00:03:59,920 --> 00:04:10,220
+R ناقص B في S كله مضلمين Moduli اذا بضرب طرفي
+
+41
+00:04:10,830 --> 00:04:15,290
+التطابق الأولى في D وطرفي التطابق الثانية في B
+
+42
+00:04:15,290 --> 00:04:21,170
+وطرح اللى هو الأولى ناقص الثانية بطلع عندى اللى هو
+
+43
+00:04:21,170 --> 00:04:27,850
+اللى أمامى Model 1 الان هو معطينى أن العامل
+
+44
+00:04:27,850 --> 00:04:34,150
+المشترك الأعلى ال greatest common divisor since ال
+
+45
+00:04:34,150 --> 00:04:40,520
+greatest common divisor بين الـDA ناقص BCوالـ N
+
+46
+00:04:40,520 --> 00:04:46,960
+بساوي واحد ثم الآن
+
+47
+00:04:46,960 --> 00:04:57,680
+التطابقة اللي هي AD ناقص BC في Z تطابق الواحد
+
+48
+00:04:57,680 --> 00:05:06,140
+Modulo N has a unique solution
+
+49
+00:05:07,650 --> 00:05:12,170
+Modulo N ايش اللي سويته؟ ايش عملت تيك؟ احنا غربنا
+
+50
+00:05:12,170 --> 00:05:18,170
+ايه؟ عشان نوجد قيمة مين؟ قيمة X ماشي؟ الان بدي
+
+51
+00:05:18,170 --> 00:05:22,910
+اعمل اللي هو بدي اواجد قيمة T اللي بتحقق طرفي
+
+52
+00:05:22,910 --> 00:05:29,010
+المعادلة هذه ايش معنى هذه؟ بعد شوية هوصل هذا الطرف
+
+53
+00:05:29,010 --> 00:05:35,150
+للطرف هنا بطريقة معينة ومن خلالها هصل لقيمة X شوف
+
+54
+00:05:35,150 --> 00:05:39,580
+عليها ايش اللي بقولهالان المتطابقة هذه تطابق واحد
+
+55
+00:05:39,580 --> 00:05:43,320
+مضلوان بما ان العام المشترك اللي على بين هذه و هذه
+
+56
+00:05:43,320 --> 00:05:47,260
+بيساوي واحد اذا it has a unique solution هذه
+
+57
+00:05:47,260 --> 00:05:50,560
+بالظبط مشابهة للي كنا نحكي فيه في ال linear
+
+58
+00:05:50,560 --> 00:05:55,300
+congruences لما نوجد قيمة اللي هو ال X في ال
+
+59
+00:05:55,300 --> 00:05:58,540
+linear congruences العادية و في الآخر نعوضها في
+
+60
+00:05:58,540 --> 00:06:03,180
+الحل العام و نوجد قيمة ال X bar نفس المتطابقة لكن
+
+61
+00:06:03,180 --> 00:06:07,710
+اللي هي العام اللي اختلف الاناتفاجرنا ان هذا الوضع
+
+62
+00:06:07,710 --> 00:06:13,230
+لديه حلول إيميجية Say then أو then there exist T
+
+63
+00:06:13,230 --> 00:06:21,470
+element in Z such that AD-BC في T يطابق الواحد
+
+64
+00:06:21,470 --> 00:06:26,850
+مضلومين مضلوا عنه سميلي هذه التي هي اتنين وهذه
+
+65
+00:06:26,850 --> 00:06:33,940
+سميها واحد معايا يا شبابماذا يعني أن هذه المعادلة
+
+66
+00:06:33,940 --> 00:06:38,100
+لديها solution يعني صارت بين إيديا في T في Z
+
+67
+00:06:38,100 --> 00:06:41,880
+بتحقيق الطرفين يعني بمعنى آخر هذه في T تطابق
+
+68
+00:06:41,880 --> 00:06:46,560
+الواحد مدلومين مدلون اضرب لي هذه المعادلة هذه
+
+69
+00:06:46,560 --> 00:06:58,540
+اضربها في X بيصير عندي AD-BC في X في T تطابق ال X
+
+70
+00:06:58,540 --> 00:07:04,220
+مدلومين مدلون واضح أه؟بصيرنا عارفين وحالنا و اين
+
+71
+00:07:04,220 --> 00:07:13,360
+رايحين الان واحد اضربها برضه في مين؟ في T ليش؟ لما
+
+72
+00:07:13,360 --> 00:07:20,200
+اضرب في T بيصير عبارة عن AD ناقص BC في X في T
+
+73
+00:07:20,200 --> 00:07:28,280
+تطابق الـDR ناقص BS في مين؟ في T كله مين؟ Modulo N
+
+74
+00:07:28,280 --> 00:07:33,920
+تنسوش ان الـT صار رقم بين إيدياوهذه كلها المددات
+
+75
+00:07:33,920 --> 00:07:38,520
+بين إيديها لأن من هذه ومن هذه خاصية التعدي معناته
+
+76
+00:07:38,520 --> 00:07:46,180
+صارت X أشمالها X تطابق T في DR ناقص BS كله مدلوا
+
+77
+00:07:46,180 --> 00:07:51,300
+مين والـ T unique وحيدة من الأول مدلوا أن إذا صار
+
+78
+00:07:51,300 --> 00:07:56,200
+عند X has a unique value مدلوا أن اللي هي مين
+
+79
+00:07:56,200 --> 00:08:03,410
+بالظبط الـ T في DR ناقص مينباس هذه الآن قيمة X
+
+80
+00:08:03,410 --> 00:08:09,530
+بدوجن قيمة مين؟ قيمة Y Similarly بالنسبة لقيمة Y
+
+81
+00:08:09,530 --> 00:08:15,150
+بضرب المعادلة الأولى الآن والمعادلة التانية أو
+
+82
+00:08:15,150 --> 00:08:20,330
+التطابق الأولى والتطابق الثانية بضرب الأولى عشان
+
+83
+00:08:20,330 --> 00:08:26,750
+أضيع مين الآن؟اللي هو X بضرب الهدف C وهدف مين في A
+
+84
+00:08:26,750 --> 00:08:34,790
+و بترحل من بعض فبصير عنده C في B C في B ناقص A في
+
+85
+00:08:34,790 --> 00:08:45,270
+D الكل في Y تطابق اللي هو CR ناقص AS كله مضلوا مين
+
+86
+00:08:45,270 --> 00:08:48,070
+مضلوا يعني واضح أه
+
+87
+00:08:51,220 --> 00:09:00,520
+معنى يا عزيزي اه؟ الان
+
+88
+00:09:00,520 --> 00:09:06,880
+هذه الان هي التطابقه اللي بدها توصلي لقيمة اللي هي
+
+89
+00:09:06,880 --> 00:09:11,900
+ل .. اللي هي لما اضربها الان في X الجهتين بعد ما
+
+90
+00:09:11,900 --> 00:09:18,070
+وصلت لجتياللي هي هذه أداء للوصول لربط اللي هي
+
+91
+00:09:18,070 --> 00:09:21,750
+التطابق اللي بتطلع منها بالتطابق الأصلي من أجل
+
+92
+00:09:21,750 --> 00:09:27,060
+الحصول على X كيف وصلنا لجينة T؟طب كيف لجينا الـ T؟
+
+93
+00:09:27,060 --> 00:09:31,440
+قولنا هذا و هذا عاملهم واحد إذا فيه أكيد T و وجدنا
+
+94
+00:09:31,440 --> 00:09:35,740
+الـ T هذا الآن جسر وصلنا من خلاله ضربناه في X
+
+95
+00:09:35,740 --> 00:09:40,620
+حصلنا على هذه و الأولى ضربناها في T و حصلنا على
+
+96
+00:09:40,620 --> 00:09:44,720
+هذا هو نفس الطرف هذا صار عندي هذا بيساوي في T
+
+97
+00:09:44,720 --> 00:09:49,900
+بيساوي مين؟ قيمة X إذا هي عبارة عن مفتاح الأمر
+
+98
+00:09:49,900 --> 00:09:55,660
+للحلأي بني هذي هتكون مفتاح لحل اللي عندي شوف كيف
+
+99
+00:09:55,660 --> 00:10:00,200
+وصلنا لهذه فاهمين كيف وصلنا ضربنا الطرفين هذولة
+
+100
+00:10:00,200 --> 00:10:04,320
+الأول في C والتاني في A وطرحناها من بعض طيبنا قيمة
+
+101
+00:10:04,320 --> 00:10:09,480
+X وطلعت عندي القيمة اللي أمامي الآن بالضبط بهذه
+
+102
+00:10:09,480 --> 00:10:13,080
+المعادلة كلها في مين في T T صرت جيبها أنا وعرفها
+
+103
+00:10:13,080 --> 00:10:21,360
+فبصير عندي الآن CBنقص A في D في Y في T تطابق CR
+
+104
+00:10:21,360 --> 00:10:28,240
+نقص AS في T كله مدلون مين مدلون حصلت على هذه برجع
+
+105
+00:10:28,240 --> 00:10:34,580
+لمين لأكتر طابق اتنين اللي هي مفتاح الحل هذه بدرب
+
+106
+00:10:34,580 --> 00:10:43,720
+في مين الطرفين في Y بيصير عندك الان Y AD نقص BC في
+
+107
+00:10:43,720 --> 00:10:54,110
+Yفى T نضربها فى مين فى سالب تطابق ال AS نقص CR فى
+
+108
+00:10:54,110 --> 00:11:00,950
+مين فاش ضربنا احنا لأ اش ضربنا احنا ضربنا في مين
+
+109
+00:11:00,950 --> 00:11:05,750
+انا اللى برا اتكلم ده ضربنا في Y فبصير عندى تطابق
+
+110
+00:11:05,750 --> 00:11:14,850
+Y مظبوطة Modulo مين Modulo Nواضح؟ الان عندي هذا هو
+
+111
+00:11:14,850 --> 00:11:18,490
+هذا مع هذا سالب إذا من التنتين مع بعض بخاصية
+
+112
+00:11:18,490 --> 00:11:23,390
+التعدي بالسير Y تطابق اللي هو الآن سالب بتاخد هذا
+
+113
+00:11:23,390 --> 00:11:31,350
+بالسير AS نقص CR في T modulo mean مفهوم أه؟ هذا
+
+114
+00:11:31,350 --> 00:11:36,910
+اللي هو قيمة mean قيمة Y إذا صار عندي the unique
+
+115
+00:11:36,910 --> 00:11:47,080
+solution modulo Nاللي هو X بتساوي كده و
+
+116
+00:11:47,080 --> 00:11:55,020
+Y بتساوي كده من هنا مفتاح الأمر إلينا اللي هي
+
+117
+00:11:55,020 --> 00:11:56,500
+التطابق اللي أمامنا
+
+118
+00:12:00,340 --> 00:12:02,920
+والـ T أشمالها واحدة إذاً هي كأثباتنا unique
+
+119
+00:12:02,920 --> 00:12:09,900
+solution مدلوق لاحظ الآن إذا عمليا عشان اللي هو
+
+120
+00:12:09,900 --> 00:12:13,360
+نتذكر إيش اللي بنعمله عشان نحل السؤال من هذا النوع
+
+121
+00:12:14,180 --> 00:12:19,380
+إيش اللي بلزمني؟ بلزمني بس أحل التطابق هذه طبعاً
+
+122
+00:12:19,380 --> 00:12:22,000
+واحد بده يحل بنفس الطريقة اللي حلناها ويمشي نفس
+
+123
+00:12:22,000 --> 00:12:26,980
+الاشي بنفع بس كل مرة إيش ماله بده يطول في الحل لكن
+
+124
+00:12:26,980 --> 00:12:32,460
+أنا الأن فهمت روح البرهان وفهمت روح الحديث لحل
+
+125
+00:12:32,460 --> 00:12:36,780
+التطابق تاني إذا بس خليني أركز على اللي هي كيف
+
+126
+00:12:36,780 --> 00:12:40,640
+اللي هو بحل هذا التطابق ومن ثم أعوض عن X وY ويكون
+
+127
+00:12:40,640 --> 00:12:46,510
+خلصناه شوف عنديوانتبه علي أيش اللي بقوله إذا الأول
+
+128
+00:12:46,510 --> 00:12:49,230
+خطوة أن أنا بفحص
+
+129
+00:12:51,970 --> 00:12:55,690
+A×D مُعامل X في الأولى مضروب في مُعامل Y في
+
+130
+00:12:55,690 --> 00:12:59,990
+الثانية ناقص مُعامل X في الثانية مضروب في مُعامل Y
+
+131
+00:12:59,990 --> 00:13:03,830
+في الأولى إذا كان هذا العدد مع اللي هو الآن الـ
+
+132
+00:13:03,830 --> 00:13:06,090
+Grade-Sum Indivisor بساوي واحد معناته فيه عندي إيش
+
+133
+00:13:06,090 --> 00:13:09,790
+مال و بضمن فيه عندي unique solution مُدرُع ماشي
+
+134
+00:13:09,790 --> 00:13:13,830
+الحالة طيب الآن لجيته اللي هو بساوي بطابق الواحد
+
+135
+00:13:13,830 --> 00:13:18,560
+إيش بسوي الخطوة الثانية باجياللي فحصت فيه ركزوا في
+
+136
+00:13:18,560 --> 00:13:22,020
+اللي بحكي اللي فحصت فيه اللي هو هذا بضربه في T
+
+137
+00:13:22,020 --> 00:13:25,960
+تطابق واحد مضلقا و بوجد ال solution لأنه أنا ضامن
+
+138
+00:13:25,960 --> 00:13:28,640
+ال answer ان هو هذا و هذا واحد معناته في unique
+
+139
+00:13:28,640 --> 00:13:32,660
+solution بوجد قيمة مين الآن قيمة T بصير T بين
+
+140
+00:13:32,660 --> 00:13:36,720
+إيديا بعد ما صير ال T بين إيديا باجي بقول إذا ال
+
+141
+00:13:36,720 --> 00:13:41,920
+solution هو X بتساوي ال T اللي لجيتها مضروبة في D
+
+142
+00:13:41,920 --> 00:13:53,810
+في مين؟ في Rهذا قيمة X باخد معامل Y في الثانية
+
+143
+00:13:53,810 --> 00:13:58,290
+وبضربه في مين في الحد المطلق اللي هو في الأولى
+
+144
+00:14:04,780 --> 00:14:12,440
+في الثانية فاهمين هذا مين اللي هو X و Y بعكس ببدأ
+
+145
+00:14:12,440 --> 00:14:16,300
+بمين بالمعامل X في الأولى و بضربه في الحد المطلق
+
+146
+00:14:16,300 --> 00:14:20,120
+في الثانية و نفس الاشي في الثانية و بضربه في الحد
+
+147
+00:14:20,120 --> 00:14:25,630
+المطلق في الأولى اللي هومعامل X عشان الـ Y وهنا
+
+148
+00:14:25,630 --> 00:14:29,010
+معامل Y عشان الـ X مضروب في الحد المطلق في كل
+
+149
+00:14:29,010 --> 00:14:32,070
+منهما و مرة باخد المعادلة الأولى قبل و مرة باخد
+
+150
+00:14:32,070 --> 00:14:35,030
+المعادلة الثانية قبل عساس إشارة النقص واضح اللي
+
+151
+00:14:35,030 --> 00:14:45,690
+بحكيه طيب نيجي الآن بدنا ناخد مثال example
+
+152
+00:14:45,690 --> 00:14:50,970
+find the solution example
+
+153
+00:14:54,360 --> 00:15:07,260
+Find the solution of the system 7x
+
+154
+00:15:07,260 --> 00:15:11,820
+plus 3y تطابق
+
+155
+00:15:11,820 --> 00:15:24,180
+العشرة modulo 16 2x plus 5yتطابق التسعة modulo 16
+
+156
+00:15:24,180 --> 00:15:30,020
+الآن
+
+157
+00:15:30,020 --> 00:15:35,880
+بدي أحل هذا ال system of two linear congruences of
+
+158
+00:15:35,880 --> 00:15:39,040
+two variables يعني بدي أحل بمعنى أخر بدي أجد قيمة
+
+159
+00:15:39,040 --> 00:15:45,380
+XY اللي بتحقق اللي هو التطابقتين الآن أول شيء بقول
+
+160
+00:15:45,380 --> 00:15:46,540
+solution
+
+161
+00:15:48,420 --> 00:15:51,940
+بقول الـ greatest بما انه الـ greatest common
+
+162
+00:15:51,940 --> 00:15:58,640
+divisor بين سبعة في خمسة خمسة و تلاتين ناقص اتنين
+
+163
+00:15:58,640 --> 00:16:05,260
+في تلاتة بستة مع الست عشر بساوي ال greatest common
+
+164
+00:16:05,260 --> 00:16:10,180
+divisor هذا العدد من هو تسعة و عشرين مع الست عشر
+
+165
+00:16:10,180 --> 00:16:15,540
+ايش هيساوي طبيعي واحد اذا ال system
+
+166
+00:16:18,430 --> 00:16:24,210
+Has a unique solution
+
+167
+00:16:24,210 --> 00:16:30,110
+modulo 16 معاه؟ بدنا نوجد هذا ال solution قولنا
+
+168
+00:16:30,110 --> 00:16:39,250
+مفتاح الحل مين هي؟ الـ هي هذه الآن عندياللي فحصت
+
+169
+00:16:39,250 --> 00:16:44,890
+فيها هي اللي هي الـ 29 بضربها في T اللي فحصت فيها
+
+170
+00:16:44,890 --> 00:16:51,490
+تطابق الواحد modulo 16 معايا وهي اللي بتوجد الـ T
+
+171
+00:16:51,490 --> 00:16:57,630
+فيها او جد الـ T بكون خلصت الان الان 29 بدي أشيل
+
+172
+00:16:57,630 --> 00:17:02,370
+منها 16 أو تنتين يمكن 16 أسهل لي اللي هي بشيل 32
+
+173
+00:17:02,370 --> 00:17:10,420
+يعني بيصير ناقص 3T ناقص 3Tتطابق الـ 1 الـ 1 سأجعل
+
+174
+00:17:10,420 --> 00:17:15,600
+شيء يقبل الجسم على ثلاثة واضح لو أجهزت من الـ 1 16
+
+175
+00:17:15,600 --> 00:17:22,040
+يصبح ناقص 15 ناقص 15 يعني جاي على طول مضله مين
+
+176
+00:17:22,040 --> 00:17:25,600
+مضله 16 بقسم الجهتين على مين على ناقص ثلاثة لو
+
+177
+00:17:25,600 --> 00:17:29,340
+جلسكم الـ divisor مع السلطه عشان يساوي واحد يصبح
+
+178
+00:17:29,340 --> 00:17:36,410
+عند الـ T تطابق الخمسةمعدل مين 16 الان ال
+
+179
+00:17:36,410 --> 00:17:43,410
+solutions او solution the solution is
+
+180
+00:17:43,410 --> 00:17:53,670
+لان كنا وحيد ايش هو X بتساوي الان وين معدلتنا اللي
+
+181
+00:17:53,670 --> 00:18:00,230
+هو الان اباجي لمين لو Y ماشي عندى خمسة في عشرة
+
+182
+00:18:00,230 --> 00:18:13,600
+خمسينناقص 3×9 هو 27 وهو عبارة عن جداش 23 مظبوط
+
+183
+00:18:13,600 --> 00:18:25,820
+مدله 16 الـ 23 جداش بيكون X تطابق 7 مدله 16 هذا
+
+184
+00:18:25,820 --> 00:18:34,020
+اللي هو قيمة X الـ Y Y تساوي الآن أخدتأه في T أسف
+
+185
+00:18:34,020 --> 00:18:40,560
+أسف جدش T خمسة خمسة بتطلع خمسة في تلاتة و عشرين
+
+186
+00:18:40,560 --> 00:18:46,700
+جدش بتطلع عندنا قولوا معنا 115 هي جدش طلعت هنا
+
+187
+00:18:46,700 --> 00:18:51,440
+سبعة خمسة و تلاتين تلاتة يعني عارفين كيف حسبتها
+
+188
+00:18:51,440 --> 00:18:54,940
+طلعت هذه جدش أنا في الأول سبعة في خمسة و خمسة و
+
+189
+00:18:54,940 --> 00:18:57,400
+تلاتين خمسة و تلاتين شيل اتنين اتنين و تلاتين ضال
+
+190
+00:18:57,400 --> 00:18:59,380
+جدش تلاتة فاهمين why
+
+191
+00:19:02,640 --> 00:19:06,860
+الحسابات كلها why نجيب خواي ايش ال why اللي هو
+
+192
+00:19:06,860 --> 00:19:12,380
+سبعة في تسعة عكس تشايفين تلاتة و ستين ناقص اتنين
+
+193
+00:19:12,380 --> 00:19:18,520
+فعشرة بعشرين في ال T جداش ال T خمسة بلاش ننسيها زي
+
+194
+00:19:18,520 --> 00:19:22,660
+قبل شوية تلاتة و أربعين في خمسةاللي هي بتساوي
+
+195
+00:19:22,660 --> 00:19:26,680
+الستة عشر اتنين و تلاتين اتنين و تلاتين بزيد قداش
+
+196
+00:19:26,680 --> 00:19:31,580
+احداش احداش في خمسة خمسة و خمسين خمسة و خمسين شيل
+
+197
+00:19:31,580 --> 00:19:38,300
+منها شيل منها اتنين و تلاتين سبعة سبعة مضله ستة
+
+198
+00:19:38,300 --> 00:19:42,000
+عشر شيل منها اتنين و تلاتين التمانية و اربعين شيل
+
+199
+00:19:42,000 --> 00:19:45,140
+منها تمانية و اربعين من التلاتة من ال .. من ال ..
+
+200
+00:19:45,140 --> 00:19:51,040
+مضال مضال قداش سبعة باضح
+
+201
+00:19:51,040 --> 00:19:51,380
+اه؟
+
+202
+00:19:55,760 --> 00:20:04,320
+هذا اللي هو عندى y تطابق السبعة مدله 16 اتنين هذا
+
+203
+00:20:04,320 --> 00:20:07,840
+اللي هو the unique solution مدله 16 ال X وY هكذا
+
+204
+00:20:07,840 --> 00:20:11,960
+نكون خلصنا شبتر أربعة اللي هو the theory of
+
+205
+00:20:11,960 --> 00:20:17,660
+congruences الآن بدنا ننتقل إلى شبتر خمسة
+
+206
+00:21:24,530 --> 00:21:29,690
+الجزء الثاني من المحاضرة هو عبارة عن .. هندخل في
+
+207
+00:21:29,690 --> 00:21:33,810
+شقطر 5 اللي هو الـ Fermat's theorem أول section
+
+208
+00:21:33,810 --> 00:21:36,250
+هنبدأ فيه اللي هو خمسة اتنين اللي هو Fermat's
+
+209
+00:21:36,250 --> 00:21:41,170
+little theorem and pseudo-primes نحكي عن اللي هو
+
+210
+00:21:41,170 --> 00:21:49,070
+ال Fermat's little theoremالنظرية هي كما يلي بتقول
+
+211
+00:21:49,070 --> 00:21:54,950
+إذا كان عند بي برايم and
+
+212
+00:21:54,950 --> 00:22:03,130
+ال b لا يقسم ال a then ال a to the b minus one
+
+213
+00:22:03,130 --> 00:22:09,410
+تطابق الواحد modulo b a proof برايم number
+
+214
+00:22:15,080 --> 00:22:21,360
+عند بي الزبران معاياis a prime number والـ A is
+
+215
+00:22:21,360 --> 00:22:26,180
+any integer بحقق مالي أن الـ B لا تقسم من الـ A
+
+216
+00:22:26,180 --> 00:22:30,900
+إذا الـ A to the B minus واحد تطابق الواحد أشماله
+
+217
+00:22:30,900 --> 00:22:35,960
+modulo B طبعا هذه النظرية بتسهل علي كتير كتير كتير
+
+218
+00:22:35,960 --> 00:22:42,100
+كتير لعملية إيجاد ال remainder اللي هو عند القسمة
+
+219
+00:22:42,100 --> 00:22:46,260
+على A prime الأعداد اللي هو مرفوعة لقوة عالية جدا
+
+220
+00:22:47,010 --> 00:22:53,550
+خلّيني أبرهن النظرية والاشياء النظرية برهانها
+
+221
+00:22:53,550 --> 00:22:58,750
+يعتمد على الـ 6 التالية بدا أقول لك consider الـ
+
+222
+00:22:58,750 --> 00:23:05,290
+6S إيش الـ 6S هذا اللي بتداخلها؟ هي عبارة عن A و
+
+223
+00:23:05,290 --> 00:23:12,350
+2Aوتلاتة ايه لما أصل بي ماينس واحد في مين فيه ماشي
+
+224
+00:23:12,350 --> 00:23:17,850
+consider us بتساوي زي ما هى أمامى الآن هذه الست
+
+225
+00:23:17,850 --> 00:23:23,130
+بتثبتلك شغلتين فيها بتثبتلك ان ولا واحد من هدولة
+
+226
+00:23:23,130 --> 00:23:29,180
+عبارة عن سفرمدلبي يعني لا يطابق السفر مدلبي ولا
+
+227
+00:23:29,180 --> 00:23:34,240
+واحد منها اي واحد اتنين بدي اثبتلك انه كل العناصر
+
+228
+00:23:34,240 --> 00:23:38,580
+اللي موجودة هنا are incongruent ماشي ولا واحد
+
+229
+00:23:38,580 --> 00:23:42,340
+congruent لمين لا التاني طيب ايش علاقته بموضوعنا
+
+230
+00:23:42,340 --> 00:23:46,880
+هل جيت نشوف ايش علاقته بموضوعنا الان بدي افرض عشان
+
+231
+00:23:46,880 --> 00:23:53,540
+اثبت to prove thatاللي هو S Contains No Element
+
+232
+00:23:53,540 --> 00:23:58,920
+Congruent to Zero Modulo B We Assume Not يعني بدنا
+
+233
+00:23:58,920 --> 00:24:06,130
+نقول صبازبدأ أقول suppose that there exists S A في
+
+234
+00:24:06,130 --> 00:24:13,610
+الـ S S A as small S A المتنقض such that S A يطابق
+
+235
+00:24:13,610 --> 00:24:18,490
+الـ Zero modulo Min modulo B يعني فرضت أنه في يوجد
+
+236
+00:24:18,490 --> 00:24:23,050
+عنصر هنا اللي هو اسمه S A يطابق الـ Zero Min
+
+237
+00:24:23,050 --> 00:24:26,460
+modulo B و أسأل a contradictionمدام الاس ايه في
+
+238
+00:24:26,460 --> 00:24:30,980
+الاس؟ معناته الأصل الصغيرة هذه، يا واحد، يا اتنين،
+
+239
+00:24:30,980 --> 00:24:35,520
+يا تلاتة، يا مين، يعني صارت الاس هذه وين موجودة في
+
+240
+00:24:35,520 --> 00:24:42,130
+الواحد والتنين اللي عند البي ماقص واحدواضح؟ الـ S
+
+241
+00:24:42,130 --> 00:24:45,970
+A هذا اللي موجود في الـ S الكبيرة سيصبح الـ S A يا
+
+242
+00:24:45,970 --> 00:24:49,910
+صورة A يا اتنين A يا تلاتة A يا B minus واحد في A
+
+243
+00:24:49,910 --> 00:24:54,150
+يعني الـ S هذا عامل الـ A هيكون يا واحد يا اتنين
+
+244
+00:24:54,150 --> 00:24:57,810
+يا تلاتة يا B minus واحد يعني عامل الـ A هذا هيكون
+
+245
+00:24:57,810 --> 00:25:03,370
+في الست واحد اتنين عند مين B minus واحد طيب الآن
+
+246
+00:25:04,940 --> 00:25:08,380
+مدام S A تطبق الـ Zero modulo B وانا بعرف ان
+
+247
+00:25:08,380 --> 00:25:12,860
+العامل المشترك الأعلى B لا تقسم الـ A يعني بي مش
+
+248
+00:25:12,860 --> 00:25:17,540
+موجودة من الـ A من أصله إذا أكيد العامل المشترك
+
+249
+00:25:17,540 --> 00:25:20,640
+الأعلى بين الـ B و الـ A مش بساوي واحد مش عامل
+
+250
+00:25:20,640 --> 00:25:23,460
+بينهم لأن بي is a prime إذا صار عند ال greatest
+
+251
+00:25:23,460 --> 00:25:29,200
+common divisor بين الـ B و الـ A بساوي واحد إذا
+
+252
+00:25:29,200 --> 00:25:34,040
+معناته أنه بقدر أختصر الـ A من هنا و بيصير عند S
+
+253
+00:25:35,230 --> 00:25:40,970
+then S تطابق الـ 0 مضنوا مين مضنوا B صارت الـ S
+
+254
+00:25:40,970 --> 00:25:45,990
+small تطابق الـ 0 يعني بمعنى أخر الـ S الـ B بيكسب
+
+255
+00:25:45,990 --> 00:25:50,230
+من الـ S يعني الـ B الـ S من مضاعفات الـ B وهنا
+
+256
+00:25:50,230 --> 00:25:55,230
+أصلا الـ S مستحيل تكون اللي هي من مضاعفات الـ B
+
+257
+00:25:55,230 --> 00:26:00,590
+لأن الـ S عبارة عن واحد أو 2 أو B minus 1واضح وهذا
+
+258
+00:26:00,590 --> 00:26:07,530
+which is a contradiction يدن therefore therefore S
+
+259
+00:26:07,530 --> 00:26:12,930
+A لا تطابق ال zero modulo B for every S A element
+
+260
+00:26:12,930 --> 00:26:17,390
+in me هنا إذا فش ولا واحد فين بطابق ال zero اي
+
+261
+00:26:17,390 --> 00:26:24,810
+واحد اتنين بدي أثبت لك انه فش شيءأي واحد متطابق
+
+262
+00:26:24,810 --> 00:26:29,230
+التاني جوا ماشي الحال بدي أقولك برضه suppose not
+
+263
+00:26:29,230 --> 00:26:34,330
+يعني نفترض أنه في اتنين هنا متطابقين يعني بدي
+
+264
+00:26:34,330 --> 00:26:43,490
+أقولك suppose that there exist sr or sa or ra
+
+265
+00:26:43,490 --> 00:26:51,400
+element in s such that sa يطابق الra مضلمينفرضت
+
+266
+00:26:51,400 --> 00:26:58,040
+إنه فيه اتنين في الـ S متطابقين أكيد الـ S والـ R
+
+267
+00:26:58,040 --> 00:27:02,140
+مدام الـ S أيه هنا والـ R أيه موجودة هنا هيكون الـ
+
+268
+00:27:02,140 --> 00:27:06,280
+S أيه الـ S والـ R موجودات في الواحد والتانية اللي
+
+269
+00:27:06,280 --> 00:27:12,670
+عند مين بـ-1بما أن B لا يقسم الـA وB زبرايما، إذاً
+
+270
+00:27:12,670 --> 00:27:14,850
+العامل المشترك الأعلى بين الـB والـA زي ما قلنا
+
+271
+00:27:14,850 --> 00:27:19,410
+بـS1 إذاً بختصر هذه محادثة تظهر عند الـS تطابق
+
+272
+00:27:19,410 --> 00:27:24,950
+الـR Modulo B لكن هذا أصلاً كل العناصر اللي فيها
+
+273
+00:27:24,950 --> 00:27:28,410
+incomplete .. اللي هو incongruent، ليش؟ لأن أصلاً
+
+274
+00:27:28,410 --> 00:27:31,730
+هذا هو جزء من الـComplete Residue System Modulo B
+
+275
+00:27:31,730 --> 00:27:34,250
+يعني هذا Complete Residue System Modulo B إذا
+
+276
+00:27:34,250 --> 00:27:38,730
+دفنانه بالـ0إذاً أكيد العناصر أشمالهم are
+
+277
+00:27:38,730 --> 00:27:42,510
+incongruent إذاً هذا صار أشماله contradiction
+
+278
+00:27:42,510 --> 00:27:48,430
+Therefore .. Therefore صار S A لايطابق الـ R A في
+
+279
+00:27:48,430 --> 00:27:53,150
+كل العناصر الموجودة في مين فاس إذاً صار عندي اللي
+
+280
+00:27:53,150 --> 00:27:57,450
+صار عندي ما يليه أن الـ S هذه اللي هي عبارة عن الـ
+
+281
+00:27:57,450 --> 00:28:05,940
+A و 2A لعند الـ B-1 في الـ A عبارة عناللي هو
+
+282
+00:28:05,940 --> 00:28:11,800
+مجموعة فيها كم عنصر بي ماينس واحد من العناصر ركز
+
+283
+00:28:11,800 --> 00:28:18,860
+ولا واحد من هدولة بطابق إيش الآخر ولا واحد بطابق
+
+284
+00:28:18,860 --> 00:28:22,820
+الـ Zero إذا يعني لو بتناله الـ Zero هيصير
+
+285
+00:28:22,820 --> 00:28:29,320
+Complete Residue System مضلمين مضلبينبالظبط بالظبط
+
+286
+00:28:29,320 --> 00:28:35,900
+هذا صفر و واحد لعند الـ B- واحد ايش برضه Complete
+
+287
+00:28:35,900 --> 00:28:42,060
+Residue System Modulo B Modulo B نعرف هذا طيب يعني
+
+288
+00:28:42,060 --> 00:28:46,660
+الآن هذا الصفر اللي هنا والصفر اللي هنا لو شلناها
+
+289
+00:28:47,560 --> 00:28:51,480
+بصير هذا هو عبارة عن الـ Complete Residue مع هذا
+
+290
+00:28:51,480 --> 00:28:55,360
+الـ 0 وهذا الـ Complete Residue مع هذا الـ 2 يعني
+
+291
+00:28:55,360 --> 00:29:00,380
+بمعنى أخر كل عصر من هنا is congruent to one and
+
+292
+00:29:00,380 --> 00:29:05,730
+only one element هنايعني كل واحد فيه الواحد و بس
+
+293
+00:29:05,730 --> 00:29:09,490
+واحد عددهم هدولة بيه minus واحد وبعدها عددهم مين
+
+294
+00:29:09,490 --> 00:29:14,570
+بيه minus واحد يعني كل واحد من هان congruent one
+
+295
+00:29:14,570 --> 00:29:19,210
+and only one in this set إذا صار حاصل ضرب هدولة
+
+296
+00:29:19,210 --> 00:29:23,670
+أكيد أشماله يطابق حاصل ضرب هدولة يعني بمعنى أخر
+
+297
+00:29:23,670 --> 00:29:29,100
+صار عندك الفى الاتنين ايه لما أصل لعند الـ B-1 في
+
+298
+00:29:29,100 --> 00:29:35,640
+A يطابق الواحد فى التنين لعند ما أصل لعند مين مضله
+
+299
+00:29:35,640 --> 00:29:42,720
+مين مضله B طيب الان هذولة الآن ال A عدد هنا كم
+
+300
+00:29:42,720 --> 00:29:49,220
+واحدة واحدة تنتين لعند B-1 يعني فى عندك A مضروبة
+
+301
+00:29:49,220 --> 00:29:54,480
+في حالها B-1 من المرات معايا له A بيصير A أقصد B-1
+
+302
+00:29:55,650 --> 00:30:06,150
+مضروبة في 1 في 2 في B-1 تطابق هذه مين هي أصلاً B-1
+
+303
+00:30:06,150 --> 00:30:13,690
+فكتوريال وهذه مين برضه B-1 فكتوريال مضلوا مين
+
+304
+00:30:13,690 --> 00:30:17,650
+مضلوا B لاحظ العامل المشترك الأعلى بين ال B وB-1
+
+305
+00:30:17,650 --> 00:30:21,250
+فكتوريال ليش مثاوى لأن هذي 1 2 3 فاش فيهم B
+
+306
+00:30:21,250 --> 00:30:24,580
+بالمعروف أن ال B أكبر منه برأيإذا صار عند الان
+
+307
+00:30:24,580 --> 00:30:30,440
+اشماله الـ a to the b minus واحد تطابق الواحد
+
+308
+00:30:30,440 --> 00:30:43,260
+modulo b وهو المطلوب أي سؤال؟ طيب نيجي
+
+309
+00:30:43,260 --> 00:30:45,100
+الآن في عندنا corollary
+
+310
+00:30:50,020 --> 00:31:00,100
+بتقول if B is prime then A أُس B تطابق الـ A
+
+311
+00:31:00,100 --> 00:31:08,480
+modulo B الآن بيقول لي بغض النظر عن علاقة ال B و
+
+312
+00:31:08,480 --> 00:31:14,140
+ال A في بعض دايما هتلاقي أن A أُس B تطابق ال A
+
+313
+00:31:14,140 --> 00:31:14,980
+modulo A
+
+314
+00:31:21,340 --> 00:31:28,180
+الان عندى حلتين proof عندى
+
+315
+00:31:28,180 --> 00:31:35,740
+يال بى بتقسمش ال a يال بى بتقسماش ال a فى غير هيك
+
+316
+00:31:35,740 --> 00:31:40,220
+ليش جزأتين هيك لإنه أصلا نظريتي اللى بتعتمد عليها
+
+317
+00:31:40,220 --> 00:31:43,580
+اللى بتدرب الطرفين فيه زى ما قلته بس بتيجينانى لل
+
+318
+00:31:43,580 --> 00:31:49,800
+بى ده تقسم ال a لإن الحلتين هى trivialالأهل جاي
+
+319
+00:31:49,800 --> 00:31:55,280
+بتشوف الآن الـ B لتقسم مين الـ A مدام الـ B لتقسم
+
+320
+00:31:55,280 --> 00:31:58,960
+الـ A إذا by ال theorem اللي قبل بشوية A to the B
+
+321
+00:31:58,960 --> 00:32:03,140
+minus واحد تطابق الواحد مضلوا مين؟ مضلوا B اضرب
+
+322
+00:32:03,140 --> 00:32:10,400
+الجهتين في مين؟ في A فبصير الـ A تطابق الـ A مضلوا
+
+323
+00:32:10,400 --> 00:32:14,520
+مين؟ في A إيش أعمل اضربت الطرفين؟ في A مدن هذه
+
+324
+00:32:14,520 --> 00:32:16,300
+صحيحة
+
+325
+00:32:17,720 --> 00:32:20,580
+الـ B تقسم الـ A مادام الـ B تقسم الـ A أصلا على
+
+326
+00:32:20,580 --> 00:32:28,240
+طول الـ B هتقسم الـ A to the B minus 1 أو A to the
+
+327
+00:32:28,240 --> 00:32:32,740
+B أو A to the أي إشي مظبوط؟ A to the أي positive
+
+328
+00:32:32,740 --> 00:32:37,300
+number فاهمين؟ إذا هتقسم مين أي linear combination
+
+329
+00:32:37,300 --> 00:32:41,700
+بينهم يعني الـ A الـ B هتقسم الـ A to the B نقص
+
+330
+00:32:41,700 --> 00:32:47,720
+الـ A صح؟ يعني معناته أن الـ B الـ A to the Bتطابق
+
+331
+00:32:47,720 --> 00:32:54,280
+الـ A مضله مين؟ مضله B وهو المصطلح إذن أصلاً هذه
+
+332
+00:32:54,280 --> 00:33:00,200
+في حالة الـ B بتقسم الـ A في حالة الـ B اللي هي لا
+
+333
+00:33:00,200 --> 00:33:03,040
+تقسم الـ A الـ A تده B مانس واحد تطابق الواحد مضله
+
+334
+00:33:03,040 --> 00:33:08,260
+B على طول وفي حالة الـ B بتقسم الـ A على طول ما هي
+
+335
+00:33:08,260 --> 00:33:10,780
+الـ B بتقسم الـ B الـ A تده B إذن الـ B بتقسم الـ
+
+336
+00:33:10,780 --> 00:33:14,960
+A تده B نقص A إذن الـ A تده B تطابق الـ A مضله B
+
+337
+00:33:14,960 --> 00:33:19,620
+فاهمين علشان ما أقول؟ طيبيجي ناخد مثالنا الأخير
+
+338
+00:33:19,620 --> 00:33:25,080
+وننهي فيه المحاضرة المثال
+
+339
+00:33:25,080 --> 00:33:35,020
+كما يلي example
+
+340
+00:33:35,020 --> 00:33:38,360
+example
+
+341
+00:33:38,360 --> 00:33:46,340
+find the remainder of
+
+342
+00:33:47,900 --> 00:33:54,060
+خمسة مثلا زي ما هو الكاتب أس سبعة ستة أربعة تلاتة
+
+343
+00:33:54,060 --> 00:34:09,240
+اتنين تلاتة تمانية when it is divided by 11 اه بدي
+
+344
+00:34:09,240 --> 00:34:15,580
+اللي هو ال remainder لهذا العدد لو قسمناه على مين
+
+345
+00:34:15,580 --> 00:34:22,130
+على 11الـ solution أكيد صار بده إيش هو؟ بده إيه؟
+
+346
+00:34:22,130 --> 00:34:26,630
+خمسة لإن سبعة، ستة، أربعة، تلاتة، اتنين، تلاتة،
+
+347
+00:34:26,630 --> 00:34:35,270
+تمانية تطابق ماذا مدلوا مين مدلوا أحداشر الآن أكيد
+
+348
+00:34:35,270 --> 00:34:38,910
+هنحلوا على مين، هنسهل على حالة مش معقول واحد ييجي
+
+349
+00:34:38,910 --> 00:34:55,070
+يحسب هذولةماذا نفعل حسب نظرية الهان ال 11 لا تقسم
+
+350
+00:34:55,070 --> 00:35:02,730
+الخمسة اذا عندي خمسة أس بي ماينس واحد اللي هو عشرة
+
+351
+00:35:02,730 --> 00:35:08,710
+هي بي تطابق الواحد مدله مين مدله 11
+
+352
+00:35:12,310 --> 00:35:20,010
+أس سبعة ستة أربعة تلاتة اتنين تلاتة سفر هي نفسها
+
+353
+00:35:20,010 --> 00:35:25,730
+عبارة عن خمسة أس عشرة أس فاهمين عليها سبعة ستة
+
+354
+00:35:25,730 --> 00:35:32,490
+أربعة تلاتة اتنين تلاتة ماشي
+
+355
+00:35:32,490 --> 00:35:39,430
+سلت التمانية متفقين على هذا احنا اه اه ده ايش ماله
+
+356
+00:35:39,430 --> 00:35:46,710
+هو هذالأن رفعت يعني الواحد لهذا الأُس بيصير هذا
+
+357
+00:35:46,710 --> 00:35:51,250
+بطابق برضه مين مُدُل ومين مُدُل واحد عاشر إذا ان
+
+358
+00:35:51,250 --> 00:35:53,290
+رقمنا هذا بطابق الواحد مُدُل واحد عاشر ضال مين
+
+359
+00:35:53,290 --> 00:35:57,810
+عنده إذا نسأله ضال بس خمسة أُس إيش تمانية لو
+
+360
+00:35:57,810 --> 00:36:02,490
+ضربناها في الطرفين بنحصل اللي بدناها الآن اتطلع
+
+361
+00:36:02,490 --> 00:36:07,260
+على خمساش تمانية اتطلع عليهاحسبة بسيطة خمسة أقصى
+
+362
+00:36:07,260 --> 00:36:10,680
+اتنين اشمالها اللي هي خمسة وعشرين الخمسة وعشرين
+
+363
+00:36:10,680 --> 00:36:16,180
+بالنسبة للأحداش جديش تلاتة تلاتة modulo مين modulo
+
+364
+00:36:16,180 --> 00:36:21,540
+أحداش التلاتة ارفعليها دا أقصى اتنين بصير أقصى
+
+365
+00:36:21,540 --> 00:36:24,400
+اتنين تطابق تلاتة أقصى اتنين اللي هي مين تسعة
+
+366
+00:36:24,400 --> 00:36:31,270
+التسعة اشمالها ناقص اتنين modulo أحداشواضح ها ارفع
+
+367
+00:36:31,270 --> 00:36:34,290
+للتنين طبعا باي طريقة ممكن تحسبها مرة واحدة ارفع
+
+368
+00:36:34,290 --> 00:36:37,650
+للتنين بإيش لو ماعكاش قلب اعمل زي هيك الان ارفع
+
+369
+00:36:37,650 --> 00:36:41,910
+ليها اللي اقص تنين كمان بيصير خمسة اقص ثمانية
+
+370
+00:36:41,910 --> 00:36:47,230
+تطابق نقص اتنين اقص اتنين مظبوط اللي هي جداش اربعة
+
+371
+00:36:47,230 --> 00:36:53,210
+مدلو احداش صار عندي هذه الحسبة اليدوية وهذه الحسبة
+
+372
+00:36:53,210 --> 00:36:58,460
+الوسطى النظريةبصير together اتنتين مع بعض اذا
+
+373
+00:36:58,460 --> 00:37:05,720
+اضربهم في بعض اذا خمسة أس سبعة ستة تلاتة اتنين
+
+374
+00:37:05,720 --> 00:37:11,240
+تلاتة تمانية تطابق أربعة في مين في واحد اللي هي
+
+375
+00:37:11,240 --> 00:37:20,100
+تطابق الأربعة Modulo 11 عشان تشوف كم تسهل علينا
+
+376
+00:37:20,100 --> 00:37:23,100
+نظرية من هذا النوع وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/38AIlUjh8EM_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/38AIlUjh8EM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5676ccc663a9a3350da91d8c0ab6c17c0b38976a
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/38AIlUjh8EM_raw.json
@@ -0,0 +1 @@
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"probability": 0.8798828125}, {"start": 124.46, "end": 124.9, "word": " أخدناها", "probability": 0.88486328125}, {"start": 124.9, "end": 125.16, "word": " المرة", "probability": 0.925048828125}, {"start": 125.16, "end": 125.76, "word": " الماضية", "probability": 0.9938151041666666}, {"start": 125.76, "end": 126.44, "word": " بعد", "probability": 0.92333984375}, {"start": 126.44, "end": 126.68, "word": " هي", "probability": 0.88134765625}, {"start": 126.68, "end": 127.3, "word": " أخدنا", "probability": 0.846923828125}, {"start": 127.3, "end": 127.94, "word": " قلنا", "probability": 0.72509765625}, {"start": 127.94, "end": 128.4, "word": " أنه", "probability": 0.5565185546875}, {"start": 128.4, "end": 128.76, "word": " أي", "probability": 0.78564453125}], "temperature": 1.0}, {"id": 5, "seek": 15685, "start": 129.65, "end": 156.85, "text": "even perfect number هيكون اللي هو أن تطابق الستة مدله عشرة or أن تطابق التمانية مدله عشرة يعني أي even perfect number هيكون اللي هو الحد الأخير أو خانة الأحد فيه يا ستة يا تمانية الآن اطلع خليني ناخد الأسئلة المطلوبة انزل على الأسئلة المطلوبة", "tokens": [27170, 2176, 1230, 39896, 30544, 13672, 1829, 31439, 14739, 6055, 9566, 16758, 4587, 21136, 2655, 3660, 3714, 3215, 43761, 6225, 8592, 25720, 420, 14739, 6055, 9566, 16758, 4587, 16712, 2304, 7649, 10632, 3714, 3215, 43761, 6225, 8592, 25720, 37495, 22653, 36632, 754, 2176, 1230, 39896, 30544, 13672, 1829, 31439, 21542, 3215, 16247, 9778, 13546, 34051, 16490, 7649, 3660, 16247, 24401, 8978, 3224, 35186, 8608, 2655, 3660, 35186, 46811, 7649, 10632, 6024, 48506, 1975, 9566, 1211, 3615, 16490, 1211, 9957, 1829, 8717, 47283, 3215, 16247, 3794, 19986, 37977, 9673, 9566, 1211, 37746, 3660, 16472, 11622, 1211, 15844, 16247, 3794, 19986, 37977, 9673, 9566, 1211, 37746, 3660], "avg_logprob": -0.19192216390708708, "compression_ratio": 2.126315789473684, "no_speech_prob": 3.039836883544922e-06, "words": [{"start": 129.65, "end": 130.13, "word": "even", "probability": 0.397705078125}, 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"word": " الحد", "probability": 0.955322265625}, {"start": 145.99, "end": 146.61, "word": " الأخير", "probability": 0.9514973958333334}, {"start": 146.61, "end": 146.79, "word": " أو", "probability": 0.650390625}, {"start": 146.79, "end": 147.11, "word": " خانة", "probability": 0.9070638020833334}, {"start": 147.11, "end": 147.61, "word": " الأحد", "probability": 0.883544921875}, {"start": 147.61, "end": 147.99, "word": " فيه", "probability": 0.955078125}, {"start": 147.99, "end": 148.25, "word": " يا", "probability": 0.10443115234375}, {"start": 148.25, "end": 148.95, "word": " ستة", "probability": 0.9329427083333334}, {"start": 148.95, "end": 149.55, "word": " يا", "probability": 0.8427734375}, {"start": 149.55, "end": 150.07, "word": " تمانية", "probability": 0.9864908854166666}, {"start": 150.07, "end": 151.23, "word": " الآن", "probability": 0.5986328125}, {"start": 151.23, "end": 151.79, "word": " اطلع", "probability": 0.92529296875}, {"start": 151.79, "end": 152.13, "word": " 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" prove", "probability": 0.63037109375}, {"start": 164.84, "end": 165.36, "word": " that", "probability": 0.93505859375}, {"start": 165.36, "end": 166.7, "word": " the", "probability": 0.71142578125}, {"start": 166.7, "end": 167.24, "word": " integer", "probability": 0.92822265625}, {"start": 167.24, "end": 169.02, "word": " معطيني", "probability": 0.764404296875}, {"start": 169.02, "end": 169.5, "word": " الان", "probability": 0.5272216796875}, {"start": 169.5, "end": 169.88, "word": " ان", "probability": 0.55419921875}, {"start": 169.88, "end": 171.72, "word": " بساوة", "probability": 0.64150390625}, {"start": 171.72, "end": 172.02, "word": " اتنين", "probability": 0.8033447265625}, {"start": 172.02, "end": 172.2, "word": " اص", "probability": 0.5921630859375}, {"start": 172.2, "end": 172.7, "word": " عشرة", "probability": 0.93505859375}, {"start": 172.7, "end": 173.6, "word": " في", "probability": 0.421142578125}, {"start": 173.6, "end": 173.94, "word": " اتنين", "probability": 0.96923828125}, {"start": 173.94, "end": 174.18, "word": " اص", "probability": 0.9296875}, {"start": 174.18, "end": 174.92, "word": " احداش", "probability": 0.6223958333333334}, {"start": 174.92, "end": 176.12, "word": " ناقص", "probability": 0.928466796875}, {"start": 176.12, "end": 176.56, "word": " واحد", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 7, "seek": 20391, "start": 177.29, "end": 203.91, "text": "بقول اثبت ان هذا is not a perfect number الان هو ماعطيني في الكتاب hint بقول اتنين اقصى احداش ناقص واحد عبارة عن بتساوي اللي هو تلاتة و عشرين في تسعة و تمانين الان بدأ نثبت انه ا prove that n is not", "tokens": [3555, 39648, 1975, 12984, 3555, 2655, 16472, 23758, 307, 406, 257, 2176, 1230, 2423, 7649, 31439, 19446, 3615, 9566, 9957, 1829, 8978, 33251, 2655, 16758, 12075, 4724, 39648, 1975, 2655, 1863, 9957, 1975, 4587, 9381, 7578, 1975, 24401, 33599, 8717, 995, 4587, 9381, 36764, 24401, 6225, 3555, 9640, 3660, 18871, 39894, 3794, 995, 45865, 13672, 1829, 31439, 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"word": " number", "probability": 0.97802734375}, {"start": 180.87, "end": 181.91, "word": " الان", "probability": 0.6802978515625}, {"start": 181.91, "end": 182.07, "word": " هو", "probability": 0.802734375}, {"start": 182.07, "end": 182.59, "word": " ماعطيني", "probability": 0.7441162109375}, {"start": 182.59, "end": 182.69, "word": " في", "probability": 0.88818359375}, {"start": 182.69, "end": 183.27, "word": " الكتاب", "probability": 0.974609375}, {"start": 183.27, "end": 184.05, "word": " hint", "probability": 0.67919921875}, {"start": 184.05, "end": 184.47, "word": " بقول", "probability": 0.6441650390625}, {"start": 184.47, "end": 184.87, "word": " اتنين", "probability": 0.78948974609375}, {"start": 184.87, "end": 185.19, "word": " اقصى", "probability": 0.744140625}, {"start": 185.19, "end": 185.81, "word": " احداش", "probability": 0.7353515625}, {"start": 185.81, "end": 186.97, "word": " ناقص", "probability": 0.9146728515625}, {"start": 186.97, "end": 187.59, "word": " واحد", 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تساوي 2N نحسب الآن sigma of N", "tokens": [32, 2176, 1230, 2423, 26890, 38688, 6225, 8592, 7649, 8717, 12984, 3555, 2655, 14739, 426, 37893, 2176, 1230, 7251, 4117, 41185, 8717, 12984, 3555, 2655, 14739, 12771, 295, 426, 5551, 8592, 2304, 6027, 11296, 5296, 10721, 6055, 3794, 995, 45865, 568, 45, 8717, 5016, 35457, 6024, 48506, 12771, 295, 426], "avg_logprob": -0.2991728046361138, "compression_ratio": 1.3359375, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 206.78, "end": 207.04, "word": "A", "probability": 0.1448974609375}, {"start": 207.04, "end": 207.64, "word": " perfect", "probability": 0.59326171875}, {"start": 207.64, "end": 211.22, "word": " number", "probability": 0.93310546875}, {"start": 211.22, "end": 214.1, "word": " البروف", "probability": 0.487060546875}, {"start": 214.1, "end": 216.62, "word": " عشان", "probability": 0.9197591145833334}, {"start": 216.62, "end": 217.06, "word": " نثبت", "probability": 0.9949951171875}, {"start": 217.06, "end": 217.18, 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{"start": 241.88, "end": 242.28, "word": " 1", "probability": 0.66162109375}, {"start": 242.28, "end": 243.6, "word": " و", "probability": 0.78759765625}, {"start": 243.6, "end": 244.44, "word": " يساوي", "probability": 0.8408203125}, {"start": 244.44, "end": 245.32, "word": " إذن", "probability": 0.6627604166666666}, {"start": 245.32, "end": 245.68, "word": " Sigma", "probability": 0.626953125}, {"start": 245.68, "end": 245.92, "word": " of", "probability": 0.876953125}, {"start": 245.92, "end": 246.38, "word": " 10", "probability": 0.8466796875}, {"start": 246.38, "end": 247.54, "word": " بنعرف", "probability": 0.8370768229166666}, {"start": 247.54, "end": 247.72, "word": " اللي", "probability": 0.874755859375}, {"start": 247.72, "end": 247.88, "word": " هو", "probability": 0.97998046875}, {"start": 247.88, "end": 248.26, "word": " نوجد", "probability": 0.8580729166666666}, {"start": 248.26, "end": 248.42, "word": " اللي", "probability": 0.913330078125}, {"start": 248.42, "end": 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{"start": 610.69, "end": 611.19, "word": " هيصغر", "probability": 0.8502197265625}, {"start": 611.19, "end": 611.61, "word": " أكتر", "probability": 0.974609375}, {"start": 611.61, "end": 612.23, "word": " لذا", "probability": 0.42041015625}, {"start": 612.23, "end": 612.51, "word": " هذا", "probability": 0.83544921875}, {"start": 612.51, "end": 612.85, "word": " أكيد", "probability": 0.958984375}, {"start": 612.85, "end": 613.31, "word": " هيصير", "probability": 0.8798828125}, {"start": 613.31, "end": 614.03, "word": " أصغر", "probability": 0.99072265625}, {"start": 614.03, "end": 614.71, "word": " من", "probability": 0.990234375}, {"start": 614.71, "end": 614.95, "word": " B", "probability": 0.76806640625}, {"start": 614.95, "end": 615.19, "word": " أس", "probability": 0.98779296875}, {"start": 615.19, "end": 616.73, "word": " ألفة", "probability": 0.9484049479166666}, {"start": 616.73, "end": 617.29, "word": " زائد", "probability": 0.84521484375}, {"start": 617.29, "end": 617.71, 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622.67, "end": 649.47, "text": "إذا صار عندى sigma of B of Alpha أصغر strictly من 2B ألفة إذا صار عندى sigma of B ألفة لا يساوي 2B ألفة ومنه and so B ألفة is not a perfect number إذا اللى وصلتله الآن", "tokens": [28814, 15730, 20328, 9640, 43242, 7578, 12771, 295, 363, 295, 20588, 5551, 9381, 17082, 2288, 20792, 9154, 568, 33, 5551, 46538, 3660, 11933, 15730, 20328, 9640, 43242, 7578, 12771, 295, 363, 5551, 46538, 3660, 20193, 7251, 3794, 995, 45865, 568, 33, 5551, 46538, 3660, 4032, 27842, 3224, 293, 370, 363, 5551, 46538, 3660, 307, 406, 257, 2176, 1230, 11933, 15730, 13672, 7578, 4032, 36520, 2655, 43761, 6024, 48506], "avg_logprob": -0.2283740898837214, "compression_ratio": 1.490566037735849, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 622.67, "end": 623.01, "word": "إذا", "probability": 0.49114990234375}, {"start": 623.01, "end": 623.33, "word": " صار", "probability": 0.889404296875}, {"start": 623.33, "end": 623.75, "word": " عندى", "probability": 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No bar of prime can be a perfect number أي سؤال؟ نجي للسؤال اللي بعده أو الفرع C المطلوب منها Name C", "tokens": [4540, 2176, 4386, 883, 2159, 295, 5835, 393, 312, 257, 2176, 1230, 36632, 8608, 33604, 6027, 22807, 8717, 7435, 1829, 24976, 3794, 33604, 6027, 13672, 1829, 39182, 3224, 34051, 27188, 2288, 3615, 383, 9673, 9566, 1211, 37746, 9154, 11296, 13866, 383], "avg_logprob": -0.2790178528853825, "compression_ratio": 1.1818181818181819, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 650.34, "end": 650.8, "word": "No", "probability": 0.2027587890625}, {"start": 650.8, "end": 651.66, "word": " perfect", "probability": 0.4921875}, {"start": 651.66, "end": 652.06, "word": " ..", "probability": 0.257568359375}, {"start": 652.06, "end": 652.32, "word": " No", "probability": 0.64794921875}, {"start": 652.32, "end": 652.94, "word": " bar", "probability": 0.87744140625}, {"start": 652.94, "end": 653.18, "word": " of", "probability": 0.88720703125}, {"start": 653.18, "end": 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"probability": 0.7392578125}, {"start": 665.36, "end": 665.76, "word": " الفرع", "probability": 0.8916015625}, {"start": 665.76, "end": 665.98, "word": " C", "probability": 0.564453125}, {"start": 665.98, "end": 666.6, "word": " المطلوب", "probability": 0.9588623046875}, {"start": 666.6, "end": 670.18, "word": " منها", "probability": 0.706298828125}, {"start": 670.18, "end": 676.74, "word": " Name", "probability": 0.432861328125}, {"start": 676.74, "end": 677.26, "word": " C", "probability": 0.8154296875}], "temperature": 1.0}, {"id": 25, "seek": 70875, "start": 680.23, "end": 708.75, "text": "ماذا يقول الـ C؟ يقول الـ product of two odd-primes is never perfect يعني مش ممكن يكون حاصل ضرب two odd-primes ليكون perfect number", "tokens": [2304, 45636, 995, 7251, 39648, 2423, 39184, 383, 22807, 7251, 39648, 2423, 39184, 1674, 295, 732, 7401, 12, 1424, 1532, 307, 1128, 2176, 37495, 22653, 37893, 3714, 43020, 7251, 30544, 11331, 33546, 1211, 48812, 25513, 732, 7401, 12, 1424, 1532, 32239, 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"probability": 0.8916015625}, {"start": 722.21, "end": 723.99, "word": " to", "probability": 0.365966796875}, {"start": 723.99, "end": 724.99, "word": " the", "probability": 0.2315673828125}, {"start": 724.99, "end": 726.13, "word": " odd", "probability": 0.486328125}, {"start": 726.13, "end": 728.75, "word": " primes", "probability": 0.628173828125}, {"start": 728.75, "end": 731.51, "word": " اه", "probability": 0.5755615234375}, {"start": 731.51, "end": 732.25, "word": " بدنا", "probability": 0.789306640625}, {"start": 732.25, "end": 732.55, "word": " ناخد", "probability": 0.99072265625}, {"start": 732.55, "end": 732.77, "word": " B", "probability": 0.7353515625}, {"start": 732.77, "end": 733.01, "word": " and", "probability": 0.884765625}, {"start": 733.01, "end": 733.29, "word": " Q", "probability": 0.9765625}, {"start": 733.29, "end": 733.67, "word": " any", "probability": 0.78369140625}, {"start": 733.67, "end": 734.23, "word": " to", "probability": 0.943359375}, {"start": 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"probability": 0.9775390625}, {"start": 767.45, "end": 768.23, "word": " فى", "probability": 0.724853515625}, {"start": 768.23, "end": 768.47, "word": " غير", "probability": 0.993408203125}, {"start": 768.47, "end": 768.81, "word": " هيك", "probability": 0.700439453125}, {"start": 768.81, "end": 768.95, "word": " ده", "probability": 0.509521484375}, {"start": 768.95, "end": 769.39, "word": " بيساوي", "probability": 0.83056640625}, {"start": 769.39, "end": 770.05, "word": " واحد", "probability": 0.633056640625}, {"start": 770.05, "end": 771.09, "word": " زائد", "probability": 0.5987955729166666}, {"start": 771.09, "end": 771.49, "word": " B", "probability": 0.837890625}, {"start": 771.49, "end": 772.49, "word": " زائد", "probability": 0.8336588541666666}, {"start": 772.49, "end": 773.01, "word": " Q", "probability": 0.97314453125}, {"start": 773.01, "end": 773.89, "word": " زائد", "probability": 0.9680989583333334}, {"start": 773.89, "end": 774.59, "word": " B", "probability": 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{"start": 784.97, "end": 785.17, "word": " فى", "probability": 0.984619140625}, {"start": 785.17, "end": 785.53, "word": " Q", "probability": 0.978515625}, {"start": 785.53, "end": 786.29, "word": " زائد", "probability": 0.9640299479166666}, {"start": 786.29, "end": 786.67, "word": " B", "probability": 0.9716796875}, {"start": 786.67, "end": 787.25, "word": " فى", "probability": 0.989501953125}, {"start": 787.25, "end": 787.51, "word": " Q", "probability": 0.96533203125}], "temperature": 1.0}, {"id": 29, "seek": 81695, "start": 788.87, "end": 816.95, "text": "معايا؟ بدي أقول لكم لا يسوي لا يمكن يسوي اللاحظ أن هذا هو هذا بضل هذا قاتبته بسويش هذا فهو بقى معايا؟ الآن بدي أقارن بينهم بدي أقارن بينهم بإيش بين إيدايا أو من خلال إيش بين إيدايا معطيني هو الـP والـQ إيش مالهم؟ of the primes ماشي الآن", "tokens": [2304, 3615, 995, 25528, 22807, 4724, 16254, 5551, 39648, 5296, 24793, 20193, 7251, 3794, 45865, 20193, 7251, 43020, 7251, 3794, 45865, 13672, 39319, 19913, 14739, 23758, 31439, 23758, 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1.0}, {"id": 40, "seek": 109123, "start": 1083.85, "end": 1091.23, "text": "يعني الـ sigma و الان بيساوي اتنين انا ال proof ده ال summation واحد على دي دي بتكسب عنه ايش بيساوي بيساوي اتنين", "tokens": [40228, 22653, 2423, 39184, 12771, 4032, 2423, 7649, 4724, 1829, 3794, 995, 45865, 1975, 2655, 1863, 9957, 1975, 8315, 2423, 8177, 11778, 3224, 2423, 28811, 36764, 24401, 15844, 11778, 1829, 11778, 1829, 39894, 4117, 35457, 18871, 3224, 1975, 1829, 8592, 4724, 1829, 3794, 995, 45865, 4724, 1829, 3794, 995, 45865, 1975, 2655, 1863, 9957], "avg_logprob": -0.46448864936828616, "compression_ratio": 1.512396694214876, "no_speech_prob": 2.86102294921875e-06, "words": [{"start": 1083.85, "end": 1084.31, "word": "يعني", "probability": 0.5382080078125}, {"start": 1084.31, "end": 1084.65, "word": " الـ", "probability": 0.6351318359375}, {"start": 1084.65, "end": 1084.79, "word": " sigma", "probability": 0.226318359375}, {"start": 1084.79, "end": 1084.97, "word": " و", "probability": 0.36328125}, 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"word": " 5", "probability": 0.53125}, {"start": 1140.05, "end": 1145.41, "word": " اللي", "probability": 0.95654296875}, {"start": 1145.41, "end": 1146.01, "word": " معطيني", "probability": 0.71197509765625}, {"start": 1146.01, "end": 1147.25, "word": " في", "probability": 0.47509765625}, {"start": 1147.25, "end": 1147.55, "word": " السؤال", "probability": 0.86376953125}, {"start": 1147.55, "end": 1148.17, "word": " الخامسة", "probability": 0.8486328125}], "temperature": 1.0}, {"id": 43, "seek": 116823, "start": 1149.71, "end": 1168.23, "text": "بقول لي given N as an even perfect number عندي N is even perfect number ومعطيك الـ N بتساوي", "tokens": [3555, 39648, 32239, 2212, 426, 382, 364, 754, 2176, 1230, 18871, 16254, 426, 307, 754, 2176, 1230, 4032, 2304, 3615, 9566, 1829, 4117, 2423, 39184, 426, 39894, 3794, 995, 45865], "avg_logprob": -0.2583165418717169, "compression_ratio": 1.1485148514851484, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1149.71, "end": 1150.19, 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"probability": 0.8017578125}, {"start": 1158.25, "end": 1160.27, "word": " perfect", "probability": 0.9052734375}, {"start": 1160.27, "end": 1162.65, "word": " number", "probability": 0.97705078125}, {"start": 1162.65, "end": 1165.81, "word": " ومعطيك", "probability": 0.9287923177083334}, {"start": 1165.81, "end": 1167.23, "word": " الـ", "probability": 0.72509765625}, {"start": 1167.23, "end": 1167.41, "word": " N", "probability": 0.86572265625}, {"start": 1167.41, "end": 1168.23, "word": " بتساوي", "probability": 0.949462890625}], "temperature": 1.0}, {"id": 44, "seek": 119722, "start": 1169.6, "end": 1197.22, "text": "اللي هو 2 to the k minus 1 في 2 to the k ناقص واحد حسب النظرية اللي قبل بي شوية مدام un even perfect number على الصورة اللي أمامي هيكون ومش هي كمان وهيكون هذا 2 أُس k ناقص واحد is إيش ال zebrain fine number طيب هذا المقطع إيش بقولك الآن prove that prove", "tokens": [6027, 20292, 31439, 568, 281, 264, 350, 3175, 502, 8978, 568, 281, 264, 350, 8717, 995, 4587, 9381, 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"text": "معايا؟ نعم الان أخدناها قبل هيه ال corollary انه عندي إذا كان بده يكون اللي هو and composite إذا there exist there must exist بي أصغر أو ساوي جدر الان والبي بيكسبنيين الان if no such بي exist then and will be اشماله prime", "tokens": [2304, 3615, 995, 25528, 22807, 8717, 25957, 2423, 7649, 5551, 9778, 3215, 8315, 11296, 12174, 36150, 39896, 3224, 2423, 1181, 1833, 822, 16472, 3224, 18871, 16254, 11933, 15730, 25961, 47525, 3224, 7251, 30544, 13672, 1829, 31439, 293, 25557, 11933, 15730, 456, 2514, 456, 1633, 2514, 4724, 1829, 5551, 9381, 17082, 2288, 34051, 8608, 995, 45865, 10874, 3215, 2288, 2423, 7649, 16070, 21292, 4724, 1829, 4117, 35457, 22653, 9957, 2423, 7649, 498, 572, 1270, 4724, 1829, 2514, 550, 293, 486, 312, 1975, 8592, 2304, 6027, 3224, 5835], "avg_logprob": -0.3511134927300201, "compression_ratio": 1.5235849056603774, "no_speech_prob": 1.0132789611816406e-06, "words": [{"start": 1866.4700000000003, "end": 1867.5700000000002, "word": "معايا؟", "probability": 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"probability": 0.2978515625}, {"start": 2096.1, "end": 2096.4, "word": " أول", "probability": 0.809814453125}, {"start": 2096.4, "end": 2096.86, "word": " واحد", "probability": 0.978515625}, {"start": 2096.86, "end": 2098.38, "word": " نجي", "probability": 0.9833984375}, {"start": 2098.38, "end": 2098.86, "word": " لبعده", "probability": 0.81219482421875}], "temperature": 1.0}, {"id": 77, "seek": 212757, "start": 2099.81, "end": 2127.57, "text": "كيف جداش؟ بتلاتة اتنين في تلاتة بستة ستة في تلتاش تبعين وسبعين مظبوط واحد تسعة وسبعين تأكدولي من الأرقام اللي بعده اللي هو اربعة اتنين في اربعة تمانية تمانية في تلتاش حينط مين خلاص بكفيني اذا بس we only investigate from fifty three and seventy nine", "tokens": [4117, 33911, 10874, 3215, 33599, 22807, 39894, 1211, 9307, 3660, 1975, 2655, 1863, 9957, 8978, 6055, 1211, 9307, 3660, 4724, 14851, 3660, 8608, 2655, 3660, 8978, 6055, 1211, 2655, 33599, 6055, 3555, 3615, 9957, 4032, 35457, 3615, 9957, 3714, 19913, 3555, 2407, 9566, 36764, 24401, 6055, 3794, 27884, 4032, 35457, 3615, 9957, 6055, 10721, 4117, 3215, 12610, 1829, 9154, 16247, 2288, 4587, 10943, 13672, 1829, 39182, 3224, 13672, 1829, 31439, 1975, 25513, 27884, 1975, 2655, 1863, 9957, 8978, 1975, 25513, 27884, 46811, 7649, 10632, 46811, 7649, 10632, 8978, 6055, 1211, 2655, 33599, 11331, 9957, 9566, 3714, 9957, 16490, 1211, 33546, 4724, 4117, 5172, 9957, 1829, 1975, 15730, 4724, 3794, 321, 787, 15013, 490, 13442, 1045, 293, 25662, 4949], "avg_logprob": -0.2373949577327536, "compression_ratio": 1.8538812785388128, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2099.81, "end": 2100.13, "word": "كيف", "probability": 0.759765625}, {"start": 2100.13, "end": 2100.73, "word": " جداش؟", "probability": 0.67041015625}, {"start": 2100.73, "end": 2101.35, "word": " بتلاتة", "probability": 0.79766845703125}, {"start": 2101.35, "end": 2102.25, "word": " اتنين", "probability": 0.78802490234375}, {"start": 2102.25, "end": 2102.39, "word": " في", "probability": 0.61962890625}, {"start": 2102.39, "end": 2102.71, "word": " تلاتة", "probability": 0.9417724609375}, {"start": 2102.71, "end": 2103.31, "word": " بستة", "probability": 0.8697916666666666}, {"start": 2103.31, "end": 2104.03, "word": " ستة", "probability": 0.8429361979166666}, {"start": 2104.03, "end": 2104.11, "word": " في", "probability": 0.87255859375}, {"start": 2104.11, "end": 2104.83, "word": " تلتاش", "probability": 0.813232421875}, {"start": 2104.83, "end": 2106.47, "word": " تبعين", "probability": 0.535400390625}, {"start": 2106.47, "end": 2107.01, "word": " وسبعين", "probability": 0.8748779296875}, {"start": 2107.01, "end": 2107.91, "word": " مظبوط", "probability": 0.83427734375}, {"start": 2107.91, "end": 2108.51, "word": " واحد", "probability": 0.843994140625}, {"start": 2108.51, "end": 2109.33, "word": " تسعة", "probability": 0.8790690104166666}, {"start": 2109.33, "end": 2109.75, "word": " وسبعين", "probability": 0.97265625}, {"start": 2109.75, "end": 2110.25, "word": " تأكدولي", "probability": 0.7027587890625}, {"start": 2110.25, "end": 2110.33, "word": " من", "probability": 0.90283203125}, {"start": 2110.33, "end": 2110.75, "word": " الأرقام", "probability": 0.966796875}, {"start": 2110.75, "end": 2111.55, "word": " اللي", "probability": 0.928466796875}, {"start": 2111.55, "end": 2112.39, "word": " بعده", "probability": 0.838134765625}, {"start": 2112.39, "end": 2114.27, "word": " اللي", "probability": 0.970703125}, {"start": 2114.27, "end": 2114.59, "word": " هو", "probability": 0.9794921875}, {"start": 2114.59, "end": 2115.27, "word": " اربعة", "probability": 0.8186848958333334}, {"start": 2115.27, "end": 2115.51, "word": " اتنين", "probability": 0.9234619140625}, {"start": 2115.51, "end": 2115.63, "word": " في", "probability": 0.943359375}, {"start": 2115.63, "end": 2115.89, "word": " اربعة", "probability": 0.853515625}, {"start": 2115.89, "end": 2116.37, "word": " تمانية", "probability": 0.93505859375}, {"start": 2116.37, "end": 2116.99, "word": " تمانية", "probability": 0.9697265625}, {"start": 2116.99, "end": 2117.07, "word": " في", "probability": 0.8974609375}, {"start": 2117.07, "end": 2117.67, "word": " تلتاش", "probability": 0.9573974609375}, {"start": 2117.67, "end": 2118.15, "word": " حينط", "probability": 0.5448404947916666}, {"start": 2118.15, "end": 2118.59, "word": " مين", "probability": 0.876220703125}, {"start": 2118.59, "end": 2119.73, "word": " خلاص", "probability": 0.8185221354166666}, {"start": 2119.73, "end": 2121.25, "word": " بكفيني", "probability": 0.83271484375}, {"start": 2121.25, "end": 2121.61, "word": " اذا", "probability": 0.6182861328125}, {"start": 2121.61, "end": 2122.85, "word": " بس", "probability": 0.958740234375}, {"start": 2122.85, "end": 2123.07, "word": " we", "probability": 0.580078125}, {"start": 2123.07, "end": 2123.49, "word": " only", "probability": 0.81494140625}, {"start": 2123.49, "end": 2124.61, "word": " investigate", "probability": 0.953125}, {"start": 2124.61, "end": 2125.05, "word": " from", "probability": 0.1434326171875}, {"start": 2125.05, "end": 2125.97, "word": " fifty", "probability": 0.79443359375}, {"start": 2125.97, "end": 2126.43, "word": " three", "probability": 0.59619140625}, {"start": 2126.43, "end": 2126.81, "word": " and", "probability": 0.9345703125}, {"start": 2126.81, "end": 2127.19, "word": " seventy", "probability": 0.87744140625}, {"start": 2127.19, "end": 2127.57, "word": " nine", "probability": 0.90380859375}], "temperature": 1.0}, {"id": 78, "seek": 215873, "start": 2130.97, "end": 2158.73, "text": "الـ 53 لتقسم الـ M 13 بالـ .. بالطبع .. بالـ calculations and الـ 79 لتقسم الـ M 13 برضه by calculations hence اللي هو M 13 must be a prime واضح؟ طيب", "tokens": [6027, 39184, 21860, 5296, 2655, 4587, 38251, 2423, 39184, 376, 3705, 20666, 39184, 4386, 20666, 9566, 3555, 3615, 4386, 20666, 39184, 20448, 293, 2423, 39184, 32803, 5296, 2655, 4587, 38251, 2423, 39184, 376, 3705, 4724, 43042, 3224, 538, 20448, 16678, 13672, 1829, 31439, 376, 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{"start": 2163.89, "end": 2164.23, "word": " تلاتة", "probability": 0.868896484375}, {"start": 2164.23, "end": 2164.55, "word": " اللي", "probability": 0.53857421875}, {"start": 2164.55, "end": 2164.91, "word": " المطلوب", "probability": 0.9044189453125}, {"start": 2164.91, "end": 2165.09, "word": " يا", "probability": 0.125244140625}, {"start": 2165.09, "end": 2165.25, "word": " أخي", "probability": 0.8767903645833334}, {"start": 2165.25, "end": 2166.43, "word": " السؤال", "probability": 0.7893880208333334}, {"start": 2166.43, "end": 2166.81, "word": " تلاتة", "probability": 0.972900390625}, {"start": 2166.81, "end": 2167.21, "word": " كمان", "probability": 0.9820963541666666}, {"start": 2167.21, "end": 2173.11, "word": " ال", "probability": 0.487060546875}, {"start": 2173.11, "end": 2173.39, "word": " proof", "probability": 0.89990234375}, {"start": 2173.39, "end": 2173.63, "word": " ده", "probability": 0.8857421875}, {"start": 2173.63, "end": 2173.81, "word": " ده", "probability": 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"probability": 0.947265625}, {"start": 2180.17, "end": 2180.69, "word": " الآن", "probability": 0.719482421875}, {"start": 2180.69, "end": 2182.61, "word": " هيظهر", "probability": 0.86517333984375}, {"start": 2182.61, "end": 2183.27, "word": " عندى", "probability": 0.8115234375}, {"start": 2183.27, "end": 2184.17, "word": " هيظهر", "probability": 0.86663818359375}, {"start": 2184.17, "end": 2184.95, "word": " عندى", "probability": 0.825927734375}, {"start": 2184.95, "end": 2185.51, "word": " اللي", "probability": 0.9228515625}, {"start": 2185.51, "end": 2185.81, "word": " هو", "probability": 0.9921875}, {"start": 2185.81, "end": 2188.51, "word": " انه", "probability": 0.743408203125}, {"start": 2188.51, "end": 2190.19, "word": " في", "probability": 0.86279296875}], "temperature": 1.0}, {"id": 80, "seek": 220391, "start": 2191.35, "end": 2203.91, "text": "الـ prime factor للـ M29 من بين ال factors الممكنة اللي ع صورة 2K بزائد 1 ده نشوف إيش سؤالنا سؤال تلاتة", "tokens": [6027, 39184, 5835, 5952, 24976, 39184, 376, 11871, 9154, 49374, 2423, 6771, 9673, 43020, 3660, 13672, 1829, 6225, 20328, 13063, 3660, 568, 42, 4724, 11622, 16373, 3215, 502, 11778, 3224, 8717, 8592, 38688, 11933, 1829, 8592, 8608, 33604, 6027, 8315, 8608, 33604, 6027, 6055, 1211, 9307, 3660], "avg_logprob": -0.26334636472165585, "compression_ratio": 1.2290076335877862, "no_speech_prob": 2.2649765014648438e-06, "words": [{"start": 2191.35, "end": 2191.63, "word": "الـ", "probability": 0.636474609375}, {"start": 2191.63, "end": 2191.93, "word": " prime", "probability": 0.1995849609375}, {"start": 2191.93, "end": 2192.59, "word": " factor", "probability": 0.904296875}, {"start": 2192.59, "end": 2193.01, "word": " للـ", "probability": 0.7000732421875}, {"start": 2193.01, "end": 2193.61, "word": " M29", "probability": 0.905517578125}, {"start": 2193.61, "end": 2194.81, "word": " من", "probability": 0.87451171875}, {"start": 2194.81, "end": 2195.25, "word": " بين", "probability": 0.99560546875}, 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{"start": 2201.07, "end": 2201.61, "word": " سؤالنا", "probability": 0.9901123046875}, {"start": 2201.61, "end": 2203.33, "word": " سؤال", "probability": 0.9361979166666666}, {"start": 2203.33, "end": 2203.91, "word": " تلاتة", "probability": 0.8785400390625}], "temperature": 1.0}, {"id": 81, "seek": 223777, "start": 2208.51, "end": 2237.77, "text": "طبعا الجزء الثاني على طول بطلع اللي هو العدد اللي بطلع مدان هذا طلع عندى prime إذا الـ 2 وصوله 12 ف2 وصوله 13 نقص 1 هيطلع إيه شماله perfect number sigma of n بتطلع 2n سؤال تلاتة هنزلكم الحلول لا تجلبوش", "tokens": [9566, 3555, 3615, 995, 25724, 11622, 38207, 6024, 104, 7649, 1829, 15844, 23032, 12610, 4724, 9566, 1211, 3615, 13672, 1829, 31439, 18863, 3215, 3215, 13672, 1829, 4724, 9566, 1211, 3615, 3714, 3215, 7649, 23758, 23032, 1211, 3615, 43242, 7578, 5835, 11933, 15730, 2423, 39184, 568, 4032, 9381, 12610, 3224, 2272, 6156, 17, 4032, 9381, 12610, 3224, 3705, 8717, 4587, 9381, 502, 8032, 1829, 9566, 1211, 3615, 11933, 1829, 3224, 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0.153564453125}, {"start": 2220.21, "end": 2220.67, "word": " of", "probability": 0.91162109375}, {"start": 2220.67, "end": 2222.05, "word": " n", "probability": 0.36083984375}, {"start": 2222.05, "end": 2222.49, "word": " بتطلع", "probability": 0.9371337890625}, {"start": 2222.49, "end": 2223.31, "word": " 2n", "probability": 0.55511474609375}, {"start": 2223.31, "end": 2230.61, "word": " سؤال", "probability": 0.9622395833333334}, {"start": 2230.61, "end": 2231.55, "word": " تلاتة", "probability": 0.8695068359375}, {"start": 2231.55, "end": 2234.37, "word": " هنزلكم", "probability": 0.670556640625}, {"start": 2234.37, "end": 2234.81, "word": " الحلول", "probability": 0.9928385416666666}, {"start": 2234.81, "end": 2235.05, "word": " لا", "probability": 0.1531982421875}, {"start": 2235.05, "end": 2237.77, "word": " تجلبوش", "probability": 0.80810546875}], "temperature": 1.0}, {"id": 82, "seek": 226708, "start": 2251.24, "end": 2267.08, "text": "السؤال اللي بيقولي prove that المرسيل number", "tokens": [6027, 3794, 33604, 6027, 13672, 1829, 4724, 1829, 39648, 1829, 7081, 300, 2423, 29973, 3794, 26895, 1230], "avg_logprob": -0.5755208333333334, "compression_ratio": 1.0634920634920635, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2251.24, "end": 2252.52, "word": "السؤال", "probability": 0.67303466796875}, {"start": 2252.52, "end": 2252.64, "word": " اللي", "probability": 0.56494140625}, {"start": 2252.64, "end": 2252.98, "word": " بيقولي", "probability": 0.708099365234375}, {"start": 2252.98, "end": 2253.28, "word": " prove", "probability": 0.70166015625}, {"start": 2253.28, "end": 2253.92, "word": " that", "probability": 0.93408203125}, {"start": 2253.92, "end": 2262.64, "word": " المرسيل", "probability": 0.5416259765625}, {"start": 2262.64, "end": 2267.08, "word": " number", "probability": 0.52783203125}], "temperature": 1.0}, {"id": 83, "seek": 229890, "start": 2270.66, "end": 2298.9, "text": "م تسعة و عشرين is composite prove by theorem أحداشر خمسة the possible prime factors of M تسعة و عشرين", "tokens": [2304, 6055, 3794, 27884, 4032, 6225, 46309, 9957, 307, 25557, 7081, 538, 20904, 5551, 24401, 33599, 2288, 16490, 2304, 3794, 3660, 264, 1944, 5835, 6771, 295, 376, 6055, 3794, 27884, 4032, 6225, 46309, 9957], "avg_logprob": -0.2999999965940203, "compression_ratio": 1.168141592920354, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2270.66, "end": 2271.14, "word": "م", "probability": 0.583984375}, {"start": 2271.14, "end": 2272.72, "word": " تسعة", "probability": 0.706787109375}, {"start": 2272.72, "end": 2272.84, "word": " و", "probability": 0.9072265625}, {"start": 2272.84, "end": 2273.38, "word": " عشرين", "probability": 0.8592122395833334}, {"start": 2273.38, "end": 2274.02, "word": " is", "probability": 0.171142578125}, {"start": 2274.02, "end": 2276.52, "word": " composite", "probability": 0.8916015625}, {"start": 2276.52, "end": 2278.38, "word": " prove", "probability": 0.06610107421875}, {"start": 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2298.08, "end": 2298.9, "word": " عشرين", "probability": 0.9640299479166666}], "temperature": 1.0}, {"id": 84, "seek": 232663, "start": 2302.13, "end": 2326.63, "text": "R of the form اتنين ك بي زائد واحد بيهم تسعة و عشرين يعني اتنين ك في تسعة و عشرين زائد واحد و يساوي تمانية و خمسين ك زائد واحد", "tokens": [49, 295, 264, 1254, 1975, 2655, 1863, 9957, 9122, 4724, 1829, 30767, 16373, 3215, 36764, 24401, 4724, 1829, 16095, 6055, 3794, 27884, 4032, 6225, 46309, 9957, 37495, 22653, 1975, 2655, 1863, 9957, 9122, 8978, 6055, 3794, 27884, 4032, 6225, 46309, 9957, 30767, 16373, 3215, 36764, 24401, 4032, 7251, 3794, 995, 45865, 46811, 7649, 10632, 4032, 16490, 2304, 3794, 9957, 9122, 30767, 16373, 3215, 36764, 24401], "avg_logprob": -0.17826705042159918, "compression_ratio": 1.7459016393442623, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 2302.13, "end": 2303.29, "word": "R", "probability": 0.51806640625}, {"start": 2303.29, "end": 2304.45, "word": " of", "probability": 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{"start": 2540.25, "end": 2540.71, "word": " 7", "probability": 0.6806640625}, {"start": 2540.71, "end": 2541.49, "word": " و", "probability": 0.1099853515625}, {"start": 2541.49, "end": 2542.39, "word": " 11", "probability": 0.434814453125}, {"start": 2542.39, "end": 2542.85, "word": " دل", "probability": 0.4874267578125}, {"start": 2542.85, "end": 2543.13, "word": " عنا", "probability": 0.5667724609375}, {"start": 2543.13, "end": 2543.51, "word": " chapter", "probability": 0.7822265625}, {"start": 2543.51, "end": 2544.21, "word": " 7", "probability": 0.97265625}, {"start": 2544.21, "end": 2544.63, "word": " خلاص", "probability": 0.70361328125}, {"start": 2544.63, "end": 2544.91, "word": " ماشي", "probability": 0.7511393229166666}, {"start": 2544.91, "end": 2545.09, "word": " الله", "probability": 0.7998046875}, {"start": 2545.09, "end": 2545.45, "word": " يعطيكوا", "probability": 0.644677734375}, {"start": 2545.45, "end": 2545.71, "word": " العفو", "probability": 0.7677408854166666}, {"start": 2545.71, "end": 2545.99, "word": " المرة", "probability": 0.6099853515625}, {"start": 2545.99, "end": 2546.27, "word": " الجاية", "probability": 0.7696940104166666}, {"start": 2546.27, "end": 2546.33, "word": " ان", "probability": 0.5712890625}, {"start": 2546.33, "end": 2546.53, "word": " شاء", "probability": 0.982177734375}, {"start": 2546.53, "end": 2547.05, "word": " الله", "probability": 0.94677734375}, {"start": 2547.05, "end": 2548.07, "word": " بنكمل", "probability": 0.7826334635416666}, {"start": 2548.07, "end": 2549.17, "word": " و", "probability": 0.4345703125}, {"start": 2549.17, "end": 2549.43, "word": " إلى", "probability": 0.53662109375}, {"start": 2549.43, "end": 2549.89, "word": " لقايا", "probability": 0.8426513671875}, {"start": 2549.89, "end": 2550.25, "word": " اخر", "probability": 0.72509765625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2550.6655625, "duration_after_vad": 2362.4356249999905}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/38AIlUjh8EM_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/38AIlUjh8EM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f7cdbc8313f897e65de72c6b13e13ad978a136a3
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/38AIlUjh8EM_raw.srt
@@ -0,0 +1,1556 @@
+1
+00:00:21,530 --> 00:00:26,290
+بسم الله الرحمن الرحيم محاضر رقم 35 مساق نظرية
+
+2
+00:00:26,290 --> 00:00:33,090
+الاعداد لطلاب الجامعة الإسلامية قسم غياضيات كلياتي
+
+3
+00:00:33,090 --> 00:00:38,430
+العلوم والتربية اليوم حيكون عندنا اللي هو مناقشة
+
+4
+00:00:38,430 --> 00:00:43,170
+لشرطر 11 او للموضوعين اللي أخدناها في شرطر 11 اللي
+
+5
+00:00:43,170 --> 00:00:47,720
+هو ال perfect numbers and Mercien numbersمراجعة
+
+6
+00:00:47,720 --> 00:00:52,780
+سريعة لما أخدناه في الـ perfect number قلنا إنه
+
+7
+00:00:52,780 --> 00:00:55,960
+بنقول عن الـ N is a perfect number إذا كان الـ
+
+8
+00:00:55,960 --> 00:01:00,420
+Sigma of N بساوة 2N بنقول عن الـ N is a perfect
+
+9
+00:01:00,420 --> 00:01:06,160
+number أخدنا نظرية إنه لو كان عندي 2 to the K
+
+10
+00:01:06,160 --> 00:01:11,540
+minus 1 is prime و K أكبر من 1بكون اللي هو n to
+
+11
+00:01:11,540 --> 00:01:17,820
+the 2k-1×2k-1 is a perfect number و أي even
+
+12
+00:01:17,820 --> 00:01:22,680
+perfect number هيكون على هذه الصورة يعني الآن لو
+
+13
+00:01:22,680 --> 00:01:30,360
+كان عندى اللي هو 2 to the k-1 is prime و هيكون
+
+14
+00:01:30,360 --> 00:01:37,400
+العدد n بيساوي 2k-1×2k-1 هيطلع عندى perfect
+
+15
+00:01:37,400 --> 00:01:39,320
+perfect
+
+16
+00:01:41,140 --> 00:01:46,520
+number و أيضا أي perfect أي even perfect number
+
+17
+00:01:46,520 --> 00:01:50,260
+هيكون على هذه الصورة بمعنى آخر أي even perfect
+
+18
+00:01:50,260 --> 00:01:56,580
+number هيكون على صورة 2k-1 في 2 أُس k ناقص الواحد
+
+19
+00:01:56,580 --> 00:02:03,400
+حيث هذا العدد اللي هو 2k ناقص واحد is a prime هذا
+
+20
+00:02:03,400 --> 00:02:07,300
+اللي هي النظرية أخدناها المرة الماضية بعد هي أخدنا
+
+21
+00:02:07,300 --> 00:02:13,890
+قلنا أنه أيeven perfect number هيكون اللي هو أن
+
+22
+00:02:13,890 --> 00:02:21,050
+تطابق الستة مدله عشرة or أن تطابق التمانية مدله
+
+23
+00:02:21,050 --> 00:02:25,430
+عشرة يعني أي even perfect number هيكون اللي هو
+
+24
+00:02:25,430 --> 00:02:30,070
+الحد الأخير أو خانة الأحد فيه يا ستة يا تمانية
+
+25
+00:02:30,070 --> 00:02:35,830
+الآن اطلع خليني ناخد الأسئلة المطلوبة انزل على
+
+26
+00:02:35,830 --> 00:02:36,850
+الأسئلة المطلوبة
+
+27
+00:02:40,400 --> 00:02:44,840
+الاسئلة المطلوبة نجي للسؤال الأول بقولني ا prove
+
+28
+00:02:44,840 --> 00:02:52,200
+that the integer معطيني الان ان بساوة اتنين اص
+
+29
+00:02:52,200 --> 00:02:58,710
+عشرة في اتنين اص احداش ناقص واحدبقول اثبت ان هذا
+
+30
+00:02:58,710 --> 00:03:03,270
+is not a perfect number الان هو ماعطيني في الكتاب
+
+31
+00:03:03,270 --> 00:03:09,210
+hint بقول اتنين اقصى احداش ناقص واحد عبارة عن
+
+32
+00:03:09,210 --> 00:03:16,150
+بتساوي اللي هو تلاتة و عشرين في تسعة و تمانين الان
+
+33
+00:03:16,150 --> 00:03:23,910
+بدأ نثبت انه ا prove that n is not
+
+34
+00:03:26,780 --> 00:03:31,220
+A perfect number
+
+35
+00:03:31,220 --> 00:03:39,340
+البروف عشان نثبت أن N مش perfect number يكفي نثبت
+
+36
+00:03:39,340 --> 00:03:44,520
+أن sigma of N أشمالها لأ تساوي 2N نحسب الآن sigma
+
+37
+00:03:44,520 --> 00:03:50,440
+of Nبساوي عند الـ 2 أُس 10 و 2 أُس 11 ناقص 1 are
+
+38
+00:03:50,440 --> 00:03:54,040
+relatively prime و الـ Sigma is multiplicative إذن
+
+39
+00:03:54,040 --> 00:03:58,800
+سيكون الـ Sigma بساوي Sigma 2 أُس 10 في Sigma أُس
+
+40
+00:03:58,800 --> 00:04:06,380
+2 2 أُس 11 ناقص مين ناقص 1 و يساوي إذن Sigma of 10
+
+41
+00:04:06,380 --> 00:04:11,000
+بنعرف اللي هو نوجد اللي هو الـ Sigma اللي عبارة عن
+
+42
+00:04:11,000 --> 00:04:13,740
+Sigma أس 2 أُس 10 إيش بتساوي
+
+43
+00:04:20,040 --> 00:04:26,280
+تنين أُس كزائد واحد اللي هي اتنين أُس إحداش ناقص
+
+44
+00:04:26,280 --> 00:04:32,900
+واحد اللي هي اتنين ناقص واحد اتنين في سيجما of
+
+45
+00:04:32,900 --> 00:04:36,600
+اتنين أُس إحداش ناقص واحد هذا يقول لي أيش معنى
+
+46
+00:04:36,600 --> 00:04:41,200
+اللي هو عطيني هنت اللي هو تلاتة عشرين في مين في
+
+47
+00:04:41,200 --> 00:04:44,580
+تسعة و تمانين بيصير سيجما of تلاتة و عشرين في
+
+48
+00:04:44,580 --> 00:04:47,200
+سيجما of تسعة و تمانين
+
+49
+00:04:50,020 --> 00:04:54,820
+معايا لأن التنين relative ل prime لإنه بيصير عند
+
+50
+00:04:54,820 --> 00:05:00,220
+الأولاني اتنين أس احداش ناقص واحد فهذا هو عبارة عن
+
+51
+00:05:00,220 --> 00:05:04,160
+اربع وعشرين عارفين كيف اربع وعشرين تلاتة وعشرين
+
+52
+00:05:04,160 --> 00:05:08,740
+زائد واحد اللي هو sum of divisors اللي هو مدان ال
+
+53
+00:05:08,740 --> 00:05:11,380
+prime اذا مجموحا تلاتة وعشرين زائد واحد اللي اربع
+
+54
+00:05:11,380 --> 00:05:14,980
+وعشرين والتاني برضه prime اللي هو تسعة وتمانين
+
+55
+00:05:14,980 --> 00:05:22,500
+زائد واحد اللي هو جداش تسعينالان هذا العدد عندى
+
+56
+00:05:22,500 --> 00:05:25,520
+اتنين اصحى احداش ناقص واحد هى اتنين اصحى احداش
+
+57
+00:05:25,520 --> 00:05:31,980
+ناقص واحد هذا المقدار لا يساوي اتنين اصحى عشرة
+
+58
+00:05:31,980 --> 00:05:36,400
+اكيد لان هذا فيه ايش فيه تلاتة هذا مش فيه تلاتة
+
+59
+00:05:36,400 --> 00:05:41,380
+اذا اكيد هذا لا يساوي اتنين اصحى احداش ناقص واحد
+
+60
+00:05:41,380 --> 00:05:48,420
+اربع عشرين فهذا لايساوي اتنينلا يساوى اتنين اصلا
+
+61
+00:05:48,420 --> 00:05:51,480
+طبعا
+
+62
+00:05:51,480 --> 00:05:55,720
+هو بالظبط لا يساوى اتنين اصلا احداش اكيد فبصير لا
+
+63
+00:05:55,720 --> 00:06:03,360
+يساوى اتنين ان اي سؤال اذا سبعين الان is not a
+
+64
+00:06:03,360 --> 00:06:14,160
+perfect number نيجينا اللي هو السؤال الثاني فرع a
+
+65
+00:06:19,530 --> 00:06:27,330
+Prove that no bar
+
+66
+00:06:27,330 --> 00:06:39,310
+of a prime can be a perfect number
+
+67
+00:06:51,110 --> 00:06:57,970
+Power of Ibrahim هو Ibrahim ب مرفوع لpower أي رقم
+
+68
+00:06:57,970 --> 00:07:06,550
+ألف أكبر أو أسوأ واحد Let B to the alpha be a
+
+69
+00:07:06,550 --> 00:07:17,550
+prime and alpha أكبر أو أسوأ واحد بأي bar of
+
+70
+00:07:17,550 --> 00:07:23,520
+Ibrahimبنثبت ان هذا P to the alpha لا يمكن ان يكون
+
+71
+00:07:23,520 --> 00:07:28,920
+الهو perfect number يعني بمعنى اخر ال sigma لل P
+
+72
+00:07:28,920 --> 00:07:32,880
+قص Alpha لاتساوي
+
+73
+00:07:32,880 --> 00:07:39,200
+2P Alpha قص Alpha معايا ال sigma of P of Alpha حسب
+
+74
+00:07:39,200 --> 00:07:44,500
+القانون ايش بتساوي P قص Alpha زائد واحد ماقص واحد
+
+75
+00:07:44,500 --> 00:07:54,070
+على P ماقص ايهاش ماقص واحدمعايا الان هذا بدي اصلك
+
+76
+00:07:54,070 --> 00:08:02,170
+انه لا يساوي بي اتنين بي اص الفة يعني بمعنى اخر لا
+
+77
+00:08:02,170 --> 00:08:08,910
+يساوي بي اص الفة زائد بي اص الفة الان عليك بدي
+
+78
+00:08:08,910 --> 00:08:14,540
+اجزلك هذا الى دي زينالى بيوز ألفة زائد some number
+
+79
+00:08:14,540 --> 00:08:18,440
+والـ some number اللى بيطلع يكون سهل أقارنه
+
+80
+00:08:18,440 --> 00:08:23,420
+بالبيوز ألفة مايسويش ماشي الحالة بناء على هيك بدي
+
+81
+00:08:23,420 --> 00:08:28,560
+أحسب هذا مقص البيوز ألف على جهة ومنها بقدر أكتب
+
+82
+00:08:28,560 --> 00:08:33,220
+هذا على صورة بيوز ألف زائد something إذا الأن على
+
+83
+00:08:33,220 --> 00:08:39,620
+جهةبأجي بحسب اللي هو B أس Alpha زائد واحد ناقص
+
+84
+00:08:39,620 --> 00:08:46,660
+واحد على B ناقص واحد ناقص B أس Alpha بساوي B ناقص
+
+85
+00:08:46,660 --> 00:08:52,720
+واحد بيصير هذا عبارة عن B أس Alpha زائد واحد ناقص
+
+86
+00:08:52,720 --> 00:09:01,000
+واحد ناقص B أس Alpha زائد واحد زائد B أس Alpha
+
+87
+00:09:01,000 --> 00:09:03,440
+باشي الحال
+
+88
+00:09:06,140 --> 00:09:11,280
+طيب وي ساوي اللي هو بي أس ألفة ناقص واحد على بي
+
+89
+00:09:11,280 --> 00:09:17,800
+ناقص واحد ماشي الحال بصير عندى الآن هذا المقدار
+
+90
+00:09:17,800 --> 00:09:23,040
+كتبته على صورة بي أس ألفة زائد هذا وهذا اللي بدي
+
+91
+00:09:23,040 --> 00:09:31,800
+انا اذا الان عشان أصل اللي بديه هذا كتبت هذا
+
+92
+00:09:31,800 --> 00:09:38,250
+المقدار بساويهذا المقدار حسب الـ dot ناقص P ألفة
+
+93
+00:09:38,250 --> 00:09:45,390
+بساوي هذا بيصير هذا بساوي P ألفة زائد هذا P ألفة
+
+94
+00:09:45,390 --> 00:09:58,150
+هذا زائد P ألفة ناقص واحد على P ناقص واحدالآن سهل
+
+95
+00:09:58,150 --> 00:10:04,830
+أقارن هذا بـ B أس ألفة لأن B أس ألفة ناقص واحد
+
+96
+00:10:04,830 --> 00:10:09,890
+أصغر من B أس ألفة أكيد فما بالك أن ناقص ما على B
+
+97
+00:10:09,890 --> 00:10:14,950
+ناقص واحد هيصغر أكتر لذا هذا أكيد هيصير أصغر من B
+
+98
+00:10:14,950 --> 00:10:20,390
+أس ألفة زائد B أس ألفة لأن B أس ألفة أكبر من هذا
+
+99
+00:10:20,390 --> 00:10:25,230
+المقدار strictlyإذا صار عندى sigma of B of Alpha
+
+100
+00:10:25,230 --> 00:10:32,030
+أصغر strictly من 2B ألفة إذا صار عندى sigma of B
+
+101
+00:10:32,030 --> 00:10:43,190
+ألفة لا يساوي 2B ألفة ومنه and so B ألفة is not a
+
+102
+00:10:43,190 --> 00:10:52,060
+perfect number إذا اللى وصلتله الآنNo perfect ..
+
+103
+00:10:52,060 --> 00:11:01,540
+No bar of prime can be a perfect number أي
+
+104
+00:11:01,540 --> 00:11:10,180
+سؤال؟ نجي للسؤال اللي بعده أو الفرع C المطلوب منها
+
+105
+00:11:10,180 --> 00:11:16,740
+Name
+
+106
+00:11:16,740 --> 00:11:17,260
+C
+
+107
+00:11:20,230 --> 00:11:27,930
+ماذا يقول الـ C؟ يقول الـ product of
+
+108
+00:11:27,930 --> 00:11:35,850
+two odd-primes is
+
+109
+00:11:35,850 --> 00:11:45,630
+never perfect يعني مش ممكن يكون حاصل ضرب two odd
+
+110
+00:11:45,630 --> 00:11:50,950
+-primes ليكون perfect numberperfect numbers a
+
+111
+00:11:50,950 --> 00:12:06,130
+proof a proof let B let B and Q be any to the odd
+
+112
+00:12:06,130 --> 00:12:15,710
+primes اه بدنا ناخد B and Q any to other primes
+
+113
+00:12:15,710 --> 00:12:21,820
+بدأ اثبت لكم الآن ان B في Qis not perfect كيف
+
+114
+00:12:21,820 --> 00:12:26,060
+بتتبتركم ان ال sigma of B في Q ماتطلعش تساوي B في
+
+115
+00:12:26,060 --> 00:12:33,160
+Q لاتطلعش تساوي 2 في B في Q then ال
+
+116
+00:12:33,160 --> 00:12:39,480
+sigma of B في Q تساوي العدد اللي عندي هو B في Q
+
+117
+00:12:39,480 --> 00:12:45,750
+prime في prime ايش ال divisors اللي قلوه واحدو B و
+
+118
+00:12:45,750 --> 00:12:53,010
+Q و B فى Q فى غير هيك ده بيساوي واحد زائد B زائد Q
+
+119
+00:12:53,010 --> 00:13:02,610
+زائد B فى Q معايا أه؟ الآن بيدكبتلك أن هذا لا يمكن
+
+120
+00:13:02,610 --> 00:13:10,390
+يساوي B فى Q زائد B فى Qمعايا؟ بدي أقول لكم لا
+
+121
+00:13:10,390 --> 00:13:15,690
+يسوي لا يمكن يسوي اللاحظ أن هذا هو هذا بضل هذا
+
+122
+00:13:15,690 --> 00:13:21,270
+قاتبته بسويش هذا فهو بقى معايا؟ الآن بدي أقارن
+
+123
+00:13:21,270 --> 00:13:28,210
+بينهم بدي أقارن بينهم بإيش بين إيدايا أو من خلال
+
+124
+00:13:28,210 --> 00:13:33,590
+إيش بين إيدايا معطيني هو الـP والـQ إيش مالهم؟ of
+
+125
+00:13:33,590 --> 00:13:42,000
+the primes ماشي الآناللي ممكن يجيبلي المقارنة اللي
+
+126
+00:13:42,000 --> 00:13:45,560
+ممكن يجيبلي الـ 1 و الـ B و الـ Q و الـ B في الـ Q
+
+127
+00:13:45,560 --> 00:13:54,860
+هو حاصل ضرب اللي هو 1-B في 1-Q أو Q-1 و B-1 اللي
+
+128
+00:13:54,860 --> 00:13:58,120
+ممكن يجيبلي الـ 1 و الـ B و الـ Q و الـ B في الـ Q
+
+129
+00:13:58,120 --> 00:14:05,060
+اللي هو ال term لعبة Q-1 لو ضربته في B-1 إيش بطلع
+
+130
+00:14:05,060 --> 00:14:12,080
+عليه؟ بطلع ليه الـ Q في B؟زائد بي ناقص بي ناقص q
+
+131
+00:14:12,080 --> 00:14:19,380
+زائد واحد هذا فيه ظهر الواحد و ال b و ال q و مين و
+
+132
+00:14:19,380 --> 00:14:24,740
+ال b في ال q طيب لو جيتط طلعت لهذا المقدار اللي هو
+
+133
+00:14:24,740 --> 00:14:30,830
+هذا هذا المقدار q قد براين و b قد براينإذا هذا
+
+134
+00:14:30,830 --> 00:14:35,490
+اكيد اتنين وطالع و هذا اتنين وطالع، مظبوط؟ إذا
+
+135
+00:14:35,490 --> 00:14:40,650
+حاصل جربهم أكبر من مين؟ من اتنين، إذا الأن نقطة
+
+136
+00:14:40,650 --> 00:14:45,390
+الانطلاق since bq-1
+
+137
+00:14:48,430 --> 00:14:55,710
+في b-1 أكبر من 2 إذن أكيد قيمتين هدولة مين هي الـ
+
+138
+00:14:55,710 --> 00:15:03,190
+q في b حصل ضربهم نقص b نقص q سائد واحد أكبر من مين
+
+139
+00:15:03,190 --> 00:15:11,710
+من اتنين مظبوط ولا لأ ومن ثم عند so عند ال q في b
+
+140
+00:15:13,660 --> 00:15:18,000
+أكبر من بالدنجل هذا على الجهة مين؟ الثانية فبصير
+
+141
+00:15:18,000 --> 00:15:24,000
+أكبر من 2 زائد بي زائد كيو ناقص واحد اللي هي
+
+142
+00:15:24,000 --> 00:15:31,980
+بالظبط مين؟ واحد زائد بي زائد كيو هذه الآن سميها
+
+143
+00:15:31,980 --> 00:15:40,060
+اتنين وهذه سميها ايش؟ واحد لأن
+
+144
+00:15:40,060 --> 00:15:41,160
+from واحد
+
+145
+00:15:46,690 --> 00:16:06,110
+واتمتنا ان واحد
+
+146
+00:16:06,110 --> 00:16:10,570
+زائد بي زائد كيو أصغر
+
+147
+00:16:10,570 --> 00:16:16,750
+من 100من بي في كيو معايا هذا بساوي واحد زائد بي
+
+148
+00:16:16,750 --> 00:16:23,870
+زائد كيو كله مع بعض زائد بي في كيو من اتنين الواحد
+
+149
+00:16:23,870 --> 00:16:29,490
+زائد بي زائد كيو strictly أصغر من مين واضح هذا
+
+150
+00:16:29,490 --> 00:16:32,990
+المقدار أصغر strictly من مين من بي في كيو إذا صار
+
+151
+00:16:32,990 --> 00:16:37,370
+هذا المقدار أصغر strictly من بي في كيو زائد ال بي
+
+152
+00:16:37,370 --> 00:16:42,370
+في كيو اللي هو اتنين بي في كيوإذا صار هذا المقدار
+
+153
+00:16:42,370 --> 00:16:48,630
+أصغر strictly من بي في اتنين بي في كيو hence ال
+
+154
+00:16:48,630 --> 00:16:55,110
+sigma of بي في كيو لا يساوي اتنين بي في كيو وهذا
+
+155
+00:16:55,110 --> 00:16:59,830
+ايش يعني ان ال sigma of انا لا ساوي اتنين انا يعني
+
+156
+00:16:59,830 --> 00:17:06,130
+اشمل و ال بي في كيو is not perfect hence and so بي
+
+157
+00:17:06,130 --> 00:17:21,430
+في كيو is notPerfect هو المطلوب أي سؤال نفسه
+
+158
+00:17:21,430 --> 00:17:29,850
+نفسه أي سؤال
+
+159
+00:17:35,800 --> 00:17:39,060
+if n is a perfect number prove that summation 1
+
+160
+00:17:39,060 --> 00:17:43,240
+على d دي بتجسم n بيساوي ايش بيساوي اتنين هذا بيتمد
+
+161
+00:17:43,240 --> 00:17:50,600
+على على سؤال قبل هيك أخدناه في شبطر 6 1 اللي هو
+
+162
+00:17:50,600 --> 00:17:54,640
+problem 8 بقولنا
+
+163
+00:17:54,640 --> 00:17:57,800
+خلوكم
+
+164
+00:17:57,800 --> 00:18:04,310
+معايا لأن اللي بقول if n is a perfect numberيعني
+
+165
+00:18:04,310 --> 00:18:07,310
+الـ sigma و الان بيساوي اتنين انا ال proof ده ال
+
+166
+00:18:07,310 --> 00:18:09,750
+summation واحد على دي دي بتكسب عنه ايش بيساوي
+
+167
+00:18:09,750 --> 00:18:16,700
+بيساوي اتنينسؤال 8 في 6 واحد اثبتنا ان ال
+
+168
+00:18:16,700 --> 00:18:21,460
+summation 1 على d d تجسم n بساوي sigma of n على
+
+169
+00:18:21,460 --> 00:18:27,520
+مين على n وبما ان في سؤالنا ال n is perfect فبصير
+
+170
+00:18:27,520 --> 00:18:31,020
+ال sigma of n ايش بساوي اتنين n على ال n ايش
+
+171
+00:18:31,020 --> 00:18:34,960
+هيساوي بساوي اتنين اذا انصار ال summation بساوي
+
+172
+00:18:34,960 --> 00:18:41,050
+اتنين طيب نيجي لسؤال خمسةالسؤال اللي جابله إذا
+
+173
+00:18:41,050 --> 00:18:46,270
+سؤال يعتمد على سؤال سابق بس
+
+174
+00:18:46,270 --> 00:18:51,830
+يستخدمنا معلومة sigma of n بساوت in n اللي هو as
+
+175
+00:18:51,830 --> 00:18:56,690
+an imperfect number now we are going to prove
+
+176
+00:18:56,690 --> 00:19:05,410
+problem 5 اللي
+
+177
+00:19:05,410 --> 00:19:13,550
+معطيني في السؤال الخامسةبقول لي given N as an even
+
+178
+00:19:13,550 --> 00:19:22,650
+perfect number عندي N is even perfect number
+
+179
+00:19:22,650 --> 00:19:25,810
+ومعطيك
+
+180
+00:19:25,810 --> 00:19:33,580
+الـ N بتساوياللي هو 2 to the k minus 1 في 2 to the
+
+181
+00:19:33,580 --> 00:19:38,840
+k ناقص واحد حسب النظرية اللي قبل بي شوية مدام un
+
+182
+00:19:38,840 --> 00:19:43,100
+even perfect number على الصورة اللي أمامي هيكون
+
+183
+00:19:43,100 --> 00:19:49,140
+ومش هي كمان وهيكون هذا 2 أُس k ناقص واحد is إيش ال
+
+184
+00:19:49,140 --> 00:19:54,520
+zebrain fine number طيب هذا المقطع إيش بقولك الآن
+
+185
+00:19:54,520 --> 00:19:57,220
+prove that prove
+
+186
+00:19:59,870 --> 00:20:08,030
+that أن تبعتنا هذه بتساوي واحد زاد اتنين زاد اتنين
+
+187
+00:20:08,030 --> 00:20:14,290
+أس كي ناقص واحد هاي أول واحد وبيقولك prove that
+
+188
+00:20:14,290 --> 00:20:21,470
+كمان prove that واحد اتنين اثبت انه five of n
+
+189
+00:20:21,470 --> 00:20:27,330
+بساوي اتنين أس كي ناقص واحد في اتنين أس كي ناقص
+
+190
+00:20:27,330 --> 00:20:28,550
+واحد ناقص
+
+191
+00:20:32,260 --> 00:20:50,140
+معايا تنحلوا مع بعض ا proof اذكركم
+
+192
+00:20:50,140 --> 00:20:56,340
+بس بال file of M كيف نوجدها عندي احنا لو ال M أكبر
+
+193
+00:20:56,340 --> 00:21:02,410
+من واحد و كتبناها على صورة P1 α1 لعين PR αRبكون
+
+194
+00:21:02,410 --> 00:21:08,890
+اللي هو Phi of N بساوي الـ N نفسها في واحد نقص
+
+195
+00:21:08,890 --> 00:21:15,410
+واحد على P واحد لما أصل عند واحد نقص واحد على PR
+
+196
+00:21:15,410 --> 00:21:21,870
+معايا هذه اللي هي ال main ال Phi of N اللي هو
+
+197
+00:21:21,870 --> 00:21:29,430
+الأعداد اللي بتكون اللي هو relatively prime to N
+
+198
+00:21:32,770 --> 00:21:41,250
+طيب او عدد الأعداد من البرهن هذه في اللي هو
+
+199
+00:21:41,250 --> 00:21:46,490
+المتتابع
+
+200
+00:21:46,490 --> 00:21:52,290
+اللي عندي لحد الأول واحد و بعدين الأساس واحد زاد
+
+201
+00:21:52,290 --> 00:21:58,590
+اتنين زاد تلاتة زاد ان عدد حدودها ان ايش قولها
+
+202
+00:21:58,590 --> 00:22:06,830
+بساوي انعدد الحدود فان زائد واحد على مين على اتنين
+
+203
+00:22:06,830 --> 00:22:11,910
+هذا قانون مر علينا سواء في ال calculus او اللي هو
+
+204
+00:22:11,910 --> 00:22:17,050
+في التنوية او الإعدادية واحد زائد اتنين زائد تلاتة
+
+205
+00:22:17,050 --> 00:22:20,590
+زائد ألف سواء فان زايد واحد على ايش على اتنين الان
+
+206
+00:22:20,590 --> 00:22:26,290
+بدأت أخدم هذه عندي اللي هو هذه المقدار هذاالمقدار
+
+207
+00:22:26,290 --> 00:22:31,190
+هذا واحد زائد اتنين زائد اخر حد اللي هو اتنين K
+
+208
+00:22:31,190 --> 00:22:35,450
+ناقص واحد كل مرة بنزيد ايه ليش بنزيد واحد لما
+
+209
+00:22:35,450 --> 00:22:39,170
+وصلنا لاخر حد هو هذا هذا اللي بمثل الان اذا ايش
+
+210
+00:22:39,170 --> 00:22:43,130
+بيساوي هذا اللي هي الان اللي هو اتنين أس K ناقص
+
+211
+00:22:43,130 --> 00:22:48,110
+واحد مضروب في مين في ان زائد واحد هذا زائد واحد
+
+212
+00:22:48,110 --> 00:22:51,650
+اللي هو بيطلع ايه شماله اتنين أس K لانه اتنين أس K
+
+213
+00:22:51,650 --> 00:22:56,590
+ناقص واحد زائد واحد بيطلع اتنين أس Kعلى اتنين
+
+214
+00:22:56,590 --> 00:23:01,530
+ويساوي اللي هو بيصير اتنين اث ك ناقص واحد في اتنين
+
+215
+00:23:01,530 --> 00:23:08,850
+اث ك ناقص مين ناقص واحد هذا المجموع اللي عندك واضح
+
+216
+00:23:08,850 --> 00:23:16,610
+طيب الآن بدنا نوجد مين five of n five of n بساوي
+
+217
+00:23:16,610 --> 00:23:27,720
+حسب القانون بساوياللي هو Phi of 2K-1 في Phi أُس 2K
+
+218
+00:23:27,720 --> 00:23:36,420
+-1-1 since Phi is multiplicative and the greatest
+
+219
+00:23:36,420 --> 00:23:41,520
+common divisor بين 2K-1 و2K-1
+
+220
+00:23:54,560 --> 00:24:03,360
+أدك هي اه مساوي واحد معايا اه يا شباب هد و هد
+
+221
+00:24:03,360 --> 00:24:05,840
+relative ال prime و Phi is multiplicative عشان هي
+
+222
+00:24:05,840 --> 00:24:12,960
+كه اللي هو انا وزعت هنا ال Phi و يساوي Phi هي اد
+
+223
+00:24:12,960 --> 00:24:17,900
+ايش هي ابقى عن اتنين حسب القانون K minus واحد اللي
+
+224
+00:24:17,900 --> 00:24:25,760
+هي N في مضروف واحد ناقص نصحسب القانون اللي هو 5n
+
+225
+00:24:25,760 --> 00:24:32,440
+بساوة n في 1 ناقص 1 على ال prime factors ال .. ال
+
+226
+00:24:32,440 --> 00:24:35,540
+.. ال primes اللي هنا بس مين هو ال factorization
+
+227
+00:24:35,540 --> 00:24:41,380
+لعددها ده بس التنين فاهمين علشان بحكي مضروب في مين
+
+228
+00:24:41,380 --> 00:24:47,740
+فاي هذا، هذه إيش مالها؟ is a prime فاي of بي لما
+
+229
+00:24:47,740 --> 00:24:51,240
+يكون بي prime إيش بيساوي؟ فاي of بي
+
+230
+00:24:55,550 --> 00:25:02,630
+الـ Euler function Phi of B بسوا B ناقص واحد Phi
+
+231
+00:25:02,630 --> 00:25:07,270
+of B بسوا B ناقص واحد عدد الأعداد اللي relative to
+
+232
+00:25:07,270 --> 00:25:12,850
+the primes مع الـ B واحد و اتنين و التلاتة لمّا
+
+233
+00:25:12,850 --> 00:25:16,850
+اصلا عند B minus واحد اكم واحد هنا B minus واحد
+
+234
+00:25:16,850 --> 00:25:21,610
+إذن اللي هي Phi of the prime بسوا B ناقص واحد يعني
+
+235
+00:25:21,610 --> 00:25:26,760
+بما ناخر اتنين أسكيه ناقص واحد ناقص1 الـ prime
+
+236
+00:25:26,760 --> 00:25:31,800
+ناقص مين؟ ناقص واحد و2 أُس K ماينس واحد مايساوي
+
+237
+00:25:31,800 --> 00:25:39,440
+هذا عبارة عن مين؟ 2 أُس K ناقص واحد في نص في ..
+
+238
+00:25:39,440 --> 00:25:46,840
+هذا عبارة عن مين؟ 2 أُس K ناقص 2 معايا يا شباب
+
+239
+00:25:46,840 --> 00:25:53,410
+ويساوي 2 أُس K ماينس واحد في نصهذا نسحب الاتنين
+
+240
+00:25:53,410 --> 00:25:58,150
+عامل مشترك هان بيصير اتنين في اتنين أس ك ناقص واحد
+
+241
+00:25:58,150 --> 00:26:03,870
+ناقص الواحد هذا اتنين مع النص عشان ايه كما طيرتوش
+
+242
+00:26:03,870 --> 00:26:09,670
+في الأول هو يساوي اتنين أس ك ناقص واحد في اتنين أس
+
+243
+00:26:09,670 --> 00:26:14,850
+ك ناقص واحد ناقص واحد مارضيتش اختصره دخله لهذه
+
+244
+00:26:14,850 --> 00:26:17,830
+اللي هو النص هذا عشان نختصر
+
+245
+00:26:20,950 --> 00:26:26,190
+صار عندى الـPhi of n نين أسكيه مانسة واحد نين
+
+246
+00:26:26,190 --> 00:26:32,770
+أسكيه نقص واحد نقص واحد وهو المقلوب نيجي
+
+247
+00:26:32,770 --> 00:26:39,310
+لإحداش تلاتة خلصنا إحداش اتنين بدنا ناخد إحداش
+
+248
+00:26:39,310 --> 00:26:42,610
+تلاتة طلعلي على أسلت إحداش تلاتة من الكتاب هاي
+
+249
+00:26:42,610 --> 00:26:44,930
+إحداش تلاتة الآن
+
+250
+00:27:01,580 --> 00:27:07,100
+الـ Mercier numbers عندي بعض الأسئلة سؤالين عن الـ
+
+251
+00:27:07,100 --> 00:27:14,380
+Mercier numbers الهمواك ال 113 سؤال واحد prove
+
+252
+00:27:14,380 --> 00:27:22,320
+that ال
+
+253
+00:27:22,320 --> 00:27:30,460
+M13 ال M13 is upright
+
+254
+00:27:33,630 --> 00:27:42,590
+هنس هيكون عندي n بساوة 2 اقصى 13 ولا 2 اقصى 12 ف2
+
+255
+00:27:42,590 --> 00:27:49,610
+اقصى 13 ناقص واحد is perfect
+
+256
+00:28:25,390 --> 00:28:30,890
+بس في نظرية هعتمد عليها في الحالة الـ theorem
+
+257
+00:28:30,890 --> 00:28:36,090
+أخدناها الـ 11.5 أظن و 11.6 .. 11.5 بقول إذا كانت
+
+258
+00:28:36,090 --> 00:28:45,320
+بي قد إبراهيموكان الـ Q عبارة عن الـ Prime و بجسم
+
+259
+00:28:45,320 --> 00:28:52,460
+الـ MB غِم الـ Q لازم يكون على صورة 2K في B زائد
+
+260
+00:28:52,460 --> 00:28:58,420
+واحد كمان مرة النظرية بتقول مالي هي الحقيقة
+
+261
+00:28:58,420 --> 00:29:02,930
+بتاعتها متعلقة في حال السؤالين اللي عنديالنظرية
+
+262
+00:29:02,930 --> 00:29:07,590
+بتقول if B is an odd prime and the Q is a prime
+
+263
+00:29:07,590 --> 00:29:12,990
+factor of MB يعني كيوبكس من ال MB لـ Q هذا لازم
+
+264
+00:29:12,990 --> 00:29:19,810
+يكون على صورة 2KB زائد 1 يعني لو بد يكون لل MB فيه
+
+265
+00:29:19,810 --> 00:29:24,770
+prime factors بس هتلاقيهم من وين من اللي على صورة
+
+266
+00:29:24,770 --> 00:29:29,790
+2KB زائد 1 okay بس هو 1 و 2 الاخرين واضح؟
+
+267
+00:29:31,420 --> 00:29:36,700
+الان بيقوللي اثبت ان الام تلتاش is a prime و من ثم
+
+268
+00:29:36,700 --> 00:29:40,680
+مادام الام تلتاش is a prime ايش الام تلتاش هو الام
+
+269
+00:29:40,680 --> 00:29:44,920
+تلتاش اللي هو عبارة عن مرسيم number اللي هو اتنين
+
+270
+00:29:44,920 --> 00:29:50,500
+اص تلتاش ناقص واحد لان المرسيم number mn ايش هيكون
+
+271
+00:29:50,500 --> 00:29:56,780
+ع صورة اتنين اص ام ناقصأولا يطلب مني أن أثبت أن
+
+272
+00:29:56,780 --> 00:30:01,240
+الان تلتاش is a prime number كيف؟ لكي أثبت أنه
+
+273
+00:30:01,240 --> 00:30:07,140
+prime نحن قبل ما جابنا معلومة مثل هذه أنه لأي عدد
+
+274
+00:30:07,140 --> 00:30:13,860
+ان عشان أوجد ال prime factors اللي لهأو اللي هو
+
+275
+00:30:13,860 --> 00:30:18,560
+عشان اللي هو أثبت ان الـ N is composite ولا .. ولا
+
+276
+00:30:18,560 --> 00:30:23,860
+.. ولا إبراهيم كنا نقول إذا كان بدو يكون composite
+
+277
+00:30:23,860 --> 00:30:32,220
+بدو يكون في عند D أو B اللي هو إبراهيم بيبسم الـ N
+
+278
+00:30:32,220 --> 00:30:38,980
+والـ B أصغر من مين أصغر و سوء إيش جدر الـ N إذا
+
+279
+00:30:38,980 --> 00:30:44,970
+عشان أفحصاللي هو الـ M is composite او لا يكفيني
+
+280
+00:30:44,970 --> 00:30:51,210
+ان افحص اللي هو الـ prime factors اللي جاب المين
+
+281
+00:30:51,210 --> 00:30:56,430
+الجابرن الـ N ال primes اللي ممكن يكون factors ده
+
+282
+00:30:56,430 --> 00:31:00,110
+مين للـ N مالجيتش ولا واحد معناته الـ M على طول
+
+283
+00:31:00,110 --> 00:31:10,390
+ايش ماله is M is a primeمعايا؟ نعم الان أخدناها
+
+284
+00:31:10,390 --> 00:31:17,030
+قبل هيه ال corollary انه عندي إذا كان بده يكون
+
+285
+00:31:17,030 --> 00:31:23,190
+اللي هو and composite إذا there exist there must
+
+286
+00:31:23,190 --> 00:31:28,590
+exist بي أصغر أو ساوي جدر الان والبي بيكسبنيين
+
+287
+00:31:28,590 --> 00:31:34,550
+الان if no such بي exist then and will be اشماله
+
+288
+00:31:34,550 --> 00:31:40,480
+primeإذا من الآن عشان أثبت ال M13 أنه براين باجي
+
+289
+00:31:40,480 --> 00:31:45,820
+باخد الجدر التربيعي إلى ال M13 و باخد كل ال brains
+
+290
+00:31:45,820 --> 00:31:51,020
+اللي جابله و بفحصها بجسمي ال M13 ولا لأ إذا بجسميه
+
+291
+00:31:51,020 --> 00:31:57,460
+ولا واحد من ال M13 صار إيش ماله is a brainطيب الآن
+
+292
+00:31:57,460 --> 00:32:01,140
+ماعطيني انت في الكتاب جالي الجدر التربيع لل M13
+
+293
+00:32:01,140 --> 00:32:04,920
+أصغر من مين؟ من 91 يعني الآن لو جيت أخدت الجدر
+
+294
+00:32:04,920 --> 00:32:10,600
+التربيع لهذا العدد هتلاقي أصغر من مين؟ من 91 الان
+
+295
+00:32:10,600 --> 00:32:22,080
+note that اللي هو الجدر التربيع لل M13 less than
+
+296
+00:32:22,080 --> 00:32:23,020
+91
+
+297
+00:32:26,100 --> 00:32:31,040
+الأن المعلومات الأولية تبعت زمان بتقول عشان تثبت
+
+298
+00:32:31,040 --> 00:32:35,950
+ان الام طلعت على شهادة براين بدك تيجي تاخداللي هو
+
+299
+00:32:35,950 --> 00:32:41,170
+كل الأعداد لـ Brines اللي جاب للـ 91 واتجربها تكسب
+
+300
+00:32:41,170 --> 00:32:44,790
+الـ M 13 ولا لا؟ غلبة يعني بدي أجيب التنين
+
+301
+00:32:44,790 --> 00:32:48,570
+والتلاتة والخمسة والسبعة والأحداشر والتلاتاشر
+
+302
+00:32:48,570 --> 00:32:52,990
+والسبعتاشر والتسعتاشر والتلاتة وعشرين لما أصل لـ
+
+303
+00:32:52,990 --> 00:32:57,350
+Brines اللي عند الـ 91 فيرة وغلبة الآن اللي
+
+304
+00:32:57,350 --> 00:33:01,210
+بيخففلي هذه الغلبة مين؟ اللي هو النظرية التالية
+
+305
+00:33:01,780 --> 00:33:05,760
+بتقولي إذا كان بده يكون فيه prime factors للن بي
+
+306
+00:33:05,760 --> 00:33:12,260
+إذا صورتها هتكون على صورة مين؟ اتنين كب زائد واحد
+
+307
+00:33:12,260 --> 00:33:16,680
+إذا يكفي لي .. يكفي لي أني أفحص الأعداد لـprimes
+
+308
+00:33:16,680 --> 00:33:21,240
+اللي أقل من واحد وتسعين وعلى صورة مين؟ اتنين كب
+
+309
+00:33:21,240 --> 00:33:32,900
+زائد واحد but أو by theorem أحداشر خمسة أناIbrahim
+
+310
+00:33:32,900 --> 00:33:40,720
+and Ibrahim factor of
+
+311
+00:33:40,720 --> 00:33:57,360
+M13 must be of the form 2KB زائد 1 so we only
+
+312
+00:33:57,360 --> 00:33:59,420
+investigate
+
+313
+00:34:01,590 --> 00:34:14,830
+the primes less than ninety one and of the form
+
+314
+00:34:14,830 --> 00:34:24,390
+اتنين ك بيه اللي هو جداش بيه جداش هيها تلتاش تلتاش
+
+315
+00:34:24,390 --> 00:34:27,570
+زائد واحد اه
+
+316
+00:34:32,600 --> 00:34:38,180
+these primes are من هما ناخد أول الشكلة بالساعة
+
+317
+00:34:38,180 --> 00:34:42,720
+واحد اتنين في التلات عشر ستة و عشرين زاد واحد سبعة
+
+318
+00:34:42,720 --> 00:34:48,200
+و عشرين مش primes سيبه نجي للي بعده اتنين في اتنين
+
+319
+00:34:48,200 --> 00:34:54,260
+اربعة اربعة في تلات عشر اربعة في تلات عشر اتنين و
+
+320
+00:34:54,260 --> 00:34:58,380
+خمسين و احد تلاتة و خمسين إذا هي أول واحد نجي
+
+321
+00:34:58,380 --> 00:35:04,110
+لبعدهكيف جداش؟ بتلاتة اتنين في تلاتة بستة ستة في
+
+322
+00:35:04,110 --> 00:35:10,250
+تلتاش تبعين وسبعين مظبوط واحد تسعة وسبعين تأكدولي
+
+323
+00:35:10,250 --> 00:35:15,890
+من الأرقام اللي بعده اللي هو اربعة اتنين في اربعة
+
+324
+00:35:15,890 --> 00:35:22,850
+تمانية تمانية في تلتاش حينط مين خلاص بكفيني اذا بس
+
+325
+00:35:22,850 --> 00:35:27,190
+we only investigate from fifty three and seventy
+
+326
+00:35:27,190 --> 00:35:27,570
+nine
+
+327
+00:35:30,970 --> 00:35:36,670
+الـ 53 لتقسم الـ M 13 بالـ .. بالطبع .. بالـ
+
+328
+00:35:36,670 --> 00:35:43,410
+calculations and الـ 79 لتقسم الـ M 13 برضه by
+
+329
+00:35:43,410 --> 00:35:53,410
+calculations hence اللي هو M 13 must be a prime
+
+330
+00:35:53,410 --> 00:35:57,750
+واضح؟
+
+331
+00:35:57,750 --> 00:35:58,730
+طيب
+
+332
+00:36:03,190 --> 00:36:06,810
+نجي لسؤال تلاتة اللي المطلوب يا أخي السؤال تلاتة
+
+333
+00:36:06,810 --> 00:36:13,110
+كمان ال
+
+334
+00:36:13,110 --> 00:36:17,490
+proof ده ده ال number 29 is composite فكرة نفس
+
+335
+00:36:17,490 --> 00:36:24,170
+فكرة السؤال اللي عندى بس الآن هيظهر عندى هيظهر
+
+336
+00:36:24,170 --> 00:36:35,250
+عندى اللي هو انه فيالـ prime factor للـ M29 من بين
+
+337
+00:36:35,250 --> 00:36:40,890
+ال factors الممكنة اللي ع صورة 2K بزائد 1 ده نشوف
+
+338
+00:36:40,890 --> 00:36:43,910
+إيش سؤالنا سؤال تلاتة
+
+339
+00:36:48,510 --> 00:36:51,690
+طبعا الجزء الثاني على طول بطلع اللي هو العدد اللي
+
+340
+00:36:51,690 --> 00:36:55,150
+بطلع مدان هذا طلع عندى prime إذا الـ 2 وصوله 12 ف2
+
+341
+00:36:55,150 --> 00:36:59,190
+وصوله 13 نقص 1 هيطلع إيه شماله perfect number
+
+342
+00:36:59,190 --> 00:37:10,610
+sigma of n بتطلع 2n سؤال
+
+343
+00:37:10,610 --> 00:37:17,770
+تلاتة هنزلكم الحلول لا تجلبوش
+
+344
+00:37:31,240 --> 00:37:42,640
+السؤال اللي بيقولي prove that المرسيل
+
+345
+00:37:42,640 --> 00:37:47,080
+number
+
+346
+00:37:50,660 --> 00:38:02,160
+م تسعة و عشرين is composite prove by
+
+347
+00:38:02,160 --> 00:38:16,700
+theorem أحداشر خمسة the possible prime factors of
+
+348
+00:38:16,700 --> 00:38:18,900
+M تسعة و عشرين
+
+349
+00:38:22,130 --> 00:38:31,330
+R of the form
+
+350
+00:38:31,330 --> 00:38:38,230
+اتنين ك بي زائد واحد بيهم تسعة و عشرين يعني اتنين
+
+351
+00:38:38,230 --> 00:38:44,790
+ك في تسعة و عشرين زائد واحد و يساوي تمانية و خمسين
+
+352
+00:38:44,790 --> 00:38:46,630
+ك زائد واحد
+
+353
+00:38:52,620 --> 00:38:57,960
+النظرية هذه نظرية هذه استخدمت النظرية اللي بتقول
+
+354
+00:38:57,960 --> 00:39:05,260
+لو كان P of the brine ال Q هتكسب M P إذا Q بتكسب م
+
+355
+00:39:05,260 --> 00:39:08,140
+ال M P لازم ال Q تطلع على صورة 2 K P زائد إذا مش
+
+356
+00:39:08,140 --> 00:39:15,190
+واحد إذا ال possible the brine factors of M PR of
+
+357
+00:39:15,190 --> 00:39:19,610
+the form تمانية و خمسين K زائد واحد اللي هو اتنين
+
+358
+00:39:19,610 --> 00:39:25,550
+KB زائد واحد إذا بدي يكون الفحص من خلال هذه الأقام
+
+359
+00:39:25,550 --> 00:39:30,010
+الآن الرقم الأول اللي هو K بساوي واحد تمانية و
+
+360
+00:39:30,010 --> 00:39:38,470
+خمسين زائد واحد ايش معنوه تسعة و خمسين الان four K
+
+361
+00:39:38,470 --> 00:39:46,970
+بساوي واحد تسعة و خمسينis prime is prime but
+
+362
+00:39:46,970 --> 00:39:52,190
+التسعة و خمسين لو جيت فحصلت مش هلاقيك سنين الام
+
+363
+00:39:52,190 --> 00:39:59,070
+تسعة و عشرين الام four كيه بيساوي اتنين بيصير عندى
+
+364
+00:39:59,070 --> 00:40:03,230
+اتنين في تمانية و خمسين اللي هو عبارة عن مية و
+
+365
+00:40:03,230 --> 00:40:07,990
+ستاش زاد واحد مية و سبعتاش مية و سبعتاش is prime
+
+366
+00:40:07,990 --> 00:40:17,660
+is not prime is notبرايم فلا نبحث عن هذا الرقم لأن
+
+367
+00:40:17,660 --> 00:40:27,380
+توريمنا يتكلم عن الواقعات البرايم و أكيد و أكيد
+
+368
+00:40:27,380 --> 00:40:35,840
+هيطلع 117 إش ماله لا يقسم من 29 4
+
+369
+00:40:35,840 --> 00:40:44,930
+كيه بيساوي 103 إيش هيطلع عندي العدد؟أضرب الآن 58
+
+370
+00:40:44,930 --> 00:40:52,650
+في 3 اضرب لي العدد 175
+
+371
+00:40:52,650 --> 00:40:59,950
+برضه ايش ماله it's not a prime اه الان four كيف
+
+372
+00:40:59,950 --> 00:41:04,790
+يساوي اربعة بطلع اللي هو اربعة في خمسة اتنين
+
+373
+00:41:04,790 --> 00:41:08,050
+واربعة في تمانية اتنين و تلاتين اتنين و تلاتين
+
+374
+00:41:08,050 --> 00:41:11,930
+اتنين و تلاتة و تلاتين اتنين و تلاتة و تلاتين اه
+
+375
+00:41:12,510 --> 00:41:26,030
+and we will find that 233 تقسم من M29 by
+
+376
+00:41:26,030 --> 00:41:26,990
+calculations
+
+377
+00:41:30,690 --> 00:41:35,130
+إذا مافيش غلبة كتير، اللي هو عندي، هاي عدد، عددين،
+
+378
+00:41:35,130 --> 00:41:38,150
+تلاتة وصلنا لقى الرابع، أيه أش معله؟ مائتين و
+
+379
+00:41:38,150 --> 00:41:40,530
+تلاتة و تلاتين، دي اكسب منها متساع و عشرين، لو بده
+
+380
+00:41:40,530 --> 00:41:45,010
+يطلع اللي هو prime، بكون أخدت مين، لو أنا مش عارف
+
+381
+00:41:45,010 --> 00:41:47,590
+إنه prime أو مش prime، باخده الجدر التربيهي و ببحث
+
+382
+00:41:47,590 --> 00:41:51,030
+اللي جابني جاي السؤال الأول يعني، إذا في منهم شي
+
+383
+00:41:51,030 --> 00:41:53,710
+بيجسم، معناته say are composite، في شي بيجسم
+
+384
+00:41:53,710 --> 00:41:59,790
+معناته أيش معله، is primeوالأم تسعة و عشرين اشماله
+
+385
+00:41:59,790 --> 00:42:05,590
+is composite و
+
+386
+00:42:05,590 --> 00:42:12,850
+الام تسعة و عشرين اكيد مش هي متين و تلتة و تلتين
+
+387
+00:42:16,110 --> 00:42:21,490
+أوى سؤال بكونى خلصنا ال discussion of chapter 7 و
+
+388
+00:42:21,490 --> 00:42:25,710
+11 دل عنا chapter 7 خلاص ماشي الله يعطيكوا العفو
+
+389
+00:42:25,710 --> 00:42:30,250
+المرة الجاية ان شاء الله بنكمل و إلى لقايا اخر
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/4ffxvgnWBKc_postprocess.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/4ffxvgnWBKc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c447c3d71fdb359c5db5bab82158a991f46be714
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/4ffxvgnWBKc_postprocess.srt
@@ -0,0 +1,2124 @@
+1
+00:00:20,990 --> 00:00:25,690
+بسم الله الرحمن الرحيم محاضرة رقم 37 مساق نظرية
+
+2
+00:00:25,690 --> 00:00:30,690
+الأعداد هذه المحاضرة هي المحاضرة الأخيرة في المادة
+
+3
+00:00:30,690 --> 00:00:41,850
+إذا تمكننا في وقت لاحق نحل ونصور محاضرة حول امتحان
+
+4
+00:00:41,850 --> 00:00:46,250
+نهائي أو امتحانات سابقة سنقوم بذلك أما هذه هي
+
+5
+00:00:46,250 --> 00:00:50,590
+المحاضرة الأخيرة في مساق نظرية الأعداداليوم
+
+6
+00:00:50,590 --> 00:01:00,390
+هنستكمل مناقشة chapter 7 نقشنا المرة الماضية 7
+
+7
+00:01:00,390 --> 00:01:06,190
+ثلاثة و 7 اتنين دال في 7 ثلاثة فينا سؤال و هنناقش
+
+8
+00:01:06,190 --> 00:01:16,130
+أيضا 7 أربعة سؤال 7 ثلاثة اللي هو بقول ما يلي سؤال
+
+9
+00:01:16,130 --> 00:01:17,890
+13
+
+10
+00:01:19,180 --> 00:01:25,640
+وقولّي إذا كانت بي is an odd prime بي is an odd
+
+11
+00:01:25,640 --> 00:01:31,180
+prime بدنا
+
+12
+00:01:31,180 --> 00:01:38,960
+نثبت أنه الناقص بي زائد واحد على اتنين
+
+13
+00:01:43,670 --> 00:01:50,130
+باقية سؤال 13 في سبعة تلاتة السؤال بيقول مالي إذا
+
+14
+00:01:50,130 --> 00:01:54,890
+كانت بي is an odd prime بدنا نثبت show that the
+
+15
+00:01:54,890 --> 00:02:00,210
+integers ناقص بي واحد على اتنين لما أصل لعند ناقص
+
+16
+00:02:00,210 --> 00:02:06,850
+اتنين وناقص واحد وواحد واتنين لعند البي ناقص واحد
+
+17
+00:02:06,850 --> 00:02:12,630
+على اتنين بتعملي form a reduced
+
+18
+00:02:15,500 --> 00:02:27,940
+set of residues modulo n proof الان
+
+19
+00:02:27,940 --> 00:02:38,400
+احنا بنعرف ان الواحد والتنين والتلاتة وال بي زائد
+
+20
+00:02:38,400 --> 00:02:43,320
+واحد على اتنين لما اصل ل عند ال
+
+21
+00:02:46,080 --> 00:02:56,260
+اللي عند الـ P نقص واحد هذه form a reduced set
+
+22
+00:02:56,260 --> 00:02:59,360
+of
+
+23
+00:02:59,360 --> 00:03:09,910
+residue modulo N لأن هي عبارة عنعند الـ B تعمل
+
+24
+00:03:09,910 --> 00:03:14,450
+Complete Residue System Modulo N ومن ثم أخذنا كل
+
+25
+00:03:14,450 --> 00:03:17,890
+الـ Relatively Prime مع الـ B لأن B is a Lot وقالت
+
+26
+00:03:17,890 --> 00:03:20,790
+عندي اللي هي الأعداد من واحد لعند الـ B minus واحد
+
+27
+00:03:20,790 --> 00:03:26,670
+فتعمل Reduce Residue System Modulo N ومن ثم هذه
+
+28
+00:03:26,670 --> 00:03:34,340
+الأعداد أكيد Are Incongruent Modulo Nوكل مدلو أ بي
+
+29
+00:03:34,340 --> 00:03:39,720
+وكل مدلو أ بي وكل مدلو أ بي وكل مدلو أ بي وكل مدلو
+
+30
+00:03:39,720 --> 00:03:39,920
+مدلو أ بي وكل مدلو أ بي وكل مدلو أ بي وكل مدلو أ
+
+31
+00:03:39,920 --> 00:03:40,000
+بي وكل مدلو أ بي وكل مدلو أ بي وكل مدلو أ بي وكل
+
+32
+00:03:40,000 --> 00:03:41,180
+مدلو أ بي وكل مدلو أ بي وكل مدلو أ بي وكل مدلو أ
+
+33
+00:03:41,180 --> 00:03:45,440
+بي وكل مدلو أ بي وكل مدلو أ بي وكل مدلو أ بي وكل
+
+34
+00:03:45,440 --> 00:03:54,700
+مدلو أ بي وكل مدلو أ بي وكل مدلو أ ب
+
+35
+00:03:55,440 --> 00:04:01,600
+من عند 1 لعند الـ B-1 بالاضافة للأعداد من ناقص B-1
+
+36
+00:04:01,600 --> 00:04:05,980
+على 2 لعند ناقص 1 كلهم هذولة كل واحد فيهم
+
+37
+00:04:05,980 --> 00:04:11,200
+congruent لواحد و بس واحد من هذوللو أثبتنا هيك
+
+38
+00:04:11,200 --> 00:04:14,880
+معناه تصارت اللي هي الأعداد هذولة in congrant مع
+
+39
+00:04:14,880 --> 00:04:20,600
+بعض هذه واحد اتنين وعددهم هذولة هذولة five of B
+
+40
+00:04:20,600 --> 00:04:24,400
+لأن عددهم معدد هذولة بالظبط فبتعمل ي reduce
+
+41
+00:04:24,400 --> 00:04:31,640
+residue system modulo B الان نلاحظ ان الأعداد من
+
+42
+00:04:31,640 --> 00:04:40,840
+واحد لعند ال B minus واحد على اتنينهذه الأعداد هي
+
+43
+00:04:40,840 --> 00:04:45,500
+نفس الأعداد اللي كانت هنا فأكيد اشمال متطابقات كل
+
+44
+00:04:45,500 --> 00:04:52,580
+واحد بطابق اللي هو نظيره modulo B دل علينا نثبت ان
+
+45
+00:04:52,580 --> 00:04:57,380
+هذول الأعداد بطابق من الأعداد المتبقية عندي اللي
+
+46
+00:04:57,380 --> 00:05:09,720
+كانت هنا لاحظ مالي Note that انه عندي الـ Bناقص
+
+47
+00:05:09,720 --> 00:05:21,560
+واحد او b زائد واحد على اتنين تطابق ال b ناقص ال b
+
+48
+00:05:21,560 --> 00:05:28,900
+زائد واحد على اتنين تطابق اللي هو ناقص ال b minus
+
+49
+00:05:28,900 --> 00:05:37,900
+واحد على اتنين modulo b طبعا اللي سبب بسيط ان ال b
+
+50
+00:05:39,220 --> 00:05:44,340
+زائد واحد على اتنين زائد بي مقص واحد على اتنين
+
+51
+00:05:44,340 --> 00:05:49,960
+مساوى اتنين بي على اتنين ويساوي ال بي فاكيد
+
+52
+00:05:49,960 --> 00:05:54,800
+العددين متطابقين والعدد اللي بعده هنا اللي بعده
+
+53
+00:05:54,800 --> 00:05:58,260
+اللي هو بي زائد تلاتة على اتنين اللي بعد هذا
+
+54
+00:05:58,260 --> 00:06:03,820
+مباشرة اللي هو بي زائد تلاتة على اتنينباضح ها
+
+55
+00:06:03,820 --> 00:06:10,420
+تطابق ناقص العدد اللي قبله هنا اللي هو بي ناقص
+
+56
+00:06:10,420 --> 00:06:21,280
+ثلاثة على اتنين modulo بي وهكذا لما نقصل عند العدد
+
+57
+00:06:21,280 --> 00:06:30,290
+الأخير اللي هو بي زائدبنقص 2 على 2 اللي هو في
+
+58
+00:06:30,290 --> 00:06:38,170
+الواقع هيطلع من هو بي ناقص واحد بضل
+
+59
+00:06:38,170 --> 00:06:43,030
+ازيد واحد واحد كل واحد بيكون على اللي عاجباله عندي
+
+60
+00:06:43,030 --> 00:06:47,730
+ال بي زائد واحد على اتنين مع هذا ال بي زائد تلاتة
+
+61
+00:06:47,730 --> 00:06:50,850
+على اتنين اللي بعده مع اللي جنبه هذا اللي هو بي
+
+62
+00:06:50,850 --> 00:06:58,580
+ناقص تلاتة على اتنين بالسالمو هكذا لما نقصل لعند
+
+63
+00:06:58,580 --> 00:07:03,620
+اللي هو اخر عدد ناقص واحد هلاقيه بطابق اللي هو الـ
+
+64
+00:07:03,620 --> 00:07:06,660
+B زائد B ناقص اتنين على اتنين هذا اللي هو الـ B
+
+65
+00:07:06,660 --> 00:07:12,960
+ماينس واحد اكيد بطابق ناقص واحد modulo B صار عند
+
+66
+00:07:12,960 --> 00:07:20,160
+الاعداداللي هو ناقص واحد بطابق ال B- واحد ناقص
+
+67
+00:07:20,160 --> 00:07:25,260
+اتنين بطابق ال B- اتنين و بضلني انزل لما اصل لآخر
+
+68
+00:07:25,260 --> 00:07:29,660
+واحد ناقص B- واحد على اتنين بطابق ال B زاد واحد
+
+69
+00:07:29,660 --> 00:07:30,260
+على اتنين
+
+70
+00:07:33,450 --> 00:07:37,590
+الواحد بطابق الواحد والتنين بطابق التنين وال بي
+
+71
+00:07:37,590 --> 00:07:40,630
+نقص واحد على اتنين بطابق البي نقص واحد على اتنين
+
+72
+00:07:40,630 --> 00:07:41,550
+على اتنين
+
+73
+00:07:45,010 --> 00:07:50,610
+عبارة عن Incongruent لبعض وحيكون الـ Relative
+
+74
+00:07:50,610 --> 00:07:57,810
+prime مع الـ B طبقا لمن يطابقن في اللي هو من واحد
+
+75
+00:07:57,810 --> 00:08:01,850
+عند الـ B minus واحد اللي هنا بيعمل reduce
+
+76
+00:08:01,850 --> 00:08:07,730
+residual system modulo B يعني بمعنى أخر كلتين غير
+
+77
+00:08:07,730 --> 00:08:12,590
+متطابقات بالإضافة أن الـ Relative prime مع مين مع
+
+78
+00:08:12,590 --> 00:08:16,980
+Bإذا صارت هذه الـ set اللي أمامي اللي هو
+
+79
+00:08:16,980 --> 00:08:22,860
+relatively prime كل عنصر فيها مع البيئة و
+
+80
+00:08:22,860 --> 00:08:27,780
+incongruent مع الآخر إذا بعمل ال reduced residue
+
+81
+00:08:27,780 --> 00:08:34,580
+system modulo LB الآن هذا السؤال المتبقى من
+
+82
+00:08:34,580 --> 00:08:44,300
+chapter أو من section 7-3 الآن هنروحالناقش أو نحل
+
+83
+00:08:44,300 --> 00:08:51,860
+بعض الأسئلة في section 7-4 خلّينا نشوف السؤال
+
+84
+00:08:51,860 --> 00:08:58,800
+الأول إيش بيقول اطلعلنا على الأسئلة سبعة أربعة
+
+85
+00:08:58,800 --> 00:09:05,960
+السؤال الأول إيش بيقول بيقول four a positive
+
+86
+00:09:05,960 --> 00:09:08,940
+integer and a positive
+
+87
+00:09:12,580 --> 00:09:23,420
+انتجر ان prove that ال
+
+88
+00:09:23,420 --> 00:09:32,760
+summation ناقص واحد ان على دي فاي of دي دي بتجسم
+
+89
+00:09:32,760 --> 00:09:47,670
+ان بتساوي سفر if n is evenمناقص ان فان از قط proof
+
+90
+00:09:47,670 --> 00:09:52,670
+اللي
+
+91
+00:09:52,670 --> 00:10:01,210
+بتنسب تمايالي نثبت مايالي انهالـ summation لـ ناقص
+
+92
+00:10:01,210 --> 00:10:07,210
+1 N على D حيث D يقسم N الـ summation بيشتغل على كل
+
+93
+00:10:07,210 --> 00:10:14,210
+قواسم من الـ N 5D هذا المقدر هيساوي سفر إذا كانت N
+
+94
+00:10:14,210 --> 00:10:18,990
+اللي بنحكي عنها عبارة عن even number هتساوي ناقص N
+
+95
+00:10:18,990 --> 00:10:25,010
+إذا كانت إش N أزقد نيجي ناخد الحالة الأولى الأسهل
+
+96
+00:10:25,010 --> 00:10:28,170
+F N
+
+97
+00:10:29,010 --> 00:10:37,190
+is odd then مدام ان is odd اذا اكيد اكيد اكيد الان
+
+98
+00:10:37,190 --> 00:10:41,370
+على دي مدام دي بتقسم الان اذا ان على دي برضه ايه
+
+99
+00:10:41,370 --> 00:10:50,410
+اشمالها is odd لكل دي لكل دي بتقسم الانإذا صار
+
+100
+00:10:50,410 --> 00:10:55,610
+عندى الـ summation هذا N على D دا ناقص واحد بس N
+
+101
+00:10:55,610 --> 00:10:59,470
+على D دايما اللي هو ده المقدرش بيساوي ناقص واحد،
+
+102
+00:10:59,470 --> 00:11:04,330
+مظبوط؟ إذا صار عندى then صار عندى ال summation
+
+103
+00:11:04,330 --> 00:11:11,570
+ناقص واحد بس N على D Phi of D دي بتجسم ال N بساوي
+
+104
+00:11:11,570 --> 00:11:16,650
+ناقص واحد دايما اللي هو ناقص ال summation Phi of D
+
+105
+00:11:17,180 --> 00:11:22,960
+دي بتجسم الان لكن ال summation 5D دي بتجسم الان
+
+106
+00:11:22,960 --> 00:11:28,760
+ايش بيساوي حسب نظرية سابقة بيساوي هذا بيساوي الان
+
+107
+00:11:28,760 --> 00:11:34,780
+فبصير بيساوي سالر الان لإن احنا أخدنا نظرية في ال
+
+108
+00:11:34,780 --> 00:11:40,580
+section 7-4 بتقول ان ال summation 5D لدي بتجسم
+
+109
+00:11:40,580 --> 00:11:47,390
+الان دايما ايش بتساوي بتساوي الانإذا نادي الجزئية
+
+110
+00:11:47,390 --> 00:11:57,310
+الأولى الان بدنا ناخد if if if if if and is even
+
+111
+00:11:57,310 --> 00:12:00,830
+if and is even
+
+112
+00:12:04,270 --> 00:12:08,870
+then الان اللي حكيناه في حالة الان is odd طلع عنده
+
+113
+00:12:08,870 --> 00:12:13,210
+ال summation بسبب ناقص ان زي ما هو مطلوب الان ييجي
+
+114
+00:12:13,210 --> 00:12:16,550
+عند حالة الان is even مدام ان is even إذا الان can
+
+115
+00:12:16,550 --> 00:12:23,090
+be written as ان بسوء two to the k في ان where k
+
+116
+00:12:23,090 --> 00:12:29,130
+أكبر و سوء واحد عشان نضمن اللي هو ان even and الان
+
+117
+00:12:29,130 --> 00:12:36,690
+is oddالان بدنا ندى نحسب summation نقص واحد بس N
+
+118
+00:12:36,690 --> 00:12:44,710
+على D Phi of D D بتجسم ال N الان انا بدى افصل ال
+
+119
+00:12:44,710 --> 00:12:50,250
+divisors الى جزئين جزء بسببلى ان ال N على D يكون
+
+120
+00:12:50,250 --> 00:12:55,100
+odd والجزء التانى يسببلى ان ال N على D is evenإذا
+
+121
+00:12:55,100 --> 00:13:01,100
+هذا بيساوي two summations ناقص واحد أس N على D Phi
+
+122
+00:13:01,100 --> 00:13:08,220
+of D D بتكسب ال N زائد summation ناقص واحد أس N
+
+123
+00:13:08,220 --> 00:13:13,800
+على D prime مثلا D prime بتكسب ال N Phi of D prime
+
+124
+00:13:13,800 --> 00:13:23,890
+where اللي هو ال N على D is odd and ال Nعلى D
+
+125
+00:13:23,890 --> 00:13:35,230
+prime as even as even ماشي الحال ويساوي او خلّيني
+
+126
+00:13:35,230 --> 00:13:40,790
+نسمي هذه as even وهذه as odd عشان نكون يتلافق مع
+
+127
+00:13:40,790 --> 00:13:45,450
+التلخيص اللي في الأسئلة
+
+128
+00:13:45,450 --> 00:13:53,350
+عشان يكون عندك أسلحة المراجعة بالنسبالك ويساويالان
+
+129
+00:13:53,350 --> 00:13:59,030
+تبعتنا في الواقع ايش هي بتساوي اتنين اث ك في ان
+
+130
+00:13:59,030 --> 00:14:05,300
+والان تبعتنا ايش بتساوي اتنين اث ك في انالأن اللي
+
+131
+00:14:05,300 --> 00:14:11,140
+بده يخلّي هذه اللي هو 2K N على D إنها even بده
+
+132
+00:14:11,140 --> 00:14:17,800
+يكون في اللي تحت أقصى حد أقصى حد أقصى حد 2K-1 عساس
+
+133
+00:14:17,800 --> 00:14:29,560
+إنه تضمن إنه 2K N على اللي القواسم للـ2K-1 يطلع
+
+134
+00:14:29,560 --> 00:14:35,250
+الناتج عبارة عن فيه 2الأن الـ D هنا سواء الـ
+
+135
+00:14:35,250 --> 00:14:42,410
+summation ناقص واحد قصة اتنين K في M على D حيث الـ
+
+136
+00:14:42,410 --> 00:14:47,070
+D بتجسم اتنين K ماينس واحد في مين في N في هذا
+
+137
+00:14:47,070 --> 00:14:53,290
+الحالة بأضمن ان انا حصلت على كل ال devices اللي
+
+138
+00:14:53,290 --> 00:14:59,110
+بتعمل لهذا عبارة عن even number اللي هو Phi of D
+
+139
+00:14:59,740 --> 00:15:04,920
+زاد الـ summation اللى عندى اللى هو هذا ناقص واحد
+
+140
+00:15:04,920 --> 00:15:11,260
+قصه اتنين قصه K and على الان ال divisor اللى هنا
+
+141
+00:15:11,260 --> 00:15:15,760
+بده اضمن انه يخلينى هذا قد اذا ال divisor هذا لازم
+
+142
+00:15:15,760 --> 00:15:20,460
+يكون فيه موجود مين اللى هو اتنين قصه K عشان نروح
+
+143
+00:15:20,460 --> 00:15:25,610
+مع اللى فوقفي الـ Divisor اللي بيبقى هنا D' هيكون
+
+144
+00:15:25,610 --> 00:15:32,490
+بس بديها Divisor لمن؟ لـ N فبصير عندي D' بتقسم ل N
+
+145
+00:15:32,490 --> 00:15:40,930
+فى Of اللي هو صار عند مين ال Divisor
+
+146
+00:15:40,930 --> 00:15:47,550
+في هذه الحالة لكل هذا فبصير هو عبارة عن 2K في مين
+
+147
+00:15:47,550 --> 00:15:55,230
+في ال D'بدل اللي هو الـ divisor لكل اتنين كف دي
+
+148
+00:15:55,230 --> 00:15:58,830
+صار عند ال divisor في هذه الحالة اللي هو عبارة عن
+
+149
+00:15:58,830 --> 00:16:02,710
+اتنين كف دي prime الـ D prime ينبغي بجسم ال N في
+
+150
+00:16:02,710 --> 00:16:07,710
+هذه الحالة ان انا فصلت ال even لحاله و ال odd
+
+151
+00:16:07,710 --> 00:16:13,230
+لحاله وهذا سيسبب لي بساويالان هذا مادام even
+
+152
+00:16:13,230 --> 00:16:16,790
+معناته صار هذا عبارة عن واحد إذا هذا عبارة عن
+
+153
+00:16:16,790 --> 00:16:25,780
+summation لل 5D لل D بتكسب mean 2K-1 في H في Nالان
+
+154
+00:16:25,780 --> 00:16:32,240
+هذا قد كله مادام قده ده نقش ماله ناقص واحد ناقص
+
+155
+00:16:32,240 --> 00:16:38,580
+واحد ده بيصير ناقص ال summation فاي of اتنين K في
+
+156
+00:16:38,580 --> 00:16:46,180
+D prime لدى D prime اللى بتكسر نين الان طيب الان
+
+157
+00:16:46,180 --> 00:16:46,780
+ويساوي
+
+158
+00:16:49,700 --> 00:16:53,800
+هذا حسب النظرية summation للـ5 of D دي بتكسب الان
+
+159
+00:16:53,800 --> 00:16:58,400
+على طول ايش بساوي بساوي الان لأن 5 of D دي بتكسب
+
+160
+00:16:58,400 --> 00:17:01,780
+هذا المقدار اذا كل ال summation هذا ايش هيساوي
+
+161
+00:17:01,780 --> 00:17:11,180
+اتنين اص كمانس واحد في ايش في ان طيب ماقصالان الـ
+
+162
+00:17:11,180 --> 00:17:14,620
+Summation الـ Phi is multiplicative function وهدي
+
+163
+00:17:14,620 --> 00:17:18,860
+Odd وهدي Even وما فيش بينهم اي عامل مشتركة لأن هو
+
+164
+00:17:18,860 --> 00:17:22,380
+دي بس Power of Two إذا بيصير عبارة عن Summation
+
+165
+00:17:22,380 --> 00:17:28,560
+Phi of 2 أس K في Phi of D Prime وSummation شغالة
+
+166
+00:17:28,560 --> 00:17:37,860
+على D Prime بتجسمين الان واضح ها؟ طيب خليني أكتب
+
+167
+00:17:37,860 --> 00:17:47,340
+فوقأكمل هنا بصينعين D التكملة
+
+168
+00:17:47,340 --> 00:17:53,860
+ويساوي summation تبعنا هنا هي طلع بيساوي هذا
+
+169
+00:17:53,860 --> 00:18:02,440
+المقدار ناقص هذا المقدار ويساوي ويساوي اتنين أسكي
+
+170
+00:18:02,440 --> 00:18:08,910
+minus واحد في N ناقصالان فاي اف اتنين كاشغبتها
+
+171
+00:18:08,910 --> 00:18:15,030
+اتنين اث كمانس واحد اللي هو بساوي summation اتنين
+
+172
+00:18:15,030 --> 00:18:23,490
+اث كمانس واحدلدي برايم تجسم الـ N فاي of دي برايم
+
+173
+00:18:23,490 --> 00:18:26,830
+اتنين K أس K ماينس واحد independent of the
+
+174
+00:18:26,830 --> 00:18:29,570
+summation لأن ال summation شغالة على ال device و
+
+175
+00:18:29,570 --> 00:18:34,810
+مالوش علاقة إذا ثابت بالنسبة لل summation إذا بقدر
+
+176
+00:18:34,810 --> 00:18:38,570
+أطلعه برا ال summation إذا بيساوي اتنين K أس K
+
+177
+00:18:38,570 --> 00:18:42,760
+ماينس واحد N ناقص اتنين K أس K ماينس واحدفي الـ
+
+178
+00:18:42,760 --> 00:18:46,820
+summation للـ phi of D prime الـ D prime أيش
+
+179
+00:18:46,820 --> 00:18:52,300
+معناها؟ بتجسم الـ N هذا المقدار حسب النظرية اللي
+
+180
+00:18:52,300 --> 00:18:55,900
+هي الـ 5DD بتجسم الـ N بيساوي مين الـ N إذا إيش
+
+181
+00:18:55,900 --> 00:19:01,080
+هيساوي هذا؟ الـ N capital ويساوي 2 أُس K minus 1
+
+182
+00:19:01,080 --> 00:19:04,660
+في الـ N نقص 2 أُس K minus 1 في الـ N capital
+
+183
+00:19:04,660 --> 00:19:10,820
+ويساوي 0إذا في حالة الان is even طالع عند ال
+
+184
+00:19:10,820 --> 00:19:16,720
+summation هذا اللي هو بساوي صفر إذا حصلنا على
+
+185
+00:19:16,720 --> 00:19:27,780
+المطلوب في السؤال الأول أي سؤال نجي الآن للسؤال
+
+186
+00:19:27,780 --> 00:19:32,800
+التالت لسؤال
+
+187
+00:19:32,800 --> 00:19:33,620
+التالت
+
+188
+00:19:42,790 --> 00:19:51,790
+for a positive integer
+
+189
+00:19:51,790 --> 00:20:03,190
+and a proof that a proof that summation mu تربيه
+
+190
+00:20:03,190 --> 00:20:13,280
+of D على فاي of D دي بتقسم الانبساوي N على Phi of
+
+191
+00:20:13,280 --> 00:20:13,520
+N
+
+192
+00:20:42,810 --> 00:20:47,450
+طيب خلّيني أبدن السؤال نشوف إيش السؤال اللي عندي
+
+193
+00:20:47,450 --> 00:20:53,150
+عندي for a positive integer n بيدنالت بيت ال
+
+194
+00:20:53,150 --> 00:20:56,570
+summation ميوتر بيعديها على 5DD بتكسم N هو بسوء N
+
+195
+00:20:56,570 --> 00:21:02,610
+على مين على Phi of N لو جينا لاحظنا ال N على ال
+
+196
+00:21:02,610 --> 00:21:07,130
+Phi of N ال N على Phi of N is a multiplicative
+
+197
+00:21:07,130 --> 00:21:11,350
+function وسهل اعتبادهاو لو جينا طلعنا لهذا اللي
+
+198
+00:21:11,350 --> 00:21:14,730
+جوا ال summation اللي هو اللي مُ multiplicative و
+
+199
+00:21:14,730 --> 00:21:18,250
+ال file مُ multiplicative إذا كل هذا على بعض إيش
+
+200
+00:21:18,250 --> 00:21:21,370
+ماله مُ multiplicative و مادام هذا مُ
+
+201
+00:21:21,370 --> 00:21:24,390
+multiplicative إذا كل على بعض إيش ماله مُ
+
+202
+00:21:24,390 --> 00:21:28,430
+multiplicative إذا ال multiplicative بشجعني أن
+
+203
+00:21:28,430 --> 00:21:35,050
+أروح باتجاه الإثبات بس ل prime b to the alpha و
+
+204
+00:21:35,050 --> 00:21:38,230
+بيصير حصل الدرب هو بحصل ليه كل اللي بديها
+
+205
+00:21:41,750 --> 00:21:45,510
+الان اذا بناقن عليه مادان بدك تبقى على صورة الان
+
+206
+00:21:45,510 --> 00:21:47,790
+على صورة ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+207
+00:21:47,790 --> 00:21:49,870
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+208
+00:21:49,870 --> 00:21:50,930
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+209
+00:21:50,930 --> 00:21:51,350
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+210
+00:21:51,350 --> 00:21:51,410
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+211
+00:21:51,410 --> 00:21:53,570
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+212
+00:21:53,570 --> 00:21:57,270
+ال ال ال ال ال ال ال ال ال
+
+213
+00:21:57,270 --> 00:21:57,650
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+214
+00:22:01,580 --> 00:22:09,080
+to see that summation mu تربيع of D على فاي of D
+
+215
+00:22:09,080 --> 00:22:14,100
+دي بتكسب الواحد اللي هي الآن بساوي ميو of واحد ميو
+
+216
+00:22:14,100 --> 00:22:18,460
+تربيع of واحد على فاي of واحد ويساوي واحد ويساوي
+
+217
+00:22:18,460 --> 00:22:22,020
+واحد على فايل of واحد اللي هي الآن على
+
+218
+00:22:28,050 --> 00:22:37,690
+الحلقة الصحيحة في حالة M بتساوي 1 اذا M أكبر من 1
+
+219
+00:22:37,690 --> 00:22:42,570
+فالـ M يمكن أن يكون كذلك الـ Rhyme factorization
+
+220
+00:22:42,570 --> 00:22:53,750
+لها B1 Alpha 1 لعند PR Alpha RP1 لعند PR are
+
+221
+00:22:53,750 --> 00:23:04,090
+distinct primes والألفة I أكبر أو يساوي واحد لكل I
+
+222
+00:23:04,090 --> 00:23:10,170
+من واحد لعند ال R وال R أكبر أو يساوي واحد طيب
+
+223
+00:23:10,170 --> 00:23:20,010
+الان let let F of N بساوي ال summationميو تربيع of
+
+224
+00:23:20,010 --> 00:23:30,630
+D على فاي of D لدى D بتجسم الان الان هذه سميها
+
+225
+00:23:30,630 --> 00:23:40,190
+واحد لأن since ميو تربيع of D او ميو تربيع على فاي
+
+226
+00:23:40,190 --> 00:23:45,210
+of D is multiplicative
+
+227
+00:23:47,320 --> 00:23:52,500
+How؟ How سهلة على طول بما أن U مُلتبليكاتف و F
+
+228
+00:23:52,500 --> 00:23:56,500
+مُلتبليكاتف إذا التربيع، الدرب هذا على القسمة
+
+229
+00:23:56,500 --> 00:24:01,380
+بيطلع أشماله مُلتبليكاتف مدام هذا مُلتبليكاتف in
+
+230
+00:24:01,380 --> 00:24:08,420
+then by theorem then by theorem 6 أربعة مدام اللي
+
+231
+00:24:08,420 --> 00:24:14,460
+جوا مُلتبليكاتف هتطلع F is مُلتبليكاتف
+
+232
+00:24:15,820 --> 00:24:20,460
+بناء عليه بدأ من الـ F capital multiplicative بناء
+
+233
+00:24:20,460 --> 00:24:27,080
+عليه هيكون عندي F of N الـ N تباعتنا اللي هي P1
+
+234
+00:24:27,080 --> 00:24:32,240
+Alpha 1 عند P R سواء Alpha R بتساوي ال product
+
+235
+00:24:32,240 --> 00:24:40,120
+معايا ال product للـ F of P I Alpha I I من عند 1
+
+236
+00:24:40,120 --> 00:24:47,700
+لعند R وسمي هذه اتنينالان اذا يكفي عشان احسب ان
+
+237
+00:24:47,700 --> 00:24:52,580
+احسب لمين لل F of P I قصة Alpha I بكون خلصت السؤال
+
+238
+00:24:52,580 --> 00:24:56,760
+و هثبت لك ان ال product هذا هيطلع ان هو بالظبط N
+
+239
+00:24:56,760 --> 00:25:05,080
+في A في مين على Phi of N الان اطلع عندي في تلخيص
+
+240
+00:25:05,080 --> 00:25:11,460
+كامل اللي هو على الصفحه السؤال اذا عندي بدي احسب
+
+241
+00:25:11,460 --> 00:25:20,910
+الان F nowWe compute f of bi alpha i وإي ساوي حسب
+
+242
+00:25:20,910 --> 00:25:26,790
+التعريف ايه حكاية وإي ساوي So summation Mu تربيع
+
+243
+00:25:26,790 --> 00:25:34,830
+of D على Phi of D لدى D تجسم ال Bi Alpha Iالـ
+
+244
+00:25:34,830 --> 00:25:38,750
+divisor للبي آلف آي سهل حساباتها هي عبارة عن
+
+245
+00:25:38,750 --> 00:25:43,170
+الواحد و البي آي و البي آي تربية لما أصل لعندين
+
+246
+00:25:43,170 --> 00:25:49,630
+البي آي آلف آي و يساويهو عبارة عن ميو تربيع اف
+
+247
+00:25:49,630 --> 00:25:57,430
+واحد على في اف واحد زاد ميو تربيع اف بي اي على في
+
+248
+00:25:57,430 --> 00:26:05,730
+اف بي اي زاد ميو تربيع اف بي اي تربيع على في اف بي
+
+249
+00:26:05,730 --> 00:26:14,130
+اي تربيع زاد لما أصل الاخر واحدة ميو ن او رميو
+
+250
+00:26:14,130 --> 00:26:23,330
+تربيع of بي آلف آي على في of بي آلف آي الان ميو
+
+251
+00:26:23,330 --> 00:26:30,130
+احنا عارفين الميو الميو الها تلت قيم ميو of ان
+
+252
+00:26:30,130 --> 00:26:37,700
+بتساوي واحد في حالة الان بتساوي واحدوبتساوي ن و
+
+253
+00:26:37,700 --> 00:26:43,200
+صفر إذا كان الان فيها مربع كامل يعني بيه تربيع بين
+
+254
+00:26:43,200 --> 00:26:48,060
+بيقسم الان وبساوي ماقص واحد أُص R إذا كانت الان
+
+255
+00:26:48,060 --> 00:26:52,380
+على صورة بي واحد لعند مين بي ار Distinct Primes،
+
+256
+00:26:52,380 --> 00:26:56,540
+مظبوط؟ إذا هذه المقادير الـ Mu of Bi تربيع الـ Mu
+
+257
+00:26:56,540 --> 00:27:01,160
+of Bi تكعيب لما الـ Mu of Bi Alpha I كله أصفر، إذا
+
+258
+00:27:01,160 --> 00:27:08,080
+هذا كله صفرو بيظهر عندي بس بساوي المقدار الـ Mu
+
+259
+00:27:08,080 --> 00:27:11,640
+الـ Mu of واحد واحد و الـ Phi of واحد واحد ده
+
+260
+00:27:11,640 --> 00:27:16,160
+بيصير واحد زاد الـ Mu تربيه على الـ Bi الـ Mu Bi
+
+261
+00:27:16,160 --> 00:27:19,920
+اللي هو سالب واحد حسب اللي هنا لإنه ناقص واحد قُس
+
+262
+00:27:19,920 --> 00:27:23,800
+واحد لإن الارواح بتصير واحد وتربيه بتصير واحد إذا
+
+263
+00:27:23,800 --> 00:27:29,540
+زاد واحد على Phi of Bi إيش الـ Phi of Bi اللي هو
+
+264
+00:27:29,540 --> 00:27:32,740
+بي آي ناقص واحد
+
+265
+00:27:35,690 --> 00:27:45,790
+مظبوط؟ و .. و يساوي .. و يساوي عبارة عن bi ناقص
+
+266
+00:27:45,790 --> 00:27:53,390
+واحد زائد واحد على bi ناقص واحد و يساوي bi على bi
+
+267
+00:27:53,390 --> 00:28:02,780
+ناقص واحد صح؟إذا صار عندي الان f of bi alpha bi
+
+268
+00:28:02,780 --> 00:28:11,740
+بسوى bi على bi نقص واحد هذا تلاتة الان من اللي هو
+
+269
+00:28:11,740 --> 00:28:20,860
+اتنين و تلاتة from from اتنين
+
+270
+00:28:20,860 --> 00:28:30,950
+and تلاتة we getwe get ماذا؟ we get F of N F of N
+
+271
+00:28:30,950 --> 00:28:42,330
+بسوّله product A حصل الدرب ل B I على B I ناقص واحد
+
+272
+00:28:42,330 --> 00:28:50,760
+I من عند واحد لعند مين لعند Rمعايا اه الان بس اضرب
+
+273
+00:28:50,760 --> 00:28:56,440
+لفوق عشان اقول لك ايه اضرب لفوق في بي اي اص الف اي
+
+274
+00:28:56,440 --> 00:29:02,440
+ماقص واحد و تحت في بي اي اص الف اي ماقص واحد في
+
+275
+00:29:02,440 --> 00:29:09,820
+نفس النقطة اضربت و يساوي ال product لأ ال بي اي اص
+
+276
+00:29:09,820 --> 00:29:22,650
+الف اي معايا على اللي هوالـ Product لـ Bi أُس
+
+277
+00:29:22,650 --> 00:29:28,250
+Alpha I ناقص واحد مضروب في الـ Bi ناقص واحد I من
+
+278
+00:29:28,250 --> 00:29:33,390
+واحد لعند R و I من عند واحد لعند R اللي فوق هذه
+
+279
+00:29:33,390 --> 00:29:42,530
+مين هي أصلا؟ هذه مين هي؟ هي عبارة عن الـ NP1 α1 P2
+
+280
+00:29:42,530 --> 00:29:48,710
+α2 لعند PR αR و اللي تحت مين هي Phi of N واضح انها
+
+281
+00:29:48,710 --> 00:29:54,850
+Phi of N و هي ساوي اللي هو على Phi of N لأن Phi of
+
+282
+00:29:54,850 --> 00:30:00,410
+N Phi of N عارفين ايش Phi of N Phi of N بساوي N
+
+283
+00:30:01,530 --> 00:30:05,990
+نفسها في مضروبة واحد ناقص واحد على بي واحد لما اصل
+
+284
+00:30:05,990 --> 00:30:10,870
+لعند واحد ناقص واحد على بي ار او بتعبير اخر لما
+
+285
+00:30:10,870 --> 00:30:16,170
+اضرب الان جوا بيصير عندي او اضرب الان عبارة عن بي
+
+286
+00:30:16,170 --> 00:30:19,030
+واحد الف واحد بي اتنين الف اتنين الاخره بيصير بي
+
+287
+00:30:19,030 --> 00:30:25,010
+واحد الف واحد لعند ال بي ار الف ار الان مضروبة في
+
+288
+00:30:25,010 --> 00:30:29,370
+المقدار واحد ناقص واحد على بي واحد لعند واحد ناقص
+
+289
+00:30:29,370 --> 00:30:35,410
+واحد على بي ارو يساوي ان الصورة اللي قبل قليل دخل
+
+290
+00:30:35,410 --> 00:30:43,060
+هنا بي واحد و هنا بي ار واحدة بيظل هنا بي واحدأس
+
+291
+00:30:43,060 --> 00:30:47,560
+ألف واحد ناقص واحد لما أصل عند بي ار أس ألف ار
+
+292
+00:30:47,560 --> 00:30:52,440
+ناقص واحد مضروبة في بي واحد ناقص واحد لما أصل عند
+
+293
+00:30:52,440 --> 00:30:57,680
+بي ار ناقص واحد يا الصورة هذه يا الصورة هذه اللي
+
+294
+00:30:57,680 --> 00:31:02,040
+هي لل file الان احنا وصلنا للصورة الأخيرة هذه اذا
+
+295
+00:31:02,040 --> 00:31:06,780
+صار عندي اللي هو ال f of n بسوو ال n على five of n
+
+296
+00:31:06,780 --> 00:31:18,190
+الان هي هذه أربعة from fromواحد and أربعة بنحصل
+
+297
+00:31:18,190 --> 00:31:23,510
+إنه ال summation لـ mu تربيه of D اللي هو ال FN
+
+298
+00:31:23,510 --> 00:31:30,190
+على فاي of D دي بتجسم N بساوي ال FN اللي طلعت عندي
+
+299
+00:31:30,190 --> 00:31:36,730
+بتساوي هذا المقدار بساوي ال N على فاي of N وهو
+
+300
+00:31:36,730 --> 00:31:37,390
+المطلوب
+
+301
+00:31:44,220 --> 00:31:49,080
+الان نجي لسؤال خمسة سؤال خمسة
+
+302
+00:32:22,580 --> 00:32:28,000
+سؤال الخامسة a
+
+303
+00:32:28,000 --> 00:32:32,400
+الان for if n أكبر من واحد has the prime
+
+304
+00:32:32,400 --> 00:32:36,800
+factorization ماعطيني ال n الها ال prime
+
+305
+00:32:36,800 --> 00:32:41,080
+factorization و ال n أكبر من واحد ماعطينيها n أكبر
+
+306
+00:32:41,080 --> 00:32:44,580
+من واحد و ال n بيساوي بيه و ال alpha واحد لعند ال
+
+307
+00:32:44,580 --> 00:32:53,000
+b r alpha r بقول لي ايهمش مشكلة انا بقول ال A
+
+308
+00:32:53,000 --> 00:32:59,500
+summation اثبت ان ال summation ميو of D فاي of D
+
+309
+00:32:59,500 --> 00:33:06,900
+دي بتكسب N بساوي اتنين ناقص بي واحد لما اصلا عند
+
+310
+00:33:06,900 --> 00:33:09,120
+اتنين ناقص ال PR
+
+311
+00:33:19,830 --> 00:33:29,630
+عندنا سؤال Problem 3 Section 6-2 Problem 3-6-2
+
+312
+00:33:29,630 --> 00:33:34,170
+Problem 3-6-2 Problem
+
+313
+00:33:34,170 --> 00:33:42,090
+3-6-2 Problem 3-6-2 Problem 3-6
+
+314
+00:33:42,090 --> 00:33:49,130
+-2 Problem 3-6-2 Problem 3-6-2 Problem 3-6
+
+315
+00:33:49,130 --> 00:33:49,270
+-2 Problem 3-6-2 Problem 3-6-2 Problem 3-6-2
+
+316
+00:33:49,270 --> 00:33:58,520
+3فى 6 اتنين summation عندي ميو اف دى اف اف دى
+
+317
+00:33:58,520 --> 00:34:07,340
+بساوي واحد ناقص اف اف دى لما اصل عند واحد ناقص دى
+
+318
+00:34:07,340 --> 00:34:13,780
+بتجسم اللى هو ان لكل ال divisors اللى هى اف اف بى
+
+319
+00:34:13,780 --> 00:34:17,440
+اف
+
+320
+00:34:17,440 --> 00:34:28,220
+اف بىوحد لعند F أو PR summation هذا يساوي هذا
+
+321
+00:34:28,220 --> 00:34:36,240
+المفتاح هذا سؤال ستة سؤال تلاتة في ستة اتنين معايا
+
+322
+00:34:36,240 --> 00:34:42,820
+اه الان ال proof ال
+
+323
+00:34:42,820 --> 00:34:46,380
+proof طبعا
+
+324
+00:34:46,380 --> 00:34:51,670
+ال F في السؤال F ايه شمالهاis multiplicative هنا
+
+325
+00:34:51,670 --> 00:35:00,630
+بس بجربة التطبيق اللي قال let f of d بسوة five of
+
+326
+00:35:00,630 --> 00:35:10,130
+d and problem تلاتة ستة
+
+327
+00:35:10,130 --> 00:35:13,930
+اتنين where
+
+328
+00:35:13,930 --> 00:35:24,120
+five is multiplicativeto get أو we get مالي
+
+329
+00:35:24,120 --> 00:35:31,120
+summation mu of d phi of d دي بتكسب الان بساوي
+
+330
+00:35:31,120 --> 00:35:40,160
+عبارة عن واحد ناقص phi of b واحد لعند واحد ناقص
+
+331
+00:35:40,160 --> 00:35:49,010
+phi of br ويساوي واحد ناقص5 بواحد ايش بتساوي بواحد
+
+332
+00:35:49,010 --> 00:35:57,830
+الزبران بواحد ناقص واحد صح لما
+
+333
+00:35:57,830 --> 00:36:07,350
+اصل عند واحد ناقص واحد ناقص بار أي ساوياحد نقص بي
+
+334
+00:36:07,350 --> 00:36:12,650
+زائد بيصير اتنين نقص بي واحد لما اصل عند اتنين نقص
+
+335
+00:36:12,650 --> 00:36:19,410
+بي احد مجرد تطبيق مباشر نجي للشؤال بي .. بي بي اش
+
+336
+00:36:19,410 --> 00:36:27,470
+بي بيقول بي بيقول ما يلي summation
+
+337
+00:36:27,470 --> 00:36:40,950
+summation phi of D في D D بتقسم ال Nبساوي بي واحد
+
+338
+00:36:40,950 --> 00:36:47,730
+اتنين ك واحد زائد واحد زائد واحد على بي واحد زائد
+
+339
+00:36:47,730 --> 00:36:54,350
+واحد لمؤاصر الاخر واحد بي ار اتنين ك ار زائد واحد
+
+340
+00:36:54,350 --> 00:37:04,750
+زائد واحد على بي ار زائد واحد proof الملاحظة
+
+341
+00:37:04,750 --> 00:37:09,750
+الأولىإنه عندي الـ Phi is multiplicative و ال
+
+342
+00:37:09,750 --> 00:37:13,090
+identity function multiplicative إذا D في Phi of D
+
+343
+00:37:13,090 --> 00:37:19,850
+أشمالها is multiplicative بناء عليه لأن since اللي
+
+344
+00:37:19,850 --> 00:37:28,210
+هو N في Phi of Nis multiplicative than by theorem
+
+345
+00:37:28,210 --> 00:37:33,270
+لأن الشغل مكرر الان by theorem 6 أربعة هيطلع عندي
+
+346
+00:37:33,270 --> 00:37:39,730
+f of n اللي هي سوى summation في of دي في دي دي
+
+347
+00:37:39,730 --> 00:37:48,450
+بتجسم n is multiplicative معايا اذا الان عشان اوجد
+
+348
+00:37:48,450 --> 00:37:54,750
+ال f of nبدي أوجد اللي هو بس f of b i alpha i لأنه
+
+349
+00:37:54,750 --> 00:37:59,750
+في النهاية f of n بساوي حاصل ضرب ال f of b i alpha
+
+350
+00:37:59,750 --> 00:38:09,330
+i لأن now now f of b i alpha i بساوي في القرأن
+
+351
+00:38:09,330 --> 00:38:16,170
+طبعا i أكبر سوى 1 أصغر سوى r بساوي حسب اللي هو
+
+352
+00:38:16,170 --> 00:38:24,160
+المقطعf of bi المسمينه احنا بساوي summation d phi
+
+353
+00:38:24,160 --> 00:38:30,240
+of d دي بتكسمين ال bi الف i قاسم ال bi الف i
+
+354
+00:38:30,240 --> 00:38:34,080
+معروفة واحد بي اي بي اي تربيع الاخ لما صلى بي اي
+
+355
+00:38:34,080 --> 00:38:40,660
+الف اي و يساوي اللي هو عبارة عن بي اي اللي هي ال d
+
+356
+00:38:40,660 --> 00:38:49,170
+واحد يعني phi of واحد ذاتbi file of bi معايا زاد
+
+357
+00:38:49,170 --> 00:38:58,410
+bi تربيع file of bi تربيع زاد لما أصل عند file او
+
+358
+00:38:58,410 --> 00:39:08,210
+bi أس الف اي في file of bi أس الف اي واضح اه
+
+359
+00:39:08,210 --> 00:39:14,930
+ويساوياعمل الـ summation تطلع هذه واحد زائد بي اي
+
+360
+00:39:14,930 --> 00:39:22,330
+five بي اي بي اي ناقص واحد زائد بي اي تربيع اللي
+
+361
+00:39:22,330 --> 00:39:26,710
+هي في five بي اي اش بي اي five بي اي تربيع اللي هو
+
+362
+00:39:26,710 --> 00:39:30,350
+بي اي تربيع ناقص بي اي
+
+363
+00:39:33,160 --> 00:39:37,680
+زائد لما أصل الأخر واحدة بي آي Alpha I مضروبة في
+
+364
+00:39:37,680 --> 00:39:43,120
+بي آي Alpha I ناقص بي آي Alpha I minus واحد هدين
+
+365
+00:39:43,120 --> 00:39:48,600
+إن هي Phi of بي آي Alpha I ويساوي الال موضوع موضوع
+
+366
+00:39:48,600 --> 00:39:52,400
+حسابات اللي هو في عندي series أو final geometric
+
+367
+00:39:52,400 --> 00:39:59,780
+series بساوي واحد زائد بي آي تربيع ناقص بي آيزاد
+
+368
+00:39:59,780 --> 00:40:10,980
+بي قص أربعة ناقص بي تكعيد زاد لما أصل لعند بي قص
+
+369
+00:40:10,980 --> 00:40:17,100
+اتنين ألف اي ناقص بي اتنين ألف اي ناقص واحد ضربتها
+
+370
+00:40:17,100 --> 00:40:28,110
+هو يساوي نرتبها بيصير واحد ناقص بي ايزائد bi تربيع
+
+371
+00:40:28,110 --> 00:40:33,530
+ناقص bi تكعيب زائد bi أُس أربعة زائد الاخرى زائد
+
+372
+00:40:33,530 --> 00:40:39,610
+ناقص زائد ناقص لعندي اللي هو ناقص bi اتنين Alpha I
+
+373
+00:40:39,610 --> 00:40:45,070
+ناقص واحد زائد bi اتنين Alpha I ويساوي هذه الـ
+
+374
+00:40:45,070 --> 00:40:49,170
+Finite Geometric Series اللي هي أساسها عبارة عن
+
+375
+00:40:49,170 --> 00:40:53,750
+ناقص bi بصير عندي bi
+
+376
+00:40:55,750 --> 00:41:02,770
+اس بالسالب طبعا الاساس هذا عدد انجداش 2000I زائد
+
+377
+00:41:02,770 --> 00:41:09,510
+واحد 2000I زائد واحد ناقص الواحد على بي اي اللي هو
+
+378
+00:41:09,510 --> 00:41:19,990
+ناقص بي اي ناقص الواحد هذا الأساس هذا الأساس رحل
+
+379
+00:41:19,990 --> 00:41:26,680
+أسنون ناقص واحد على رحل ناقص واحد هذا اللي هيمجموع
+
+380
+00:41:26,680 --> 00:41:33,060
+الـ Finite Geometric Series ويساوي هذا قد الأس
+
+381
+00:41:33,060 --> 00:41:38,080
+وهذا اللي هو السلب بيطلع برا و السلب بيطلع برا فى
+
+382
+00:41:38,080 --> 00:41:42,180
+سلب فوق وسلب تحت بيصير عبارة عن بي آي أسنين اتنين
+
+383
+00:41:42,180 --> 00:41:47,900
+ألف آي زائد واحد مفهوم اه زائد واحد على بي آي زائد
+
+384
+00:41:47,900 --> 00:41:53,480
+واحد واضح اه هذا مين هو F of بي آي بساوي هذا
+
+385
+00:41:53,480 --> 00:41:58,630
+المقدارحنا قلنا الـ F إيه شمالها is multiplicative
+
+386
+00:41:58,630 --> 00:42:08,910
+حكينا
+
+387
+00:42:08,910 --> 00:42:14,850
+إن الـ F is multiplicative هي الـ F تبعتنا of P I
+
+388
+00:42:14,850 --> 00:42:20,290
+Alpha I طلعت هذا المقدار و بما إنه F is
+
+389
+00:42:20,290 --> 00:42:26,700
+multiplicative thenاللي هو الـ summation تبعنا هذا
+
+390
+00:42:26,700 --> 00:42:33,420
+D Phi of D D بتقسم N اللي هو بساوي F of N ال F of
+
+391
+00:42:33,420 --> 00:42:39,900
+N إيش حيساوي؟ ال F of N إيش حيساوي؟ عبارة عن اللي
+
+392
+00:42:39,900 --> 00:42:45,240
+هو مدام Multiplicative عبارة عن ال product ال
+
+393
+00:42:45,240 --> 00:42:47,500
+product لل F
+
+394
+00:42:50,300 --> 00:42:54,840
+ن عبارة عن بي واحد الف واحد لعند بي ار الف ار ال
+
+395
+00:42:54,840 --> 00:43:00,640
+product لل F of بي ار الف اي اي من عند واحد لعند
+
+396
+00:43:00,640 --> 00:43:06,600
+ار هو يساوي ال product او جبنا ال F of بي اي الف
+
+397
+00:43:06,600 --> 00:43:14,490
+اي هيها بساوي ال product لالـ PI 2 α I زائد واحد
+
+398
+00:43:14,490 --> 00:43:19,410
+زائد واحد على PI زائد واحد I من عند واحد لعند R
+
+399
+00:43:19,410 --> 00:43:26,190
+وهو المطلوب عصر ضرب لنا اللي عندنا
+
+400
+00:43:54,890 --> 00:44:01,010
+فرع C في السؤال الخامسة مشابه لفرع B بدل مكان اللي
+
+401
+00:44:01,010 --> 00:44:05,250
+هو فرع B عبارة عن D في 5D طلق اللي الآن عندنا
+
+402
+00:44:05,250 --> 00:44:10,870
+ماعطينا 5D على D بل انه بسهل عملية الحسابات عن
+
+403
+00:44:10,870 --> 00:44:15,990
+اللي حلناه في اللي هو فرع الـ B الآن بنفس الطريقة
+
+404
+00:44:15,990 --> 00:44:22,090
+هكون عندى اللي هو الـ 5D على D البروف
+
+405
+00:44:23,890 --> 00:44:27,570
+الـ 5d على d عبارة عن multiplicative لأن 5
+
+406
+00:44:27,570 --> 00:44:33,170
+ملتبليكاتيف ورسبروكال 1 على d ملتبليكاتيف لأن 5d
+
+407
+00:44:33,170 --> 00:44:35,210
+على d ملتبليكاتيف لأن 5d على d ملتبليكاتيف لأن 5d
+
+408
+00:44:35,210 --> 00:44:35,930
+على d ملتبليكاتيف لأن 5d على d ملتبليكاتيف لأن 5d
+
+409
+00:44:35,930 --> 00:44:36,070
+على d ملتبليكاتيف لأن 5d على d ملتبليكاتيف لأن 5d
+
+410
+00:44:36,070 --> 00:44:36,610
+على d ملتبليكاتيف لأن 5d على d ملتبليكاتيف لأن 5d
+
+411
+00:44:36,610 --> 00:44:38,310
+على d ملتبليكاتيف لأن 5d على d ملتبليكاتيف لأن 5d
+
+412
+00:44:38,310 --> 00:44:43,610
+على d ملتبليكاتيف لأن 5d على d ملتبليكاتيف لأن 5d
+
+413
+00:44:43,610 --> 00:44:50,010
+على d ملتبليكاتيف
+
+414
+00:44:52,220 --> 00:44:57,960
+Phi of N بسعر الـ summation Phi of D على D D بتجسم
+
+415
+00:44:57,960 --> 00:45:08,740
+N is multiplicative because Phi of N على N is
+
+416
+00:45:08,740 --> 00:45:13,480
+multiplicative لأن الـ function الأصلية Phi is
+
+417
+00:45:13,480 --> 00:45:19,980
+multiplicative ندى الآن حسب ستجد الخطوات تقريبا
+
+418
+00:45:20,870 --> 00:45:30,110
+متشابهة ومتكررة فاي عند F of N بيساوي ال product
+
+419
+00:45:30,110 --> 00:45:36,570
+لل F of P I Alpha I I من عند واحد لعند آخر نحسب
+
+420
+00:45:36,570 --> 00:45:44,610
+الآن F of P I Alpha I بيساوي ال summation لفاي of
+
+421
+00:45:44,610 --> 00:45:56,950
+P I Alpha I على P Iأسف دي على دي حيث دي بتقسم البي
+
+422
+00:45:56,950 --> 00:46:06,290
+الف آي واضح أه هو يساوي الآن القواسم زي ما قلنا
+
+423
+00:46:06,290 --> 00:46:13,470
+عبارة عن five واحد على واحد زائد five of bi على bi
+
+424
+00:46:13,470 --> 00:46:24,550
+زائد لما أصل لآخر واحد fiveof bi αi على bi αi هذه
+
+425
+00:46:24,550 --> 00:46:31,410
+اللي هي قوة سمين الـ bi αi واضحة ويساوي واحد زائد
+
+426
+00:46:31,410 --> 00:46:38,090
+bi minus واحد اللي هي five of bi على biزائد لما
+
+427
+00:46:38,090 --> 00:46:44,210
+أصل الأخر واحدة اللي هو bi قص ألف آي ناقص bi قص
+
+428
+00:46:44,210 --> 00:46:51,530
+ألف آي ناقص واحد على bi قص ألف آي هو يساوي اللي هو
+
+429
+00:46:51,530 --> 00:46:57,970
+واحد زائد bi ناقص واحد على bi زائد لما أصل الأخر
+
+430
+00:46:57,970 --> 00:47:03,710
+واحد خد ال bi قص ألف آي minus واحد عام مشترك بيصير
+
+431
+00:47:03,710 --> 00:47:11,670
+bi ناقص واحدعلى بي اص الف اي لو جيبنا ال term اللي
+
+432
+00:47:11,670 --> 00:47:16,830
+هنا عساس انه ال code الاحسابات الاحسابات اللي
+
+433
+00:47:16,830 --> 00:47:23,050
+بقوله اوضح five of bi تربيع على بي اي تربيع عساس
+
+434
+00:47:23,050 --> 00:47:28,890
+تتضح الصورة لكم اكثر زائد اللي هو بي اي تربيع ناقص
+
+435
+00:47:28,890 --> 00:47:36,680
+بي اي على بي اي تربيع زائدالـ term هذا هو بيطلع بي
+
+436
+00:47:36,680 --> 00:47:45,700
+اي في بي اي ناقص واحد على بي اي تربيع واضح
+
+437
+00:47:45,700 --> 00:47:57,080
+اه ويساوي واحد زائد بي اي ناقص واحد على بي اي زائد
+
+438
+00:47:57,080 --> 00:48:01,980
+ال بي اي مع ال بي اي تربيع بيصير بي اي ناقص واحد
+
+439
+00:48:01,980 --> 00:48:03,460
+على بي اي
+
+440
+00:48:09,680 --> 00:48:16,320
+زائد زائد بنختصر بيطلع بي اي ناقص واحد على بي اي
+
+441
+00:48:16,320 --> 00:48:20,500
+واضح انه كل term بيبقى فيه ايش بي اي على ناقص واحد
+
+442
+00:48:20,500 --> 00:48:23,840
+على ناقص واحد على بي اي بي اي ناقص واحد على بي اي
+
+443
+00:48:23,840 --> 00:48:25,880
+بي اي ناقص واحد على بي اي بي اي ناقص واحد على بي
+
+444
+00:48:25,880 --> 00:48:26,420
+اي بي اي ناقص واحد على بي اي بي اي ناقص واحد على
+
+445
+00:48:26,420 --> 00:48:26,720
+واحد على بي اي ناقص واحد على بي اي ناقص واحد على
+
+446
+00:48:26,720 --> 00:48:31,320
+بي اي ناقص واحد على بي اي ناقص واحد على بي اي نا
+
+447
+00:48:31,780 --> 00:48:36,840
+اللي أُس جدّاش اللي هو Alpha I أو Ki سماه هو نسميه
+
+448
+00:48:36,840 --> 00:48:44,000
+واحد زاد Alpha I في Bi ناقص واحد على Bi هذي بيه
+
+449
+00:48:44,000 --> 00:48:49,920
+مين ال F of Bi Alpha I F of N in general هتساوي
+
+450
+00:48:49,920 --> 00:48:56,800
+then ال F of N عبارة عن ال product هذا قايم من عند
+
+451
+00:48:56,800 --> 00:49:03,840
+واحد لعند R لكل ال terms هذي اللي هو عبارة عن واحد
+
+452
+00:49:03,840 --> 00:49:10,160
+زي ال alpha I في بي I نقص واحد على بي I قايمة عند
+
+453
+00:49:10,160 --> 00:49:15,160
+واحد لعند R وهي الصورة اللي مخلوبة اللي هو أنا
+
+454
+00:49:15,160 --> 00:49:19,640
+طبعا مسميها Alpha I هي مسميها Ki بس كرموز اختلفت
+
+455
+00:49:19,640 --> 00:49:31,140
+طيب نيجي لسؤال تمانية لسؤال تمانيةعندي سؤال تمانية
+
+456
+00:49:31,140 --> 00:49:35,660
+بيقول ميالي if
+
+457
+00:49:35,660 --> 00:49:43,700
+n أو for a square free integer for a square free
+
+458
+00:49:43,700 --> 00:49:52,260
+integer n أكبر
+
+459
+00:49:52,260 --> 00:49:56,820
+من واحد show that
+
+460
+00:49:58,130 --> 00:50:05,250
+Tau of N تربيع بساوي N if and only if N بتساوي
+
+461
+00:50:05,250 --> 00:50:11,790
+تلاتة الـ proof الان
+
+462
+00:50:11,790 --> 00:50:21,770
+الاتجاه الأول سهل if N بتساوي تلاتة then Tau of N
+
+463
+00:50:21,770 --> 00:50:25,410
+تربيع يعني تلاتة تربيع بساوي اللي هو بتعرف كيف
+
+464
+00:50:25,410 --> 00:50:31,760
+نوجد Tau ofTau of B أُس Alpha بساوي اللي هو Alpha
+
+465
+00:50:31,760 --> 00:50:37,980
+ثائد واحد عدد ال divisors دمية لل B Alpha بيصير
+
+466
+00:50:37,980 --> 00:50:42,460
+عندي Tau تلاتة تربيع عيش بساوي اتنين زائد واحد
+
+467
+00:50:42,460 --> 00:50:47,480
+ويساوي تلاتة اذا واضح انه في حالة الان بتساوي
+
+468
+00:50:47,480 --> 00:50:53,420
+تلاتة Tau of N تربيع بساوي الان conversely
+
+469
+00:50:53,420 --> 00:50:55,280
+conversely
+
+470
+00:50:58,180 --> 00:51:06,320
+Suppose that Tau of N تربيع بساوي N باشي لإن ما
+
+471
+00:51:06,320 --> 00:51:10,680
+أعطيك ال N إيه اشمله three three او square three
+
+472
+00:51:10,680 --> 00:51:19,560
+integer لإن since N أكبر من واحد is square او the
+
+473
+00:51:19,560 --> 00:51:23,840
+square three integer
+
+474
+00:51:25,250 --> 00:51:29,710
+إذا مافيش فيه أي مربع كامل، then N can be written
+
+475
+00:51:29,710 --> 00:51:42,310
+as B1 لعندي R where B1 لعندي R are distinct
+
+476
+00:51:42,310 --> 00:51:49,800
+primes لأنه في Ray Squareأو square free مافيش فيه
+
+477
+00:51:49,800 --> 00:51:53,820
+أي مربع كامل يعني مانعته أنه الأسس اللي عندي هنا
+
+478
+00:51:53,820 --> 00:51:58,280
+بس واحد وال بي لعند واحد لعند ال بي ار اللي هو
+
+479
+00:51:58,280 --> 00:52:07,100
+distinct primes هذا يعني then tau of n تربيع
+
+480
+00:52:07,100 --> 00:52:14,700
+معطيني ايه ايه ايش بيساوي n تساوي tau of n تربيع
+
+481
+00:52:14,700 --> 00:52:20,890
+هذا مقطع مين ال nهذا المقطة مفترضينه مين الان بي
+
+482
+00:52:20,890 --> 00:52:24,470
+واحد لعندي ال بي ار التاو في ان تربيع هنا بدنا
+
+483
+00:52:24,470 --> 00:52:31,170
+نحسبها هو يساوي تاو of بي واحد تربيع لعندي بي ار
+
+484
+00:52:31,170 --> 00:52:35,510
+تربيع ايش بيساوي التاو is multiplicative اللي هو
+
+485
+00:52:35,510 --> 00:52:38,410
+تاولة الأولة في تاولة التانية لتاولة الأخيرة يعني
+
+486
+00:52:38,410 --> 00:52:42,230
+بيصير عندى اتنين زائد واحد مضروبة في نفسها اتنين
+
+487
+00:52:42,230 --> 00:52:48,940
+زائد واحد اكم مرة ارTimes انها تبدأ من واحد لآخر
+
+488
+00:52:49,430 --> 00:52:54,930
+إذاً هذا بيساوي تلاتة مكررة R من الميوات إذاً
+
+489
+00:52:54,930 --> 00:52:59,750
+تلاتة قص إيش قص R إذا صار عندي بي واحد بي اتنين
+
+490
+00:52:59,750 --> 00:53:05,110
+عند بي R إيش بتساوي تلاتة قص R و ال بي واحد و ال
+
+491
+00:53:05,110 --> 00:53:09,110
+بي اتنين و ال بي R إيش مالهم Distinct Primes وهذا
+
+492
+00:53:09,110 --> 00:53:14,090
+لن يحدث إلا إذا كانت ال R إيش بتساوي و بتساوي واحد
+
+493
+00:53:14,090 --> 00:53:20,450
+لأنه مافيش عندي لمر مين التلاتة قص Rالان ال R عشان
+
+494
+00:53:20,450 --> 00:53:24,230
+تحافظ على انها هذه square free لازم ال R بتساوي
+
+495
+00:53:24,230 --> 00:53:32,870
+واحد then R بتساوي واحد ومنه hence هيكون عندي اللي
+
+496
+00:53:32,870 --> 00:53:40,090
+هو ال N تبعتنا هتساوي ثلاثة
+
+497
+00:53:40,090 --> 00:53:49,280
+اي سؤالأذا صارت عندي R بتساوي واحد والـ B واحد
+
+498
+00:53:49,280 --> 00:53:57,580
+بتساوي اللي هو التلاتة نيجي
+
+499
+00:53:57,580 --> 00:54:01,860
+الأن للسؤال الأخير اللي هو السؤال السؤال الأتناشر
+
+500
+00:54:01,860 --> 00:54:08,400
+آخر سؤال الأسئلة اللي مطلوبة homework أو اللي بدنا
+
+501
+00:54:08,400 --> 00:54:19,270
+نحلها كان مادج عنأسئلة الكتاب أجي
+
+502
+00:54:19,270 --> 00:54:22,290
+سؤال
+
+503
+00:54:22,290 --> 00:54:27,310
+اتن عشر
+
+504
+00:54:27,310 --> 00:54:30,370
+أكبر
+
+505
+00:54:30,370 --> 00:54:41,770
+من اتنين اكبر من اتنين اكبر من اتنين اكبر من اتنين
+
+506
+00:54:45,550 --> 00:54:54,590
+5 of n زائد واحد لكل تربيع أصغر أو يساوي 2 of n
+
+507
+00:54:54,590 --> 00:55:01,990
+تربيع proof الحل
+
+508
+00:55:01,990 --> 00:55:11,150
+للسؤال هذا اخدنا المرة الماضية انه في سؤال 5 of n
+
+509
+00:55:11,150 --> 00:55:18,640
+تربيع بساوي n في 5 of nوهذا كان جزء من سؤال أثبتنا
+
+510
+00:55:18,640 --> 00:55:23,580
+five of n M بساوي N في five of M عندما تكون اللي
+
+511
+00:55:23,580 --> 00:55:27,740
+بيقسم ال M ال M بيقسم مين ال primes اللي بيقسم ال
+
+512
+00:55:27,740 --> 00:55:33,080
+N بيقسم ال M إذن ال N هذه بدنا نعتمد عليها في هذا
+
+513
+00:55:33,080 --> 00:55:40,100
+السؤال الان five of N تربيع زائد five of N زائد
+
+514
+00:55:40,100 --> 00:55:46,180
+واحد تربيع بساوي من اللي هو السؤال السابقاللي
+
+515
+00:55:46,180 --> 00:55:51,260
+حلناه المرة الماضية بيطلع N في five of N زائد هذه
+
+516
+00:55:51,260 --> 00:55:58,780
+N زائد واحد في five of N زائد واحد واضح؟
+
+517
+00:55:58,780 --> 00:56:06,860
+وهذا دايما ال five of N ال five of N دايما أصغر
+
+518
+00:56:06,860 --> 00:56:14,460
+يساومين ال N قاقص واحد ماشي؟5n أعلى قيمة إلا لما
+
+519
+00:56:14,460 --> 00:56:19,580
+تكون الـ n برايم اللي هي 5b بـ-1 ما دون ذلك بيكون
+
+520
+00:56:19,580 --> 00:56:23,020
+الـ relative الـ prime with n لأن أصغر من الـ n
+
+521
+00:56:23,020 --> 00:56:28,620
+ناقص واحد فبصير هذا أصغر يساوي n في n ناقص واحد
+
+522
+00:56:28,620 --> 00:56:32,480
+لأن هذا أصغر يساوي n ناقص واحد زائد n زائد واحد
+
+523
+00:56:32,480 --> 00:56:37,940
+وهذا أصغر أو يساوي هذا ناقص واحد يعني الـ n زائد
+
+524
+00:56:37,940 --> 00:56:45,680
+واحد ناقص واحد وهذا بساويمن هنا ان تربيع ماقص ان
+
+525
+00:56:45,680 --> 00:56:56,220
+وهذا يذهب مع هذا بسبب ان تربيع زائد من الان هذا
+
+526
+00:56:56,220 --> 00:57:03,390
+يذهب مع هذا يصبح اتنين ان تربية وهو المطلوبوبهيك
+
+527
+00:57:03,390 --> 00:57:10,910
+بيكون احنا خلصنا discussion لشبتر سبعة شبتر سبعة
+
+528
+00:57:10,910 --> 00:57:17,710
+وبيكون انتهينا من اللي هو محاضرات نظرية الاعداد ان
+
+529
+00:57:17,710 --> 00:57:24,490
+شاء الله اذا كان سنحت الفرصة ممكن يكون في عندنا
+
+530
+00:57:24,490 --> 00:57:31,300
+تصوير لامتحان سابقوكيف انحله وبرك الله فيكم
+
+531
+00:57:31,300 --> 00:57:34,080
+والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/4ffxvgnWBKc_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/4ffxvgnWBKc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..311cf6513014d49c92c6f5a619a3a0d5166a1fa7
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/4ffxvgnWBKc_raw.json
@@ -0,0 +1 @@
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صار عندى ال summation ناقص واحد بس N على D Phi of D دي بتجسم ال N بساوي ناقص واحد دايما اللي هو ناقص ال summation Phi of D", "tokens": [28814, 15730, 20328, 9640, 43242, 7578, 2423, 39184, 28811, 23758, 426, 15844, 413, 11778, 995, 8717, 995, 4587, 9381, 36764, 24401, 4724, 3794, 426, 15844, 413, 11778, 47302, 15042, 13672, 1829, 31439, 11778, 3224, 9673, 28543, 2288, 8592, 4724, 1829, 3794, 995, 45865, 8717, 995, 4587, 9381, 36764, 24401, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 11933, 15730, 20328, 9640, 43242, 7578, 550, 20328, 9640, 43242, 7578, 2423, 28811, 8717, 995, 4587, 9381, 36764, 24401, 4724, 3794, 426, 15844, 413, 41435, 295, 413, 11778, 1829, 39894, 7435, 38251, 2423, 426, 4724, 3794, 995, 45865, 8717, 995, 4587, 9381, 36764, 24401, 11778, 47302, 15042, 13672, 1829, 31439, 8717, 995, 4587, 9381, 2423, 28811, 41435, 295, 413], "avg_logprob": -0.25080820224408445, "compression_ratio": 2.2044198895027622, "no_speech_prob": 0.0, "words": [{"start": 649.79, "end": 650.11, 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الـ D prime ينبغي بجسم ال N في هذه الحالة ان انا فصلت ال even لحاله و ال odd لحاله وهذا سيسبب لي بساوي", "tokens": [3555, 3215, 1211, 13672, 1829, 31439, 2423, 39184, 25974, 284, 5296, 28820, 1975, 2655, 1863, 9957, 9122, 5172, 11778, 1829, 20328, 9640, 43242, 2423, 25974, 284, 8978, 29538, 21542, 6027, 3660, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 1975, 2655, 1863, 9957, 9122, 5172, 11778, 1829, 5835, 2423, 39184, 413, 5835, 7251, 1863, 3555, 17082, 1829, 4724, 7435, 38251, 2423, 426, 8978, 29538, 21542, 6027, 3660, 16472, 1975, 8315, 6156, 36520, 2655, 2423, 754, 5296, 5016, 6027, 3224, 4032, 2423, 7401, 5296, 5016, 6027, 3224, 37037, 15730, 8608, 1829, 35457, 3555, 32239, 4724, 3794, 995, 45865], "avg_logprob": -0.31106504098493226, "compression_ratio": 1.92090395480226, "no_speech_prob": 2.1457672119140625e-06, "words": [{"start": 950.77, "end": 951.33, "word": "بدل", "probability": 0.575927734375}, {"start": 951.33, "end": 951.67, "word": " اللي", "probability": 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980.51, "end": 980.97, "word": " mean", "probability": 0.58447265625}, {"start": 980.97, "end": 981.71, "word": " 2K", "probability": 0.653076171875}, {"start": 981.71, "end": 982.59, "word": "-1", "probability": 0.580078125}, {"start": 982.59, "end": 982.81, "word": " في", "probability": 0.50732421875}, {"start": 982.81, "end": 983.33, "word": " H", "probability": 0.125732421875}, {"start": 983.33, "end": 984.01, "word": " في", "probability": 0.564453125}, {"start": 984.01, "end": 984.21, "word": " N", "probability": 0.85400390625}], "temperature": 1.0}, {"id": 40, "seek": 100678, "start": 985.38, "end": 1006.78, "text": "الان هذا قد كله مادام قده ده نقش ماله ناقص واحد ناقص واحد ده بيصير ناقص ال summation فاي of اتنين K في D prime لدى D prime اللى بتكسر نين الان طيب الان ويساوي", "tokens": [6027, 7649, 23758, 12174, 3215, 28242, 3224, 3714, 18513, 10943, 12174, 3215, 3224, 11778, 3224, 8717, 4587, 8592, 3714, 6027, 3224, 8717, 995, 4587, 9381, 36764, 24401, 8717, 995, 4587, 9381, 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{"start": 988.64, "end": 988.98, "word": " نقش", "probability": 0.5931803385416666}, {"start": 988.98, "end": 989.3, "word": " ماله", "probability": 0.8740234375}, {"start": 989.3, "end": 991.04, "word": " ناقص", "probability": 0.728729248046875}, {"start": 991.04, "end": 991.54, "word": " واحد", "probability": 0.983154296875}, {"start": 991.54, "end": 992.24, "word": " ناقص", "probability": 0.880126953125}, {"start": 992.24, "end": 992.48, "word": " واحد", "probability": 0.9619140625}, {"start": 992.48, "end": 992.62, "word": " ده", "probability": 0.864013671875}, {"start": 992.62, "end": 992.96, "word": " بيصير", "probability": 0.7713623046875}, {"start": 992.96, "end": 993.82, "word": " ناقص", "probability": 0.9830322265625}, {"start": 993.82, "end": 994.52, "word": " ال", "probability": 0.416748046875}, {"start": 994.52, "end": 995.04, "word": " summation", "probability": 0.7841796875}, {"start": 995.04, "end": 996.04, "word": " فاي", "probability": 0.3873697916666667}, {"start": 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"word": " الان", "probability": 0.6435546875}, {"start": 1003.28, "end": 1005.28, "word": " طيب", "probability": 0.9615885416666666}, {"start": 1005.28, "end": 1006.18, "word": " الان", "probability": 0.863525390625}, {"start": 1006.18, "end": 1006.78, "word": " ويساوي", "probability": 0.76796875}], "temperature": 1.0}, {"id": 41, "seek": 102902, "start": 1009.7, "end": 1029.02, "text": "هذا حسب النظرية summation للـ5 of D دي بتكسب الان على طول ايش بساوي بساوي الان لأن 5 of D دي بتكسب هذا المقدار اذا كل ال summation هذا ايش هيساوي اتنين اص كمانس واحد في ايش في ان طيب ماقص", "tokens": [3224, 15730, 11331, 35457, 28239, 19913, 2288, 10632, 28811, 24976, 39184, 20, 295, 413, 11778, 1829, 39894, 4117, 35457, 2423, 7649, 15844, 23032, 12610, 1975, 1829, 8592, 4724, 3794, 995, 45865, 4724, 3794, 995, 45865, 2423, 7649, 5296, 33456, 1025, 295, 413, 11778, 1829, 39894, 4117, 35457, 23758, 9673, 28543, 9640, 1975, 15730, 28242, 2423, 28811, 23758, 1975, 1829, 8592, 39896, 3794, 995, 45865, 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"probability": 0.89599609375}, {"start": 1013.56, "end": 1013.8, "word": " الان", "probability": 0.5958251953125}, {"start": 1013.8, "end": 1013.98, "word": " على", "probability": 0.59912109375}, {"start": 1013.98, "end": 1014.16, "word": " طول", "probability": 0.98095703125}, {"start": 1014.16, "end": 1014.3, "word": " ايش", "probability": 0.683349609375}, {"start": 1014.3, "end": 1014.84, "word": " بساوي", "probability": 0.89990234375}, {"start": 1014.84, "end": 1015.72, "word": " بساوي", "probability": 0.828125}, {"start": 1015.72, "end": 1016.02, "word": " الان", "probability": 0.895263671875}, {"start": 1016.02, "end": 1016.9, "word": " لأن", "probability": 0.753662109375}, {"start": 1016.9, "end": 1017.28, "word": " 5", "probability": 0.3828125}, {"start": 1017.28, "end": 1017.58, "word": " of", "probability": 0.955078125}, {"start": 1017.58, "end": 1017.82, "word": " D", "probability": 0.958984375}, {"start": 1017.82, "end": 1018.04, "word": " دي", "probability": 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في", "probability": 0.3994140625}, {"start": 1350.81, "end": 1351.39, "word": " حالة", "probability": 0.86328125}, {"start": 1351.39, "end": 1351.55, "word": " M", "probability": 0.1751708984375}, {"start": 1351.55, "end": 1352.09, "word": " بتساوي", "probability": 0.646453857421875}, {"start": 1352.09, "end": 1352.27, "word": " 1", "probability": 0.51806640625}, {"start": 1352.27, "end": 1355.19, "word": " اذا", "probability": 0.54742431640625}, {"start": 1355.19, "end": 1356.51, "word": " M", "probability": 0.642578125}, {"start": 1356.51, "end": 1356.91, "word": " أكبر", "probability": 0.8815104166666666}, {"start": 1356.91, "end": 1357.11, "word": " من", "probability": 0.97021484375}, {"start": 1357.11, "end": 1357.69, "word": " 1", "probability": 0.81787109375}, {"start": 1357.69, "end": 1358.81, "word": " فالـ", "probability": 0.34954833984375}, {"start": 1358.81, "end": 1359.05, "word": " M", "probability": 0.72265625}, {"start": 1359.05, "end": 1359.49, "word": " يمكن", "probability": 0.71728515625}, {"start": 1359.49, "end": 1359.49, "word": " أن", "probability": 0.560546875}, {"start": 1359.49, "end": 1359.83, "word": " يكون", "probability": 0.622802734375}, {"start": 1359.83, "end": 1361.07, "word": " كذلك", "probability": 0.655517578125}, {"start": 1361.07, "end": 1361.37, "word": " الـ", "probability": 0.3572998046875}, {"start": 1361.37, "end": 1361.71, "word": " Rhyme", "probability": 0.3943074544270833}, {"start": 1361.71, "end": 1362.57, "word": " factorization", "probability": 0.81640625}, {"start": 1362.57, "end": 1363.03, "word": " لها", "probability": 0.828125}, {"start": 1363.03, "end": 1364.19, "word": " B1", "probability": 0.578857421875}, {"start": 1364.19, "end": 1365.27, "word": " Alpha", "probability": 0.315673828125}, {"start": 1365.27, "end": 1365.75, "word": " 1", "probability": 0.765625}, {"start": 1365.75, "end": 1366.61, "word": " لعند", "probability": 0.7122395833333334}, {"start": 1366.61, "end": 1367.27, "word": " PR", "probability": 0.255615234375}, {"start": 1367.27, "end": 1368.05, "word": " Alpha", "probability": 0.9189453125}, {"start": 1368.05, "end": 1368.61, "word": " R", "probability": 0.9716796875}], "temperature": 1.0}, {"id": 55, "seek": 139725, "start": 1370.27, "end": 1397.25, "text": "P1 لعند PR are distinct primes والألفة I أكبر أو يساوي واحد لكل I من واحد لعند ال R وال R أكبر أو يساوي واحد طيب الان let let F of N بساوي ال summation", "tokens": [47, 16, 5296, 3615, 41260, 11568, 366, 10644, 582, 1532, 16070, 10721, 46538, 3660, 286, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 36764, 24401, 5296, 28820, 286, 9154, 36764, 24401, 5296, 3615, 41260, 2423, 497, 16070, 497, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 36764, 24401, 23032, 1829, 3555, 2423, 7649, 718, 718, 479, 295, 426, 4724, 3794, 995, 45865, 2423, 28811], "avg_logprob": -0.25721153846153844, "compression_ratio": 1.4933333333333334, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1370.27, "end": 1371.27, "word": "P1", "probability": 0.5089111328125}, {"start": 1371.27, "end": 1371.71, "word": " لعند", "probability": 0.7958984375}, {"start": 1371.71, "end": 1372.43, "word": " PR", "probability": 0.84423828125}, {"start": 1372.43, "end": 1373.75, "word": " are", "probability": 0.351806640625}, {"start": 1373.75, "end": 1375.69, "word": " distinct", "probability": 0.9345703125}, {"start": 1375.69, "end": 1377.85, "word": " primes", "probability": 0.749755859375}, {"start": 1377.85, "end": 1379.71, "word": " والألفة", "probability": 0.65045166015625}, {"start": 1379.71, "end": 1380.73, "word": " I", "probability": 0.85107421875}, {"start": 1380.73, "end": 1381.81, "word": " أكبر", "probability": 0.94189453125}, {"start": 1381.81, "end": 1381.99, "word": " أو", "probability": 0.82080078125}, {"start": 1381.99, "end": 1382.27, "word": " يساوي", "probability": 0.7125244140625}, {"start": 1382.27, "end": 1382.79, "word": " واحد", "probability": 0.9248046875}, {"start": 1382.79, "end": 1383.57, "word": " لكل", "probability": 0.981689453125}, {"start": 1383.57, "end": 1384.09, "word": " I", "probability": 0.97216796875}, {"start": 1384.09, "end": 1384.31, "word": " من", "probability": 0.9873046875}, {"start": 1384.31, "end": 1384.67, "word": " واحد", "probability": 0.934814453125}, {"start": 1384.67, "end": 1385.25, "word": " لعند", "probability": 0.9552408854166666}, {"start": 1385.25, "end": 1385.53, "word": " ال", "probability": 0.86083984375}, {"start": 1385.53, "end": 1385.83, "word": " R", "probability": 0.498046875}, {"start": 1385.83, "end": 1386.43, "word": " وال", "probability": 0.81640625}, {"start": 1386.43, "end": 1386.69, "word": " R", "probability": 0.317138671875}, {"start": 1386.69, "end": 1387.13, "word": " أكبر", "probability": 0.9827473958333334}, {"start": 1387.13, "end": 1387.37, "word": " أو", "probability": 0.90576171875}, {"start": 1387.37, "end": 1387.87, "word": " يساوي", "probability": 0.97021484375}, {"start": 1387.87, "end": 1388.57, "word": " واحد", "probability": 0.98876953125}, {"start": 1388.57, "end": 1390.17, "word": " طيب", "probability": 0.83837890625}, {"start": 1390.17, "end": 1391.51, "word": " الان", "probability": 0.562744140625}, {"start": 1391.51, "end": 1392.07, "word": " let", "probability": 0.8046875}, {"start": 1392.07, "end": 1393.75, "word": " let", "probability": 0.442626953125}, {"start": 1393.75, "end": 1394.49, "word": " F", "probability": 0.5869140625}, {"start": 1394.49, "end": 1394.75, "word": " of", "probability": 0.54931640625}, {"start": 1394.75, "end": 1395.13, "word": " N", "probability": 0.8896484375}, {"start": 1395.13, "end": 1396.53, "word": " بساوي", "probability": 0.862548828125}, {"start": 1396.53, "end": 1396.67, "word": " ال", "probability": 0.798828125}, {"start": 1396.67, "end": 1397.25, "word": " summation", "probability": 0.82421875}], "temperature": 1.0}, {"id": 56, "seek": 142521, "start": 1398.21, "end": 1425.21, "text": "ميو تربيع of D على فاي of D لدى D بتجسم الان الان هذه سميها واحد لأن since ميو تربيع of D او ميو تربيع على فاي of D is multiplicative", "tokens": [2304, 1829, 2407, 6055, 2288, 21292, 3615, 295, 413, 15844, 6156, 47302, 295, 413, 5296, 3215, 7578, 413, 39894, 7435, 38251, 2423, 7649, 2423, 7649, 29538, 8608, 2304, 1829, 11296, 36764, 24401, 5296, 33456, 1670, 3714, 1829, 2407, 6055, 2288, 21292, 3615, 295, 413, 1975, 2407, 3714, 1829, 2407, 6055, 2288, 21292, 3615, 15844, 6156, 47302, 295, 413, 307, 17596, 1166], "avg_logprob": -0.25214214622974396, "compression_ratio": 1.5419847328244274, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1398.21, "end": 1399.11, "word": "ميو", "probability": 0.67041015625}, {"start": 1399.11, "end": 1399.79, "word": " تربيع", "probability": 0.9251708984375}, {"start": 1399.79, "end": 1400.01, "word": " of", "probability": 0.472900390625}, {"start": 1400.01, "end": 1400.41, "word": " D", "probability": 0.5341796875}, {"start": 1400.41, "end": 1401.35, "word": " على", "probability": 0.7236328125}, {"start": 1401.35, "end": 1401.73, "word": " فاي", "probability": 0.4649658203125}, {"start": 1401.73, "end": 1401.93, "word": " of", "probability": 0.90869140625}, {"start": 1401.93, "end": 1402.37, "word": " D", "probability": 0.970703125}, {"start": 1402.37, "end": 1403.65, "word": " لدى", "probability": 0.69384765625}, {"start": 1403.65, "end": 1403.71, "word": " D", "probability": 0.78759765625}, {"start": 1403.71, "end": 1404.47, "word": " بتجسم", "probability": 0.7369791666666666}, {"start": 1404.47, "end": 1404.83, "word": " الان", "probability": 0.6513671875}, {"start": 1404.83, "end": 1407.73, "word": " الان", "probability": 0.6370849609375}, {"start": 1407.73, "end": 1409.17, "word": " هذه", "probability": 0.2376708984375}, {"start": 1409.17, "end": 1410.63, "word": " سميها", "probability": 0.77325439453125}, {"start": 1410.63, "end": 1412.15, "word": " واحد", "probability": 0.949951171875}, {"start": 1412.15, "end": 1413.53, "word": " لأن", "probability": 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0.99267578125}, {"start": 1421.09, "end": 1422.47, "word": " is", "probability": 0.890625}, {"start": 1422.47, "end": 1425.21, "word": " multiplicative", "probability": 0.912353515625}], "temperature": 1.0}, {"id": 57, "seek": 145446, "start": 1427.32, "end": 1454.46, "text": "How؟ How سهلة على طول بما أن U مُلتبليكاتف و F مُلتبليكاتف إذا التربيع، الدرب هذا على القسمة بيطلع أشماله مُلتبليكاتف مدام هذا مُلتبليكاتف in then by theorem then by theorem 6 أربعة مدام اللي جوا مُلتبليكاتف هتطلع F is مُلتبليكاتف", "tokens": [6462, 22807, 1012, 8608, 3224, 37977, 15844, 23032, 12610, 4724, 15042, 14739, 624, 3714, 10859, 1211, 2655, 3555, 20292, 4117, 9307, 5172, 4032, 479, 3714, 10859, 1211, 2655, 3555, 20292, 4117, 9307, 5172, 11933, 15730, 16712, 2288, 21292, 3615, 12399, 32748, 25513, 23758, 15844, 25062, 38251, 3660, 4724, 1829, 9566, 1211, 3615, 5551, 8592, 2304, 6027, 3224, 3714, 10859, 1211, 2655, 3555, 20292, 4117, 9307, 5172, 3714, 3215, 10943, 23758, 3714, 10859, 1211, 2655, 3555, 20292, 4117, 9307, 5172, 294, 550, 538, 20904, 550, 538, 20904, 1386, 5551, 25513, 27884, 3714, 3215, 10943, 13672, 1829, 10874, 14407, 3714, 10859, 1211, 2655, 3555, 20292, 4117, 9307, 5172, 8032, 2655, 9566, 1211, 3615, 479, 307, 3714, 10859, 1211, 2655, 3555, 20292, 4117, 9307, 5172], "avg_logprob": -0.23666158221601472, "compression_ratio": 2.0105820105820107, "no_speech_prob": 1.0728836059570312e-06, "words": [{"start": 1427.32, "end": 1428.36, "word": "How؟", "probability": 0.3624267578125}, {"start": 1428.36, "end": 1428.8, "word": " How", "probability": 0.33544921875}, {"start": 1428.8, "end": 1429.36, "word": " سهلة", "probability": 0.8466796875}, {"start": 1429.36, "end": 1430.22, "word": " على", "probability": 0.88427734375}, {"start": 1430.22, "end": 1430.64, "word": " طول", "probability": 0.991455078125}, {"start": 1430.64, "end": 1431.28, "word": " بما", "probability": 0.886474609375}, {"start": 1431.28, "end": 1431.4, "word": " أن", "probability": 0.60693359375}, {"start": 1431.4, "end": 1431.58, "word": " U", "probability": 0.360595703125}, {"start": 1431.58, "end": 1432.3, "word": " مُلتبليكاتف", "probability": 0.5885009765625}, {"start": 1432.3, "end": 1432.46, "word": " و", "probability": 0.9443359375}, {"start": 1432.46, "end": 1432.5, "word": " F", "probability": 0.1912841796875}, {"start": 1432.5, "end": 1433.52, "word": " مُلتبليكاتف", "probability": 0.96142578125}, {"start": 1433.52, "end": 1434.06, "word": " إذا", "probability": 0.653076171875}, {"start": 1434.06, "end": 1434.84, "word": " التربيع،", "probability": 0.7309814453125}, {"start": 1434.84, "end": 1435.36, "word": " الدرب", "probability": 0.71826171875}, {"start": 1435.36, "end": 1435.7, "word": " هذا", "probability": 0.8330078125}, {"start": 1435.7, "end": 1436.0, "word": " على", "probability": 0.86279296875}, {"start": 1436.0, "end": 1436.5, "word": " القسمة", "probability": 0.8447265625}, {"start": 1436.5, "end": 1436.76, "word": " بيطلع", "probability": 0.727685546875}, {"start": 1436.76, "end": 1437.4, "word": " أشماله", "probability": 0.8228515625}, {"start": 1437.4, "end": 1438.62, "word": " مُلتبليكاتف", "probability": 0.9635959201388888}, {"start": 1438.62, "end": 1439.8, "word": " مدام", "probability": 0.7626953125}, {"start": 1439.8, "end": 1440.1, "word": " هذا", "probability": 0.91796875}, {"start": 1440.1, "end": 1441.1, "word": " مُلتبليكاتف", "probability": 0.9690755208333334}, {"start": 1441.1, "end": 1441.38, "word": " in", "probability": 0.353759765625}, {"start": 1441.38, "end": 1441.62, "word": " then", "probability": 0.60791015625}, {"start": 1441.62, "end": 1441.9, "word": " by", "probability": 0.85546875}, {"start": 1441.9, "end": 1442.56, "word": " theorem", "probability": 0.69140625}, {"start": 1442.56, "end": 1443.9, "word": " then", "probability": 0.6337890625}, {"start": 1443.9, "end": 1444.9, "word": " by", "probability": 0.9521484375}, {"start": 1444.9, "end": 1445.52, "word": " theorem", "probability": 0.8173828125}, {"start": 1445.52, "end": 1446.52, "word": " 6", "probability": 0.626953125}, {"start": 1446.52, "end": 1447.24, "word": " أربعة", "probability": 0.7982584635416666}, {"start": 1447.24, "end": 1448.22, "word": " مدام", "probability": 0.9327799479166666}, {"start": 1448.22, "end": 1448.42, "word": " اللي", "probability": 0.90185546875}, {"start": 1448.42, "end": 1448.64, "word": " جوا", "probability": 0.845703125}, {"start": 1448.64, "end": 1449.52, "word": " مُلتبليكاتف", "probability": 0.9620768229166666}, {"start": 1449.52, "end": 1450.16, "word": " هتطلع", "probability": 0.89638671875}, {"start": 1450.16, "end": 1450.72, "word": " F", "probability": 0.9384765625}, {"start": 1450.72, "end": 1452.0, "word": " is", "probability": 0.80224609375}, {"start": 1452.0, "end": 1454.46, "word": " مُلتبليكاتف", "probability": 0.9417317708333334}], "temperature": 1.0}, {"id": 58, "seek": 148426, "start": 1455.82, "end": 1484.26, "text": "بناء عليه بدأ من الـ F capital multiplicative بناء عليه هيكون عندي F of N الـ N تباعتنا اللي هي P1 Alpha 1 عند P R سواء Alpha R بتساوي ال product معايا ال product للـ F of P I Alpha I I من عند 1 لعند R وسمي هذه اتنين", "tokens": [3555, 1863, 16606, 47356, 4724, 3215, 10721, 9154, 2423, 39184, 479, 4238, 17596, 1166, 4724, 1863, 16606, 47356, 39896, 30544, 18871, 16254, 479, 295, 426, 2423, 39184, 426, 6055, 3555, 995, 34268, 8315, 13672, 1829, 39896, 430, 16, 20588, 502, 43242, 430, 497, 8608, 2407, 16606, 20588, 497, 39894, 3794, 995, 45865, 2423, 1674, 20449, 995, 25528, 2423, 1674, 24976, 39184, 479, 295, 430, 286, 20588, 286, 286, 9154, 43242, 502, 5296, 3615, 41260, 497, 4032, 38251, 1829, 29538, 1975, 2655, 1863, 9957], "avg_logprob": -0.39471726261434104, "compression_ratio": 1.5396039603960396, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1455.82, "end": 1456.42, "word": "بناء", "probability": 0.86962890625}, {"start": 1456.42, "end": 1456.98, "word": " عليه", "probability": 0.61669921875}, {"start": 1456.98, "end": 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ساوي So summation Mu تربيع of D على Phi of D لدى D تجسم ال Bi Alpha I", "tokens": [4360, 14722, 283, 295, 3228, 8961, 741, 4032, 28814, 1829, 8608, 995, 45865, 11331, 35457, 16712, 3615, 16572, 5172, 1975, 1829, 3224, 11331, 4117, 995, 10632, 4032, 28814, 1829, 8608, 995, 45865, 407, 28811, 15601, 6055, 2288, 21292, 3615, 295, 413, 15844, 41435, 295, 413, 5296, 3215, 7578, 413, 6055, 7435, 38251, 2423, 13007, 20588, 286], "avg_logprob": -0.45586622388739334, "compression_ratio": 1.2328767123287672, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 1514.77, "end": 1515.03, "word": "We", "probability": 0.15283203125}, {"start": 1515.03, "end": 1515.69, "word": " compute", "probability": 0.91796875}, {"start": 1515.69, "end": 1516.19, "word": " f", "probability": 0.4296875}, {"start": 1516.19, "end": 1517.19, "word": " of", "probability": 0.67431640625}, {"start": 1517.19, "end": 1517.93, "word": " bi", "probability": 0.373291015625}, {"start": 1517.93, "end": 1518.71, "word": 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{"start": 1647.3, "end": 1647.72, "word": " إيش", "probability": 0.7345784505208334}, {"start": 1647.72, "end": 1647.92, "word": " الـ", "probability": 0.845458984375}, {"start": 1647.92, "end": 1648.68, "word": " Phi", "probability": 0.32177734375}, {"start": 1648.68, "end": 1648.88, "word": " of", "probability": 0.90771484375}, {"start": 1648.88, "end": 1649.24, "word": " Bi", "probability": 0.9228515625}, {"start": 1649.24, "end": 1649.42, "word": " اللي", "probability": 0.6700439453125}, {"start": 1649.42, "end": 1649.54, "word": " هو", "probability": 0.98876953125}, {"start": 1649.54, "end": 1649.8, "word": " بي", "probability": 0.59521484375}, {"start": 1649.8, "end": 1650.44, "word": " آي", "probability": 0.701171875}, {"start": 1650.44, "end": 1652.26, "word": " ناقص", "probability": 0.9649658203125}, {"start": 1652.26, "end": 1652.74, "word": " واحد", "probability": 0.99365234375}], "temperature": 1.0}, {"id": 66, "seek": 167651, "start": 1655.69, "end": 1676.51, "text": "مظبوط؟ و .. و يساوي .. و يساوي عبارة عن bi ناقص واحد زائد واحد على bi ناقص واحد و يساوي bi على bi ناقص واحد صح؟", "tokens": [2304, 19913, 3555, 2407, 9566, 22807, 4032, 4386, 4032, 7251, 3794, 995, 45865, 4386, 4032, 7251, 3794, 995, 45865, 6225, 3555, 9640, 3660, 18871, 3228, 8717, 995, 4587, 9381, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 15844, 3228, 8717, 995, 4587, 9381, 36764, 24401, 4032, 7251, 3794, 995, 45865, 3228, 15844, 3228, 8717, 995, 4587, 9381, 36764, 24401, 20328, 5016, 22807], "avg_logprob": -0.14629536626800413, "compression_ratio": 1.84, "no_speech_prob": 1.3709068298339844e-06, "words": [{"start": 1655.6899999999998, "end": 1656.87, "word": "مظبوط؟", "probability": 0.7183024088541666}, {"start": 1656.87, "end": 1656.87, "word": " و", "probability": 0.8837890625}, {"start": 1656.87, "end": 1657.03, "word": " ..", "probability": 0.286865234375}, {"start": 1657.03, "end": 1658.23, "word": " و", "probability": 0.947265625}, {"start": 1658.23, "end": 1658.67, "word": " يساوي", "probability": 0.90185546875}, {"start": 1658.67, "end": 1659.01, "word": " ..", "probability": 0.43359375}, {"start": 1659.01, "end": 1660.35, "word": " و", "probability": 0.94921875}, {"start": 1660.35, "end": 1660.83, "word": " يساوي", "probability": 0.9879150390625}, {"start": 1660.83, "end": 1662.77, "word": " عبارة", "probability": 0.982666015625}, {"start": 1662.77, "end": 1662.99, "word": " عن", "probability": 0.97900390625}, {"start": 1662.99, "end": 1663.35, "word": " bi", "probability": 0.213134765625}, {"start": 1663.35, "end": 1665.79, "word": " ناقص", "probability": 0.80804443359375}, {"start": 1665.79, "end": 1666.31, "word": " واحد", "probability": 0.97802734375}, {"start": 1666.31, "end": 1667.01, "word": " زائد", "probability": 0.9396158854166666}, {"start": 1667.01, "end": 1667.53, "word": " واحد", "probability": 0.98779296875}, {"start": 1667.53, "end": 1667.85, "word": " على", "probability": 0.67041015625}, {"start": 1667.85, "end": 1668.51, "word": " bi", "probability": 0.9345703125}, {"start": 1668.51, "end": 1669.31, "word": " ناقص", "probability": 0.99365234375}, {"start": 1669.31, "end": 1669.77, "word": " واحد", "probability": 0.991943359375}, {"start": 1669.77, "end": 1670.27, "word": " و", "probability": 0.94287109375}, {"start": 1670.27, "end": 1670.79, "word": " يساوي", "probability": 0.957763671875}, {"start": 1670.79, "end": 1671.55, "word": " bi", "probability": 0.9375}, {"start": 1671.55, "end": 1672.57, "word": " على", "probability": 0.77685546875}, {"start": 1672.57, "end": 1673.39, "word": " bi", "probability": 0.97021484375}, {"start": 1673.39, "end": 1674.45, "word": " ناقص", "probability": 0.9949951171875}, {"start": 1674.45, "end": 1674.93, "word": " واحد", "probability": 0.992919921875}, {"start": 1674.93, "end": 1676.51, "word": " صح؟", "probability": 0.9352213541666666}], "temperature": 1.0}, {"id": 67, "seek": 170530, "start": 1677.56, "end": 1705.3, "text": "إذا صار عندي الان f of bi alpha bi بسوى bi على bi نقص واحد هذا تلاتة الان من اللي هو اتنين و تلاتة from from اتنين and تلاتة we get", "tokens": [28814, 15730, 20328, 9640, 18871, 16254, 2423, 7649, 283, 295, 3228, 8961, 3228, 4724, 3794, 2407, 7578, 3228, 15844, 3228, 8717, 4587, 9381, 36764, 24401, 23758, 6055, 1211, 9307, 3660, 2423, 7649, 9154, 13672, 1829, 31439, 1975, 2655, 1863, 9957, 4032, 6055, 1211, 9307, 3660, 490, 490, 1975, 2655, 1863, 9957, 293, 6055, 1211, 9307, 3660, 321, 483], "avg_logprob": -0.29555083937564136, "compression_ratio": 1.5037593984962405, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1677.56, "end": 1677.86, "word": "إذا", "probability": 0.5433349609375}, {"start": 1677.86, "end": 1678.18, "word": " صار", "probability": 0.7205810546875}, {"start": 1678.18, "end": 1678.48, "word": " عندي", "probability": 0.62939453125}, {"start": 1678.48, "end": 1678.84, "word": " الان", "probability": 0.622802734375}, {"start": 1678.84, "end": 1680.02, "word": " f", "probability": 0.38916015625}, {"start": 1680.02, "end": 1680.46, "word": " of", "probability": 0.67431640625}, {"start": 1680.46, "end": 1681.22, "word": " bi", "probability": 0.59423828125}, {"start": 1681.22, "end": 1682.08, "word": " alpha", "probability": 0.0706787109375}, {"start": 1682.08, "end": 1682.78, "word": " bi", "probability": 0.50830078125}, {"start": 1682.78, "end": 1683.76, "word": " بسوى", "probability": 0.66943359375}, {"start": 1683.76, "end": 1684.34, "word": " bi", "probability": 0.783203125}, {"start": 1684.34, "end": 1684.64, "word": " على", "probability": 0.64794921875}, {"start": 1684.64, "end": 1685.32, "word": " bi", "probability": 0.87158203125}, {"start": 1685.32, "end": 1685.9, "word": " نقص", "probability": 0.8191731770833334}, {"start": 1685.9, "end": 1686.26, "word": " واحد", "probability": 0.9755859375}, {"start": 1686.26, "end": 1686.74, "word": " هذا", "probability": 0.71484375}, {"start": 1686.74, "end": 1687.34, "word": " تلاتة", "probability": 0.9149169921875}, {"start": 1687.34, "end": 1688.82, "word": " الان", "probability": 0.6868896484375}, {"start": 1688.82, "end": 1690.64, "word": " من", "probability": 0.97314453125}, {"start": 1690.64, "end": 1691.44, "word": " اللي", "probability": 0.883544921875}, {"start": 1691.44, "end": 1691.74, "word": " هو", "probability": 0.98291015625}, {"start": 1691.74, "end": 1692.16, "word": " اتنين", "probability": 0.9107666015625}, {"start": 1692.16, "end": 1692.3, "word": " و", "probability": 0.748046875}, {"start": 1692.3, "end": 1693.7, "word": " تلاتة", "probability": 0.9073486328125}, {"start": 1693.7, "end": 1694.46, "word": " from", "probability": 0.8642578125}, {"start": 1694.46, "end": 1697.02, "word": " from", "probability": 0.59033203125}, {"start": 1697.02, "end": 1700.86, "word": " اتنين", "probability": 0.937744140625}, {"start": 1700.86, "end": 1702.12, "word": " and", "probability": 0.89453125}, {"start": 1702.12, "end": 1703.1, "word": " تلاتة", "probability": 0.986083984375}, {"start": 1703.1, "end": 1704.38, "word": " we", "probability": 0.79736328125}, {"start": 1704.38, "end": 1705.3, "word": " get", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 68, "seek": 172681, "start": 1706.15, "end": 1726.81, "text": "we get ماذا؟ we get F of N F of N بسوّله product A حصل الدرب ل B I على B I ناقص واحد I من عند واحد لعند مين لعند R", "tokens": [826, 483, 3714, 45636, 995, 22807, 321, 483, 479, 295, 426, 479, 295, 426, 4724, 3794, 2407, 11703, 43761, 1674, 316, 11331, 36520, 32748, 25513, 5296, 363, 286, 15844, 363, 286, 8717, 995, 4587, 9381, 36764, 24401, 286, 9154, 43242, 36764, 24401, 5296, 3615, 41260, 3714, 9957, 5296, 3615, 41260, 497], "avg_logprob": -0.3485576934539355, "compression_ratio": 1.2790697674418605, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1706.15, "end": 1706.39, "word": "we", "probability": 0.2305908203125}, {"start": 1706.39, "end": 1706.67, "word": " get", "probability": 0.9345703125}, {"start": 1706.67, "end": 1707.67, "word": " ماذا؟", "probability": 0.61175537109375}, {"start": 1707.67, "end": 1707.85, "word": " we", "probability": 0.62451171875}, {"start": 1707.85, "end": 1708.11, "word": " get", "probability": 0.951171875}, {"start": 1708.11, "end": 1708.33, "word": " F", "probability": 0.359130859375}, {"start": 1708.33, "end": 1708.51, "word": " of", "probability": 0.72412109375}, {"start": 1708.51, "end": 1708.75, "word": " N", "probability": 0.83056640625}, {"start": 1708.75, "end": 1710.19, "word": " F", "probability": 0.51171875}, {"start": 1710.19, "end": 1710.53, "word": " of", "probability": 0.94970703125}, {"start": 1710.53, "end": 1710.95, "word": " N", "probability": 0.98828125}, {"start": 1710.95, "end": 1712.27, "word": " بسوّله", "probability": 0.61484375}, {"start": 1712.27, "end": 1713.05, "word": " product", "probability": 0.693359375}, {"start": 1713.05, "end": 1714.55, "word": " A", "probability": 0.359375}, {"start": 1714.55, "end": 1715.23, "word": " حصل", "probability": 0.765380859375}, {"start": 1715.23, "end": 1715.73, "word": " الدرب", "probability": 0.469970703125}, {"start": 1715.73, "end": 1716.69, "word": " ل", "probability": 0.814453125}, {"start": 1716.69, "end": 1716.95, "word": " B", "probability": 0.15185546875}, {"start": 1716.95, "end": 1717.63, "word": " I", "probability": 0.69287109375}, {"start": 1717.63, "end": 1719.53, "word": " على", "probability": 0.8115234375}, {"start": 1719.53, "end": 1720.01, "word": " B", "probability": 0.7861328125}, {"start": 1720.01, "end": 1720.57, "word": " I", "probability": 0.9638671875}, {"start": 1720.57, "end": 1721.67, "word": " ناقص", "probability": 0.884521484375}, {"start": 1721.67, "end": 1722.33, "word": " واحد", "probability": 0.978271484375}, {"start": 1722.33, "end": 1723.29, "word": " I", "probability": 0.88525390625}, {"start": 1723.29, "end": 1723.55, "word": " من", "probability": 0.98486328125}, {"start": 1723.55, "end": 1723.87, "word": " عند", "probability": 0.98681640625}, {"start": 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قال let f of d بسوة five of d and problem تلاتة ستة اتنين where five is multiplicative", "tokens": [271, 17596, 1166, 34105, 4724, 3794, 4724, 7435, 25513, 3660, 16712, 9566, 21292, 4587, 13672, 1829, 50239, 718, 283, 295, 274, 4724, 3794, 2407, 3660, 1732, 295, 274, 293, 1154, 6055, 1211, 9307, 3660, 8608, 2655, 3660, 1975, 2655, 1863, 9957, 689, 1732, 307, 17596, 1166], "avg_logprob": -0.27659573707174745, "compression_ratio": 1.3153846153846154, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2089.21, "end": 2089.73, "word": "is", "probability": 0.62646484375}, {"start": 2089.73, "end": 2091.41, "word": " multiplicative", "probability": 0.856201171875}, {"start": 2091.41, "end": 2091.67, "word": " هنا", "probability": 0.2186279296875}, {"start": 2091.67, "end": 2091.95, "word": " بس", "probability": 0.819091796875}, {"start": 2091.95, "end": 2092.33, "word": " بجربة", "probability": 0.636077880859375}, {"start": 2092.33, "end": 2092.95, "word": " التطبيق", 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0.7744140625}, {"start": 2103.07, "end": 2106.01, "word": " تلاتة", "probability": 0.83734130859375}, {"start": 2106.01, "end": 2110.13, "word": " ستة", "probability": 0.9060872395833334}, {"start": 2110.13, "end": 2110.81, "word": " اتنين", "probability": 0.9559326171875}, {"start": 2110.81, "end": 2113.93, "word": " where", "probability": 0.81298828125}, {"start": 2113.93, "end": 2115.73, "word": " five", "probability": 0.693359375}, {"start": 2115.73, "end": 2116.41, "word": " is", "probability": 0.9482421875}, {"start": 2116.41, "end": 2117.93, "word": " multiplicative", "probability": 0.91650390625}], "temperature": 1.0}, {"id": 83, "seek": 214580, "start": 2119.3, "end": 2145.8, "text": "to get أو we get مالي summation mu of d phi of d دي بتكسب الان بساوي عبارة عن واحد ناقص phi of b واحد لعند واحد ناقص phi of br ويساوي واحد ناقص", "tokens": [1353, 483, 34051, 321, 483, 3714, 6027, 1829, 28811, 2992, 295, 274, 13107, 295, 274, 11778, 1829, 39894, 4117, 35457, 2423, 7649, 4724, 3794, 995, 45865, 6225, 3555, 9640, 3660, 18871, 36764, 24401, 8717, 995, 4587, 9381, 13107, 295, 272, 36764, 24401, 5296, 3615, 41260, 36764, 24401, 8717, 995, 4587, 9381, 13107, 295, 738, 4032, 1829, 3794, 995, 45865, 36764, 24401, 8717, 995, 4587, 9381], "avg_logprob": -0.3025568276643753, "compression_ratio": 1.5909090909090908, "no_speech_prob": 0.0, "words": [{"start": 2119.3, "end": 2119.54, "word": "to", "probability": 0.7119140625}, {"start": 2119.54, "end": 2120.14, "word": " get", "probability": 0.95751953125}, {"start": 2120.14, "end": 2121.4, "word": " أو", "probability": 0.5751953125}, {"start": 2121.4, "end": 2121.66, "word": " we", "probability": 0.61376953125}, {"start": 2121.66, "end": 2122.46, "word": " get", "probability": 0.9599609375}, {"start": 2122.46, "end": 2124.12, "word": " مالي", "probability": 0.7853190104166666}, {"start": 2124.12, "end": 2125.56, "word": " summation", "probability": 0.2022705078125}, {"start": 2125.56, "end": 2126.72, "word": " mu", "probability": 0.1474609375}, {"start": 2126.72, "end": 2127.02, "word": " of", "probability": 0.865234375}, {"start": 2127.02, "end": 2127.4, "word": " d", "probability": 0.53759765625}, {"start": 2127.4, "end": 2127.84, "word": " phi", "probability": 0.08746337890625}, {"start": 2127.84, "end": 2128.08, "word": " of", "probability": 0.9716796875}, {"start": 2128.08, "end": 2128.54, "word": " d", "probability": 0.908203125}, {"start": 2128.54, "end": 2129.62, "word": " دي", "probability": 0.558135986328125}, {"start": 2129.62, "end": 2130.06, "word": " بتكسب", "probability": 0.556640625}, {"start": 2130.06, "end": 2130.46, "word": " الان", "probability": 0.64697265625}, {"start": 2130.46, "end": 2131.12, "word": " بساوي", "probability": 0.869384765625}, {"start": 2131.12, "end": 2132.82, "word": " عبارة", "probability": 0.9873046875}, {"start": 2132.82, "end": 2133.14, "word": " عن", "probability": 0.99267578125}, {"start": 2133.14, "end": 2134.02, "word": " واحد", "probability": 0.987060546875}, {"start": 2134.02, "end": 2134.8, "word": " ناقص", "probability": 0.8544921875}, {"start": 2134.8, "end": 2135.24, "word": " phi", "probability": 0.496337890625}, {"start": 2135.24, "end": 2135.64, "word": " of", "probability": 0.9482421875}, {"start": 2135.64, "end": 2136.08, "word": " b", "probability": 0.7431640625}, {"start": 2136.08, "end": 2137.46, "word": " واحد", "probability": 0.952392578125}, {"start": 2137.46, "end": 2138.54, "word": " لعند", "probability": 0.90673828125}, {"start": 2138.54, "end": 2139.66, "word": " واحد", "probability": 0.99169921875}, {"start": 2139.66, "end": 2140.16, "word": " ناقص", "probability": 0.9930419921875}, {"start": 2140.16, "end": 2140.64, "word": " phi", "probability": 0.75341796875}, {"start": 2140.64, "end": 2141.08, "word": " of", "probability": 0.97314453125}, {"start": 2141.08, "end": 2142.62, "word": " br", "probability": 0.6181640625}, {"start": 2142.62, "end": 2144.22, "word": " ويساوي", "probability": 0.6953125}, {"start": 2144.22, "end": 2145.22, "word": " واحد", "probability": 0.93505859375}, {"start": 2145.22, "end": 2145.8, "word": " ناقص", "probability": 0.993408203125}], "temperature": 1.0}, {"id": 84, "seek": 216413, "start": 2146.25, "end": 2164.13, "text": "5 بواحد ايش بتساوي بواحد الزبران بواحد ناقص واحد صح لما اصل عند واحد ناقص واحد ناقص بار أي ساوي", "tokens": [20, 4724, 14407, 24401, 1975, 1829, 8592, 39894, 3794, 995, 45865, 4724, 14407, 24401, 2423, 11622, 26890, 7649, 4724, 14407, 24401, 8717, 995, 4587, 9381, 36764, 24401, 20328, 5016, 5296, 15042, 1975, 36520, 43242, 36764, 24401, 8717, 995, 4587, 9381, 36764, 24401, 8717, 995, 4587, 9381, 4724, 9640, 36632, 8608, 995, 45865], "avg_logprob": -0.27432192046687287, "compression_ratio": 1.7346938775510203, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 2146.25, "end": 2146.63, "word": "5", "probability": 0.460693359375}, {"start": 2146.63, "end": 2147.15, "word": " بواحد", "probability": 0.4872639973958333}, {"start": 2147.15, "end": 2147.31, "word": " ايش", "probability": 0.5033365885416666}, {"start": 2147.31, "end": 2147.93, "word": " بتساوي", "probability": 0.93798828125}, {"start": 2147.93, "end": 2149.01, "word": " بواحد", "probability": 0.9529622395833334}, {"start": 2149.01, "end": 2149.61, "word": " الزبران", "probability": 0.580108642578125}, {"start": 2149.61, "end": 2150.93, "word": " بواحد", "probability": 0.9436848958333334}, {"start": 2150.93, "end": 2151.59, "word": " ناقص", "probability": 0.94921875}, {"start": 2151.59, "end": 2152.23, "word": " واحد", "probability": 0.979736328125}, {"start": 2152.23, "end": 2153.91, "word": " صح", "probability": 0.931884765625}, {"start": 2153.91, "end": 2157.83, "word": " لما", "probability": 0.79638671875}, {"start": 2157.83, "end": 2158.21, "word": " اصل", "probability": 0.875244140625}, {"start": 2158.21, "end": 2158.55, "word": " عند", "probability": 0.9814453125}, {"start": 2158.55, "end": 2158.97, "word": " واحد", "probability": 0.993408203125}, {"start": 2158.97, "end": 2159.77, "word": " ناقص", "probability": 0.994873046875}, {"start": 2159.77, "end": 2161.09, "word": " واحد", "probability": 0.944091796875}, {"start": 2161.09, "end": 2161.61, "word": " ناقص", "probability": 0.9942626953125}, {"start": 2161.61, "end": 2162.43, "word": " بار", "probability": 0.4918212890625}, {"start": 2162.43, "end": 2163.55, "word": " أي", "probability": 0.564453125}, {"start": 2163.55, "end": 2164.13, "word": " ساوي", "probability": 0.8888346354166666}], "temperature": 1.0}, {"id": 85, "seek": 219565, "start": 2165.99, "end": 2195.65, "text": "احد نقص بي زائد بيصير اتنين نقص بي واحد لما اصل عند اتنين نقص بي احد مجرد تطبيق مباشر نجي للشؤال بي .. بي بي اش بي بيقول بي بيقول ما يلي summation summation phi of D في D D بتقسم ال N", "tokens": [995, 24401, 8717, 4587, 9381, 4724, 1829, 30767, 16373, 3215, 4724, 1829, 9381, 13546, 1975, 2655, 1863, 9957, 8717, 4587, 9381, 4724, 1829, 36764, 24401, 5296, 15042, 1975, 36520, 43242, 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224185, "start": 2226.37, "end": 2241.85, "text": "إنه عندي الـ Phi is multiplicative و ال identity function multiplicative إذا D في Phi of D أشمالها is multiplicative بناء عليه لأن since اللي هو N في Phi of N", "tokens": [28814, 1863, 3224, 18871, 16254, 2423, 39184, 41435, 307, 17596, 1166, 4032, 2423, 6575, 2445, 17596, 1166, 11933, 15730, 413, 8978, 41435, 295, 413, 5551, 8592, 2304, 6027, 11296, 307, 17596, 1166, 44945, 16606, 47356, 5296, 33456, 1670, 13672, 1829, 31439, 426, 8978, 41435, 295, 426], "avg_logprob": -0.30535240376249273, "compression_ratio": 1.3835616438356164, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2226.37, "end": 2226.91, "word": "إنه", "probability": 0.3854777018229167}, {"start": 2226.91, "end": 2227.55, "word": " عندي", "probability": 0.7197265625}, {"start": 2227.55, "end": 2228.21, "word": " الـ", "probability": 0.753662109375}, {"start": 2228.21, "end": 2228.55, "word": " Phi", "probability": 0.252685546875}, {"start": 2228.55, "end": 2228.77, "word": " is", "probability": 0.7158203125}, {"start": 2228.77, "end": 2229.53, "word": " multiplicative", "probability": 0.926513671875}, {"start": 2229.53, "end": 2229.67, "word": " و", "probability": 0.42578125}, {"start": 2229.67, "end": 2229.75, "word": " ال", "probability": 0.90478515625}, {"start": 2229.75, "end": 2230.13, "word": " identity", "probability": 0.525390625}, {"start": 2230.13, "end": 2230.55, "word": " function", "probability": 0.91162109375}, {"start": 2230.55, "end": 2231.51, "word": " multiplicative", "probability": 0.740478515625}, {"start": 2231.51, "end": 2232.21, "word": " إذا", "probability": 0.73388671875}, {"start": 2232.21, "end": 2232.43, "word": " D", "probability": 0.52783203125}, {"start": 2232.43, "end": 2232.57, "word": " في", "probability": 0.84521484375}, {"start": 2232.57, "end": 2232.79, "word": " Phi", "probability": 0.88037109375}, {"start": 2232.79, "end": 2232.95, "word": " of", "probability": 0.80615234375}, {"start": 2232.95, 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ميالي if n أو for a square free integer for a square free integer n أكبر من واحد show that", "tokens": [3615, 1863, 16254, 8608, 33604, 6027, 46811, 7649, 10632, 4724, 1829, 39648, 3714, 1829, 6027, 1829, 498, 297, 34051, 337, 257, 3732, 1737, 24922, 337, 257, 3732, 1737, 24922, 297, 5551, 4117, 26890, 9154, 36764, 24401, 855, 300], "avg_logprob": -0.23157051511299917, "compression_ratio": 1.2735042735042734, "no_speech_prob": 0.0, "words": [{"start": 2970.1, "end": 2970.46, "word": "عندي", "probability": 0.7355143229166666}, {"start": 2970.46, "end": 2970.72, "word": " سؤال", "probability": 0.8990885416666666}, {"start": 2970.72, "end": 2971.14, "word": " تمانية", "probability": 0.9007161458333334}, {"start": 2971.14, "end": 2971.42, "word": " بيقول", "probability": 0.8037109375}, {"start": 2971.42, "end": 2972.06, "word": " ميالي", "probability": 0.6513671875}, {"start": 2972.06, "end": 2975.66, "word": " if", "probability": 0.469482421875}, {"start": 2975.66, "end": 2976.16, "word": 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if", "probability": 0.69189453125}, {"start": 3015.99, "end": 3017.09, "word": " N", "probability": 0.83544921875}, {"start": 3017.09, "end": 3017.57, "word": " بتساوي", "probability": 0.9613037109375}, {"start": 3017.57, "end": 3018.29, "word": " تلاتة", "probability": 0.9586181640625}, {"start": 3018.29, "end": 3019.31, "word": " then", "probability": 0.74365234375}, {"start": 3019.31, "end": 3020.69, "word": " Tau", "probability": 0.739990234375}, {"start": 3020.69, "end": 3021.33, "word": " of", "probability": 0.958984375}, {"start": 3021.33, "end": 3021.77, "word": " N", "probability": 0.9462890625}, {"start": 3021.77, "end": 3022.27, "word": " تربيع", "probability": 0.927734375}, {"start": 3022.27, "end": 3022.49, "word": " يعني", "probability": 0.768798828125}, {"start": 3022.49, "end": 3022.89, "word": " تلاتة", "probability": 0.96875}, {"start": 3022.89, "end": 3023.39, "word": " تربيع", "probability": 0.931884765625}, {"start": 3023.39, "end": 3023.95, "word": " بساوي", "probability": 0.950927734375}, {"start": 3023.95, "end": 3024.77, "word": " اللي", "probability": 0.924072265625}, {"start": 3024.77, "end": 3024.89, "word": " هو", "probability": 0.96044921875}, {"start": 3024.89, "end": 3025.19, "word": " بتعرف", "probability": 0.9462890625}, {"start": 3025.19, "end": 3025.41, "word": " كيف", "probability": 0.73046875}, {"start": 3025.41, "end": 3025.67, "word": " نوجد", "probability": 0.8748372395833334}, {"start": 3025.67, "end": 3026.01, "word": " Tau", "probability": 0.799560546875}, {"start": 3026.01, "end": 3026.33, "word": " of", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 116, "seek": 305528, "start": 3027.34, "end": 3055.28, "text": "Tau of B أُس Alpha بساوي اللي هو Alpha ثائد واحد عدد ال divisors دمية لل B Alpha بيصير عندي Tau تلاتة تربيع عيش بساوي اتنين زائد واحد ويساوي تلاتة اذا واضح انه في حالة الان بتساوي تلاتة Tau of N تربيع بساوي الان conversely conversely", "tokens": [51, 1459, 295, 363, 5551, 10859, 3794, 20588, 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3041.88, "word": " زائد", "probability": 0.8792317708333334}, {"start": 3041.88, "end": 3042.46, "word": " واحد", "probability": 0.984619140625}, {"start": 3042.46, "end": 3043.34, "word": " ويساوي", "probability": 0.88408203125}, {"start": 3043.34, "end": 3044.16, "word": " تلاتة", "probability": 0.972412109375}, {"start": 3044.16, "end": 3044.88, "word": " اذا", "probability": 0.56756591796875}, {"start": 3044.88, "end": 3045.98, "word": " واضح", "probability": 0.9650065104166666}, {"start": 3045.98, "end": 3046.32, "word": " انه", "probability": 0.875732421875}, {"start": 3046.32, "end": 3046.42, "word": " في", "probability": 0.91015625}, {"start": 3046.42, "end": 3046.76, "word": " حالة", "probability": 0.9788411458333334}, {"start": 3046.76, "end": 3047.0, "word": " الان", "probability": 0.609619140625}, {"start": 3047.0, "end": 3047.48, "word": " بتساوي", "probability": 0.95654296875}, {"start": 3047.48, "end": 3048.2, "word": " تلاتة", "probability": 0.98681640625}, {"start": 3048.2, "end": 3048.98, "word": " Tau", "probability": 0.84326171875}, {"start": 3048.98, "end": 3049.34, "word": " of", "probability": 0.904296875}, {"start": 3049.34, "end": 3049.68, "word": " N", "probability": 0.2529296875}, {"start": 3049.68, "end": 3050.3, "word": " تربيع", "probability": 0.9293212890625}, {"start": 3050.3, "end": 3050.96, "word": " بساوي", "probability": 0.94384765625}, {"start": 3050.96, "end": 3051.98, "word": " الان", "probability": 0.83642578125}, {"start": 3051.98, "end": 3053.42, "word": " conversely", "probability": 0.60614013671875}, {"start": 3053.42, "end": 3055.28, "word": " conversely", "probability": 0.86279296875}], "temperature": 1.0}, {"id": 117, "seek": 308384, "start": 3058.18, "end": 3083.84, "text": "Suppose that Tau of N تربيع بساوي N باشي لإن ما أعطيك ال N إيه اشمله three three او square three integer لإن since N أكبر من واحد is square او the square three integer", "tokens": [50, 10504, 541, 300, 314, 1459, 295, 426, 6055, 2288, 21292, 3615, 4724, 3794, 995, 45865, 426, 4724, 33599, 1829, 5296, 28814, 1863, 19446, 5551, 3615, 9566, 1829, 4117, 2423, 426, 11933, 1829, 3224, 1975, 8592, 42213, 3224, 1045, 1045, 1975, 2407, 3732, 1045, 24922, 5296, 28814, 1863, 1670, 426, 5551, 4117, 26890, 9154, 36764, 24401, 307, 3732, 1975, 2407, 264, 3732, 1045, 24922], "avg_logprob": -0.3858173076923077, "compression_ratio": 1.4155844155844155, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 3058.1800000000003, "end": 3059.3, "word": "Suppose", "probability": 0.6521199544270834}, {"start": 3059.3, "end": 3060.42, "word": " that", "probability": 0.7265625}, {"start": 3060.42, "end": 3061.86, "word": " Tau", "probability": 0.42626953125}, {"start": 3061.86, "end": 3061.98, "word": " of", "probability": 0.6923828125}, {"start": 3061.98, "end": 3062.26, "word": " N", "probability": 0.85107421875}, {"start": 3062.26, "end": 3063.02, "word": " تربيع", "probability": 0.8819580078125}, {"start": 3063.02, "end": 3063.56, "word": " بساوي", "probability": 0.58538818359375}, {"start": 3063.56, "end": 3064.04, "word": " N", "probability": 0.880859375}, {"start": 3064.04, "end": 3065.46, "word": " باشي", "probability": 0.5717366536458334}, {"start": 3065.46, "end": 3066.24, "word": " لإن", "probability": 0.701904296875}, {"start": 3066.24, "end": 3066.32, "word": " ما", "probability": 0.86962890625}, {"start": 3066.32, "end": 3066.66, "word": " أعطيك", "probability": 0.9302734375}, {"start": 3066.66, "end": 3066.8, "word": " ال", "probability": 0.90771484375}, {"start": 3066.8, "end": 3066.96, "word": " N", "probability": 0.50634765625}, {"start": 3066.96, "end": 3067.16, "word": " إيه", "probability": 0.796875}, {"start": 3067.16, "end": 3067.72, "word": " اشمله", "probability": 0.64776611328125}, {"start": 3067.72, "end": 3068.56, "word": " three", "probability": 0.1212158203125}, {"start": 3068.56, "end": 3069.22, "word": " three", "probability": 0.41064453125}, {"start": 3069.22, "end": 3069.92, "word": " او", "probability": 0.7401123046875}, {"start": 3069.92, "end": 3070.26, "word": " square", "probability": 0.5810546875}, {"start": 3070.26, "end": 3070.68, "word": " three", "probability": 0.84814453125}, {"start": 3070.68, "end": 3071.32, "word": " integer", "probability": 0.83203125}, {"start": 3071.32, "end": 3072.16, "word": " لإن", "probability": 0.9208984375}, {"start": 3072.16, "end": 3072.7, "word": " since", "probability": 0.57421875}, {"start": 3072.7, "end": 3074.7, "word": " N", "probability": 0.8173828125}, {"start": 3074.7, "end": 3075.1, "word": " أكبر", "probability": 0.9298502604166666}, {"start": 3075.1, "end": 3075.24, "word": " من", "probability": 0.990234375}, {"start": 3075.24, "end": 3075.68, "word": " واحد", "probability": 0.931640625}, {"start": 3075.68, "end": 3076.1, "word": " is", "probability": 0.88916015625}, {"start": 3076.1, "end": 3077.72, "word": " square", "probability": 0.447509765625}, {"start": 3077.72, "end": 3079.36, "word": " او", "probability": 0.62744140625}, {"start": 3079.36, "end": 3079.56, "word": " the", "probability": 0.50048828125}, {"start": 3079.56, "end": 3080.24, "word": " square", "probability": 0.84521484375}, {"start": 3080.24, "end": 3081.08, "word": " three", "probability": 0.86962890625}, {"start": 3081.08, "end": 3083.84, "word": " integer", "probability": 0.873046875}], "temperature": 1.0}, {"id": 118, "seek": 310709, "start": 3085.25, "end": 3107.09, "text": "إذا مافيش فيه أي مربع كامل، then N can be written as B1 لعندي R where B1 لعندي R are distinct primes لأنه في Ray Square", "tokens": [28814, 15730, 19446, 41185, 8592, 8978, 3224, 36632, 3714, 25513, 3615, 9122, 10943, 1211, 12399, 550, 426, 393, 312, 3720, 382, 363, 16, 5296, 3615, 1863, 16254, 497, 689, 363, 16, 5296, 3615, 1863, 16254, 497, 366, 10644, 582, 1532, 5296, 33456, 3224, 8978, 10883, 16463], "avg_logprob": -0.33128325228995464, "compression_ratio": 1.162962962962963, "no_speech_prob": 0.0, "words": [{"start": 3085.25, "end": 3085.59, "word": "إذا", "probability": 0.873046875}, {"start": 3085.59, "end": 3085.99, "word": " مافيش", "probability": 0.8483072916666666}, {"start": 3085.99, "end": 3086.27, "word": " فيه", "probability": 0.8798828125}, {"start": 3086.27, "end": 3086.43, "word": " أي", "probability": 0.80712890625}, {"start": 3086.43, "end": 3086.87, "word": " مربع", "probability": 0.900390625}, {"start": 3086.87, "end": 3087.93, "word": " كامل،", "probability": 0.862548828125}, {"start": 3087.93, "end": 3088.27, "word": " then", "probability": 0.52294921875}, {"start": 3088.27, "end": 3088.61, "word": " N", "probability": 0.1259765625}, {"start": 3088.61, "end": 3088.97, "word": " can", "probability": 0.931640625}, {"start": 3088.97, "end": 3089.27, "word": " be", "probability": 0.9521484375}, {"start": 3089.27, "end": 3089.71, "word": " written", "probability": 0.9208984375}, {"start": 3089.71, "end": 3090.51, "word": " as", "probability": 0.96240234375}, {"start": 3090.51, "end": 3091.81, "word": " B1", "probability": 0.5377197265625}, {"start": 3091.81, "end": 3092.81, "word": " لعندي", "probability": 0.58673095703125}, {"start": 3092.81, "end": 3093.49, "word": " R", "probability": 0.4560546875}, {"start": 3093.49, "end": 3094.75, "word": " where", "probability": 0.634765625}, {"start": 3094.75, "end": 3095.97, "word": " B1", "probability": 0.96923828125}, {"start": 3095.97, "end": 3096.53, "word": " لعندي", "probability": 0.9561767578125}, {"start": 3096.53, "end": 3097.29, "word": " R", "probability": 0.97998046875}, {"start": 3097.29, "end": 3099.05, "word": " are", "probability": 0.86328125}, {"start": 3099.05, "end": 3102.31, "word": " distinct", "probability": 0.93212890625}, {"start": 3102.31, "end": 3104.35, "word": " primes", "probability": 0.656982421875}, {"start": 3104.35, "end": 3105.93, "word": " لأنه", "probability": 0.6517740885416666}, {"start": 3105.93, "end": 3106.03, "word": " في", "probability": 0.81982421875}, {"start": 3106.03, "end": 3106.31, "word": " Ray", "probability": 0.47509765625}, {"start": 3106.31, "end": 3107.09, "word": " Square", "probability": 0.22705078125}], "temperature": 1.0}, {"id": 119, "seek": 313698, "start": 3108.22, "end": 3136.98, "text": "أو square free مافيش فيه أي مربع كامل يعني مانعته أنه الأسس اللي عندي هنا بس واحد وال بي لعند واحد لعند ال بي ار اللي هو distinct primes هذا يعني then tau of n تربيع معطيني ايه ايه ايش بيساوي n تساوي tau of n تربيع هذا مقطع مين ال n", "tokens": [10721, 2407, 3732, 1737, 19446, 41185, 8592, 8978, 3224, 36632, 3714, 25513, 3615, 9122, 10943, 1211, 37495, 22653, 3714, 7649, 34268, 3224, 14739, 3224, 16247, 3794, 3794, 13672, 1829, 18871, 16254, 34105, 4724, 3794, 36764, 24401, 16070, 4724, 1829, 5296, 3615, 41260, 36764, 24401, 5296, 3615, 41260, 2423, 4724, 1829, 1975, 2288, 13672, 1829, 31439, 10644, 2886, 279, 23758, 37495, 22653, 550, 17842, 295, 297, 6055, 2288, 21292, 3615, 20449, 9566, 9957, 1829, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 8592, 4724, 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0.295654296875}, {"start": 3124.12, "end": 3124.34, "word": " of", "probability": 0.951171875}, {"start": 3124.34, "end": 3124.6, "word": " n", "probability": 0.64697265625}, {"start": 3124.6, "end": 3127.1, "word": " تربيع", "probability": 0.8885498046875}, {"start": 3127.1, "end": 3128.08, "word": " معطيني", "probability": 0.7010498046875}, {"start": 3128.08, "end": 3128.26, "word": " ايه", "probability": 0.774169921875}, {"start": 3128.26, "end": 3128.4, "word": " ايه", "probability": 0.73486328125}, {"start": 3128.4, "end": 3128.5, "word": " ايش", "probability": 0.5459391276041666}, {"start": 3128.5, "end": 3129.06, "word": " بيساوي", "probability": 0.7953125}, {"start": 3129.06, "end": 3129.98, "word": " n", "probability": 0.3720703125}, {"start": 3129.98, "end": 3130.92, "word": " تساوي", "probability": 0.88037109375}, {"start": 3130.92, "end": 3132.54, "word": " tau", "probability": 0.4208984375}, {"start": 3132.54, "end": 3133.26, "word": " of", "probability": 0.974609375}, 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316894, "start": 3165.26, "end": 3168.94, "text": "Times انها تبدأ من واحد لآخر", "tokens": [51, 1532, 16472, 11296, 6055, 44510, 10721, 9154, 36764, 24401, 5296, 148, 95, 34740], "avg_logprob": -0.5833333333333334, "compression_ratio": 0.8070175438596491, "no_speech_prob": 0.0, "words": [{"start": 3165.26, "end": 3166.14, "word": "Times", "probability": 0.5928955078125}, {"start": 3166.14, "end": 3166.86, "word": " انها", "probability": 0.2137451171875}, {"start": 3166.86, "end": 3167.3, "word": " تبدأ", "probability": 0.90234375}, {"start": 3167.3, "end": 3167.34, "word": " من", "probability": 0.79931640625}, {"start": 3167.34, "end": 3167.92, "word": " واحد", "probability": 0.6883544921875}, {"start": 3167.92, "end": 3168.94, "word": " لآخر", "probability": 0.7031707763671875}], "temperature": 1.0}, {"id": 122, "seek": 319821, "start": 3169.43, "end": 3198.21, "text": "إذاً هذا بيساوي تلاتة مكررة R من الميوات إذاً تلاتة قص إيش قص R إذا صار عندي بي واحد بي اتنين عند بي R إيش بتساوي 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0.8507486979166666}, {"start": 3451.84, "end": 3452.34, "word": " عليكم", "probability": 0.970458984375}, {"start": 3452.34, "end": 3452.86, "word": " ورحمة", "probability": 0.9857177734375}, {"start": 3452.86, "end": 3453.24, "word": " الله", "probability": 0.9716796875}, {"start": 3453.24, "end": 3454.08, "word": " وبركاته", "probability": 0.95439453125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3456.3599375, "duration_after_vad": 3229.3012499999886}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5797fPCm51A_postprocess.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5797fPCm51A_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ce190c9369ac6c78794247cca9ce62d26baf29a8
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5797fPCm51A_postprocess.srt
@@ -0,0 +1,1752 @@
+1
+00:00:19,350 --> 00:00:23,970
+بسم الله الرحمن الرحيم المحاضرة بعنوان special
+
+2
+00:00:23,970 --> 00:00:26,950
+divisibility test binary and decimal
+
+3
+00:00:26,950 --> 00:00:30,890
+representation وهي عبارة عن تطبيقات على ال
+
+4
+00:00:30,890 --> 00:00:34,590
+congruences أو استغلال معلومات ال congruences
+
+5
+00:00:34,590 --> 00:00:40,190
+للدخول لأنظمة العد المختلفة نظام العد التحت اللي
+
+6
+00:00:40,190 --> 00:00:44,570
+هو بأساس بيه بصورة عامة هنحكي عن اللي هو ان أسس
+
+7
+00:00:44,570 --> 00:00:46,110
+لأنظمة العد
+
+8
+00:00:48,990 --> 00:00:56,870
+هذه المحاضرة هي محاضرة في مساق نظرية الأعداد لطلبة
+
+9
+00:00:56,870 --> 00:01:01,190
+قسم الرياضيات بالجامعة الإسلامية لكليتي العلوم
+
+10
+00:01:01,190 --> 00:01:06,650
+والتربية للحديث
+
+11
+00:01:06,650 --> 00:01:11,770
+عن النظرية خلينا في البداية ناخد بعض الأمثلة
+
+12
+00:01:13,170 --> 00:01:16,810
+العملية التحويل أو اللي هو التحويل من النظام
+
+13
+00:01:16,810 --> 00:01:21,870
+العشري إلى أنظمة أخرى والعكس ال .. ال .. الهدف من
+
+14
+00:01:21,870 --> 00:01:26,470
+اللي .. من اللي بدي أحكيه بدي أعطيك الطريقة اللي
+
+15
+00:01:26,470 --> 00:01:31,030
+أصلا إحنا اللي هو استخدمناها في البرهان وكأنه
+
+16
+00:01:31,030 --> 00:01:33,470
+طريقة التحويل اللي بنستخدمها و بتستخدموها و
+
+17
+00:01:33,470 --> 00:01:36,550
+بتعلموها للطلاب في المدارس هي في النهاية طريقة
+
+18
+00:01:36,550 --> 00:01:42,930
+للمستقام برهان النظرية شوف كيفلو أجيبنا له الرقم
+
+19
+00:01:42,930 --> 00:01:49,770
+مثلا عبارة عن 32 و بدنا اللي هو نحوله من النظام
+
+20
+00:01:49,770 --> 00:01:57,830
+العشري هذا إلى نظام العد الثلاث مثلا إيش بسوي باجي
+
+21
+00:01:57,830 --> 00:02:06,790
+بجسم 32 على 3 الآن 32 على 3 أكيد كلكم هيقول 3 في
+
+22
+00:02:06,790 --> 00:02:13,510
+10 والمتبقى جديش 2طبعاً عليكم السلام المتبقى إيش
+
+23
+00:02:13,510 --> 00:02:18,050
+هو المتبقى مادة بقسمها ثلاثة يا هيكون سفر يا هيكون
+
+24
+00:02:18,050 --> 00:02:21,950
+واحد يا هيكونين يعني الأعداد المستعملة اللي
+
+25
+00:02:21,950 --> 00:02:26,010
+هستعملها في نظام العد السلاتي هتكون تلات أعداد يا
+
+26
+00:02:26,010 --> 00:02:30,330
+سفر يا واحد يا اتنين وكل واحد انه منزلة ماشي الحال
+
+27
+00:02:30,330 --> 00:02:38,750
+الآن العشرة اللي طلعت عندي هذهبرضه أكثر من ثلاثة
+
+28
+00:02:38,750 --> 00:02:42,690
+إذا أقل من ثلاثة يعني بمعنى أخر من صفر لواحد
+
+29
+00:02:42,690 --> 00:02:46,970
+واثنين بكون خلصته بكون اللي هو العدد الأول اللي هو
+
+30
+00:02:46,970 --> 00:02:50,830
+وابنه ثابت اللي هو مقابل زي رقم الأحد عندنا في
+
+31
+00:02:50,830 --> 00:02:55,730
+العد العشري وهذا مقابل اللي هو رقم العشرات في العد
+
+32
+00:02:55,730 --> 00:03:00,610
+العشري لكن العشرة أكبر من التلاتة إذا برد أجسم
+
+33
+00:03:00,610 --> 00:03:06,430
+بصير عبارة عن تلاتة في جسمت العشرة عالمين ع تلاتة
+
+34
+00:03:06,840 --> 00:03:13,300
+العشرة بيصير تلاتة في تلاتة زائد نين زائد واحد،
+
+35
+00:03:13,300 --> 00:03:18,420
+الكل زائد نين زائد اتنين، مظبوط اللي عملته؟ طيب،
+
+36
+00:03:18,420 --> 00:03:25,420
+ويساوي، الآن الأمور جهزة عندي بيصير عبارة عن تلاتة
+
+37
+00:03:25,420 --> 00:03:33,020
+تكعيب في واحد، مظبوط؟ دخلت التلاتة، زائد تلاتة في
+
+38
+00:03:33,020 --> 00:03:39,370
+واحد زائد نين اتنينفهذا هيكون مين هو هو عبارة عن
+
+39
+00:03:39,370 --> 00:03:45,910
+العدد اللي الخانة الأولى له 2 بالنسبة للنظام العدد
+
+40
+00:03:45,910 --> 00:03:54,770
+أو للأساس تلاتة اتنين وانا واحد الآن تربيع في
+
+41
+00:03:54,770 --> 00:03:58,450
+الشيء إذا سفر في تربيع في تلاتة تربيع يعني بيصير
+
+42
+00:03:58,450 --> 00:04:04,980
+عند هذا سفر وهذا برجعش بساوي بساوي واحد طيبالان لو
+
+43
+00:04:04,980 --> 00:04:11,460
+كان في عندي العدد واحد اتنين تلاتة في نظام العد
+
+44
+00:04:11,460 --> 00:04:17,200
+مثلا نيل الخماسي بدي احوله لنظام العد عشري
+
+45
+00:04:20,350 --> 00:04:27,870
+بساوى و عبارة عن تلاتة في واحد و اتنين .. تلاتة في
+
+46
+00:04:27,870 --> 00:04:32,730
+خمسة مش سفر و اتنين في خمسة و واحد في ايش في خمسة
+
+47
+00:04:32,730 --> 00:04:39,460
+تربيع معايا؟ اذا بيصير عندي واحد في خمسة تربيعوكان
+
+48
+00:04:39,460 --> 00:04:42,440
+هذا بمثابة خانة اللي هي الخانة التالتة اللي
+
+49
+00:04:42,440 --> 00:04:46,840
+بنسميها نقات في نين اللي هي العشر يعني عشرة قصت
+
+50
+00:04:46,840 --> 00:04:52,860
+اتنين هنا خمسة قصت اتنين مفهومها زائد اتنين في
+
+51
+00:04:52,860 --> 00:04:57,890
+خمسة زائد تلاتة في خمسة قصت صفر اللي هي تلاتةWhy
+
+52
+00:04:57,890 --> 00:05:04,310
+7؟ لأن هذه بيصير 25 وهذه 10 وهذه 3 بيصير عبارة عن
+
+53
+00:05:04,310 --> 00:05:09,770
+35 يعني 38 38 هذا في النظام العد مين؟ الـ 10 طبعا
+
+54
+00:05:09,770 --> 00:05:12,650
+احنا ممكن نكتبش اللي هو 10 أساسا عشان نكون متعارف
+
+55
+00:05:12,650 --> 00:05:15,790
+عليه بيننا لأن احنا لما نكتب الأرقام العادية نقلت
+
+56
+00:05:15,790 --> 00:05:19,550
+ونكتبها في نظام العد العشرين
+
+57
+00:05:21,550 --> 00:05:27,650
+الان لو بدنا نحول هذه مثلا لنظام العد الرباعي على
+
+58
+00:05:27,650 --> 00:05:30,850
+سبيل المثال او الثلاثي او السباعي سينمي ذاكية او
+
+59
+00:05:30,850 --> 00:05:37,130
+السباعي خلينا ناخد اللي هو الـ 38 نحولها لنظام
+
+60
+00:05:37,130 --> 00:05:43,860
+العد اللي هو السباعيفبقسم هذا مين على سبعة عشان
+
+61
+00:05:43,860 --> 00:05:47,000
+أعطيك مختلف عالي فوق لأن تمنم تلاتين عالي سبعة
+
+62
+00:05:47,000 --> 00:05:53,820
+بيصير سبعة في خمسة زاد مين تلاتة هذه جاهزة السبعي
+
+63
+00:05:53,820 --> 00:05:58,240
+السبعي الخمسة أجال من السبعة ده خالص جوزت إذا صار
+
+64
+00:05:58,240 --> 00:06:04,120
+الرقم هذا مين هو عبارة عن خمسة تلاتة للأساس مين
+
+65
+00:06:04,120 --> 00:06:12,160
+سبعة واضح طيبهذا اللي هو عملية اللي هي التحويل من
+
+66
+00:06:12,160 --> 00:06:18,700
+نظام عد إلى نظام عد آخر الآن هذا النظام بدنا اللي
+
+67
+00:06:18,700 --> 00:06:24,040
+هو نحكي اللي هو النظرية تشرّعلنا لأنظمة العد أو
+
+68
+00:06:24,040 --> 00:06:29,780
+تأسسنا لأنظمة العد بشكل عام لأي أساس اسمه ياشر
+
+69
+00:06:29,780 --> 00:06:34,540
+اسمه بيه الآن النظرية بتقول التالت
+
+70
+00:06:42,370 --> 00:06:49,010
+كان عندى لان تلاتة تربيع تكعيب وماكانش فيه تلاتة
+
+71
+00:06:49,010 --> 00:06:53,630
+تربيع بالمرة اه فالتلاتة تربيع ايش معناته هذه
+
+72
+00:06:53,630 --> 00:06:59,750
+تلاتة تكعيب في واحد زائد تلاتة تربيع في سفر زائد
+
+73
+00:06:59,750 --> 00:07:04,190
+تلاتة في واحد زائد اتنين في تلاتة اقل سفر فبيصير
+
+74
+00:07:04,190 --> 00:07:07,570
+هذه الخانة الأولى وهذه الخانة التانية وهذه الخانة
+
+75
+00:07:07,570 --> 00:07:11,740
+التالتة وهذه الخانة الرابعةنسيان خانة معناته على
+
+76
+00:07:11,740 --> 00:07:15,300
+طول اللي بيجرب يفهم ان هذه خانة اللي هي اللي قُس 2
+
+77
+00:07:15,300 --> 00:07:19,760
+لكن هي في الواقع قُسمين ال .. ال .. ال .. الواحد
+
+78
+00:07:19,760 --> 00:07:23,740
+لو انت ما حطيتش هذه على طول اللي بيجرب يقول 2 1 1
+
+79
+00:07:23,740 --> 00:07:27,160
+معناته واحد مضروف تلت تربية لكن هي ايش معناه تلت
+
+80
+00:07:27,160 --> 00:07:29,900
+تقعيد فهي انا عشان هيك .. زي انا تكتب اللي هو رقم
+
+81
+00:07:29,900 --> 00:07:35,040
+ألف وواحد بنفعل جمع الـMachines فور ونحط واحد
+
+82
+00:07:35,040 --> 00:07:41,950
+واحد؟ لأ بيصير رقم تاني خالص ماشي الحالةالان نجلة
+
+83
+00:07:41,950 --> 00:07:48,130
+اللى هى النظرية تبعتنا اللى
+
+84
+00:07:48,130 --> 00:07:53,490
+بتحكى عن اللى هو أو بتأسس نظم التلعد بصورة عامة خد
+
+85
+00:07:53,490 --> 00:08:00,070
+بيه الان بيقولك let B theorem let B أكبر من واحد
+
+86
+00:08:00,070 --> 00:08:04,090
+هذا الأساس اللى بدكسم عليه let B أو بدك تكتب على
+
+87
+00:08:04,090 --> 00:08:08,390
+أساس والعدد let B أكبر من واحد النتجة
+
+88
+00:08:09,530 --> 00:08:20,250
+be an integer and an be any integer then an هذه
+
+89
+00:08:20,250 --> 00:08:29,830
+الان can be written as an بتساوي a note زائد a one
+
+90
+00:08:29,830 --> 00:08:41,200
+بي زائدA2 بي تربيع لما أصل لأخر واحد AM بيقص M
+
+91
+00:08:41,200 --> 00:08:47,560
+باشي الحالة where عندي
+
+92
+00:08:47,560 --> 00:08:57,580
+ال A note بديت A note عندي اذا ال A note و ال A1
+
+93
+00:08:57,580 --> 00:09:03,520
+عندي ال AM كل ميش نال هناموجودات بين الـ Zero
+
+94
+00:09:03,520 --> 00:09:08,600
+والواحد والاتنين اللي عندهم اللي هو الاساس اللي
+
+95
+00:09:08,600 --> 00:09:14,480
+بحكي عنه اللي هو مين هو بـ-1and this
+
+96
+00:09:14,480 --> 00:09:18,120
+representation اللي هو الان ايش ماله is unique
+
+97
+00:09:18,120 --> 00:09:24,640
+يعني على هذه الصورة بس في صورة واحدة للان على هذه
+
+98
+00:09:24,640 --> 00:09:27,440
+الصورة و .. و .. و .. و .. و .. و .. و .. و .. و
+
+99
+00:09:27,440 --> 00:09:27,760
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+100
+00:09:27,760 --> 00:09:28,300
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+101
+00:09:28,300 --> 00:09:29,340
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+102
+00:09:29,340 --> 00:09:30,520
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+103
+00:09:30,520 --> 00:09:31,660
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+104
+00:09:31,660 --> 00:09:34,220
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+105
+00:09:34,220 --> 00:09:35,180
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+106
+00:09:35,180 --> 00:09:36,180
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+107
+00:09:36,180 --> 00:09:41,600
+.. و .. و .. و .. ونكتبها بصورة ما اتفق عليها
+
+108
+00:09:41,600 --> 00:09:45,980
+والصورة اللي بنتفق عليها بنكون فاهمين ان الـ A
+
+109
+00:09:45,980 --> 00:09:50,240
+نقطة الأولى في B الصفر والـ A واحد اللي هي في B
+
+110
+00:09:50,240 --> 00:09:53,980
+والـ A اتنين في B تربيع والـ A M في B M وهذه
+
+111
+00:09:53,980 --> 00:09:56,720
+الصورة اللي بنتفق عليها والتي اتفقنا عليها قبل
+
+112
+00:09:56,720 --> 00:10:00,140
+بشوية حكينا عنها اللي هي صورة M بتساوي
+
+113
+00:10:03,410 --> 00:10:09,850
+A1 لعينك مصل لعينك مين؟ A M هذا للأساس مين؟ للأساس
+
+114
+00:10:09,850 --> 00:10:13,470
+B عادة وان حد ما نجرى العدد هذا بنقول هذا العدد
+
+115
+00:10:13,470 --> 00:10:17,230
+بالنسبة لمن؟ ل .. اللي هو الـ B مدامنا الـ B إذن
+
+116
+00:10:17,230 --> 00:10:22,090
+بنكتب على الصورة التالية Note في B الصفر One في B
+
+117
+00:10:22,090 --> 00:10:25,710
+زائد A one في B زائد A اتنين في B اتنين لمقاصة
+
+118
+00:10:25,710 --> 00:10:30,510
+لعينك A M في مين؟ في B أسامي هذا بنسميه نظام العد
+
+119
+00:10:30,510 --> 00:10:36,460
+للأساس Bطيب نيجي للبرهان البرهان اللي جيناها
+
+120
+00:10:36,460 --> 00:10:43,100
+بالظبط .. بالظبط هو .. هو كأنه algorithm ل .. اللي
+
+121
+00:10:43,100 --> 00:10:48,200
+هو تحويل العدد أو كتابة العدد على الصورة للأساس
+
+122
+00:10:48,200 --> 00:10:52,180
+المطلوب زي ما عملت قبل شوية بالظبط إيش اللي بقصده؟
+
+123
+00:10:52,180 --> 00:10:57,360
+بقصد ما هي الجروف بدي
+
+124
+00:10:57,360 --> 00:11:03,180
+أقول suppose thatاللي هو N هو اللي بدي أحكي عنه
+
+125
+00:11:03,180 --> 00:11:11,400
+يعني بدي أقول انه by division algorithm اقسمين D
+
+126
+00:11:11,400 --> 00:11:21,640
+على B there exist unique integers Q1 و A0 integers
+
+127
+00:11:21,640 --> 00:11:30,910
+such that ال N بتساويالـ Q1 ناتج القسمة في B
+
+128
+00:11:30,910 --> 00:11:37,350
+المقصوم عليه زاد المتبقى من A Not حيث طبيعي الـ A
+
+129
+00:11:37,350 --> 00:11:44,070
+Not ماله بين 0 و أصغر من B يعني A Not جاهز وين
+
+130
+00:11:44,070 --> 00:11:49,070
+موجود في الـ 6 اللي أنا بحكي عنها ماشي الحال طيب
+
+131
+00:11:49,070 --> 00:11:57,420
+إذا كان إذا Fالـ Q1 طلعت strictly أصغر من B خلصت
+
+132
+00:11:57,420 --> 00:12:02,360
+بكون حصرت الـ Q1 و الـ A0 بين السفر وبين الـ B
+
+133
+00:12:02,360 --> 00:12:09,920
+وصار العدد تلعي على صورة N بساوي A1 في B زي A0 زي
+
+134
+00:12:09,920 --> 00:12:13,700
+المثال قبل بشوية جسمنا على سبعة طلعني بس إياش جسم
+
+135
+00:12:13,700 --> 00:12:17,960
+واحدة وعلى طول طلعنا الرقمين مظبوط واحد كان خمسة
+
+136
+00:12:17,960 --> 00:12:24,870
+وواحد كان إياش تلاتة الآنكمان مرة بعد ما جسبت إذا
+
+137
+00:12:24,870 --> 00:12:29,150
+كان Q1 هتطلع عندي برضه بين الـ 0 و بين الـ B أو
+
+138
+00:12:29,150 --> 00:12:34,490
+strictly أصغر من B بكون خلصت و معناته صار عند كل
+
+139
+00:12:34,490 --> 00:12:44,520
+Q1 بساوي A1 to getلنحصل على M بتساوي A1B زاد A نوت
+
+140
+00:12:44,520 --> 00:12:49,840
+وهذا اللي هو على الصورة اللي طالبها فوق والـ M في
+
+141
+00:12:49,840 --> 00:12:57,400
+هذه الحالة طلعت أشعل D بتساوي واحد الآن إذا حدث F
+
+142
+00:12:57,400 --> 00:13:06,620
+P1 أكبر أوي وساوة Bبدنا معاود نجسم اللي هو الـ Q1
+
+143
+00:13:06,620 --> 00:13:13,600
+على مين؟ على B then by division algorithm there
+
+144
+00:13:13,600 --> 00:13:22,520
+exist unique Q2 أو A1 such that الـ Q1 بتساوي Q2
+
+145
+00:13:22,520 --> 00:13:29,300
+في B زائد A1 والـ A1 أكبر وساوي صفر وأصغر من مين؟
+
+146
+00:13:29,300 --> 00:13:37,920
+من B مظبوط؟الان برد بعوض هذا في اللي فوق بيصير عند
+
+147
+00:13:37,920 --> 00:13:47,640
+الان الان بتساوي Q1 هي عبارة عن Q2 في B زائد A1 في
+
+148
+00:13:47,640 --> 00:13:57,820
+B زائد من A0 بفردها بتصير عبارة عن Q2فى B تربيع
+
+149
+00:13:57,820 --> 00:14:03,960
+زائد A واحد فى B زائد A نوت والـ A نوت والـ A واحد
+
+150
+00:14:03,960 --> 00:14:08,140
+جاهزات لأن الـ A نوت والـ A واحد مالهم بين السفر
+
+151
+00:14:08,140 --> 00:14:15,600
+وبين الـ B باجي لمين الـ Q2 الآن وطبعا لاحظ إذا
+
+152
+00:14:15,600 --> 00:14:22,560
+كانت الـ Q2 if Q2 أصغر strictly من B then بنكون
+
+153
+00:14:22,560 --> 00:14:32,280
+خلصنا thenC Q2 بيساوي A2 to get اللي هو N بتساوي
+
+154
+00:14:32,280 --> 00:14:41,500
+A2 في B تربيع زائد A1 في B زائد A0 where A0 و A1 و
+
+155
+00:14:41,500 --> 00:14:51,310
+A2 تنتمي إلى 0 1 لعند الـ B-1، مظبوط؟ واضحمعناه يا
+
+156
+00:14:51,310 --> 00:14:55,010
+ابو حسين صورة عندي الآن على الصورة هذه لو كانت
+
+157
+00:14:55,010 --> 00:14:58,850
+الـA أصغر من الـB من الـQ و2 أصغر من الـB
+
+158
+00:15:02,340 --> 00:15:10,000
+أكبر أو يساوي بيه بنيجة اللي هو بنعوض كمان مرة في
+
+159
+00:15:10,000 --> 00:15:16,300
+المعادلة اللي عندي وبقسم كمان مرة وكذا أنا بقول
+
+160
+00:15:16,300 --> 00:15:20,660
+والمصدر من أيدي يعني في الآخر هنخلص يعني هتنتهي
+
+161
+00:15:20,660 --> 00:15:25,660
+الخطوات ليش؟ لأن أنا أصلا عند الأنت بقى اللي بدأت
+
+162
+00:15:25,660 --> 00:15:30,960
+فيها وجسمتهابتلعب اللي هو عندي الباطل اللي هو الـ
+
+163
+00:15:30,960 --> 00:15:33,220
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+164
+00:15:33,220 --> 00:15:33,280
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+165
+00:15:33,280 --> 00:15:33,720
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+166
+00:15:33,720 --> 00:15:34,220
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+167
+00:15:34,220 --> 00:15:34,680
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+168
+00:15:34,680 --> 00:15:35,140
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+169
+00:15:35,140 --> 00:15:35,680
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+170
+00:15:35,680 --> 00:15:38,570
+الـ الـ الـ الـ الـ الـ الـأنا strictly أكبر منه و
+
+171
+00:15:38,570 --> 00:15:44,450
+Q1 strictly أكبر من مين من نتيجة قسم Q2 إذا كل
+
+172
+00:15:44,450 --> 00:15:49,810
+باقي قسم عامال هينزل أنا في آخر عدد نهائي إذا بعد
+
+173
+00:15:49,810 --> 00:15:53,690
+سلسلة من الخطوات هذه هيكون أكبر أو يساوي مين ساوي
+
+174
+00:15:53,690 --> 00:15:59,890
+سفر حصل لمين للسفر بمعنى بمعنى أنه أنا في النهاية
+
+175
+00:15:59,890 --> 00:16:07,320
+في النهاية بعد أم من الخطواتهحصل على اللي هي a
+
+176
+00:16:07,320 --> 00:16:10,040
+naught زي دقيقة واحد بيه زي دقيقة اتنين بيه تربيه
+
+177
+00:16:10,040 --> 00:16:16,960
+زي دقيقة ا اميا بيقص اموبكون هيك خلصت طبعا قبل هذه
+
+178
+00:16:16,960 --> 00:16:22,360
+الخطوة قبل الأصول اللي هي مباشرة انا بقول انه حصلت
+
+179
+00:16:22,360 --> 00:16:30,320
+على QM-1 بساوي QM B زائد A-1 حيث الـ Q .. ال .. ال
+
+180
+00:16:30,320 --> 00:16:35,900
+A-1 بين ال A و ال B .. بين السفر و ال Bوالكل اللي
+
+181
+00:16:35,900 --> 00:16:42,120
+جابلها الـ A M-2 والـ A2 والـ A1 والـ A0 كلهم بصبن
+
+182
+00:16:42,120 --> 00:16:46,600
+في هذه المنطقة وانا بقول انا خلصت بعد M من الخطوات
+
+183
+00:16:46,600 --> 00:16:52,540
+خلصت اذا اخر خطوة عندي الآن اللي هي عند EQM هذه
+
+184
+00:16:52,540 --> 00:16:57,870
+بكون حصلت عليها اصغر من 100 من الـ Bفبتصير الـ
+
+185
+00:16:57,870 --> 00:17:02,850
+Representation النهائية بعوّر بيصير عند M بتساوي A
+
+186
+00:17:02,850 --> 00:17:06,950
+M B M A M مانس واحد B M مانس واحد لعند مين لعند اي
+
+187
+00:17:06,950 --> 00:17:11,570
+نوت اي سؤال؟
+
+188
+00:17:11,570 --> 00:17:17,810
+طيب هذا اللي هو ان M can be written in this form
+
+189
+00:17:17,810 --> 00:17:21,090
+اللي انا بدنا نقول ان this representation is
+
+190
+00:17:21,090 --> 00:17:25,350
+unique اذا
+
+191
+00:17:26,440 --> 00:17:30,900
+بنفترض إنه فيه Two Representations ونسأل إن هذا
+
+192
+00:17:30,900 --> 00:17:34,640
+الـ Representation لازم يكون زي بعضه الاتنين
+
+193
+00:17:34,640 --> 00:17:38,720
+يكونوا نفس الشيء يعني هنسأل الـ Contradiction
+
+194
+00:17:38,720 --> 00:17:41,900
+بمعنى واخر لما نسأل إنه فيه عندي Two Distinct
+
+195
+00:17:41,900 --> 00:17:51,430
+Representations الأن نفترض إنهان لديه اتصالات
+
+196
+00:17:51,430 --> 00:17:56,270
+مختلفة لانه
+
+197
+00:17:56,270 --> 00:18:00,610
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+198
+00:18:00,610 --> 00:18:00,710
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+199
+00:18:00,710 --> 00:18:00,950
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+200
+00:18:00,950 --> 00:18:06,570
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+201
+00:18:08,870 --> 00:18:13,750
+ونفرض .. نفترض إن في representation آخر إيش اسمه؟
+
+202
+00:18:13,750 --> 00:18:22,550
+اسمه C note مثلا زائد C1B زائد لمّا أصل C M B أُس
+
+203
+00:18:22,550 --> 00:18:28,290
+M ونفترض إن الـ two representations are different
+
+204
+00:18:28,290 --> 00:18:32,050
+ماشي الحال يعني هذا ال representation و هذا ال
+
+205
+00:18:32,050 --> 00:18:37,530
+representation مختلفات ماشي الحال طيب
+
+206
+00:18:38,980 --> 00:18:47,220
+الان جيبليها الانتهاء هذوله مع بعض وسميلي اللي هو
+
+207
+00:18:47,220 --> 00:18:56,860
+D1 بساوي او D note بساوي A note ناقص C note وD1
+
+208
+00:18:56,860 --> 00:19:06,560
+بساوي A1 ناقص C1 لما حصل ان هي DM بساوي AM ناقص CM
+
+209
+00:19:09,150 --> 00:19:13,790
+ما دام الـ two representations are different إذاً
+
+210
+00:19:13,790 --> 00:19:19,930
+على الأقل واحد من هذولهيكون لو سوء صفر وإلا لو
+
+211
+00:19:19,930 --> 00:19:23,730
+كانت كلهم صفر معناته ال representation نفس ال
+
+212
+00:19:23,730 --> 00:19:28,710
+representation إذا خلّينا ما دام الان احنا فرضنا
+
+213
+00:19:28,710 --> 00:19:34,090
+ان ال two representations مختلفات إذا في واحد من
+
+214
+00:19:34,090 --> 00:19:34,370
+ال
+
+215
+00:19:39,240 --> 00:19:45,340
+خلّينا ناخد أول واحد بن جابله مش سفر، ماشي الحال،
+
+216
+00:19:45,340 --> 00:19:51,840
+نفترض إنه DK هو عبارة عن الـ First Non-zero term
+
+217
+00:19:51,840 --> 00:19:58,440
+from these terms الـ DK أشمله أول واحد مش سفر بن
+
+218
+00:19:58,440 --> 00:20:05,660
+جابله، واضح؟ معناه يا وسيم؟طيب صار عندي الآن بناء
+
+219
+00:20:05,660 --> 00:20:09,360
+على الفرضية دي دي نوت و دي واحد و دي اتنين اللي
+
+220
+00:20:09,360 --> 00:20:15,220
+عندي دي ك مينوس واحد كلهم صفر اه و دي ك اشماله مش
+
+221
+00:20:15,220 --> 00:20:22,460
+صفر فالان جيبلي هذي جنب هذي فبصير عندي اللي هو دي
+
+222
+00:20:22,460 --> 00:20:32,190
+واحد او دي نوتفي اللي هو زائد D1 في B زائد لما أصل
+
+223
+00:20:32,190 --> 00:20:40,370
+عن Dk-1 في B أُس K-1 زائد معايا متبعين Dk B أُس K
+
+224
+00:20:40,370 --> 00:20:48,450
+زائد لما أصل لآخر واحدوخلّيني اكتب اللي بعده دي ك
+
+225
+00:20:48,450 --> 00:20:55,130
+زائد واحد بي قص ك زائد واحد لما أصل لآخر واحد دي
+
+226
+00:20:55,130 --> 00:21:01,870
+ان بي قص ان هذا كل ما حيساوي ايش يا جماعة؟ حيساوي
+
+227
+00:21:01,870 --> 00:21:07,790
+سفر عارفين ليش؟ لأنه نجلت هذا على الجهة هذه وكتبت
+
+228
+00:21:07,790 --> 00:21:11,530
+C واحد .. C .. A واحد .. A Note ناقص C Note A واحد
+
+229
+00:21:11,530 --> 00:21:16,450
+ناقص C واحد وكلنا دول لإن دي اللي سميت هناالـ Arc
+
+230
+00:21:16,450 --> 00:21:21,290
+بناءً على الفرضية اللي هان هذولا كلهم من يالهان
+
+231
+00:21:21,290 --> 00:21:27,190
+إيش مالهان؟ صفر، Zero، ماشي، إذا إيش ضال عندي؟ ضال
+
+232
+00:21:27,190 --> 00:21:35,170
+عندي هذول، هذول مجموح برضه إيش حيساوة؟ حيساوة صفر،
+
+233
+00:21:35,170 --> 00:21:39,370
+إن جمع هذول كلهم على الجهة الثانية، فبصير عندي DK
+
+234
+00:21:39,370 --> 00:21:49,870
+في B أُس K، إيش بيساوي؟بساوة لاقص dk زائد واحد
+
+235
+00:21:49,870 --> 00:21:57,750
+بيقص k زائد واحد زائد لما أصل عند dm بيقص m مظبوط
+
+236
+00:21:57,750 --> 00:22:03,810
+الآن طبعا هذا ال k أصغر واحد في الأسس اللي هنا
+
+237
+00:22:05,000 --> 00:22:11,140
+فأكيد اللي هو بدي بقسم كل هدول على الـ B كي و بضل
+
+238
+00:22:11,140 --> 00:22:15,040
+محافظ عليهم كل ال Integers فبصير عندها ده بيساوي
+
+239
+00:22:15,040 --> 00:22:22,720
+ايه ده دي كي بيساوي ناقص اللي هو دي كي زائد واحد
+
+240
+00:22:22,720 --> 00:22:28,580
+في B زائد التانية في B تربيع في B تكعيب لما أصل
+
+241
+00:22:28,580 --> 00:22:34,720
+لآخر واحدة DM في B أُس M ناقص كي صح؟
+
+242
+00:22:36,930 --> 00:22:43,510
+عند الآن كل واحدة فيها ذولة فيها بيبدي اشهر اخد
+
+243
+00:22:43,510 --> 00:22:50,590
+عامل مشترك فبتساوي ناقص بي في دي ك زائد واحد زائد
+
+244
+00:22:50,590 --> 00:22:54,470
+دي ك زائد اتنين فيها بي واللي بقى ده فيه بي لما
+
+245
+00:22:54,470 --> 00:22:58,130
+اصل الاخر واحد ده برضه فيها بي انا ناقص كيه ناقص
+
+246
+00:22:58,130 --> 00:23:03,670
+واحد هذا كله اكيد integer وهذا integer انصار الدي
+
+247
+00:23:03,670 --> 00:23:09,010
+كيه حاصل ضرب من بي في العدد اللي عندهإذا أكيد صار
+
+248
+00:23:09,010 --> 00:23:16,730
+عند الـ B هذا عامل من عامل مين الـ DK الـ B عامل
+
+249
+00:23:16,730 --> 00:23:23,730
+من عامل مين الـ DK طيب
+
+250
+00:23:23,730 --> 00:23:32,330
+الآن الـ B اللي عندي هذه صارت
+
+251
+00:23:32,330 --> 00:23:39,510
+اطلع لفوقأحنا عامال بنحكي أن الـ AK strictly أصغر
+
+252
+00:23:39,510 --> 00:23:45,570
+من B والـ CK strictly أصغر من B، مظبوط؟ إذا حصر
+
+253
+00:23:45,570 --> 00:23:51,570
+طلحن، إذا حصر طلحن اللي هو الـ DK يعني هيصير الـ
+
+254
+00:23:51,570 --> 00:24:00,010
+DK strictly ال absolute value له أصغر من مين؟ من B
+
+255
+00:24:00,900 --> 00:24:07,080
+ركز معايا هنا ال absolute value ل Dk أصغر من بيه،
+
+256
+00:24:07,080 --> 00:24:12,590
+قلت إيش السبب؟ إن عندك ال Akأصغر من B وأكبر بساوي
+
+257
+00:24:12,590 --> 00:24:17,310
+صفر Strictly والـ CK أصغر من B وأكبر بساوي صفر
+
+258
+00:24:17,310 --> 00:24:21,930
+برضه Strictly من هنا إذا حاصل ترحل اللي هو الـ DK
+
+259
+00:24:21,930 --> 00:24:27,150
+بين الماقص B وبين ميين الـ B يعني الـ Absolute
+
+260
+00:24:27,150 --> 00:24:36,070
+Value للـ DK strictly أصغر من مين من B الـ A بي من
+
+261
+00:24:36,070 --> 00:24:44,750
+عوام الميين الـ DKوعندي الآن الـDK الصغيرة وB من
+
+262
+00:24:44,750 --> 00:24:49,670
+عواملها الـ Absolute value للـDK الصغيرة إذا الـDK
+
+263
+00:24:49,670 --> 00:24:54,950
+لا يمكن إن الـB تقسم الـDK والـAbsolute value لهذه
+
+264
+00:24:54,950 --> 00:25:03,070
+أصغر من هذه إلا إذا كانت الـDK إيش بتسميه؟ كمان
+
+265
+00:25:03,070 --> 00:25:09,060
+مرةالآن للتسهيل خلّيني افترض أن تنتقش مع الـ M
+
+266
+00:25:09,060 --> 00:25:17,380
+Positive ركّز هذا العدد بيجسم هذا وهذا صغير أصغر
+
+267
+00:25:17,380 --> 00:25:23,560
+من هذا أصغر منه مستحيل
+
+268
+00:25:23,560 --> 00:25:26,840
+اللي يكون مين هو الـ DKF؟ واحدة واحدة
+
+269
+00:25:38,530 --> 00:25:43,290
+أنا أريد أن أوصلك إلى مفاحش للسفر كمان مرة كمان
+
+270
+00:25:43,290 --> 00:25:49,650
+مرة عندي الآن أدرُب لك مثال التلاتة
+
+271
+00:25:49,650 --> 00:25:56,330
+بتجسم الـDK ماشي الحال والـDK
+
+272
+00:25:56,330 --> 00:26:02,360
+قيمتها المطلقة أصغر من 3مستحيل تكون يعني إن هو
+
+273
+00:26:02,360 --> 00:26:06,800
+الـDK والمباعثات التلاتة إلا إذا كانت الـDK صفر
+
+274
+00:26:06,800 --> 00:26:12,620
+لأن الصفر كل الدنيا من عوارله إذا مافيش إمكانية إن
+
+275
+00:26:12,620 --> 00:26:16,900
+التلاتة تكسب الـDK والـDK ال absolute value يكون
+
+276
+00:26:16,900 --> 00:26:20,380
+أكبر من التلاتة أصغر من التلاتة إلا يكون الـDK
+
+277
+00:26:20,380 --> 00:26:27,820
+أشمالهبساوي سفر إذا صار عندى ملخص الحديث بما انه
+
+278
+00:26:27,820 --> 00:26:33,480
+ال b تقسم ال dk وال absolute value ل ال dk
+
+279
+00:26:33,480 --> 00:26:39,360
+strictly أصغر من ال b إذا لا يمكن إلا أن يكون ال
+
+280
+00:26:39,360 --> 00:26:44,400
+dk ايش بتساوي؟ بتساوي اللى هو سفرالـ DK بيساوي سفر
+
+281
+00:26:44,400 --> 00:26:47,000
+Contradiction ليش Contradiction؟ لأن احنا اصلا
+
+282
+00:26:47,000 --> 00:26:51,140
+مفترضين أشماله لا يساوي سفر، فالفرضية الأولى مش
+
+283
+00:26:51,140 --> 00:26:55,800
+صحيحة، إذا الـ two representations must be equal
+
+284
+00:26:55,800 --> 00:27:02,540
+إذا في عندي بس only one representationأي سؤال؟
+
+285
+00:27:02,540 --> 00:27:06,520
+اللي خلّيني أساسي أنه البعض اللي حتى الآن هدم شوية
+
+286
+00:27:06,520 --> 00:27:12,300
+B بتكسب مين الـDK يعني الـDK من المباعثات مين اللي
+
+287
+00:27:12,300 --> 00:27:20,100
+هو الـB إذا الـDK الـDK هتكون يا إما 0 يا إما 2B
+
+288
+00:27:20,100 --> 00:27:27,250
+يا تلتة B يا أربعة B يا آخري، مظبوط؟أو أو أو سالب
+
+289
+00:27:27,250 --> 00:27:34,430
+بي سالب اتنين بي سالب تلاتة بي الاخرية لكن أصلا ال
+
+290
+00:27:34,430 --> 00:27:39,410
+absolute value of dk أصغر من بي إذا هدولة كلهم مش
+
+291
+00:27:39,410 --> 00:27:42,390
+وردات و هدولة كلهم مش وردات إذا مين بيبقى الباس من
+
+292
+00:27:42,390 --> 00:27:50,190
+المضاعفاته السفر مانفعش ما تفهمش هيك بعد هيك طيب
+
+293
+00:27:50,190 --> 00:27:54,880
+صلوا على النبي عليه الصلاة والسلامالان الاتفاق مع
+
+294
+00:27:54,880 --> 00:27:58,960
+ال notation ان هي الان العبارة عن الان اللي عنده
+
+295
+00:27:58,960 --> 00:28:02,880
+عبارة عن اللي هو مكتوب بال decimal representation
+
+296
+00:28:02,880 --> 00:28:08,420
+او بالنظام العد العشري بالنظام العد العشري اذا ..
+
+297
+00:28:08,420 --> 00:28:13,630
+اذانظام العد للأساس B على أساس الـ Representation
+
+298
+00:28:13,630 --> 00:28:19,070
+هذا هيه والـ B خدها إيش ما بدك أكبر من واحد ماشي
+
+299
+00:28:19,070 --> 00:28:21,950
+الحاجة إتنين، تلاتة، أربعة، خمسة، إذاً كل .. إذاً
+
+300
+00:28:21,950 --> 00:28:26,810
+الآن كل أنظمة العد إذاً هي الطريقة لعملية التحويل
+
+301
+00:28:26,810 --> 00:28:31,130
+من وإلى استنادا إلى هذه النظرية أو لبروهان هذه
+
+302
+00:28:31,130 --> 00:28:32,950
+النظرية اطلع للبعده
+
+303
+00:28:36,760 --> 00:28:42,520
+المثال اللي موجود، حلّينا، أحنا عملنا أنثى خلّينا
+
+304
+00:28:42,520 --> 00:28:48,000
+نذكر مثال العدد اللي موجود المعزز برضه اللي حكيناه
+
+305
+00:28:48,000 --> 00:28:53,340
+لأنه يعني صار اللي هو الأصل الأهل أنه بكل سهولة
+
+306
+00:28:53,340 --> 00:28:57,380
+أنك أنت تقدر تتحول من نظام عد إلى نظام عد لأنه أنا
+
+307
+00:28:57,380 --> 00:29:01,680
+بعتقد أنه ما زال في الابتدائية بيعطوا النظام العد
+
+308
+00:29:01,680 --> 00:29:06,200
+الخماسي أظلفأكيد بدي يعني المستقبل عن حد درسوه
+
+309
+00:29:06,200 --> 00:29:12,160
+معناته أنه منيح تارف أساسه العلميوالله يبقى ..
+
+310
+00:29:12,160 --> 00:29:16,120
+بدّك الصحيحة أنا سألت نفس السؤال يعني الواحد لو
+
+311
+00:29:16,120 --> 00:29:20,660
+جالس ثنائي استخداماته كبيرة .. كبيرة في إيش؟ في
+
+312
+00:29:20,660 --> 00:29:24,260
+اللي في الكمبيوتر والآخرين ال .. ال .. السداسي أو
+
+313
+00:29:24,260 --> 00:29:27,600
+الـ 16 أو كذا فيه له استخدامات في اللي هي
+
+314
+00:29:27,600 --> 00:29:30,960
+applications في القهربة وفي الآخرين نظام العدد
+
+315
+00:29:30,960 --> 00:29:35,800
+الخماسي قد تكون شغلة يعني مرتبطة نفسيا بإنه بدل ما
+
+316
+00:29:35,800 --> 00:29:38,740
+نحكي عن العشرة نحكي عن الخمسة الخمسة عدد نيح يعني
+
+317
+00:29:38,740 --> 00:29:45,680
+زي العشرةهو قد تكون حسب علمي انه تطبيقات خاصة
+
+318
+00:29:45,680 --> 00:29:53,260
+بالخماسي انا مابعرفش طيب شوف عليها انا اول ما
+
+319
+00:29:53,260 --> 00:30:04,120
+سمعتش قبل هيك شوف الان
+
+320
+00:30:04,120 --> 00:30:10,210
+بساوي 104 على الأساس 105عندى منى أربعة للأساس خمسة
+
+321
+00:30:10,210 --> 00:30:16,570
+عشان يساوي قولوا معايا أربعة
+
+322
+00:30:16,570 --> 00:30:22,730
+زائد سفر في خمسة فهمين زائد واحد في خمس تاربيع
+
+323
+00:30:22,730 --> 00:30:27,310
+نظبط اللى بعمله زى ما عملنا ال presentation اللى
+
+324
+00:30:27,310 --> 00:30:33,150
+لنا هو يساوي طبعا عندك تبدأيا كله جائز خمسة وعشرين
+
+325
+00:30:33,150 --> 00:30:39,120
+هو أربعة تسعة وعشرينبالدنيا أولى العدد مين النظام
+
+326
+00:30:39,120 --> 00:30:42,960
+العدد الثنائي النظام العدد الثنائي تسعة وعشرين
+
+327
+00:30:42,960 --> 00:30:50,140
+اتنين بديك تيجي تجسم اه؟ خلّينا نعرف انك تسعة
+
+328
+00:30:50,140 --> 00:30:53,740
+اتنين ما يساوي، اذا لأ هي جيت بدي استخدم مين؟
+
+329
+00:30:53,740 --> 00:30:58,500
+برهانة نظرية، في الواقع برهانة نظرية، لأ عبارة عن
+
+330
+00:30:58,500 --> 00:31:06,910
+جدشة تسعة عشر في اتنينأربعة عشر في اتنين زي
+
+331
+00:31:06,910 --> 00:31:13,870
+الدياشر واحد كويساوي صح لأن هذه صارت عبارة عن
+
+332
+00:31:13,870 --> 00:31:19,650
+الاربعة عشر عبارة عن سبعة في اتنين في اتنين مظبوط
+
+333
+00:31:19,650 --> 00:31:26,450
+هذا واضحة مافيش داعي نعملها اه سبعة في اتنين تربيع
+
+334
+00:31:28,490 --> 00:31:34,990
+معايا زايد ايش واحد ويساوي سبعة عبارة عن مين تلاتة
+
+335
+00:31:34,990 --> 00:31:40,650
+في اتنين زايد واحد الكل في مين زايد واحد فاهمين
+
+336
+00:31:40,650 --> 00:31:45,830
+ايش اللي بحكيه سبعة مدلة مكتر اتنين بكسبها ويساوي
+
+337
+00:31:45,830 --> 00:31:50,330
+الان التلاتة تقبل من اتنين لأ اذا بكسبها بيصير
+
+338
+00:31:50,330 --> 00:31:53,830
+عبارة عن تلاتة في اتنين خلينا نبسطها بالسادس قبل
+
+339
+00:31:53,830 --> 00:32:02,440
+اللي هي عبارة عن تلاتة2 تكعيب زائد 2 تربيع زائد 1
+
+340
+00:32:02,440 --> 00:32:07,180
+هدول جنزن، مظبوط؟ لأنه انا واحد في اتنين تربيع
+
+341
+00:32:07,180 --> 00:32:14,200
+ويساوي تلاتة هي عبارة عن 2 زائد 1 في اتنين تكعيب
+
+342
+00:32:14,200 --> 00:32:23,200
+تلاتة على اتنين اتنين في واحد زائد واحد صح؟ زائد
+
+343
+00:32:23,200 --> 00:32:28,750
+واحد في اتنين تربيع زائد واحدY ساوي اتنين أقصى
+
+344
+00:32:28,750 --> 00:32:33,790
+أربعة زائد واحد في اتنين تكعيب زائد واحد في اتنين
+
+345
+00:32:33,790 --> 00:32:37,930
+تربيع زائد واحد مظبوط اللي بكتبه Y ساوي الخانة
+
+346
+00:32:37,930 --> 00:32:42,130
+الأولى واحد الأساسي اتنين الخانة التانية واحد
+
+347
+00:32:42,130 --> 00:32:47,170
+الخانة التالكة واحد الخانة الرابعة برضه يعيش واحد
+
+348
+00:32:47,170 --> 00:32:51,490
+واحدات كلها في شغل مخربطين فيه احنا
+
+349
+00:32:57,120 --> 00:33:05,860
+سبعة هي تلاتة في مين؟ في اتنين في اتنين
+
+350
+00:33:05,860 --> 00:33:13,600
+أس واحد زائد و Zero في اتنين أس واحد زائد مين؟
+
+351
+00:33:13,600 --> 00:33:17,960
+زائد واحد واضح
+
+352
+00:33:17,960 --> 00:33:20,440
+اه؟ ماشي الحل
+
+353
+00:33:26,440 --> 00:33:38,140
+طيب يا جماعة للتسهيل
+
+354
+00:33:38,140 --> 00:33:47,720
+الحسابات دلوقت طيب
+
+355
+00:33:47,720 --> 00:33:52,780
+شوف طيب
+
+356
+00:33:52,780 --> 00:33:59,150
+ليه جي احناالـ let B of X بيساوي summation CK X K
+
+357
+00:33:59,150 --> 00:34:02,310
+بيه polynomial function of X with integral
+
+358
+00:34:02,310 --> 00:34:05,650
+coefficients CK ده كانت الـ A تطابق B modulo N
+
+359
+00:34:05,650 --> 00:34:08,550
+هتكون ال polynomial عند ال A تطابق ال polynomial
+
+360
+00:34:08,550 --> 00:34:16,730
+عند ال B الأمر سهل، خلّينا بس قبل نذكركم شغلة أنه
+
+361
+00:34:16,730 --> 00:34:25,010
+لو كانت A تطابق ال B modulo N مثلاأخدنا قبل ذلك
+
+362
+00:34:25,010 --> 00:34:29,250
+أنه على طول بتصير .. بما أن هذه تطابق هذه إذا هذا
+
+363
+00:34:29,250 --> 00:34:37,010
+يؤدي إلى AK تطابق الـ BK مضنؤا لكل مين K اللي هو
+
+364
+00:34:37,010 --> 00:34:43,760
+element NL بناء عليهلو ضربنا الطرفين في
+
+365
+00:34:43,760 --> 00:34:48,500
+coefficients سموه CK مثلاً فبصير الـ CK تطابق في
+
+366
+00:34:48,500 --> 00:34:55,060
+AK تطابق الـ CK بـ K مدلون الآن هذا لـ K بساوي 0 و
+
+367
+00:34:55,060 --> 00:35:01,500
+1 و 2 و 3 و 4 و 5 لكل الـ K صفر و واحد و اتنين
+
+368
+00:35:01,500 --> 00:35:08,180
+لعند مين لعند الـ A لعند مثلا الجردش لعند ايش بدهو
+
+369
+00:35:08,180 --> 00:35:18,290
+لعند Mماشي لعيد ان واضح اه؟ اذا اكيد مجموح هنا
+
+370
+00:35:18,290 --> 00:35:22,890
+اللي هان بطابق المجموع اللي هان بناء على ايش على a
+
+371
+00:35:22,890 --> 00:35:30,350
+تطابق b modulo n و c تطابق d modulo n اذا صار عندي
+
+372
+00:35:30,350 --> 00:35:35,970
+a زائد c تطابق b زائد d بناء على هذه الخاصية بصير
+
+373
+00:35:35,970 --> 00:35:45,070
+عند ال summation ck akK من صفر لعند M تتعدق
+
+374
+00:35:45,070 --> 00:35:54,590
+summation CK BK K من صفر لعند M Modulo N هذه عبارة
+
+375
+00:35:54,590 --> 00:36:05,320
+عن P of A وP of Bبناء على افتراضنا ان b of x
+
+376
+00:36:05,320 --> 00:36:10,940
+بيساوي summation of ck x of k كمن سفر لعند مين
+
+377
+00:36:10,940 --> 00:36:15,080
+لعندها إذا صار عند لما ال a تطابق ال b مضله n
+
+378
+00:36:15,080 --> 00:36:22,660
+بيعطينا b of a تطابق ال b of b مضله n في حال ال b
+
+379
+00:36:22,660 --> 00:36:28,800
+of x بيساوي ck x كمن سفر لعندهاالرقص معايا كمان
+
+380
+00:36:28,800 --> 00:36:36,980
+مرة خلّينا نرتب أموركم لل .. يعني في عنده شوية لسه
+
+381
+00:36:36,980 --> 00:36:42,040
+غباش let P of X بتساوي ال summation CK X أُس K K
+
+382
+00:36:42,040 --> 00:36:46,000
+من صفر لحد مين ع الدم هذا عبارة عن polynomial ال
+
+383
+00:36:46,000 --> 00:36:48,740
+coefficients اللي لها أشمالها عبارة عن integers
+
+384
+00:36:49,710 --> 00:36:53,810
+معايا ومعطيني بيقول لي لو كانت عند ال A تطابق ال B
+
+385
+00:36:53,810 --> 00:37:02,490
+مدنو مين مدرعا حيكون ال B of A يطابق ال B مين of B
+
+386
+00:37:02,490 --> 00:37:09,040
+مدرعا باضح إذا كانتالـ B of X عبارة عن بلو نورميل
+
+387
+00:37:09,040 --> 00:37:15,660
+C0 زائد C1X زائد C2X تربيع زائد C3X تكعيب لما أصل
+
+388
+00:37:15,660 --> 00:37:20,780
+عند CM X أُس M وكانت عند الـ A تطابق الـ B Modulo
+
+389
+00:37:20,780 --> 00:37:26,440
+M إذن الـ B of A تطابق الـ B بإيش ما لها Modulo M
+
+390
+00:37:26,950 --> 00:37:30,390
+هذا الكلام برهنة وسهل جلّا مدارة الـ A تطابق الـ B
+
+391
+00:37:30,390 --> 00:37:35,110
+إذا الـ A K تطابق الـ B K ومن ثم نضرب الجهتين في C
+
+392
+00:37:35,110 --> 00:37:39,850
+K بتظل تطابقها صحيحة نجمحهم كلهم مع بعض، اللي
+
+393
+00:37:39,850 --> 00:37:44,390
+بيصير تطابق هذه، هذه اللي هي B of A وهذه اللي هي B
+
+394
+00:37:44,390 --> 00:37:53,190
+of B أي سؤال مصر إعلانه سهل الكلام نجنا الكوريلر
+
+395
+00:37:53,190 --> 00:37:53,910
+اللي عندنا
+
+396
+00:37:59,740 --> 00:38:09,060
+الـ Corollary بتقول ما يلي إذا كان في عندي
+
+397
+00:38:09,060 --> 00:38:22,480
+if A is a solution of B of X تطابق الـ Zero modulo
+
+398
+00:38:22,480 --> 00:38:23,100
+N
+
+399
+00:38:26,830 --> 00:38:40,710
+A تطابق الـ B مضلوان then B is a solution of الـ
+
+400
+00:38:40,710 --> 00:38:48,070
+star اللي فوق هذه بظبط؟ بقول إذا كانت A solution
+
+401
+00:38:48,070 --> 00:38:54,010
+لهذه و A تطابق الـ B مضلوان هيكون برضه B solution
+
+402
+00:38:54,010 --> 00:38:59,370
+للـ starالكلام سهل، لماذا؟ لأن الـProof بيقول
+
+403
+00:38:59,370 --> 00:39:02,830
+التالي الـProof
+
+404
+00:39:02,830 --> 00:39:10,950
+الشيء معناه A solution since A is a solution of
+
+405
+00:39:10,950 --> 00:39:19,530
+star then B of X تطابق الـ0 B of A تطابق الـ0 مدنه
+
+406
+00:39:19,530 --> 00:39:26,420
+مين؟ مدنه أنا، مدام A solutionلمن؟ للمتطابقة اللي
+
+407
+00:39:26,420 --> 00:39:31,360
+عندي هذه إذا أكيد تحقق طرفيا المتطابقة فبصير B of
+
+408
+00:39:31,360 --> 00:39:35,780
+A تطابق Zero modulo مين؟ Modulo N الآن بقولك أيضًا
+
+409
+00:39:35,780 --> 00:39:42,920
+since A تطابق الـ B modulo N then by theorem اللي
+
+410
+00:39:42,920 --> 00:39:48,960
+قبل بشوية اللي برهنها هيكون عندك الـ B of A تطابق
+
+411
+00:39:48,960 --> 00:39:55,430
+الـ B of BModulo N لأن من الجهتين هذول بخاصية
+
+412
+00:39:55,430 --> 00:40:03,750
+التعدي للتطابقة بيطلع الـ B together B of B تطابق
+
+413
+00:40:03,750 --> 00:40:10,590
+الـ Zero Modulo N وهذا إيش يعني أن B is a solution
+
+414
+00:40:10,590 --> 00:40:18,430
+of a star أي
+
+415
+00:40:18,430 --> 00:40:19,050
+سؤال؟
+
+416
+00:40:24,280 --> 00:40:31,640
+طيب احنا خلّينا الموضوع الجاي ان شاء الله هنحكي عن
+
+417
+00:40:31,640 --> 00:40:39,720
+اللي هو بعض الاختبارات لقابلية القسمة لبعض الإعداد
+
+418
+00:40:39,720 --> 00:40:44,060
+من الشغلات المشهورة اللي انتوا بتعرفوها أول إشي
+
+419
+00:40:44,060 --> 00:40:50,840
+قابلية القسمة على 9بنقول .. ناخد test الآن بيقوللي
+
+420
+00:40:50,840 --> 00:40:57,760
+التسعة بتقسم الان إذا التسعة بتقسم إيش؟ مجموعة
+
+421
+00:40:57,760 --> 00:41:04,400
+اللي هو ال coefficients لمن؟ لعشر أقص كي اللي بقصد
+
+422
+00:41:04,400 --> 00:41:09,520
+فيها يعني مجموعة أرقام العددماشي اللي هي يعني
+
+423
+00:41:09,520 --> 00:41:14,300
+النظرية بتقولك لو ال M كتبناها على صورة انتبه
+
+424
+00:41:14,300 --> 00:41:18,060
+معايا لو ال M كتبناها على صورة اللي هو ال decimal
+
+425
+00:41:18,060 --> 00:41:22,420
+representation ايش ال decimal representation يعني
+
+426
+00:41:22,420 --> 00:41:27,100
+A M عشرة أقص M يعني الأساس في النظرية الأولى بدل
+
+427
+00:41:27,100 --> 00:41:31,790
+مكان B صار ايش معنوه عشرةالـ N بيساوي A M عشر
+
+428
+00:41:31,790 --> 00:41:35,790
+أوسام A M minus واحد عشر أوسام minus واحد لعند A
+
+429
+00:41:35,790 --> 00:41:39,570
+واحد فعشرة زايد A Note لو كانت الـ N على يد الصورة
+
+430
+00:41:39,570 --> 00:41:43,990
+إذن طبعاً والـ A Note والـ A واحد لعند الـ A M
+
+431
+00:41:43,990 --> 00:41:48,370
+كلهم بالهم من صفر لعشر يعني الـ N مكتوبة على صورة
+
+432
+00:41:48,370 --> 00:41:54,110
+اللي هو الصورة العشريةإذن التسعة بتقسم العدد N إذا
+
+433
+00:41:54,110 --> 00:41:58,710
+و فقط إذا التسعة بتقسم الاس الاس اللي بيحكي عنها
+
+434
+00:41:58,710 --> 00:42:04,170
+اللي هو A0 زي دي واحد زي دي اتنين عند مين AM و ده
+
+435
+00:42:04,170 --> 00:42:08,130
+اللي هو ال test المشهور اللي انتوا عارفينه المرة
+
+436
+00:42:08,130 --> 00:42:13,230
+الجاية ان شاء الله بنكمل طبعاً برهانه سهل على ال
+
+437
+00:42:13,230 --> 00:42:16,690
+.. لأنه بولونوميرد وطبق بولونوميرد بنشوف المرة
+
+438
+00:42:16,690 --> 00:42:19,450
+القادمة ان شاء الله الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5XQIwHNIvj0_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5XQIwHNIvj0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0387610a3993be15d3dcb079784989dae2fcdd8c
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5XQIwHNIvj0_raw.json
@@ -0,0 +1 @@
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الـ X بيساوي الـ Grass Integer إلها هي الـ 1 زائد الكسر الآن اللي هي 2 و 2 من 10 أه نبدأ فيها هتساوي ال Grass Integer إلها زائد من اللي هو كسرها هذه الـ θ اللي بنقول عنها اللي بنقصد في suitable θ طيب اطلع على فوق الآن هذا ما يهمنا الآن", "tokens": [40228, 22653, 2423, 39184, 502, 4032, 805, 9154, 1266, 13672, 1829, 39896, 2423, 39184, 1783, 4724, 1829, 3794, 995, 45865, 2423, 39184, 39891, 5681, 30744, 11933, 1211, 11296, 39896, 2423, 39184, 502, 30767, 16373, 3215, 33251, 3794, 2288, 6024, 48506, 13672, 1829, 39896, 568, 4032, 568, 9154, 1266, 5551, 3224, 8717, 44510, 10721, 8978, 11296, 8032, 2655, 3794, 995, 45865, 2423, 39891, 5681, 30744, 11933, 1211, 11296, 30767, 16373, 3215, 9154, 13672, 1829, 31439, 9122, 3794, 2288, 11296, 29538, 2423, 39184, 12622, 13672, 1829, 44945, 39648, 18871, 11296, 13672, 1829, 44945, 4587, 9381, 3215, 8978, 12873, 12622, 23032, 1829, 3555, 1975, 9566, 1211, 3615, 15844, 6156, 30543, 6024, 48506, 23758, 19446, 7251, 16095, 8315, 6024, 48506], 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in n factorial بي appears بي is إبراهيم بي appears in n factorial", "tokens": [2407, 4724, 1829, 11933, 3555, 23557, 3224, 32640, 9154, 6225, 2407, 10943, 9673, 9957, 2423, 7649, 38637, 2304, 4724, 1829, 4724, 1829, 7038, 34051, 4724, 1829, 307, 364, 11933, 3555, 23557, 3224, 32640, 3714, 33599, 1829, 7038, 294, 297, 36916, 4724, 1829, 7038, 4724, 1829, 307, 11933, 3555, 23557, 3224, 32640, 4724, 1829, 7038, 294, 297, 36916], "avg_logprob": -0.28744610784382657, "compression_ratio": 1.7606837606837606, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 461.16, "end": 461.4, "word": "و", "probability": 0.8974609375}, {"start": 461.4, "end": 462.12, "word": " بي", "probability": 0.603515625}, {"start": 462.12, "end": 462.96, "word": " إبراهيم", "probability": 0.82734375}, {"start": 462.96, "end": 464.76, "word": " من", "probability": 0.9169921875}, {"start": 464.76, "end": 465.18, "word": " عوام", "probability": 0.96435546875}, {"start": 465.18, "end": 465.74, "word": " 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0.79022216796875}, {"start": 2603.38, "end": 2605.08, "word": " ستة", "probability": 0.900390625}, {"start": 2605.08, "end": 2606.42, "word": " على", "probability": 0.6728515625}, {"start": 2606.42, "end": 2606.94, "word": " واحد", "probability": 0.99072265625}, {"start": 2606.94, "end": 2608.26, "word": " زاد", "probability": 0.75927734375}, {"start": 2608.26, "end": 2609.78, "word": " دين", "probability": 0.52618408203125}, {"start": 2609.78, "end": 2610.94, "word": " ستة", "probability": 0.8816731770833334}, {"start": 2610.94, "end": 2611.06, "word": " على", "probability": 0.8779296875}, {"start": 2611.06, "end": 2611.44, "word": " اتنين", "probability": 0.97021484375}, {"start": 2611.44, "end": 2611.6, "word": " و", "probability": 0.29296875}, {"start": 2611.6, "end": 2611.7, "word": " انا", "probability": 0.7061767578125}, {"start": 2611.7, "end": 2611.78, "word": " كنت", "probability": 0.755126953125}, {"start": 2611.78, "end": 2611.98, "word": " واحد", "probability": 0.89208984375}, {"start": 2611.98, "end": 2612.42, "word": " يختصر", "probability": 0.962890625}, {"start": 2612.42, "end": 2612.56, "word": " من", "probability": 0.99267578125}, {"start": 2612.56, "end": 2612.76, "word": " دروة", "probability": 0.5381673177083334}, {"start": 2612.76, "end": 2612.92, "word": " ولا", "probability": 0.1680908203125}, {"start": 2612.92, "end": 2613.2, "word": " درا", "probability": 0.4537353515625}], "temperature": 1.0}, {"id": 107, "seek": 264693, "start": 2618.93, "end": 2646.93, "text": "مسدد دلدالك يا أبو يحيان زائد أربعة في ستة على أربعة زائد خمسة في ستة على خمسة زائد ستة في ستة على ستة كويس أوي أنا ستة أنا ستة أنا ستة أنا أربعة في عدد أربعة زائد خمسة زائد ستة صح؟", "tokens": [2304, 3794, 3215, 3215, 11778, 1211, 3215, 6027, 4117, 35186, 5551, 3555, 2407, 7251, 5016, 1829, 7649, 30767, 16373, 3215, 5551, 25513, 27884, 8978, 8608, 2655, 3660, 15844, 5551, 25513, 27884, 30767, 16373, 3215, 16490, 2304, 3794, 3660, 8978, 8608, 2655, 3660, 15844, 16490, 2304, 3794, 3660, 30767, 16373, 3215, 8608, 2655, 3660, 8978, 8608, 2655, 3660, 15844, 8608, 2655, 3660, 9122, 45865, 3794, 34051, 1829, 41850, 8608, 2655, 3660, 41850, 8608, 2655, 3660, 41850, 8608, 2655, 3660, 41850, 5551, 25513, 27884, 8978, 6225, 3215, 3215, 5551, 25513, 27884, 30767, 16373, 3215, 16490, 2304, 3794, 3660, 30767, 16373, 3215, 8608, 2655, 3660, 20328, 5016, 22807], "avg_logprob": -0.14983784899396715, "compression_ratio": 2.4580152671755724, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2618.93, "end": 2619.59, "word": "مسدد", "probability": 0.68951416015625}, {"start": 2619.59, "end": 2620.15, "word": " دلدالك", "probability": 0.5875}, {"start": 2620.15, "end": 2620.25, "word": " يا", "probability": 0.89013671875}, {"start": 2620.25, "end": 2620.35, "word": " أبو", "probability": 0.7141927083333334}, {"start": 2620.35, "end": 2620.75, "word": " يحيان", "probability": 0.911865234375}, {"start": 2620.75, "end": 2621.55, "word": " زائد", "probability": 0.6133626302083334}, {"start": 2621.55, "end": 2622.03, "word": " أربعة", "probability": 0.8473307291666666}, {"start": 2622.03, "end": 2622.21, "word": " في", "probability": 0.69140625}, {"start": 2622.21, "end": 2622.85, "word": " ستة", "probability": 0.9777018229166666}, {"start": 2622.85, "end": 2623.39, "word": " على", "probability": 0.8583984375}, {"start": 2623.39, "end": 2623.95, "word": " أربعة", "probability": 0.9012044270833334}, {"start": 2623.95, "end": 2625.19, "word": " زائد", "probability": 0.9402669270833334}, {"start": 2625.19, "end": 2626.89, "word": " خمسة", "probability": 0.953369140625}, {"start": 2626.89, "end": 2627.17, "word": " في", "probability": 0.97607421875}, {"start": 2627.17, "end": 2627.61, "word": " ستة", "probability": 0.9825846354166666}, {"start": 2627.61, "end": 2627.75, "word": " على", "probability": 0.900390625}, {"start": 2627.75, "end": 2628.51, "word": " خمسة", "probability": 0.99365234375}, {"start": 2628.51, "end": 2629.55, "word": " زائد", "probability": 0.93603515625}, {"start": 2629.55, "end": 2630.23, "word": " ستة", "probability": 0.9938151041666666}, {"start": 2630.23, "end": 2630.51, "word": " في", "probability": 0.97900390625}, {"start": 2630.51, "end": 2631.21, "word": " ستة", "probability": 0.9943033854166666}, {"start": 2631.21, "end": 2631.55, "word": " على", "probability": 0.94287109375}, {"start": 2631.55, "end": 2632.29, "word": " ستة", "probability": 0.9931640625}, {"start": 2632.29, "end": 2633.09, "word": " كويس", "probability": 0.8557942708333334}, {"start": 2633.09, "end": 2633.45, "word": " أوي", "probability": 0.721435546875}, {"start": 2633.45, "end": 2633.85, "word": " أنا", "probability": 0.66162109375}, {"start": 2633.85, "end": 2634.79, "word": " ستة", "probability": 0.9920247395833334}, {"start": 2634.79, "end": 2635.59, "word": " أنا", "probability": 0.67529296875}, {"start": 2635.59, "end": 2637.21, "word": " ستة", "probability": 0.9856770833333334}, {"start": 2637.21, "end": 2637.61, "word": " أنا", "probability": 0.82373046875}, {"start": 2637.61, "end": 2639.59, "word": " ستة", "probability": 0.923828125}, {"start": 2639.59, "end": 2640.37, "word": " أنا", "probability": 0.83740234375}, {"start": 2640.37, "end": 2641.65, "word": " أربعة", "probability": 0.9609375}, {"start": 2641.65, "end": 2641.95, "word": " في", "probability": 0.86865234375}, {"start": 2641.95, "end": 2642.43, "word": " عدد", "probability": 0.64697265625}, {"start": 2642.43, "end": 2642.95, "word": " أربعة", "probability": 0.9464518229166666}, {"start": 2642.95, "end": 2644.01, "word": " زائد", "probability": 0.96875}, {"start": 2644.01, "end": 2644.77, "word": " خمسة", "probability": 0.9951171875}, {"start": 2644.77, "end": 2645.75, "word": " زائد", "probability": 0.97216796875}, {"start": 2645.75, "end": 2646.25, "word": " ستة", "probability": 0.994140625}, {"start": 2646.25, "end": 2646.93, "word": " صح؟", "probability": 0.9033203125}], "temperature": 1.0}, {"id": 108, "seek": 265885, "start": 2647.69, "end": 2658.85, "text": "و يساوي 4 ستات أربع عشرين تمانية عشرين وخمسة تلاتة و تلاتين و الله يعطيك العافية و إلى لقاء آخر", "tokens": [2407, 7251, 3794, 995, 45865, 1017, 8608, 2655, 9307, 5551, 25513, 3615, 6225, 46309, 9957, 46811, 7649, 10632, 6225, 46309, 9957, 4032, 9778, 2304, 3794, 3660, 6055, 1211, 9307, 3660, 4032, 6055, 1211, 9307, 9957, 4032, 21984, 37495, 9566, 1829, 4117, 18863, 31845, 10632, 4032, 30731, 5296, 4587, 16606, 19753, 34740], "avg_logprob": -0.2436898975418164, "compression_ratio": 1.4406779661016949, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 2647.69, "end": 2647.89, "word": "و", "probability": 0.5234375}, {"start": 2647.89, "end": 2648.39, "word": " يساوي", "probability": 0.789794921875}, {"start": 2648.39, "end": 2649.33, "word": " 4", "probability": 0.40380859375}, {"start": 2649.33, "end": 2649.87, "word": " ستات", "probability": 0.5513916015625}, {"start": 2649.87, "end": 2650.13, "word": " أربع", "probability": 0.666015625}, {"start": 2650.13, "end": 2650.83, "word": " عشرين", "probability": 0.9440104166666666}, {"start": 2650.83, "end": 2651.59, "word": " تمانية", "probability": 0.84228515625}, {"start": 2651.59, "end": 2652.29, "word": " عشرين", "probability": 0.9471028645833334}, {"start": 2652.29, "end": 2653.59, "word": " وخمسة", "probability": 0.8892578125}, {"start": 2653.59, "end": 2654.75, "word": " تلاتة", "probability": 0.925048828125}, {"start": 2654.75, "end": 2654.85, "word": " و", "probability": 0.56787109375}, {"start": 2654.85, "end": 2655.51, "word": " تلاتين", "probability": 0.938232421875}, {"start": 2655.51, "end": 2656.11, "word": " و", "probability": 0.355224609375}, {"start": 2656.11, "end": 2656.33, "word": " الله", "probability": 0.9052734375}, {"start": 2656.33, "end": 2656.73, "word": " يعطيك", "probability": 0.9637451171875}, {"start": 2656.73, "end": 2657.43, "word": " العافية", "probability": 0.85595703125}, {"start": 2657.43, "end": 2657.67, "word": " و", "probability": 0.91845703125}, {"start": 2657.67, "end": 2657.91, "word": " إلى", "probability": 0.8076171875}, {"start": 2657.91, "end": 2658.39, "word": " لقاء", "probability": 0.7674153645833334}, {"start": 2658.39, "end": 2658.85, "word": " آخر", "probability": 0.927978515625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2659.822625, "duration_after_vad": 2555.96374999999}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5thS97U7ozY.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5thS97U7ozY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..82e8807cec5033fd4d650198bd80867c3d46a822
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5thS97U7ozY.srt
@@ -0,0 +1,1831 @@
+1
+00:00:19,560 --> 00:00:26,980
+بسم الله الرحمن الرحيم المحاضرة رقم 22 مساق نظرية
+
+2
+00:00:26,980 --> 00:00:33,820
+الأعداد لطلاب الجامعة الإسلامية قسم رياضيات كلية
+
+3
+00:00:33,820 --> 00:00:40,120
+العلوم وكلية التربية وصلنا لعند الـ section الثاني
+
+4
+00:00:40,120 --> 00:00:45,250
+من شطر 6 تحت عنوان The Mobius Inversion Formula
+
+5
+00:00:45,250 --> 00:00:52,290
+بدنا نعرف الآن بدنا نعرف الـ function ميو هذا عبارة عن
+
+6
+00:00:52,290 --> 00:01:01,110
+دالة هنعرفها من Z positive لعند اللي هو zero واحد
+
+7
+00:01:01,110 --> 00:01:07,610
+ونقص واحد أو لعند Z إذا شئت الآن التعريفة كالتالي
+
+8
+00:01:07,610 --> 00:01:15,460
+هنعرف ميو of n تساوي بتساوي واحد إذا كانت الـ n إيش
+
+9
+00:01:15,460 --> 00:01:22,680
+بتساوي واحد وحنقول أن ميو n بتساوي صفر if اللي هو
+
+10
+00:01:22,680 --> 00:01:33,380
+b تربيع بتقاسم الـ n for some prime b وبساوي سالب
+
+11
+00:01:33,380 --> 00:01:41,340
+واحد أس r بتساوي b1 b2 لعند الـ br
+
+12
+00:01:41,340 --> 00:01:50,020
+where b1 لعند الـ br are distinct primes اللي
+
+13
+00:01:50,020 --> 00:01:56,560
+هي .. اللي هي primes مختلفة الآن لو جينا حسبنا الـ
+
+14
+00:01:56,560 --> 00:02:01,880
+mu of واحد واضح إيش بتساوي واحد لأن أنا عارف
+
+15
+00:02:01,880 --> 00:02:05,560
+الدالة إيش هي ميو of واحد بيساوي واحد إذا كانت أنا
+
+16
+00:02:05,560 --> 00:02:10,370
+بتساوي واحد إذا كانت n فيها مربع كامل في داخلها
+
+17
+00:02:10,370 --> 00:02:15,210
+يعني فيه b تربيع بتقسمها معناته صارت الـ mu n إيش
+
+18
+00:02:15,210 --> 00:02:20,470
+بتساوي صفر إذا كانت اللي هي n أكبر من واحد و
+
+19
+00:02:20,470 --> 00:02:24,310
+square free يعني مافيش فيها ولا square معناته الـ
+
+20
+00:02:24,310 --> 00:02:27,950
+n إيش هتكون على صورة b1 b2 يعني b are
+
+21
+00:02:27,950 --> 00:02:32,330
+distinct primes ومش هيتكرر الـ primes لأنه لو تكرر
+
+22
+00:02:32,330 --> 00:02:35,030
+بيصير فيه b تربيع معناته صار في الحالة الثانية
+
+23
+00:02:44,040 --> 00:02:48,060
+بناء على هذا الحديث الـ mu of واحد واحد الـ mu of
+
+24
+00:02:48,060 --> 00:02:53,360
+اثنين اللي هو اندي بس إيش one prime n بتساوي
+
+25
+00:02:53,360 --> 00:02:56,840
+اثنين إذا حيصير حسب الحديث اللي هان عبارة عن ناقص
+
+26
+00:02:56,840 --> 00:03:02,000
+واحد أس واحد لأنه إيش مالها اثنين الـ mu of اثنين
+
+27
+00:03:02,000 --> 00:03:07,710
+الـ b واحد اثنين وفيش غيرهم معايا إذا هو يساوي سالب
+
+28
+00:03:07,710 --> 00:03:12,410
+واحد إنه يقف ثلاثة من نفس الأسلوب إيش هيساوي ناقص
+
+29
+00:03:12,410 --> 00:03:16,970
+واحد قص واحد ويساوي إيش ماله سالب واحد إنه يقف
+
+30
+00:03:16,970 --> 00:03:23,450
+أربعة إيش هيساوي صفر ليش لأنه اثنين تربيع تقاسم
+
+31
+00:03:23,450 --> 00:03:28,990
+الأربعة يعني فيه في داخله إيش اللي هو مربع كامل
+
+32
+00:03:28,990 --> 00:03:35,480
+واضح أه؟ إنه يقف خمسة اللي هو سالب واحد ميو في ستة
+
+33
+00:03:35,480 --> 00:03:41,480
+اللي هو الستة إيه إيش مالها عبارة عن ثلاثة في اثنين
+
+34
+00:03:41,480 --> 00:03:45,480
+واتنين في اثنين هذا وهذا distinct primes ومفيش
+
+35
+00:03:45,480 --> 00:03:49,380
+فيهم اللي هو مين مربع كامل إذا إيش هيساوي ناقص
+
+36
+00:03:49,380 --> 00:03:55,840
+واحد قص هي واحد اثنين عدد الـ primes فاهمين قص اثنين
+
+37
+00:03:55,840 --> 00:04:01,970
+ويساوي واحد ميو في سبعة -1 يعني واضح أن ميو أي
+
+38
+00:04:01,970 --> 00:04:07,770
+prime يساوي سالب واحد ميو في ثمانية صفر لأن الثمانية
+
+39
+00:04:07,770 --> 00:04:12,350
+فيها إيش مالها اثنين تربيع بتقسم الثمانية فيها مربع
+
+40
+00:04:12,350 --> 00:04:19,110
+كامل ميو في تسعة ميو في تسعة إيش مالها صفر برضه لأن
+
+41
+00:04:19,110 --> 00:04:24,730
+ثلاثة تربيع بتقسم التسعة ميو في عشرة اللي هو العشرة
+
+42
+00:04:24,730 --> 00:04:29,370
+خمسة في اثنين اللي هو عبارة عن سالب واحد قص اثنين
+
+43
+00:04:29,370 --> 00:04:33,970
+ويساوي واحد لإن العشرة بتساوي خمسة في اثنين لو
+
+44
+00:04:33,970 --> 00:04:39,130
+قلنا ميو of سبعين
+
+45
+00:04:39,130 --> 00:04:46,910
+إيش بتساوي اللي هو عبارة عن خمسة في اثنين في سبعة
+
+46
+00:04:46,910 --> 00:04:51,390
+اللي هو عبارة عن سالب واحد قص ثلاثة ويساوي سالب
+
+47
+00:04:51,390 --> 00:05:02,130
+واحد واضح صحيح ميو of عشرين صفر لإن فيها أربعة اللي
+
+48
+00:05:02,130 --> 00:05:06,870
+هي اثنين تربيع واضح أه الآن هذه الـ function اللي
+
+49
+00:05:06,870 --> 00:05:13,650
+هي نسميها Mobius function الآن هذه أداء بتساعدنا
+
+50
+00:05:13,650 --> 00:05:18,650
+اللي هو في تسهيل اللي هو كثير من الأمور هنشوفها إن
+
+51
+00:05:18,650 --> 00:05:23,870
+شاء الله نأتي الأن لأول نظرية نظرية 6.5 اللي هي
+
+52
+00:05:23,870 --> 00:05:27,470
+مبيوظ ميو فانكشن اللي بنحكي عنها ميو is a
+
+53
+00:05:27,470 --> 00:05:31,750
+multiplicative function بدنا نثبت لك الآن أن هذا
+
+54
+00:05:31,750 --> 00:05:37,150
+الـ function ميو is a multiplicative function ميو
+
+55
+00:05:37,150 --> 00:05:39,990
+is a multiplicative function
+
+56
+00:05:47,240 --> 00:05:54,340
+قلنا لـ mu اللي هي تلت قيم يا واحد، يا صفر، يا
+
+57
+00:05:54,340 --> 00:05:59,700
+سالب واحد، إذا كانت n بتساوي واحد، إذا كانت p
+
+58
+00:05:59,700 --> 00:06:03,800
+تربيع تقاسم الـ n for some p، إذا كانت اللي هي ناقص
+
+59
+00:06:03,800 --> 00:06:09,080
+واحد أس r، إذا كانت اللي هي n بتساوي p1، لعند
+
+60
+00:06:09,080 --> 00:06:11,780
+الـ pr are distinct primes، بس خلينا أحطها أساسا
+
+61
+00:06:11,780 --> 00:06:15,900
+تتذكروا، أعطيكم تذكرينها، نيجي الآن الـ theorem
+
+62
+00:06:15,900 --> 00:06:25,000
+اللي عندي Theorem اللي هي 6 خمسة ميو is a
+
+63
+00:06:25,000 --> 00:06:31,980
+multiplicative function نبرهنها
+
+64
+00:06:31,980 --> 00:06:39,130
+الـ proof أذكركم شو .. كيف بينا .. من برهان اللي هو
+
+65
+00:06:39,130 --> 00:06:42,450
+الـ function is multiplicative، قولنا بتكون الـ
+
+66
+00:06:42,450 --> 00:06:45,890
+function f is multiplicative إذا كان حققت، إن الـ
+
+67
+00:06:45,890 --> 00:06:48,490
+greatest common divisor بين الـ m والـ n بتساوي
+
+68
+00:06:48,490 --> 00:06:54,730
+واحد يعطيني إن الـ f في m في n إيش مالها بتساوي f في m
+
+69
+00:06:54,730 --> 00:07:03,650
+في f of n يعني تتحقق أن f mn بتساوي fm fn لكل
+
+70
+00:07:03,650 --> 00:07:07,130
+الـ m والـ n العامل المشترك الأعلى بينهما بتساوي
+
+71
+00:07:07,130 --> 00:07:11,850
+واحد، واضح؟ إذا الآن يجب أن أبرهن أن ميو هي عملية
+
+72
+00:07:11,850 --> 00:07:19,490
+مرتبطة إذا افترض أن أقول لـ m و n element in z
+
+73
+00:07:19,490 --> 00:07:23,690
+positive such that the greatest common divisor بين
+
+74
+00:07:23,690 --> 00:07:29,850
+الـ m والـ n بتساوي واحد بدي أثبت لك أصلاً أنه لازم
+
+75
+00:07:29,850 --> 00:07:35,810
+يطلع عندي ميو mn بتساوي ميو m في ميو
+
+76
+00:07:35,810 --> 00:07:40,810
+n الآن كيف بدي أسوي هذه بدي آخذ cases الـ case الأول
+
+77
+00:07:40,810 --> 00:07:47,170
+إن يكون عندي بدي أجزم أموري إلى three cases الـ
+
+78
+00:07:47,170 --> 00:07:50,650
+case الأول و الـ case الثاني و الـ case الثالث الـ
+
+79
+00:07:50,650 --> 00:07:53,150
+case الأول إن يكون either
+
+80
+00:07:56,780 --> 00:08:04,240
+m or n is one or both يا إما m يا إما n بتساوي
+
+81
+00:08:04,240 --> 00:08:13,540
+واحد أو التنتين واحد الـ case الثانية إن either m
+
+82
+00:08:13,540 --> 00:08:18,120
+or n اللي هو contains a square
+
+83
+00:08:25,170 --> 00:08:30,870
+بمعنى آخر إن b تربيع تقاسم الـ m أو b تربيع تقاسم
+
+84
+00:08:30,870 --> 00:08:35,210
+الـ n يعني أو بص طبعًا ماشي الحال الـ case الثالثة
+
+85
+00:08:37,400 --> 00:08:42,640
+هذه كل الـ m و الـ n اللي عندي يا تنتين .. يا واحد
+
+86
+00:08:42,640 --> 00:08:47,220
+منهم على الأقل بتساوي واحد يا واحد منهم على الأقل
+
+87
+00:08:47,220 --> 00:08:53,520
+فيه مربع كامل يا إما التنتين الـ m و الـ n أكبر من
+
+88
+00:08:53,520 --> 00:09:04,550
+واحد and both m and n are square free يعني مافيش
+
+89
+00:09:04,550 --> 00:09:10,790
+فيه مياشي أي مربع كامل إذا الجزء اللي هو لهذا m or
+
+90
+00:09:10,790 --> 00:09:16,990
+n بتساوي واحد الجزء الثاني اللي هو m or n contains
+
+91
+00:09:16,990 --> 00:09:23,600
+a square اللي هو طبعًا الآن الجزء الثالث both of m
+
+92
+00:09:23,600 --> 00:09:28,800
+and n are greater than one and they are square of
+
+93
+00:09:28,800 --> 00:09:33,920
+free واضح هاه؟ طيب نجي للحالة الأولى الحالة
+
+94
+00:09:33,920 --> 00:09:42,500
+الأولى if mu m في n هيساوي لو كانت الآن بتساوي واحد
+
+95
+00:09:42,500 --> 00:09:48,640
+معناها صارت هذه mu m صح ولا لأ هذا f m بتساوي واحد
+
+96
+00:09:48,640 --> 00:09:56,220
+لو كانت الـ m بتساوي واحد بيصير mu m f m بتساوي واحد
+
+97
+00:09:57,100 --> 00:10:01,760
+التنتين في الحالتين في الحالتين اللي هي بتساوي
+
+98
+00:10:01,760 --> 00:10:09,200
+ميو m في ميو n لأن ميو of واحد إيش بتساوي واحد
+
+99
+00:10:09,200 --> 00:10:12,920
+معناه إن صارت ميو of m في الواحد هي ميو m في ميو
+
+100
+00:10:12,920 --> 00:10:18,140
+n وصارت الـ ميو n في الـ ميو m اللي هي واحد بتساوي
+
+101
+00:10:18,140 --> 00:10:21,820
+ميو m في ميو n صارت في هذه الحالة بتحقق شروط
+
+102
+00:10:21,820 --> 00:10:25,960
+الـ ميو is multiplicative in the first case نجي in
+
+103
+00:10:25,960 --> 00:10:33,520
+the second main case الحالة الثانية يا إما b تربيع
+
+104
+00:10:33,520 --> 00:10:37,300
+بتكسب m أو b تربيع بتكسب الـ n أو بتكسب أو الـ both
+
+105
+00:10:37,300 --> 00:10:40,320
+بتكسب الـ n يعني b1 تربيع و b2 تربيع
+
+106
+00:10:40,320 --> 00:10:43,920
+واحدة بتكسب الـ m واحدة بتكسب الـ n إيه يعني then
+
+107
+00:10:43,920 --> 00:10:50,650
+then أكيد هيكون الـ b بتكسب الـ n الـ b تربيع تكسب
+
+108
+00:10:50,650 --> 00:10:55,230
+الـ n فن، مدام الـ b تربيع تكسب هذه أو هذه، إذا
+
+109
+00:10:55,230 --> 00:11:00,050
+الـ b تربيع تكسب الـ n فن حصل الضرب، إذا صار
+
+110
+00:11:00,050 --> 00:11:10,370
+عندي الـ n then mu n فن هيساوي إيه؟ صفر، لأنه صارت
+
+111
+00:11:10,370 --> 00:11:16,390
+الـ n فن إيش مالها تحتوي على مربع كامل طيب هذا بيساوي
+
+112
+00:11:16,390 --> 00:11:22,130
+ميو m في ميو n ليش؟ لأن لو كانت الـ m يعني واحدة
+
+113
+00:11:22,130 --> 00:11:24,650
+من اللي حد تقول احتوى ميو مربع كامل لذا واحدة من
+
+114
+00:11:24,650 --> 00:11:28,270
+اللي على الأقل صفر لذا حصل ضرر من صفر إذا صار هذا
+
+115
+00:11:28,270 --> 00:11:32,650
+بيساوي هذا إذا برضه في الحالة الثانية بتحقق شروط
+
+116
+00:11:32,650 --> 00:11:36,570
+الـ multiplicative فيه نجي لأهالي الحالة الثالثة إن m
+
+117
+00:11:36,570 --> 00:11:41,690
+و n أكبر من واحد and both are square free شوف
+
+118
+00:11:41,690 --> 00:11:41,970
+كيف
+
+119
+00:11:50,730 --> 00:12:01,370
+خليني أظهر الحالة الثالثة case 3 لأن عندك الـ m
+
+120
+00:12:01,370 --> 00:12:08,790
+و الـ n أكبر من واحد و square free then أكيد by
+
+121
+00:12:08,790 --> 00:12:15,490
+unique factorization theorem m بتساوي b1 b2 لعند
+
+122
+00:12:15,490 --> 00:12:20,250
+الـ pr و لا يوجد تكرار لأن أنا فرضت هان إن إيش مالها
+
+123
+00:12:20,250 --> 00:12:23,910
+square free ونفس الشيء عند
+
+124
+00:12:47,480 --> 00:12:48,880
+n�
+
+125
+00:12:48,910 --> 00:12:51,990
+لأن لو كان فيه أي primes بين هذه وهذه مشتركة
+
+126
+00:12:51,990 --> 00:12:56,190
+معناته صار العامل المشترك الأعلى بينهم مش واحد إذا
+
+127
+00:12:56,190 --> 00:13:04,390
+أكيد then b1 b2 اللي عند pr و q1 اللي عند qs
+
+128
+00:13:04,390 --> 00:13:08,490
+are distinct
+
+129
+00:13:08,490 --> 00:13:11,570
+primes
+
+130
+00:13:11,570 --> 00:13:21,730
+معايا يا شباب الحسب السهل الآن ميو n في n بتساوي
+
+131
+00:13:21,730 --> 00:13:26,930
+اللي صار الـ factorization لها هو هذا في هذا وكل
+
+132
+00:13:26,930 --> 00:13:30,490
+index distinct primes إذا حسب القانون إيش هيطلع
+
+133
+00:13:30,490 --> 00:13:35,510
+عندي ناقص واحد أس r لإن عدد هنا دولة distinct
+
+134
+00:13:35,510 --> 00:13:40,830
+prime إيش مالها r زائد s ويساوي
+
+135
+00:13:41,860 --> 00:13:47,320
+سالب واحد أس r في سالب واحد أس s سالب واحد
+
+136
+00:13:47,320 --> 00:13:52,820
+أس r هو في الواقع مين ميو m وهذا في الواقع مين؟
+
+137
+00:13:52,820 --> 00:13:58,160
+ميو n وهو المطلوب therefore في كل الأحوال طلع
+
+138
+00:13:58,160 --> 00:14:00,440
+إن لما greatest common divisor بين الـ m و الـ n
+
+139
+00:14:00,440 --> 00:14:04,720
+بتساوي واحد طلع عندي ميو mn بتساوي ميو m في
+
+140
+00:14:04,720 --> 00:14:09,040
+ميو n therefore ميو is a multiplicative function 
+
+141
+00:14:09,040 --> 00:14:13,540
+μ is a multiplicative function أي سؤال
+
+142
+00:14:22,240 --> 00:14:24,920
+وشوف في صلة النبي عليه الصلاة والسلام المرة 
+
+143
+00:14:24,920 --> 00:14:33,260
+الماضية كان في عيننا نظرية أثبتناها بتقول
+
+144
+00:14:33,260 --> 00:14:39,620
+إذا كانت F و M F و F capital اللي هو عبارة عن
+
+145
+00:14:39,620 --> 00:14:48,200
+number theoretic functions وكانت اللي هي الـ F is 
+
+146
+00:14:48,200 --> 00:14:53,920
+multiplicative الـ F small is multiplicative ثم
+
+147
+00:14:53,920 --> 00:15:00,740
+وكان عندي الـ F capital عبارة عن summation F small من
+
+148
+00:15:00,740 --> 00:15:09,460
+D دي بتجسم N ثم F capital برضه إيش is multiplicative
+
+149
+00:15:10,120 --> 00:15:12,580
+كمان مرة أذكركم فيها نظرية هذه المرة الفاترة
+
+150
+00:15:12,580 --> 00:15:16,860
+اتخذناها النظرية بتقول مالي إذا كانت ال F و ال F 
+
+151
+00:15:16,860 --> 00:15:21,320
+كابتال are number theoretic functions و ال F small
+
+152
+00:15:21,320 --> 00:15:25,640
+is multiplicative و ال F capital مكتوبة على صورة
+
+153
+00:15:25,640 --> 00:15:31,080
+summation لل F small of D D بتجسم N بتطلع هذه ال F
+
+154
+00:15:31,080 --> 00:15:35,480
+الكبيرة أو ال F capital أشمالها is multiplicative
+
+155
+00:15:36,610 --> 00:15:40,010
+واضح ليش اللي بحكيه طبعا هنصل لـ F آخر المحاضرة
+
+156
+00:15:40,010 --> 00:15:45,890
+أنه لو كانت اللي هي ال F small multiplicative .. آسف
+
+157
+00:15:45,890 --> 00:15:49,150
+ال F capital multiplicative هتطلع ال F small برضه
+
+158
+00:15:49,150 --> 00:15:54,870
+أشمالها is multiplicative مش الحال لأن هذه النظرية
+
+159
+00:15:54,870 --> 00:16:00,430
+اللي هي اللي بحكي عنها اللي هنصلها الجسر اللي هو
+
+160
+00:16:00,430 --> 00:16:04,410
+الوصول إليها هي عبارة عن ال mobius function اللي
+
+161
+00:16:04,410 --> 00:16:10,860
+هي الميوالان بدي .. اللي هي استخدم هذه النظرية بعد
+
+162
+00:16:10,860 --> 00:16:15,220
+شوية لإثبات شغلة من خواص اللي هي الـ Mobius
+
+163
+00:16:15,220 --> 00:16:21,100
+function نيجي الان ل .. اللي هي نظرية 6-6 بقولي
+
+164
+00:16:21,100 --> 00:16:26,680
+لأي انتجار N أكبر و ساوي واحد؟
+
+165
+00:16:26,680 --> 00:16:34,660
+شوفوا
+
+166
+00:16:34,660 --> 00:16:46,490
+عنديا يا شباب عندي لو جيه اتعرفت أنا F of N ستة
+
+167
+00:16:46,490 --> 00:16:52,910
+ستة الـ N لأي N positive integer أكبر أو يساوي واحد
+
+168
+00:16:52,910 --> 00:17:01,850
+الـ F of N بدي أعرفها أنا بالساعة والصممشن Mu of D
+
+169
+00:17:01,850 --> 00:17:07,500
+دي بتقسم الـ N هكذا انت عارفه ماشي الحل الان إيش
+
+170
+00:17:07,500 --> 00:17:11,600
+النظرية بتقوللي بتقوللي هتطلع قيمة هذه هذا ال
+
+171
+00:17:11,600 --> 00:17:17,580
+summation هيطلع قيمته الان الان four ان أكبر أو يساوي
+
+172
+00:17:17,580 --> 00:17:20,700
+واحد هيطلع عندي ال F of N اللي هو ال summation هذا
+
+173
+00:17:20,700 --> 00:17:25,920
+هذا ال summation هيطلع قيمته عبارة عن واحد F of N
+
+174
+00:17:25,920 --> 00:17:32,570
+بتساوي واحد و صفر F of N أشمالها أكبر من واحد يعني
+
+175
+00:17:32,570 --> 00:17:36,530
+هتطلعلي الدالة هذه يا صفر يا إيش يا واحد يعني عندي
+
+176
+00:17:36,530 --> 00:17:40,690
+ال F of N له هذا ال summation لأن F of N أنا معرف
+
+177
+00:17:40,690 --> 00:17:43,550
+لك يهيك هذا ال summation أنا بقولك النظرية
+
+178
+00:17:43,550 --> 00:17:46,910
+هتطلعليها هذه هتثبتلك في الآخر أنه هتساوي واحد إذا
+
+179
+00:17:46,910 --> 00:17:50,970
+كانت N بتساوي واحد و Zero إذا كانت N أشمالها أكبر
+
+180
+00:17:50,970 --> 00:17:58,390
+من واحد نيجي لل proof ال proof سهل شوف F of N
+
+181
+00:17:58,390 --> 00:18:05,520
+بتساوي واحد إذا n بيتساوى واحد ثم ال f of واحد في
+
+182
+00:18:05,520 --> 00:18:10,820
+هذه الحالة هيساوي ال summation حسب ما نعرفه μ of D
+
+183
+00:18:10,820 --> 00:18:15,400
+دي بتكسب مين الواحد قسم الواحد بس مين هي الموجبة
+
+184
+00:18:15,400 --> 00:18:19,740
+واحد إذا هيساوي μ of واحد اللي هي إيش عرفناها
+
+185
+00:18:19,740 --> 00:18:24,260
+بتساوي واحد إذا صارت عندي f واحد فعلا إيش بتساوي
+
+186
+00:18:24,260 --> 00:18:31,450
+واحد لإن بتاخد n إيش مالها لإن let n أكبر strictly
+
+187
+00:18:31,450 --> 00:18:35,270
+من مين؟ من واحد مدام n أكبر من واحد اذا by unique
+
+188
+00:18:35,270 --> 00:18:37,750
+factorization theorem n can be written as a
+
+189
+00:18:37,750 --> 00:18:42,750
+canonical form then by unique factorization
+
+190
+00:18:42,750 --> 00:18:47,370
+theorem n بتساوي p1 α1 لعند p r
+
+191
+00:18:47,370 --> 00:18:51,670
+أشمالها α r where p1 و p2 و p r
+
+192
+00:18:51,670 --> 00:18:58,100
+are distinct primes مش الحال then then بدي احسب
+
+193
+00:18:58,100 --> 00:19:03,740
+الان مين انا اللي هي F of N F of N إيش بتساوي F of
+
+194
+00:19:03,740 --> 00:19:10,120
+p1 α1 لعند p r α r إيش r لاحظوا الان
+
+195
+00:19:10,120 --> 00:19:15,280
+لاحظوا الان ما يليه النظرية هذه اللي فوق بتقول لو
+
+196
+00:19:15,280 --> 00:19:17,640
+كان اللي جوا multiplicative هيكون ال summation
+
+197
+00:19:17,640 --> 00:19:21,880
+أشماله multiplicative طب ما احنا أثبتنا قبل بشوية
+
+198
+00:19:21,880 --> 00:19:25,080
+أن هاد الـ μ أشماله multiplicative إذا ال
+
+199
+00:19:25,080 --> 00:19:28,300
+summation هيطلع أشماله multiplicative بالنظرية
+
+200
+00:19:28,300 --> 00:19:32,240
+اللي فوق إذا صارت عندي ال F هذه أشمالها is a
+
+201
+00:19:32,240 --> 00:19:35,780
+multiplicative function مدام F is a multiplicative
+
+202
+00:19:35,780 --> 00:19:44,770
+function إذا بتساوي F of p1 α1 لعند F of p r α r لإيش
+
+203
+00:19:44,770 --> 00:19:48,210
+لأن الـ p1 و p2 اللي عند الـ p r are distinct primes
+
+204
+00:19:48,210 --> 00:19:51,490
+معناته الـ greatest common divisor بين item 2
+
+205
+00:19:51,490 --> 00:19:57,850
+بساوية واحد فعلا الان بل علي اوجد هذه شوف كيف بده
+
+206
+00:19:57,850 --> 00:20:06,140
+اوجدها الان F of p1 α1 إيش هتساوي حسب اللي هو
+
+207
+00:20:06,140 --> 00:20:11,520
+التعريف اللي عرفناها summation μ of D حيث الـ D بتكسب
+
+208
+00:20:11,520 --> 00:20:18,290
+p1 α1، مظبوط؟ لأن F of p1 α1
+
+209
+00:20:18,290 --> 00:20:22,410
+بتوجدها لأن وين ال formula اللي معطنيها F of N انا
+
+210
+00:20:22,410 --> 00:20:26,190
+بساوي ال summation شيله الان و أحط مكانها مين p
+
+211
+00:20:26,190 --> 00:20:29,630
+واحد α1 فبصي ال summation لأن ال μ دي لدي
+
+212
+00:20:29,630 --> 00:20:34,790
+بتكسب مين p1 α1 لأن قواسم القواسم العدب
+
+213
+00:20:34,790 --> 00:20:40,150
+p1 α1 يا الواحد يا ال p1 يا p1
+
+214
+00:20:40,150 --> 00:20:44,930
+تربيع يا p1 تكعيب لما أصل عند p1 أشمالها
+
+215
+00:20:44,930 --> 00:20:49,810
+α1 إذا ال summation هذا بيصير μ للواحد
+
+216
+00:20:49,810 --> 00:20:55,670
+أول قاسم زائد القاسم التاني مين هو p1 زائد
+
+217
+00:20:55,670 --> 00:20:59,890
+القاسم الثالث مين هو هو p1 تربيع زائد لما أصل
+
+218
+00:20:59,890 --> 00:21:07,510
+لآخر قاسم p1 α1 ويساوي μ فى واحد إيش
+
+219
+00:21:07,510 --> 00:21:12,190
+نجناها واحد μ of p1 قبل بشوية حسب انها إيش
+
+220
+00:21:12,190 --> 00:21:20,080
+بتساوي μ ل p1 سالب واحد قبل شوية كتبناها ناقص
+
+221
+00:21:20,080 --> 00:21:24,180
+واحد أسو r اللي هي واحد يعني اللي هي ناقص واحد
+
+222
+00:21:24,180 --> 00:21:29,160
+زائد هدولة كلهم إيش مالهم أصفار لإن كلهم فيهم إيش
+
+223
+00:21:29,160 --> 00:21:35,520
+p1 كربع واضح إذا زائد صفر زائد صفر ويساوي
+
+224
+00:21:35,520 --> 00:21:40,960
+واحد ناقص واحد صفر إذا صار F of p1 α1
+
+225
+00:21:40,960 --> 00:21:46,160
+إيش هيساوي صفر إذا صار عندي F of N بيساوي هذا صفر
+
+226
+00:21:46,160 --> 00:21:52,670
+و الرابع جات زيه بصير إيش مساوى F
+
+227
+00:21:52,670 --> 00:21:57,230
+of N بتساوي صفر يعني بمعنى آخر لما كانت N أكبر
+
+228
+00:21:57,230 --> 00:22:02,750
+من واحد طلعت لي ال summation هذا إيش مساوى صفر إذا
+
+229
+00:22:02,750 --> 00:22:03,410
+فضل
+
+230
+00:22:09,110 --> 00:22:12,410
+احنا عرفناها ده الـ function قبل ما تيجي عرفناها
+
+231
+00:22:12,410 --> 00:22:17,550
+ده لإنه أي عدد فيه square في داخله الـ μ له إيش
+
+232
+00:22:17,550 --> 00:22:20,670
+ما لها صفر طيب
+
+233
+00:22:23,180 --> 00:22:27,360
+هنأتي الآن لـ Mobius inversion formula الموبيوس
+
+234
+00:22:27,360 --> 00:22:31,280
+inversion formula نشوف إيش اللي بتقول الموبيوس inversion
+
+235
+00:22:31,280 --> 00:22:36,280
+formula بتقول إنه لو كانت F capital و F small two
+
+236
+00:22:36,280 --> 00:22:40,340
+number theoretic functions وكانت ال F of N بيساوي
+
+237
+00:22:40,340 --> 00:22:45,500
+ال summation F of D دي بتقسم N إذا بقدر اكتب ال F
+
+238
+00:22:45,500 --> 00:22:50,570
+N الـ F of N عند الـ F capital مكتوب على صورة summation
+
+239
+00:22:50,570 --> 00:22:54,470
+لمن؟ لـ F small الآن الـ Mobius inversion Formula
+
+240
+00:22:54,470 --> 00:22:58,730
+بتعكس للكتابة بتقول بأقدر أكتب لك الـ F small اللي
+
+241
+00:22:58,730 --> 00:23:03,870
+جوا على صورة summation برضه لمن؟ لمن؟ لـ divisors
+
+242
+00:23:03,870 --> 00:23:09,170
+دي بتكسم N بس الآن في عامل مساعد العامل المساعد مين
+
+243
+00:23:09,170 --> 00:23:13,190
+هو الـ Mobius function بيساوي summation μ of D F
+
+244
+00:23:13,190 --> 00:23:19,290
+of N على D أو μ N على D F of D D بتجسم الـ N بنشوف
+
+245
+00:23:19,290 --> 00:23:24,030
+كمان مرة بالتفصيل إيش النظرية دي بتقول وإيش
+
+246
+00:23:24,030 --> 00:23:30,230
+برهانها شوفوا
+
+247
+00:23:30,230 --> 00:23:32,330
+يا شباب عادي
+
+248
+00:23:54,280 --> 00:23:57,780
+النظرية اللي قبل شوية حكيناها هي summation μ of D
+
+249
+00:23:57,780 --> 00:24:05,080
+D بيقسم N بساوة صفر F N بساوة أكبر من واحد و واحد
+
+250
+00:24:05,080 --> 00:24:09,960
+F N بساوة واحد صح؟ طيب هذه النظرية اللي قبل شوية
+
+251
+00:24:09,960 --> 00:24:13,060
+بس عشان أنا هسا أخدمها نشوف إيش الموبيوث inversion
+
+252
+00:24:13,060 --> 00:24:18,580
+formula بتقول بتقول لو كانت F capital و F small
+
+253
+00:24:18,580 --> 00:24:24,510
+اللي هو number of theoretical functions معايا؟ و
+
+254
+00:24:24,510 --> 00:24:29,690
+بقول إن لو كانت عندي ال F of N مكتوبة على صورة
+
+255
+00:24:29,690 --> 00:24:37,410
+summation F of D small D تجسم N then ال F of N
+
+256
+00:24:37,410 --> 00:24:44,080
+مكتوبة على صورة F of D D تجسم N إذن بقدر اكتب نت مين
+
+257
+00:24:44,080 --> 00:24:49,660
+الـ F الصغيرة F of N of F small على صورة الـ
+
+258
+00:24:49,660 --> 00:24:53,540
+summation بس الـ N هذا الـ summation بعامل مساعد
+
+259
+00:24:53,540 --> 00:24:57,700
+مين هو العامل المساعد؟ الـ μ المحولة يعني اللي هي
+
+260
+00:24:57,700 --> 00:25:04,680
+μ برضه على إيش D بتقسم عنه μ of D اللي هي F
+
+261
+00:25:04,680 --> 00:25:14,580
+capital of N على D F capital of N على D هذه
+
+262
+00:25:14,580 --> 00:25:19,720
+النظرية لأن هذه طبعا بقدر اكتبها على صورة هذا قاسم
+
+263
+00:25:19,720 --> 00:25:24,320
+و هذا قاسم مظبوط ولا لا و هدولة بيحدثين مع بعض لذا
+
+264
+00:25:24,320 --> 00:25:28,120
+بقدر اكتبها على صورة بدل ما اقول μ of D بقدر اكتب
+
+265
+00:25:28,120 --> 00:25:34,580
+μ N على D و F N على D لأن هذا قاسم و هذا قاسم
+
+266
+00:25:34,580 --> 00:25:39,020
+هدولة و هدولة اكتلين أشمال لأن بيحدثن مع بعض D
+
+267
+00:25:39,590 --> 00:25:44,830
+بتكسم N الان يا الصورة هذه يا الصورة هذه قمناها
+
+268
+00:25:44,830 --> 00:25:51,550
+قبل هيك طيب إذا صار عندي الآن بدنا نثبت اللي هو F
+
+269
+00:25:51,550 --> 00:25:55,450
+capital F small of 1 بساوي ال summation اللي عندي
+
+270
+00:25:55,450 --> 00:26:03,710
+خلي هنا نشوف كيف نثبتها و بروف إيش بدنا نسوي بدنا
+
+271
+00:26:03,710 --> 00:26:08,540
+ناخد الطرف هذا و نوصله لهذا يعني أنا بالداخل اقول
+
+272
+00:26:08,540 --> 00:26:16,140
+summation μ of D F capital of N على D الـ D بتكسب
+
+273
+00:26:16,140 --> 00:26:27,500
+الان بساوة الان F of N هيها صح ولا لا هيها F of N
+
+274
+00:26:27,500 --> 00:26:31,100
+بساوة summation F of D D بتكسب الان طب F of N على
+
+275
+00:26:31,100 --> 00:26:39,120
+D أتخيل هذا C وهذا C F of F of N على D إيش هيساوي
+
+276
+00:26:39,120 --> 00:26:47,240
+F of اللي هي A اللي هي C بتكسب مين N على D فاهمين
+
+277
+00:26:47,240 --> 00:26:55,900
+اه واضح اه كمان مرة F of N بساوي F of C C بتكسب
+
+278
+00:26:55,900 --> 00:27:01,920
+مين الـ N لما تحسب مين F of N على D بيساوي .. ده
+
+279
+00:27:01,920 --> 00:27:06,460
+شيل ها دي و بدي احط قيمتها من هنا قيمتها بيساوي
+
+280
+00:27:06,460 --> 00:27:13,240
+summation μ of D D بتجسم N بدل ها دي شيل الـ N و 
+
+281
+00:27:13,240 --> 00:27:19,500
+أحط مكانها N على مين اللي هي F summation F of C C
+
+282
+00:27:19,500 --> 00:27:26,300
+بتجسم من N على D أي
+
+283
+00:27:26,300 --> 00:27:33,370
+سؤال؟ واضح أه؟ خلّي هدف الذاكرة بدي أعملك شغل هنا
+
+284
+00:27:33,370 --> 00:27:39,470
+أثبت لك شغل هنا عشان أستبدل اللي هو ال indices تبع
+
+285
+00:27:39,470 --> 00:27:44,570
+ال summation ب indices أخرى هتلزملي أه؟ بس قبلها
+
+286
+00:27:44,570 --> 00:27:49,490
+خلّينا نكمل Y ساوي بدي أضرب هدف الداخل أدخلها لجوا
+
+287
+00:27:49,490 --> 00:27:57,630
+اضرب عادي summation summation Mu of D في F of C دي
+
+288
+00:27:57,630 --> 00:28:01,730
+بتكسم الان و C بتكسم مين الان على دي ايش الفكرة
+
+289
+00:28:01,730 --> 00:28:08,150
+الآن الفكرة ان احاول اخل ال U of D هذه لحالها و
+
+290
+00:28:08,150 --> 00:28:11,870
+أشيل ال F of C تيجيها بطريقة معينة بتغيير ال
+
+291
+00:28:11,870 --> 00:28:15,880
+indices ليه؟ لأن الـSummation الـU في دي أنا بعرفه
+
+292
+00:28:15,880 --> 00:28:21,060
+يا واحد يا سفر فبصير مجموعه بس اللي هو طبعا السفر
+
+293
+00:28:21,060 --> 00:28:24,840
+خلاص بروح بظل مين عنده بس اللي عند الواحد اللي هي
+
+294
+00:28:24,840 --> 00:28:30,430
+عند اللي هي N بتساوي واحد إذا الفكرة أني أبسط هذا
+
+295
+00:28:30,430 --> 00:28:34,150
+الموضوع عن طريق اللي هو كتابة هذا على صورة أنه
+
+296
+00:28:34,150 --> 00:28:37,110
+أشيل ال F of C في الجهة دي و أخلّي ال summation
+
+297
+00:28:37,110 --> 00:28:40,190
+الميو دي لحاله الميو دي لحاله ال summation اللي هو
+
+298
+00:28:40,190 --> 00:28:43,990
+إيش بيساوي؟ بيساوي واحد و ال zero خلاص ما هو بيصير
+
+299
+00:28:43,990 --> 00:28:51,650
+ال summation سفر بيصير كمجموع بيبقى للواحد لنشوف
+
+300
+00:28:51,650 --> 00:29:00,740
+كيف؟ بتثبت لك الان شغلة بيثبت لك ان هذا ال condition
+
+301
+00:29:00,740 --> 00:29:09,120
+هي و من هنا لها دي بتقسم الان دي بتقسم الان and
+
+302
+00:29:09,120 --> 00:29:13,360
+C بتقسم N على D يكافئ
+
+303
+00:29:14,820 --> 00:29:19,080
+يكافئ condition تاني هو اللي بدو يسعفني في عملية
+
+304
+00:29:19,080 --> 00:29:22,540
+نقل ال F of C لأن F of C ماقدرش أنجلها ال gate لإن
+
+305
+00:29:22,540 --> 00:29:27,320
+ال F of C اللي هو الجمع تبعها هشغال في هذا ال
+
+306
+00:29:27,320 --> 00:29:30,860
+summation فلو طلعته بيصير .. مافعش أطلعه، على مين
+
+307
+00:29:30,860 --> 00:29:35,740
+بيشتغل؟ بيصير اللي هو مش ثابت بالنسبة لهذا عشان
+
+308
+00:29:35,740 --> 00:29:41,330
+أطلعه برا فمينش ماحكي طيب إذا بدي أثبت لك إن هذا
+
+309
+00:29:41,330 --> 00:29:48,870
+بكافي اللي هو الـ C بيقسم N و D بيقسم N على C C
+
+310
+00:29:48,870 --> 00:29:59,210
+بيقسم N و D بيقسم N على C هذا اللي بتثبته أثبته زي
+
+311
+00:29:59,210 --> 00:30:02,830
+الحسابات بس شوف كيف خلّيني أخد اتجاهه تاني
+
+312
+00:30:02,830 --> 00:30:03,750
+similarly
+
+313
+00:30:06,170 --> 00:30:13,790
+D بتقسم الـN and C بتقسم الـN على D إيش معناته
+
+314
+00:30:13,790 --> 00:30:17,050
+هذا؟ إيش هو بيعطيني؟ D بتقسم الـN معناته أن الـN
+
+315
+00:30:17,050 --> 00:30:21,810
+بتساوي D في sum K يعني انتجر صار اللي هو الـN على
+
+316
+00:30:21,810 --> 00:30:29,530
+D and .. and اللي هو إيش بتصير هذا؟ N على D بتساوي
+
+317
+00:30:29,530 --> 00:30:37,780
+CM مثلا يعني بمعنى آخر الـ N بتساوي CM في مين في D
+
+318
+00:30:37,780 --> 00:30:43,940
+صح ولا لأ؟ طيب، طيب معناته أن هذا صارت الـC عامل
+
+319
+00:30:43,940 --> 00:30:48,740
+من عامل مين؟ الـ N، واضح الـ N بتساوي CM في D إذا
+
+320
+00:30:48,740 --> 00:30:52,260
+الـ C عامل من عامل الـ N إذا صار بيعطينا هذا C
+
+321
+00:30:52,260 --> 00:31:01,540
+بتكسب مين؟ آسف، بتكسب مين؟ الـ N صح ولا لأ؟ واضحة
+
+322
+00:31:01,540 --> 00:31:06,420
+أه؟ C بتكسب الـ N يعني صار عندي هذا و كأنه N في D
+
+323
+00:31:06,420 --> 00:31:14,180
+أش بيساوي N على C لأن برضه الـ D عمل من أهم الميان
+
+324
+00:31:14,180 --> 00:31:23,760
+N على C فاهمين؟ and D بتكسب الـ N على C إذن الـ D
+
+325
+00:31:23,760 --> 00:31:27,020
+بتكسب الـ N و الـ C بتكسب الـ N على D أعطاني C
+
+326
+00:31:27,020 --> 00:31:32,990
+بتكسب الـ N و الـ D بتكسب M Similarly هذا بقى D
+
+327
+00:31:32,990 --> 00:31:38,510
+لهذا إذا صار two conditions هذول أشمالهم متكافئين
+
+328
+00:31:38,510 --> 00:31:43,850
+واضح يعني هذا بيحدث مع هذا F أندر ال F إذا صار هذا
+
+329
+00:31:43,850 --> 00:31:49,370
+ال summation بيصير عبارة عن summation ميو of D أف
+
+330
+00:31:49,370 --> 00:31:55,330
+of C الآن بدل D بيكسب M وC بيكسب M على D بدي أحط
+
+331
+00:31:55,330 --> 00:31:58,870
+ال conditions اللي هي المكافئة لها اللي هو C بيكسب
+
+332
+00:31:58,870 --> 00:32:09,620
+M و الـ D تكسب مين؟ N على C واضح أه طيب صارت الأن
+
+333
+00:32:09,620 --> 00:32:13,740
+ال F of C بقدر أطلّح أين؟ برا لإن هذا ال summation
+
+334
+00:32:13,740 --> 00:32:18,500
+بيشتغل على مين؟ على ال D إذا هو يساوي summation F
+
+335
+00:32:18,500 --> 00:32:23,520
+of C C بتكسب N هاي بتشتغل عليها ال C فال summation
+
+336
+00:32:23,520 --> 00:32:29,700
+Mu of D ال D بتكسب مين؟ N على C لأن هذا ال
+
+337
+00:32:29,700 --> 00:32:38,030
+summation سفر ما عدا لما اللي هي الـ N على C أشوى
+
+338
+00:32:38,030 --> 00:32:43,230
+تساوي واحد سفر
+
+339
+00:32:43,230 --> 00:32:48,030
+ما عدا عند مين الـ N بتساوي واحد يعني هذا هيكون
+
+340
+00:32:48,030 --> 00:32:53,190
+سفر ما عدا عند مين عند N على C بتساوي واحد لأن هذا
+
+341
+00:32:53,190 --> 00:32:59,770
+بيساوي summation F of C في واحد ومتى
+
+342
+00:33:00,780 --> 00:33:09,500
+لما الـ N بيساوي الـ C N
+
+343
+00:33:09,500 --> 00:33:16,440
+على الـ C صح؟ شو معناته دي؟ N بيساوي الـ C واضح
+
+344
+00:33:16,440 --> 00:33:25,200
+ها؟ الـ C بتكسب الـ N و هذه بتعطيني ال N بتساوي C
+
+345
+00:33:25,200 --> 00:33:32,800
+يعني بمعنى آخر ال F of C بس عند N إيش بتساوي C
+
+346
+00:33:32,800 --> 00:33:40,140
+فاهمين أه؟ طب هذه إيش مالها؟ عبارة عن F of N
+
+347
+00:33:40,140 --> 00:33:43,400
+summation
+
+348
+00:33:43,400 --> 00:33:49,770
+of F of C لما C بتساوي N إيش بتساوي F of N؟ إذا صار
+
+349
+00:33:49,770 --> 00:33:58,530
+عندي الان ال F of N أيش صار بالساوية؟ و هو المطلوب
+
+350
+00:33:58,530 --> 00:34:07,410
+أي سؤال؟ طيب نشوف تطبيق ال Mobius Invergent
+
+351
+00:34:07,410 --> 00:34:07,950
+Formula
+
+352
+00:34:34,290 --> 00:34:43,090
+ما هو اللي بيقول لي؟ بيقول لي prove that الواحد
+
+353
+00:34:43,090 --> 00:34:49,690
+بيقوم
+
+354
+00:34:49,690 --> 00:34:58,510
+بصميم mu of n على d في tau of d دي بتجسم n
+
+355
+00:35:02,640 --> 00:35:08,320
+الـ N بتساوي الـ summation ميو of N على D سيجما of
+
+356
+00:35:08,320 --> 00:35:13,860
+D دي بتكسب إيش الـ N ماشي الحالة الـ proof
+
+357
+00:35:13,860 --> 00:35:18,260
+بتستخدم
+
+358
+00:35:18,260 --> 00:35:21,900
+اللي هي ال inversion ال Mobius inversion formula
+
+359
+00:35:21,900 --> 00:35:32,650
+إيش بده أقول؟ لأن أنا بعرف لأن since Tau of N بس هو
+
+360
+00:35:32,650 --> 00:35:38,010
+الـ summation للواحد واحد اللي هو دي بتكسب مين
+
+361
+00:35:38,010 --> 00:35:42,770
+الآن التو ايش اسمها؟ بس راكزوا معايا اذاكركوا فيها
+
+362
+00:35:42,770 --> 00:35:46,730
+التو ايش هي؟ number of divisors كيف بدأت number of
+
+363
+00:35:46,730 --> 00:35:49,610
+divisors كل مرة كل divisor بدأ يعد بواحد كل
+
+364
+00:35:49,610 --> 00:35:52,550
+divisor بدأ يعد بواحد معايا يا محمد فالآن بدي
+
+365
+00:35:52,550 --> 00:35:57,670
+أصميش للواحد اللي هو العداد عالميا على كل ال
+
+366
+00:35:57,670 --> 00:36:00,810
+divisors دي بتكسب مين الآن كل ما يجي divisor بعد
+
+367
+00:36:00,810 --> 00:36:03,910
+واحد كل ما يجي divisor بعد واحد إذا أنا أصميش
+
+368
+00:36:03,910 --> 00:36:09,860
+للواحد دي بتكسب مين الآن الاقلب دي أطبّق الـ
+
+369
+00:36:09,860 --> 00:36:12,180
+Inversion Formula بكرا اللي هي المبنية الـ
+
+370
+00:36:12,180 --> 00:36:15,740
+Inversion Formula على هذه لأن هذه بتعتبرها F
+
+371
+00:36:15,740 --> 00:36:20,540
+Capital و هذه بتعتبرها مين؟ F Small يعني الـ F
+
+372
+00:36:20,540 --> 00:36:24,380
+Small إيش بتساوي دائما واحد والـ F Capital مين هي
+
+373
+00:36:24,380 --> 00:36:29,720
+التاو لأن بيصير .. إذا هذي متحققة ولا لأ؟ هذي F
+
+374
+00:36:29,720 --> 00:36:34,480
+Capital عبارة عن summation لـ F Small إذا by
+
+375
+00:36:34,480 --> 00:36:42,860
+inversion then by Mobius Inversion Formula بدي اطلع
+
+376
+00:36:42,860 --> 00:36:47,240
+عندي ال F of N مين ال F of N اللي هو الواحد فاهمين
+
+377
+00:36:47,240 --> 00:36:55,680
+واحد بساوي ال summation ميو of مين of دي أه بدك
+
+378
+00:36:55,680 --> 00:37:00,920
+تأخذ هد خد هد زي ما بدك هد أو هد مش فارق أه ميو of
+
+379
+00:37:00,920 --> 00:37:07,000
+ان على دي عشان نعمل زي ما بده في مين في F of D اللي
+
+380
+00:37:07,000 --> 00:37:15,760
+هي مين؟ F of D تاو of D D تجسم الانوار واضحة ها
+
+381
+00:37:15,760 --> 00:37:20,820
+Similarly اللي المفى ... المركز عليها دي اللي مستمع
+
+382
+00:37:20,820 --> 00:37:32,000
+بشها دي عندي التانية الآن أنا معرف since اللي هي
+
+383
+00:37:32,000 --> 00:37:34,180
+الآن بتساوي
+
+384
+00:37:35,810 --> 00:37:45,890
+الـ summation لـ 
+
+385
+00:37:45,890 --> 00:37:55,930
+sigma of n سوى summation لـ D
+
+386
+00:37:55,930 --> 00:38:00,750
+دي بتكسب main الـ n أذكركم فيها هذه اللي هي
+
+387
+00:38:00,750 --> 00:38:05,130
+الـSigma of an H هي عبارة عن مجموع الـdivisors هي
+
+388
+00:38:05,130 --> 00:38:07,670
+عبارة عن الـsummation لكل الـdivisors من الـmain
+
+389
+00:38:07,670 --> 00:38:16,030
+لأ لأ معايا then برضه by Möbius inversion formula
+
+390
+00:38:16,030 --> 00:38:21,670
+كيف؟ هذه بدأت تصير تمثل اللي هي F capital وهذه
+
+391
+00:38:21,670 --> 00:38:28,510
+بدأت تمثل لمين؟ لف صغير إيش لف صغير؟ يعني F of D
+
+392
+00:38:28,510 --> 00:38:33,500
+بتساوي D يعني ال identity يعني f of واحد واحد، f of
+
+393
+00:38:33,500 --> 00:38:38,460
+اثنين اثنين، f of ان ان، f of دي إيش بتساوي دي،
+
+394
+00:38:38,460 --> 00:38:44,100
+فاهمين؟ إذا by inversion formula بيصير عندي f
+
+395
+00:38:44,100 --> 00:38:48,580
+small of ان، مين f small of ان؟ اللي هي f of دي
+
+396
+00:38:48,580 --> 00:38:53,340
+بيساوي دي، يعني ان، فاهمين؟ بيساوي summation؟ لا
+
+397
+00:38:55,670 --> 00:38:59,550
+الـ Fsmall of N إيش هتساوي N لأنه ماخد الـ Fsmall
+
+398
+00:38:59,550 --> 00:39:04,770
+مين هي الـ Identity F of N بيستخدم الـ Summation
+
+399
+00:39:04,770 --> 00:39:10,770
+Mu N على D في
+
+400
+00:39:10,770 --> 00:39:13,570
+مين F الـ Capital اللي أخدناها إيه إيه إيش Sigma
+
+401
+00:39:13,570 --> 00:39:19,630
+في Sigma of D حيث D بتجسم مين الـ N وهو المطلوب
+
+402
+00:39:19,630 --> 00:39:22,810
+نيجي
+
+403
+00:39:22,810 --> 00:39:31,070
+لآخر نظرية في ال section اللي هي اللي وعدناكم فيها
+
+404
+00:39:31,070 --> 00:39:38,210
+في الأول اللي قلنا انه لو كانت ال F multiplicative
+
+405
+00:39:38,210 --> 00:39:41,750
+بيصير .. احنا اللي أثبتناها قبل هيك ان لو كانت ال
+
+406
+00:39:41,750 --> 00:39:45,230
+F small multiplicative هتكون ال F أشمالها
+
+407
+00:39:45,230 --> 00:39:49,970
+multiplicative اللي بتحكيها ده النظرية انه لو كان
+
+408
+00:39:49,970 --> 00:39:53,810
+اللي هو ال F capital هي ال multiplicative هتكون
+
+409
+00:39:53,810 --> 00:39:57,050
+اللي جوا ال summation برضه أشمالها multiplicative
+
+410
+00:39:57,050 --> 00:40:02,550
+إذا كانت F F small multiplicative F capital
+
+411
+00:40:02,550 --> 00:40:06,770
+multiplicative F capital multiplicative F small
+
+412
+00:40:06,770 --> 00:40:13,390
+إيه شمالها multiplicative مظبوط يا محمد معانها خير
+
+413
+00:40:13,390 --> 00:40:18,610
+نستخدم
+
+414
+00:40:18,610 --> 00:40:20,610
+هذا عشان نخليها
+
+415
+00:40:27,650 --> 00:40:41,050
+فيرم تمانية تمانية الان if F is multiplicative and
+
+416
+00:40:41,050 --> 00:40:53,830
+F of N سم F of D دي بتجسم N then F برضه أشمالة is
+
+417
+00:40:53,830 --> 00:41:01,870
+multiplicative معايا يا شباب الغروف الغروف 6 8 غروف
+
+418
+00:41:01,870 --> 00:41:07,750
+عشان اثبت ان ال F small multiplicative ايش بيدقول
+
+419
+00:41:07,750 --> 00:41:13,830
+بيدقول let M و N element in Z positive such that
+
+420
+00:41:13,830 --> 00:41:17,490
+ال greatest common divisor بين ال M و ال N بساوة 
+
+421
+00:41:17,490 --> 00:41:21,530
+واحد وأثبت لكم أن الـ F small M في N بساوة F small
+
+422
+00:41:21,530 --> 00:41:23,390
+of M في الـ F small of M
+
+423
+00:41:26,550 --> 00:41:35,130
+عندي الـ f small of n في n بساوة الآن عشان أعرف أتحرك
+
+424
+00:41:35,130 --> 00:41:41,370
+بدي أحول اللي هو fmn نفسها على صورة main على صورة
+
+425
+00:41:41,370 --> 00:41:46,150
+summation الآن الـ main اللي بده يحرك ليه يغير ليه
+
+426
+00:41:46,150 --> 00:41:54,190
+المبيوث inversion formula معايا؟ الآن عندي fn أف أن
+
+427
+00:41:54,190 --> 00:41:58,590
+إذا كانت أف أن على الصورة هذه فبتصير أف أن للي جوا
+
+428
+00:41:58,590 --> 00:42:04,430
+فاهمين عليها دي بتقسم أن أف أن بساوي الـ summation
+
+429
+00:42:04,430 --> 00:42:10,750
+ميو of دي في أف أن على دي أو ميو of أن على دي أف 
+
+430
+00:42:10,750 --> 00:42:14,630
+of دي اللي بديها باستخدامها فيساوي الـ summation
+
+431
+00:42:14,630 --> 00:42:22,910
+للي ميو of دي الآن أف كويت الـ of مين؟ M فن على D
+
+432
+00:42:22,910 --> 00:42:28,630
+لأنه أنا بوجد لمين؟ للـ M فن حيث الـ D بتكسب مين؟
+
+433
+00:42:28,630 --> 00:42:33,230
+الـ M فن الآن الـ Greatest Common Divisor بين الـ M و
+
+434
+00:42:33,230 --> 00:42:38,490
+الـ N أيش بيساوي؟ واحد هذا إذن هيساوي الـ
+
+435
+00:42:38,490 --> 00:42:48,370
+summation لـ Mu of الـ D بتكسب الـ M Nأه في 
+
+436
+00:42:48,370 --> 00:42:52,930
+الشيبان هي مشترك الـ M والـ N فبتصير عبارة عن D1
+
+437
+00:42:52,930 --> 00:42:58,770
+بتكسب الـ M و D2 بتكسب الـ M والـ D أيش بيساوي D1
+
+438
+00:42:58,770 --> 00:43:05,050
+في D2 وعملناها قبل هيك هذه اللي عبارة عن Mu D1 D2
+
+439
+00:43:05,050 --> 00:43:11,310
+في F capital of M N D1 D2
+
+440
+00:43:13,470 --> 00:43:17,790
+الـ F Multiplicative والـ Mu Multiplicative إذا
+
+441
+00:43:17,790 --> 00:43:20,810
+إيش هيساوي؟ لأن العام المشترك اللي على بين الـ D1
+
+442
+00:43:20,810 --> 00:43:23,910
+والـ D2 بيساوي واحد والعام المشترك اللي على بين
+
+443
+00:43:23,910 --> 00:43:27,170
+الـ M والـ N إيش ماله؟ بيساوي واحد إذا العام
+
+444
+00:43:27,170 --> 00:43:29,730
+المشترك اللي على بين هذه على هذه وهذه على هذه برضه
+
+445
+00:43:29,730 --> 00:43:37,810
+إيش فاهمين؟ إذا بيصير summation Mu of D1 Mu of D2
+
+446
+00:43:38,520 --> 00:43:47,320
+في F M على D 1 في F M على D 2 حيث دي واحد بتقسم الـ
+
+447
+00:43:47,320 --> 00:43:55,180
+M دي اثنين بتقسم مين الـ N هي نفسها بتساوي هذه
+
+448
+00:43:55,180 --> 00:44:00,740
+بتساوي summation summation واحد دي واحد بتقسم الـ M
+
+449
+00:44:00,740 --> 00:44:10,260
+واحد دي اثنين بتقسم مين الـ N MuF of D1 F of M على
+
+450
+00:44:10,260 --> 00:44:22,000
+D1 في ميو D2 F of M على D2 F of M على D2 F of M
+
+451
+00:44:22,000 --> 00:44:29,860
+على D2 F of M على D2 F of M على D2
+
+452
+00:44:29,940 --> 00:44:39,560
+of D1 F of M على D1 في الـ summation F of M على D2
+
+453
+00:44:39,560 --> 00:44:51,500
+ميو D2 D2 تجسم، هذه N طبعا تجسم الـ N وهذه D1
+
+454
+00:44:51,500 --> 00:44:57,820
+بتجسم الـ M الأولاني هو عبارة عن F of M F small of
+
+455
+00:44:57,820 --> 00:45:05,510
+M والثاني f of small of n صار عندي fmn سوى fm في fn
+
+456
+00:45:05,510 --> 00:45:09,990
+إذا صارت الـ f إيش ما لها is a multiplicative
+
+457
+00:45:09,990 --> 00:45:15,290
+function والمرة الجاية إن شاء الله بنكمل بنبدأ في
+
+458
+00:45:15,290 --> 00:45:17,970
+chapter 7 إن شاء الله
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5thS97U7ozY_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5thS97U7ozY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7645119ae7936bb7e719d3c661b58246259e2d5c
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/5thS97U7ozY_raw.srt
@@ -0,0 +1,1832 @@
+1
+00:00:19,560 --> 00:00:26,980
+بسم الله الرحمن الرحيم المحاضرة رقم 22 مساق نظرية
+
+2
+00:00:26,980 --> 00:00:33,820
+الأعداد لطلاب الجامعة الإسلامية قسم رياضيات كلية
+
+3
+00:00:33,820 --> 00:00:40,120
+العلوم وكلية التربية وصلنا لعند ال section الثاني
+
+4
+00:00:40,120 --> 00:00:45,250
+من شطر 6تحت عنوان The Mobius Inversion Formula
+
+5
+00:00:45,250 --> 00:00:52,290
+بدنا نعرف الآن بدنا نعرف function ميو هذا عبارة عن
+
+6
+00:00:52,290 --> 00:01:01,110
+دالة هنعرفها من z positive لعند اللي هو zero واحد
+
+7
+00:01:01,110 --> 00:01:07,610
+ونقص واحد او لعند z اذا شئت الآن التعريفة كالتالي
+
+8
+00:01:07,610 --> 00:01:15,460
+هنعرف ميو of n تساويبتساوي واحد اذا كانت الان ايش
+
+9
+00:01:15,460 --> 00:01:22,680
+بتساوي واحد وحنقول ان ميو ان بتساوي سفر if اللي هو
+
+10
+00:01:22,680 --> 00:01:33,380
+بي تربيع بتجسم الان for some prime بي وبساوي سالب
+
+11
+00:01:33,380 --> 00:01:41,340
+واحد اص ارفم بتساوي بي واحد بي اتنين لعند البر
+
+12
+00:01:41,340 --> 00:01:50,020
+where بي واحد لعند البر are distinct primes اللي
+
+13
+00:01:50,020 --> 00:01:56,560
+هي .. اللي هي primes مختلفة الآن لو جينا حسبنا الـ
+
+14
+00:01:56,560 --> 00:02:01,880
+mu of واحد واضحني ايش بتساوي واحدلأن أنا عارف
+
+15
+00:02:01,880 --> 00:02:05,560
+الدالة إيش هي ميوف واحد بيساوي واحد إذا كانت أنا
+
+16
+00:02:05,560 --> 00:02:10,370
+بتساوي واحدإذا كانت N فيها مربع كامل في داخلها
+
+17
+00:02:10,370 --> 00:02:15,210
+يعني فيه B تربيع بتقسمها معناته صارت الـ Mu N إيش
+
+18
+00:02:15,210 --> 00:02:20,470
+بتساوي سفر إذا كانت اللي هي N أكبر من واحد و
+
+19
+00:02:20,470 --> 00:02:24,310
+square free يعني مافيش فيها ولا square معناته الـ
+
+20
+00:02:24,310 --> 00:02:27,950
+N إيش هتكون على صورة بي واحد بي اتنين يعني بي are
+
+21
+00:02:27,950 --> 00:02:32,330
+distinct primes ومش هيتكرر لبرايمز لأنه لو تكرر
+
+22
+00:02:32,330 --> 00:02:35,030
+بيصير فيه بي تربيع معناته صار في الحالة الثانية
+
+23
+00:02:44,040 --> 00:02:48,060
+بناء على هذا الحديث الـ mu of واحد واحد الـ mu of
+
+24
+00:02:48,060 --> 00:02:53,360
+اتنين اللي هو اندي بس ايش one prime ان بتساوي
+
+25
+00:02:53,360 --> 00:02:56,840
+اتنين اذا حيصير حسب الحديث اللي هان عبارة عن ناقص
+
+26
+00:02:56,840 --> 00:03:02,000
+واحد اس واحد لأنه ايش مالها اتنين الـ mu of اتنين
+
+27
+00:03:02,000 --> 00:03:07,710
+الـ b واحد اتنين وفيش غيرهمعايا إذا هو يساوي سالب
+
+28
+00:03:07,710 --> 00:03:12,410
+واحد إنه يقف تلاتة من نفس الأسلوب إيش هيساوي ناقص
+
+29
+00:03:12,410 --> 00:03:16,970
+واحد قص واحد ويساوي إيش ماله سالب واحد إنه يقف
+
+30
+00:03:16,970 --> 00:03:23,450
+أربعة إيش هيساوي سفر ليش لأنه اتنين تربيع تجسم
+
+31
+00:03:23,450 --> 00:03:28,990
+الأربعة يعني فيه في داخله إيش اللي هو مربع كامل
+
+32
+00:03:28,990 --> 00:03:35,480
+واضح أه؟ إنه يقف خمسةاللي هو سالب واحد ميو في ستة
+
+33
+00:03:35,480 --> 00:03:41,480
+اللي هو الستة ايه اشمالها عبارة عن تلاتة في اتنين
+
+34
+00:03:41,480 --> 00:03:45,480
+واتنين في اتنين هذا و هذا distinct primes ومفيش
+
+35
+00:03:45,480 --> 00:03:49,380
+فيهم اللي هو مين مربع كامل إذا إيش هيساوي ناقص
+
+36
+00:03:49,380 --> 00:03:55,840
+واحد قص هيواحد اتنين عدد الprimes فاهمين قص اتنين
+
+37
+00:03:55,840 --> 00:04:01,970
+ويساوي واحد ميو في سبعة-1 يعني واضح أن ميو أي
+
+38
+00:04:01,970 --> 00:04:07,770
+prime سوى سالب واحد ميو في تمانية سفر لأن التمانية
+
+39
+00:04:07,770 --> 00:04:12,350
+فيها إيهاش اتنين تربيع بتقسم التمانية فيها مربع
+
+40
+00:04:12,350 --> 00:04:19,110
+كامل ميو في تسعة ميو في تسعة إيهاش سفر برضه لأن
+
+41
+00:04:19,110 --> 00:04:24,730
+تلاتة تربيع بتقسم التسعة ميو في عشرةاللي هو العشرة
+
+42
+00:04:24,730 --> 00:04:29,370
+خمسة في اتنين اللي هو عبارة عن سالب واحد قصة اتنين
+
+43
+00:04:29,370 --> 00:04:33,970
+ويساوي واحد لإن العشرة بتساوي خمسة في اتنين لو
+
+44
+00:04:33,970 --> 00:04:39,130
+قولنا ميو of سبعين
+
+45
+00:04:39,130 --> 00:04:46,910
+ايش بساوي اللي هو عبارة عن خمسة في اتنين في سبعة
+
+46
+00:04:46,910 --> 00:04:51,390
+اللي هو عبارة عن سالب واحد قصة تلاتة ويساوي سالب
+
+47
+00:04:51,390 --> 00:05:02,130
+واحدواضح صحيح ميوف عشرين سفر لإن فيها اربعة اللي
+
+48
+00:05:02,130 --> 00:05:06,870
+هي اتنين تربيع واضح اه الآن هذه ال function اللي
+
+49
+00:05:06,870 --> 00:05:13,650
+هي نسميها Mobius function الآن هذه أداء بتساعدنا
+
+50
+00:05:13,650 --> 00:05:18,650
+اللي هو في تسهيل اللي هو كثير من الأمور هنشوفها ان
+
+51
+00:05:18,650 --> 00:05:23,870
+شاء اللهنأتي الأن لأول نظرية نظرية 6.5 اللي هي
+
+52
+00:05:23,870 --> 00:05:27,470
+مبيوظ ميو فانكشن اللي بنحكي عنها ميو is a
+
+53
+00:05:27,470 --> 00:05:31,750
+multiplicative function بدنا نثبت لك الأن أن هذا
+
+54
+00:05:31,750 --> 00:05:37,150
+ال function ميو is a multiplicative function ميو
+
+55
+00:05:37,150 --> 00:05:39,990
+is a multiplicative function
+
+56
+00:05:47,240 --> 00:05:54,340
+قلنا لـ Mu اللي هي تلت قيم يا واحد، يا سفر، يا
+
+57
+00:05:54,340 --> 00:05:59,700
+سالف واحد، إذا كانت N بتساوي واحد، إذا كانت P
+
+58
+00:05:59,700 --> 00:06:03,800
+تربيع تجسم الـ N for some P، إذا كانت اللي هي ناقص
+
+59
+00:06:03,800 --> 00:06:09,080
+واحد أسار، إذا كانت اللي هي N بتساوي P واحد، لعند
+
+60
+00:06:09,080 --> 00:06:11,780
+الـ P are distinct primes، بس خلينا أحطها أساسا
+
+61
+00:06:11,780 --> 00:06:15,900
+تتذكروا، أعطيكم تذكرينها، نيجي الآن ال theorem
+
+62
+00:06:15,900 --> 00:06:25,000
+اللي عنديTheorem اللي هي 6 خمسة ميو is a
+
+63
+00:06:25,000 --> 00:06:31,980
+multiplicative function نبرّنها
+
+64
+00:06:31,980 --> 00:06:39,130
+ال proof أذكركم شو .. كيف بينا ..من برهيل اللي هو
+
+65
+00:06:39,130 --> 00:06:42,450
+الـ function is multiplicative، قول لأ بتكون الـ
+
+66
+00:06:42,450 --> 00:06:45,890
+function F is multiplicative إذا كان حققت، إن الـ
+
+67
+00:06:45,890 --> 00:06:48,490
+greatest common divisor بين الـ M والـ N بساوي
+
+68
+00:06:48,490 --> 00:06:54,730
+واحد يعطيني إن الـ F في M في N إشمالها سوى F في M
+
+69
+00:06:54,730 --> 00:07:03,650
+في F of Mيعني تتحقق أن فأم أن بيساوي فأم فأفأن لكل
+
+70
+00:07:03,650 --> 00:07:07,130
+الأم والأن العامل المشترك الأعلى بينهما بيساوي
+
+71
+00:07:07,130 --> 00:07:11,850
+واحد، واضح؟ إذا الأن يجب أن أبره أن ميو هي عملية
+
+72
+00:07:11,850 --> 00:07:19,490
+مرتبطة إذا أفترض أن أقول لت أم وأن element in Z
+
+73
+00:07:19,490 --> 00:07:23,690
+positive such that the greatest common divisor بين
+
+74
+00:07:23,690 --> 00:07:29,850
+الأم والأن بيساوي واحدبدي اثبت لك اصلك انه لازم
+
+75
+00:07:29,850 --> 00:07:35,810
+يطلع عندى ميو ام فان بيساوي ميو اقل الام في ميو
+
+76
+00:07:35,810 --> 00:07:40,810
+لالان كيف بدي أسوي هذه بدي اخد cases ال case الأول
+
+77
+00:07:40,810 --> 00:07:47,170
+ان يكون عندى بدي اجسم أموري الى three cases ال
+
+78
+00:07:47,170 --> 00:07:50,650
+case الأول و ال case الثاني و ال case الثالث ال
+
+79
+00:07:50,650 --> 00:07:53,150
+case الأول ان يكون either
+
+80
+00:07:56,780 --> 00:08:04,240
+m or n is one or both يا إما m يا إما n بيساوي
+
+81
+00:08:04,240 --> 00:08:13,540
+واحد أو التنتين واحد ال case التانية ان either m
+
+82
+00:08:13,540 --> 00:08:18,120
+or n اللي هو contains a square
+
+83
+00:08:25,170 --> 00:08:30,870
+بمعنى اخر ان بي تربيع تكسب الام او بي تربيع تكسب
+
+84
+00:08:30,870 --> 00:08:35,210
+مين يعني او بص طبعا ماشي الحال ال case الثالثة
+
+85
+00:08:37,400 --> 00:08:42,640
+هذه كل الـ M و الـ N اللي عندى يا تنتين .. يا واحد
+
+86
+00:08:42,640 --> 00:08:47,220
+منهم على الأقل بيساوي واحد يا واحد منهم على الأقل
+
+87
+00:08:47,220 --> 00:08:53,520
+في مربع كامل يا إما التنتين الـ M و الـ N أكبر من
+
+88
+00:08:53,520 --> 00:09:04,550
+واحد and bothm and n are square free يعني مافيش
+
+89
+00:09:04,550 --> 00:09:10,790
+فيه مياشي أي مربع كامل إذا الجزء اللي هو لهذا m or
+
+90
+00:09:10,790 --> 00:09:16,990
+n بيساوي واحد الجزء الثاني اللي هو m or n contains
+
+91
+00:09:16,990 --> 00:09:23,600
+a squareاللي هو طبعا الان الجزء الثالث both of M
+
+92
+00:09:23,600 --> 00:09:28,800
+and N are greater than one and they are square of
+
+93
+00:09:28,800 --> 00:09:33,920
+three واضح هاه؟ طيب نجي للحالة الأولى الحالة
+
+94
+00:09:33,920 --> 00:09:42,500
+الأولى if U M في Nهيساوي لو كانت الان بتساوي واحد
+
+95
+00:09:42,500 --> 00:09:48,640
+معناها تصارت هذي U M صح ولا لأ هذا F M بتساوي واحد
+
+96
+00:09:48,640 --> 00:09:56,220
+لو كانت ال M بتساوي واحد بيصير U M F M بيساوي واحد
+
+97
+00:09:57,100 --> 00:10:01,760
+التامتين في الحالتين في الحالتين اللي هي بتساوي
+
+98
+00:10:01,760 --> 00:10:09,200
+ميو ام في ميو اش ان لأن ميو اف واحد اش بيساوي واحد
+
+99
+00:10:09,200 --> 00:10:12,920
+معناه ان صارت ميو اف ام في الواحد هي ميو ام في ميو
+
+100
+00:10:12,920 --> 00:10:18,140
+ان وصارت الميو ان في الميو ام اللي هي واحد بيساوي
+
+101
+00:10:18,140 --> 00:10:21,820
+ميو ام في ميو ان صارت في هذه الحالة بتحقق شروط
+
+102
+00:10:21,820 --> 00:10:25,960
+الميو is multiplicative in the first caseنجي in
+
+103
+00:10:25,960 --> 00:10:33,520
+the second main case الحالة الثانية يا اما B تربيع
+
+104
+00:10:33,520 --> 00:10:37,300
+بتكسب M او B تربيع بتكسب مين M او بتكسب او ال both
+
+105
+00:10:37,300 --> 00:10:40,320
+بتكسب ال مين يعني بيه واحد تربيع و بيه اتنين تربيع
+
+106
+00:10:40,320 --> 00:10:43,920
+واحدة بتكسب ال M واحدة بتكسب ال مين ايه يعني then
+
+107
+00:10:43,920 --> 00:10:50,650
+then اكيد هيكون ال B بتكسب مينالـ B تربيع تكسب
+
+108
+00:10:50,650 --> 00:10:55,230
+مين؟ N فن، مدام الـ B تربيع تكسب هذه أو هذه، إذا
+
+109
+00:10:55,230 --> 00:11:00,050
+الـ B تربيع تكسب مين؟ الـ N فن حصل الضرب، إذا صار
+
+110
+00:11:00,050 --> 00:11:10,370
+عندي الـ N then Mu N فن هيساوي إيه؟ صفر، لأنه صارت
+
+111
+00:11:10,370 --> 00:11:16,390
+الـ N فن إشمالها تحتوي على مربع كاملطيب هذا بيساوي
+
+112
+00:11:16,390 --> 00:11:22,130
+ميو ام في ميو ام ليش لأن لو كانت الام يعني واحدة
+
+113
+00:11:22,130 --> 00:11:24,650
+من اللي حد تقول احتوى ميو مربع كامل لذا واحدة من
+
+114
+00:11:24,650 --> 00:11:28,270
+اللي على الأقل سفر لذا حصل ضرر من سفر إذا صار هذا
+
+115
+00:11:28,270 --> 00:11:32,650
+بساوي هذا إذا برضه في الحالة الثانية بتحقق شروط
+
+116
+00:11:32,650 --> 00:11:36,570
+المultiplicate فيه نيجي لأهالي الحالة الثالثة ان م
+
+117
+00:11:36,570 --> 00:11:41,690
+و ان أكبر من واحد and both are square every شوف
+
+118
+00:11:41,690 --> 00:11:41,970
+كيف
+
+119
+00:11:50,730 --> 00:12:01,370
+خلّيني أظهر الحالة الثالثة case a3 لأن عندك ال M
+
+120
+00:12:01,370 --> 00:12:08,790
+والL أكبر من واحد وsquare three then أكيد by
+
+121
+00:12:08,790 --> 00:12:15,490
+unique factorization theorem M بساوة بواحدB2 عند
+
+122
+00:12:15,490 --> 00:12:20,250
+الـ PR و لا يوجد تكرار لأن انا فرض اله ان اشمل ال
+
+123
+00:12:20,250 --> 00:12:23,910
+square فرى و نفس الشيء عند
+
+124
+00:12:47,480 --> 00:12:48,880
+M�
+
+125
+00:12:48,910 --> 00:12:51,990
+لأن لو كان فيه أي primes بين هذه و هذه مشتركة
+
+126
+00:12:51,990 --> 00:12:56,190
+معناته صار العامل المشترك الأعلى بينهم مش واحد اذا
+
+127
+00:12:56,190 --> 00:13:04,390
+اكيد then B1 B2 اللي عند ال PR و Q1 اللي عند QS
+
+128
+00:13:04,390 --> 00:13:08,490
+are distinct
+
+129
+00:13:08,490 --> 00:13:11,570
+primes
+
+130
+00:13:11,570 --> 00:13:21,730
+معايا يا شبابالحسب السهل الآن ميو أن في أن بساوي
+
+131
+00:13:21,730 --> 00:13:26,930
+الوصار ال factorization لها هو هذا في هذا وكل
+
+132
+00:13:26,930 --> 00:13:30,490
+index distinct primes إذا حسب القانون إيش هيطلع
+
+133
+00:13:30,490 --> 00:13:35,510
+عندي ناقص واحد أس R لإن عداد هنا دولة distinct
+
+134
+00:13:35,510 --> 00:13:40,830
+prime إيه شمالين R زائد S ويساوي
+
+135
+00:13:41,860 --> 00:13:47,320
+سالب واحد اصار في سالب واحد اص مين اصاز سالب واحد
+
+136
+00:13:47,320 --> 00:13:52,820
+اصار هو في الواقع مين ميول الاموهذا في الواقع مين؟
+
+137
+00:13:52,820 --> 00:13:58,160
+ميو للأن وهو المطلوب therefore في كل الأحوال طلع
+
+138
+00:13:58,160 --> 00:14:00,440
+اني لما great is common divisor بين الام والان
+
+139
+00:14:00,440 --> 00:14:04,720
+بيساوي واحد طلع اندي ميو ام في ان بيساوي ميو ام في
+
+140
+00:14:04,720 --> 00:14:09,040
+ميو ان therefore ميو is a multiplicative function
+
+141
+00:14:09,040 --> 00:14:13,540
+ميو is a multiplicative function أي سؤال
+
+142
+00:14:22,240 --> 00:14:24,920
+وشوف في صلة النبي عليه الصلاة والسلام المرة
+
+143
+00:14:24,920 --> 00:14:33,260
+الماضية كان في عيننا نظرية أثبتناها بتقول
+
+144
+00:14:33,260 --> 00:14:39,620
+إذا كانت F و M F و F capital اللي هو عبارة عن
+
+145
+00:14:39,620 --> 00:14:48,200
+number theoretic functions وكانت اللي هي ال Fis
+
+146
+00:14:48,200 --> 00:14:53,920
+multiplicative الـ F صغير is multiplicative ثم
+
+147
+00:14:53,920 --> 00:15:00,740
+وكان عندي الـ F كابتل عبارة عن summation F صغير من
+
+148
+00:15:00,740 --> 00:15:09,460
+D دي بتجسم N ثم F كابتل برضه إيش is multiplicative
+
+149
+00:15:10,120 --> 00:15:12,580
+كمان مرة أذكركم فيها نظرية هذه المرة الفاترة
+
+150
+00:15:12,580 --> 00:15:16,860
+اتخذناها النظرية بتقول مالي إذا كانت ال F و ال F
+
+151
+00:15:16,860 --> 00:15:21,320
+كابتال are number theoretic functions و ال F small
+
+152
+00:15:21,320 --> 00:15:25,640
+is multiplicative و ال F كابتال مكتوبة على صورة
+
+153
+00:15:25,640 --> 00:15:31,080
+summation لل F small of D D بتجسم N بتطلع هذه ال F
+
+154
+00:15:31,080 --> 00:15:35,480
+الكبيرة أو ال F كابتال أشمالها is multiplicative
+
+155
+00:15:36,610 --> 00:15:40,010
+واضح ليش اللي بحكيه طبعا هنصل لـ F آخر المحاضرة
+
+156
+00:15:40,010 --> 00:15:45,890
+انه لو كانت اللي هي ال F small multiplicate .. آسف
+
+157
+00:15:45,890 --> 00:15:49,150
+ال F capital multiplicative هتطلع ال F small برضه
+
+158
+00:15:49,150 --> 00:15:54,870
+يشمالها is multiplicative مش الحال لأن هذه النظرية
+
+159
+00:15:54,870 --> 00:16:00,430
+اللي هي اللي بحكي عنها اللي هنصلها الجسر اللي هو
+
+160
+00:16:00,430 --> 00:16:04,410
+الوصول إليها هي عبارة عن ال mobius function اللي
+
+161
+00:16:04,410 --> 00:16:10,860
+هي الميوالان بدي .. اللي هي استخدم هذه النظرية بعد
+
+162
+00:16:10,860 --> 00:16:15,220
+شوية لإثبات شغلة من خواص اللي هي الـ Mobius
+
+163
+00:16:15,220 --> 00:16:21,100
+function نيجي الان ل .. اللي هي نظرية 6-6 بقولي
+
+164
+00:16:21,100 --> 00:16:26,680
+لأي انتجار N أكبر و ساوي واحد؟
+
+165
+00:16:26,680 --> 00:16:34,660
+شوفوا
+
+166
+00:16:34,660 --> 00:16:46,490
+عنديا يا شبابعندي لو جيه اتعرفت انا F of N ستة
+
+167
+00:16:46,490 --> 00:16:52,910
+ستة الـ N لأي N positive integer أكبر أوي سوى واحد
+
+168
+00:16:52,910 --> 00:17:01,850
+الـ F of N بدي أعرفها أنا بالساعة والصممشن Mu of D
+
+169
+00:17:01,850 --> 00:17:07,500
+دي بتقسم الـ Nهك انت عارفه ماشي الحل الان ايش
+
+170
+00:17:07,500 --> 00:17:11,600
+النظرية بتقوللي بتقوللي هتطلع قيمة هذه هذا ال
+
+171
+00:17:11,600 --> 00:17:17,580
+summation هيطلع قيمته الان الان four ان اكبر سو
+
+172
+00:17:17,580 --> 00:17:20,700
+واحد هيطلع عندي ال F of N اللي هو ال summation هذا
+
+173
+00:17:20,700 --> 00:17:25,920
+هذا ال summation هيطلع قيمته عبارة عن واحد F of N
+
+174
+00:17:25,920 --> 00:17:32,570
+بتساوي واحد و سفر F of N اشمالها اكبر من واحديعني
+
+175
+00:17:32,570 --> 00:17:36,530
+هتطلعلي الدالة هذه يا سفر يا إيش يا واحد يعني عندي
+
+176
+00:17:36,530 --> 00:17:40,690
+ال F of N له هذا ال summation لأن F of N أنا معرف
+
+177
+00:17:40,690 --> 00:17:43,550
+لك يهيك هذا ال summation أنا بقولك النظرية
+
+178
+00:17:43,550 --> 00:17:46,910
+هتطلعليها هذه هتثبتلك في الآخر أنه هتساوي واحد إذا
+
+179
+00:17:46,910 --> 00:17:50,970
+كانت N بتساوي واحد و Zero إذا كانت N أشمالها أكبر
+
+180
+00:17:50,970 --> 00:17:58,390
+من واحد نيجي لل proof ال proof سهل شوف F of N
+
+181
+00:17:58,390 --> 00:18:05,520
+بتساوي واحدإذا n بيتساوى واحد ثم ال f of واحد في
+
+182
+00:18:05,520 --> 00:18:10,820
+هذه الحالة هيساوي ال summation حسب ما نعرفه ميو دي
+
+183
+00:18:10,820 --> 00:18:15,400
+دي بتكسب مين الواحد قسم الواحد بس مين هي الموجبة
+
+184
+00:18:15,400 --> 00:18:19,740
+واحد إذا هيساوي ميو of واحد اللي هي إيش عرفناها
+
+185
+00:18:19,740 --> 00:18:24,260
+بتساوي واحد إذا صارت عندي f واحد فعلا إيش بتساوي
+
+186
+00:18:24,260 --> 00:18:31,450
+واحد لإن بتاخد n إيش مالها لإن letأن أكبر strictly
+
+187
+00:18:31,450 --> 00:18:35,270
+من مين؟ من واحد مدام أن أكبر من واحد اذا by unique
+
+188
+00:18:35,270 --> 00:18:37,750
+factorization theorem أن can be written as a
+
+189
+00:18:37,750 --> 00:18:42,750
+canonical form then by unique factorization
+
+190
+00:18:42,750 --> 00:18:47,370
+theorem أن بتساوي بي واحد ألف واحد لعند بي ار
+
+191
+00:18:47,370 --> 00:18:51,670
+اشمالها الف ار where بي واحد و بي اتنين و بي ار
+
+192
+00:18:51,670 --> 00:18:58,100
+are distinct primes مش الحال thenthen بدي احسب
+
+193
+00:18:58,100 --> 00:19:03,740
+الان مين انا اللي هي F of N F of N ايش بتساوي F of
+
+194
+00:19:03,740 --> 00:19:10,120
+P واحد Alpha واحد لعند PR Alpha ايش R لاحظوا الان
+
+195
+00:19:10,120 --> 00:19:15,280
+لاحظوا الان ما يليهالنظرية هذه اللي فوق بتقول لو
+
+196
+00:19:15,280 --> 00:19:17,640
+كان اللي جوا multiplicative هيكون ال summation
+
+197
+00:19:17,640 --> 00:19:21,880
+أشماله multiplicative طب ما احنا أثبتنا قبل بشوية
+
+198
+00:19:21,880 --> 00:19:25,080
+أن هاد الـ mu أشماله multiplicative إذا ال
+
+199
+00:19:25,080 --> 00:19:28,300
+summation هيطلع أشماله multiplicative بالنظرية
+
+200
+00:19:28,300 --> 00:19:32,240
+اللي فوق إذا صارت عندي ال F هذه أشماله is a
+
+201
+00:19:32,240 --> 00:19:35,780
+multiplicative function مدام F is a multiplicative
+
+202
+00:19:35,780 --> 00:19:44,770
+function إذا بتسوي Fof B1 α1 لعند F of Br αR لإيش
+
+203
+00:19:44,770 --> 00:19:48,210
+لأن الـ B1 وB2 اللي عند الـ Br are distinct primes
+
+204
+00:19:48,210 --> 00:19:51,490
+معناته الـ greatest common divisor بين item 2
+
+205
+00:19:51,490 --> 00:19:57,850
+بساوية واحد فعلا الان بل علي اوجد هذه شوف كيف بده
+
+206
+00:19:57,850 --> 00:20:06,140
+اوجدها الان Fof B1 α1 ايش هتساوي حسب اللي هو
+
+207
+00:20:06,140 --> 00:20:11,520
+التعريف اللي عرفناها سم ميو of D حيث الـ D بتكسب
+
+208
+00:20:11,520 --> 00:20:18,290
+100 الـ B1 α1، مظبوط؟لأن أفف بي واحد ألف واحد
+
+209
+00:20:18,290 --> 00:20:22,410
+بتوجدها لأن وين ال formula اللي معطنيها أفف فانا
+
+210
+00:20:22,410 --> 00:20:26,190
+بساوي ال summation شيله الأن و أحط مكانها مين بي
+
+211
+00:20:26,190 --> 00:20:29,630
+واحد ألف واحد فبصي ال summation لأن ال ميو دي لدي
+
+212
+00:20:29,630 --> 00:20:34,790
+بتكسب مين بي واحد ألف واحد لأن قواسم القواسم العدب
+
+213
+00:20:34,790 --> 00:20:40,150
+بي واحد ألف واحديا الواحد يا ال بي واحد يا بي واحد
+
+214
+00:20:40,150 --> 00:20:44,930
+تربيع يا بي واحد تكعيب لما أصل عند بي واحد أشماله
+
+215
+00:20:44,930 --> 00:20:49,810
+Alpha واحد إذا ال summation هذا بيصير ميو للواحد
+
+216
+00:20:49,810 --> 00:20:55,670
+أول قاسم زائد القاسم التاني مين هو بي واحد زائد
+
+217
+00:20:55,670 --> 00:20:59,890
+القاسم الثالث مين هو هو بي واحد تربيع زائد لما أصل
+
+218
+00:20:59,890 --> 00:21:07,510
+لآخر قاسم بي واحد Alpha واحد ويساويميو فى واحد ايش
+
+219
+00:21:07,510 --> 00:21:12,190
+نجناها واحد ميو of لبراين قبل بشوية حسب انها ايش
+
+220
+00:21:12,190 --> 00:21:20,080
+بيساوي ميو ل لبراين سالب واحدقبل شوية كتبناها ناقص
+
+221
+00:21:20,080 --> 00:21:24,180
+واحد أسو أر اللي هي واحد يعني اللي هي ناقص واحد
+
+222
+00:21:24,180 --> 00:21:29,160
+زائد هدولة كلهم إيش مالهم إصفار لإن كلهم فيهم إيش
+
+223
+00:21:29,160 --> 00:21:35,520
+بي واحد كاربيع واضح إذا زائد سفر زائد سفر ويساوي
+
+224
+00:21:35,520 --> 00:21:40,960
+واحد ناقص واحد سفر إذا صار F of بي واحد ألف واحد
+
+225
+00:21:40,960 --> 00:21:46,160
+إيش هيساوي سفر إذا صار عندي F of N بيساوي هذا سفر
+
+226
+00:21:46,160 --> 00:21:52,670
+و الرابع جات زيهبصير أش مساوى أف
+
+227
+00:21:52,670 --> 00:21:57,230
+of أن بتساوي سفر يعني بمعنى أخر لما كانت الان أكبر
+
+228
+00:21:57,230 --> 00:22:02,750
+من واحد طلعت لي ال summation هذا أش مساوى سفر إذا
+
+229
+00:22:02,750 --> 00:22:03,410
+فضل
+
+230
+00:22:09,110 --> 00:22:12,410
+أحنا عرفناها ده الـ function قبل ما تيجي عرفناها
+
+231
+00:22:12,410 --> 00:22:17,550
+ده لإنه أي عدد فيه square في داخله الـ mu له إيش
+
+232
+00:22:17,550 --> 00:22:20,670
+ما لها سفر طيب
+
+233
+00:22:23,180 --> 00:22:27,360
+هنأتي الآن لـ Mobius inversion formula الموبيوس
+
+234
+00:22:27,360 --> 00:22:31,280
+انفرجن فورميله نشوف ايش اللي بتقول الموبيوس انفرجن
+
+235
+00:22:31,280 --> 00:22:36,280
+فورميله بتقول انه لو كانت F كابيتل و F صغير two
+
+236
+00:22:36,280 --> 00:22:40,340
+number theoretic functions وكانت ال F of N بيساوي
+
+237
+00:22:40,340 --> 00:22:45,500
+ال summation F of D دي بتقسم N اذا بقدر اكتب ال F
+
+238
+00:22:45,500 --> 00:22:50,570
+Nالـ Fn عند الـ Fcapital مكتوب على صورة summation
+
+239
+00:22:50,570 --> 00:22:54,470
+لمن؟ لـ Fsmall الآن الـ Mobius or Virgin Formula
+
+240
+00:22:54,470 --> 00:22:58,730
+بتعكس للكتابة بتقول بأقدر أكتب لك الـ Fsmall اللي
+
+241
+00:22:58,730 --> 00:23:03,870
+جوا على صورة summation برضه لمن؟ لمن؟ لـ divisors
+
+242
+00:23:03,870 --> 00:23:09,170
+دي بدكسم Nبس الآن فى عامل مساعد العامل المساعد مين
+
+243
+00:23:09,170 --> 00:23:13,190
+هو الـ Mobius function بيساوي summation mu of D F
+
+244
+00:23:13,190 --> 00:23:19,290
+of N على D أو mu N على D F of DD بتجسم الـ N بنشوف
+
+245
+00:23:19,290 --> 00:23:24,030
+كمان مرة بالتفصيل إيش النظرية دى بتقول وإيش
+
+246
+00:23:24,030 --> 00:23:30,230
+برهانها شوفوا
+
+247
+00:23:30,230 --> 00:23:32,330
+يا شباب عادي
+
+248
+00:23:54,280 --> 00:23:57,780
+النظرية اللي قبل شوية حكيناها هي summation mu of D
+
+249
+00:23:57,780 --> 00:24:05,080
+D بيقسم N بساوة سفر F N بساوة أكبر من واحد و واحد
+
+250
+00:24:05,080 --> 00:24:09,960
+F N بساوة واحد صح؟ طيب هذه النظرية اللي قبل شوية
+
+251
+00:24:09,960 --> 00:24:13,060
+بس عشان انا هسا اخدمها نشوف ايش الموبيوث inversion
+
+252
+00:24:13,060 --> 00:24:18,580
+formula بتقول بتقول لو كانت F capital و F small
+
+253
+00:24:18,580 --> 00:24:24,510
+اللي هو number of theoretical functions معايا؟و
+
+254
+00:24:24,510 --> 00:24:29,690
+بقول إن لو كانت عندي ال F of N مكتوبة على صورة
+
+255
+00:24:29,690 --> 00:24:37,410
+summation F of D small D تجسم N then ال F of N
+
+256
+00:24:37,410 --> 00:24:44,080
+مكتوبة على صورة F of DD تجسم Nذن بقدر اكتب نت مين
+
+257
+00:24:44,080 --> 00:24:49,660
+الـ F الصغيرة F of N of a small على صورة الـ
+
+258
+00:24:49,660 --> 00:24:53,540
+summation بس الـ N هذا الـ summation بعامل مساعد
+
+259
+00:24:53,540 --> 00:24:57,700
+مين هو العامل المساعد؟ الـ Mu المحولة يعني اللي هي
+
+260
+00:24:57,700 --> 00:25:04,680
+Mu برضه على إياش D بتقسم عنه Mu of D اللي هي F
+
+261
+00:25:04,680 --> 00:25:14,580
+capital of N على DF capital of H of N على D هذه
+
+262
+00:25:14,580 --> 00:25:19,720
+النظرية لأن هذه طبعا بقدر اكتبها على صورة هذا قاسم
+
+263
+00:25:19,720 --> 00:25:24,320
+و هذا قاسم مظبوط ولا لا و هدولة بيحدثين مع بعض لذا
+
+264
+00:25:24,320 --> 00:25:28,120
+بقدر اكتبها على صورة بدل ما اقول Mu of D بقدر اكتب
+
+265
+00:25:28,120 --> 00:25:34,580
+Mu N على D و F H of D لأن هذا قاسم و هذا قاسم
+
+266
+00:25:34,580 --> 00:25:39,020
+هدولة و هدولة اكتلين اشمال لأن بيحدثن مع بعض D
+
+267
+00:25:39,590 --> 00:25:44,830
+بتكسمين الان يا الصورة هذه يا الصورة هذه قمناها
+
+268
+00:25:44,830 --> 00:25:51,550
+قبل هيك طيب إذا صار عندي الآن بدنا نثبت اللي هو F
+
+269
+00:25:51,550 --> 00:25:55,450
+capital F small of 1 بساوي ال summation اللي عندي
+
+270
+00:25:55,450 --> 00:26:03,710
+خلّي هنا نشوف كيف نثبتها و بروف ايش بدنا نسوي بدنا
+
+271
+00:26:03,710 --> 00:26:08,540
+ناخد الطرف هذا و نوصله لهذايعني انا بالداخل اقول
+
+272
+00:26:08,540 --> 00:26:16,140
+summation mu of D F capital of N على D الـ D بتكسب
+
+273
+00:26:16,140 --> 00:26:27,500
+الان بساوة الان F of N هيها صح ولا لا هيها F of N
+
+274
+00:26:27,500 --> 00:26:31,100
+بساوة summation F of D D بتكسب الان طب F of N على
+
+275
+00:26:31,100 --> 00:26:39,120
+Dأتخيل هذا C وهذا C F of F of N على دي ايش هيساوي
+
+276
+00:26:39,120 --> 00:26:47,240
+F of اللي هي A اللي هي C بتكسب مين N على دي فاهمين
+
+277
+00:26:47,240 --> 00:26:55,900
+اه واضح اه كمان مرة F of N بساوي F of C C بتكسب
+
+278
+00:26:55,900 --> 00:27:01,920
+مين الـ N لما تحسب مين F of Nعلى D بيساوي .. ده
+
+279
+00:27:01,920 --> 00:27:06,460
+شيل ها دي و بدي أحط قيمتها من هنا قيمتها بيساوي
+
+280
+00:27:06,460 --> 00:27:13,240
+summation Mu of D D بتجسم N بدل ها دي شيل الـ N و
+
+281
+00:27:13,240 --> 00:27:19,500
+أحط مكانها N على مين اللي هي F summation F of C C
+
+282
+00:27:19,500 --> 00:27:26,300
+بتجسم من N على D أي
+
+283
+00:27:26,300 --> 00:27:33,370
+سؤال؟واضح أه؟ خلّي هدف الذاكرة بدي أعملك شغل هنا
+
+284
+00:27:33,370 --> 00:27:39,470
+أثبت لك شغل هنا عشان أستبدل اللي هو ال indices تبع
+
+285
+00:27:39,470 --> 00:27:44,570
+ال summation ب indices أخرى هتلزملي أه؟ بس قبلها
+
+286
+00:27:44,570 --> 00:27:49,490
+خلّينا نكمل Y ساوي بدي أضرب هدف الداخل أدخلها لجوا
+
+287
+00:27:49,490 --> 00:27:57,630
+اضرب عادي summation summation Mu of D في F of Cدي
+
+288
+00:27:57,630 --> 00:28:01,730
+بتكسم الان و C بتكسم مين الان على دي ايش الفكرة
+
+289
+00:28:01,730 --> 00:28:08,150
+الان الفكرة ان احاول اخل ال U of D هذه لحالها و
+
+290
+00:28:08,150 --> 00:28:11,870
+اشيل ال F of C تيجيها بطريقة معينة بتغيير ال
+
+291
+00:28:11,870 --> 00:28:15,880
+indicesليه؟ لأن الـSummation الـU في دي أنا بعرفه
+
+292
+00:28:15,880 --> 00:28:21,060
+يا واحد يا سفر فبصير مجموعه بس اللي هو طبعا السفر
+
+293
+00:28:21,060 --> 00:28:24,840
+خلاص بروح بظل مين عنده بس اللي عند الواحد اللي هي
+
+294
+00:28:24,840 --> 00:28:30,430
+عند اللي هي N بتساوي واحدإذا الفكرة أني أبسط هذا
+
+295
+00:28:30,430 --> 00:28:34,150
+الموضوع عن طريق اللي هو كتابة هذا على صورة أنه
+
+296
+00:28:34,150 --> 00:28:37,110
+أشيل ال F of C في الجهة دي و أخلّي ال summation
+
+297
+00:28:37,110 --> 00:28:40,190
+الميو دي لحاله الميو دي لحاله ال summation اللي هو
+
+298
+00:28:40,190 --> 00:28:43,990
+إيش بيساوي بيساوي واحد و ال zero خلاص ما هو بيصير
+
+299
+00:28:43,990 --> 00:28:51,650
+ال summation سفر بيصير كمجموع بيبقى للواحد لنشوف
+
+300
+00:28:51,650 --> 00:29:00,740
+كيفبتثبت لك الان شغلة بيثبت لك ان هذا ال condition
+
+301
+00:29:00,740 --> 00:29:09,120
+هى و من هنا لها دى بتقسم الان دى بتقسم الان and
+
+302
+00:29:09,120 --> 00:29:13,360
+C بتقسم N على D يكافئ
+
+303
+00:29:14,820 --> 00:29:19,080
+يكافئ condition تاني هو اللي بدو يسعفني في عملية
+
+304
+00:29:19,080 --> 00:29:22,540
+نقل ال F of C لأن F of C ماقدرش أنجلها ال gate لإن
+
+305
+00:29:22,540 --> 00:29:27,320
+ال F of C اللي هو الجمع تبعها هشغال في هذا ال
+
+306
+00:29:27,320 --> 00:29:30,860
+summation فلو طلعته بيصير .. مافعش أطلعه، على مين
+
+307
+00:29:30,860 --> 00:29:35,740
+بيشتغل؟ بيصير اللي هو مش ثابت بالنسبة لهذا عشان
+
+308
+00:29:35,740 --> 00:29:41,330
+أطلعه برا فمينش ماحكيطيب إذا بدي أثبت لك إن هذا
+
+309
+00:29:41,330 --> 00:29:48,870
+بكافي اللي هو الـ C بيقسم N و D بيقسم N على C C
+
+310
+00:29:48,870 --> 00:29:59,210
+بيقسم N و D بيقسم N على C هذا اللي بتثبته أثبته زي
+
+311
+00:29:59,210 --> 00:30:02,830
+الحسابات بس شوف كيف خلّيني أخد اتجاهه تاني
+
+312
+00:30:02,830 --> 00:30:03,750
+similarly
+
+313
+00:30:06,170 --> 00:30:13,790
+D بتقسم الـN and C بتقسم الـN على D إيش معناته
+
+314
+00:30:13,790 --> 00:30:17,050
+هذا؟ إيش هو بيعطيني؟ D بتقسم الـN معناته أن الـN
+
+315
+00:30:17,050 --> 00:30:21,810
+بتساوي D في sum K يعني انتجر صار اللي هو الـN على
+
+316
+00:30:21,810 --> 00:30:29,530
+D and .. and اللي هو إيش بتصير هذا؟ N على D بتساوي
+
+317
+00:30:29,530 --> 00:30:37,780
+CM مثلايعني بمعنى آخر الـ N بتساوي CM في مين في D
+
+318
+00:30:37,780 --> 00:30:43,940
+صح ولا لأ؟ طيب، طيب معناته أن هذا صارت الـC عامل
+
+319
+00:30:43,940 --> 00:30:48,740
+من عامل مين؟ الـ N، واضح الـ N بتساوي CM في D إذا
+
+320
+00:30:48,740 --> 00:30:52,260
+الـ C عامل من عامل الـ N إذا صار بيعطينا هذا C
+
+321
+00:30:52,260 --> 00:31:01,540
+بتكسب مين؟ آسف، بتكسب مين؟ الـ N صح ولا لأ؟باضحة
+
+322
+00:31:01,540 --> 00:31:06,420
+أه؟ C بتكسب الـ N يعني صار عندي هذا و كأنه N في D
+
+323
+00:31:06,420 --> 00:31:14,180
+أش بيساوي N على C لأن برضه الـ D عمل من أهم الميان
+
+324
+00:31:14,180 --> 00:31:23,760
+N على C فاهمين؟ and D بتكسب الـ N على C إذن الـ D
+
+325
+00:31:23,760 --> 00:31:27,020
+بتكسب الـ N و الـ C بتكسب الـ N على D أعطاني C
+
+326
+00:31:27,020 --> 00:31:32,990
+بتكسب الـ N و الـ D بتكسب MSimilarly هذا بقى D
+
+327
+00:31:32,990 --> 00:31:38,510
+لهذا إذا صار two conditions هذول أشمالهم متكافئين
+
+328
+00:31:38,510 --> 00:31:43,850
+واضح يعني هذا بيحدث مع هذا F أندر ال F إذا صار هذا
+
+329
+00:31:43,850 --> 00:31:49,370
+ال summation بيصير عبارة عن summation ميو of D أف
+
+330
+00:31:49,370 --> 00:31:55,330
+of C الآن بدل D بيكسب M وC بيكسب M على D بدي أحط
+
+331
+00:31:55,330 --> 00:31:58,870
+ال conditions اللي هي المكافئة لها اللي هو C بيكسب
+
+332
+00:31:58,870 --> 00:32:09,620
+Mو الـ D تكسب مين؟ N على C واضح أه طيب صارت الأن
+
+333
+00:32:09,620 --> 00:32:13,740
+ال F of C بقدر أطلّح أين؟ برا لإن هذا ال summation
+
+334
+00:32:13,740 --> 00:32:18,500
+بيشتغل على مين؟ على ال D إذا هو يساوي summation F
+
+335
+00:32:18,500 --> 00:32:23,520
+of C C بتكسب N هاي بتشتغل عليها ال C فال summation
+
+336
+00:32:23,520 --> 00:32:29,700
+Mu of D ال D بتكسب مين؟ N على C لأن هذا ال
+
+337
+00:32:29,700 --> 00:32:38,030
+summationسفر ما عدا لما اللي هي الـ N على C أشوى
+
+338
+00:32:38,030 --> 00:32:43,230
+تساوي واحد سفر
+
+339
+00:32:43,230 --> 00:32:48,030
+ما عدا عند مين الـ N بتساوي واحد يعني هذا هيكون
+
+340
+00:32:48,030 --> 00:32:53,190
+سفر ما عدا عند مين عند N على C بتساوي واحد لأن هذا
+
+341
+00:32:53,190 --> 00:32:59,770
+بيساوي summation F of C في واحد ومتى
+
+342
+00:33:00,780 --> 00:33:09,500
+لما الـ N بيساوي الـ C N
+
+343
+00:33:09,500 --> 00:33:16,440
+على الـ C صح؟ شو معناته دي؟ N بيساوي الـ C واضح
+
+344
+00:33:16,440 --> 00:33:25,200
+ها؟ الـ C بتكسب الـ Nو هذه بتعطيني ال N بتساوي C
+
+345
+00:33:25,200 --> 00:33:32,800
+يعني بمعنى آخر ال F of C بس عند N إيش بتساوي C
+
+346
+00:33:32,800 --> 00:33:40,140
+فاهمين أه؟ طب هذه إيش مالها؟ عبارة عن F of N
+
+347
+00:33:40,140 --> 00:33:43,400
+summation
+
+348
+00:33:43,400 --> 00:33:49,770
+of F of C لما C بتساوي N إيش بتساوي F of N؟إذا صار
+
+349
+00:33:49,770 --> 00:33:58,530
+عندي الان ال F of N أيش صار بالساوية؟ و هو المطلوب
+
+350
+00:33:58,530 --> 00:34:07,410
+أي سؤال؟ طيب نشوف تطبيق ال Mobius Invergent
+
+351
+00:34:07,410 --> 00:34:07,950
+Formula
+
+352
+00:34:34,290 --> 00:34:43,090
+ما هو اللي بيقوللي بيقوللي prove that الواحد
+
+353
+00:34:43,090 --> 00:34:49,690
+بيقوم
+
+354
+00:34:49,690 --> 00:34:58,510
+بصميم mu of n على d في tau of d دي بتجسم n
+
+355
+00:35:02,640 --> 00:35:08,320
+الـ N بتساوي الـ summation ميو of N على D سيجما of
+
+356
+00:35:08,320 --> 00:35:13,860
+D دي بتكسب إياش الـ N ماشي الحالة الـ proof
+
+357
+00:35:13,860 --> 00:35:18,260
+بتستخدم
+
+358
+00:35:18,260 --> 00:35:21,900
+اللي هي ال inversion ال Mobius inversion formula
+
+359
+00:35:21,900 --> 00:35:32,650
+إيش بده أقول لأن أنا بعرف لأن since Tau of Nبس هو
+
+360
+00:35:32,650 --> 00:35:38,010
+الـ summation للواحد واحد اللي هو دي بتكسب مين
+
+361
+00:35:38,010 --> 00:35:42,770
+الانالتو ايش اسمها بس راكزوا معايا اذاكركوا فيها
+
+362
+00:35:42,770 --> 00:35:46,730
+التو ايش هي number of divisors كيف بدأت number of
+
+363
+00:35:46,730 --> 00:35:49,610
+divisors كل مرة كل divisor بدأ يعد بواحد كل
+
+364
+00:35:49,610 --> 00:35:52,550
+divisor بدأ يعد بواحد معايا يا محمد فالان بدي
+
+365
+00:35:52,550 --> 00:35:57,670
+بصميش للواحد اللي هو العداد عالميا على كل ال
+
+366
+00:35:57,670 --> 00:36:00,810
+divisors دي بتكسب مين الان كل ما يجي divisor بعد
+
+367
+00:36:00,810 --> 00:36:03,910
+واحد كل ما يجي divisor بعد واحد اذا أنا صميش
+
+368
+00:36:03,910 --> 00:36:09,860
+للواحد دي بتكسب مين الان الاقلبدي أطبّق الـ
+
+369
+00:36:09,860 --> 00:36:12,180
+Inversion Formula بكرا اللي هي المبنصة الـ
+
+370
+00:36:12,180 --> 00:36:15,740
+Inversion Formula على هذه لأن هذه بتعتبرها F
+
+371
+00:36:15,740 --> 00:36:20,540
+Capital و هذه بتعتبرها مين؟ F Small يعني الـ F
+
+372
+00:36:20,540 --> 00:36:24,380
+Smallاش بتساوي دائما واحد والـ F Capital مين هي
+
+373
+00:36:24,380 --> 00:36:29,720
+التاو لأن بيصير .. إذا هذي متحققة ولا لأ؟ هذي F
+
+374
+00:36:29,720 --> 00:36:34,480
+Capital عبارة عن summation لـ F Small إذا by
+
+375
+00:36:34,480 --> 00:36:42,860
+inversion thenby Mobius Inversion Formula بدي اطلع
+
+376
+00:36:42,860 --> 00:36:47,240
+عندى ال F of N مين ال F of N اللي هو الواحد فاهمين
+
+377
+00:36:47,240 --> 00:36:55,680
+واحد بساوي ال summation ميو of مين of دي اه بدك
+
+378
+00:36:55,680 --> 00:37:00,920
+تاخد هد خد هد زي ما بدك هد او هد مش فارق اه ميو of
+
+379
+00:37:00,920 --> 00:37:07,000
+ان على دي عشان نعمل زي ما بده في مينفى F of D اللى
+
+380
+00:37:07,000 --> 00:37:15,760
+هى مين F of D تاو of D D تجسم الانوار واضحة ها
+
+381
+00:37:15,760 --> 00:37:20,820
+Similarly المفى اللى .. المركز عليها دى اللى مستمع
+
+382
+00:37:20,820 --> 00:37:32,000
+بشها دى عندى التانية الان انا معرف since اللى هى
+
+383
+00:37:32,000 --> 00:37:34,180
+الان بتساوي
+
+384
+00:37:35,810 --> 00:37:45,890
+الـ summation لـ
+
+385
+00:37:45,890 --> 00:37:55,930
+sigma of n سوى summation لـ D
+
+386
+00:37:55,930 --> 00:38:00,750
+دي بتكسب main الـ n أذكركم فيهاهذه اللي هي
+
+387
+00:38:00,750 --> 00:38:05,130
+الـSigma of an H هي عبارة عن مجموع الـdivisors هي
+
+388
+00:38:05,130 --> 00:38:07,670
+عبارة عن الـsummation لكل الـdivisors من الـmain
+
+389
+00:38:07,670 --> 00:38:16,030
+لأ لأ معايا then برضه by Möbius inversion formula
+
+390
+00:38:16,030 --> 00:38:21,670
+كيف؟ هذه بدأت تصير تمثل اللي هي F capital وهذه
+
+391
+00:38:21,670 --> 00:38:28,510
+بدأت تمثل لمين؟ لف صغير ايش لف صغير؟ يعني F of D
+
+392
+00:38:28,510 --> 00:38:33,500
+بتساوي Dيعني ال identity يعني f of واحد واحد، f of
+
+393
+00:38:33,500 --> 00:38:38,460
+اتنين اتنين، f of ان ان، f of دي ايش بتساوي دي،
+
+394
+00:38:38,460 --> 00:38:44,100
+فاهمين؟ اذا by inversion formula بيصير عندي f
+
+395
+00:38:44,100 --> 00:38:48,580
+small of ان، مين f small of ان؟ اللي هي f of دي
+
+396
+00:38:48,580 --> 00:38:53,340
+بيساوي دي، يعني ان، فاهمين؟ بيساوي summation؟ لا
+
+397
+00:38:55,670 --> 00:38:59,550
+الـ Fsmall of N إيش هتساوي N لأنه ماخد الـ Fsmall
+
+398
+00:38:59,550 --> 00:39:04,770
+مين هي الـ Identity F of N بيستخدم الـ Summation
+
+399
+00:39:04,770 --> 00:39:10,770
+Mu N على D في
+
+400
+00:39:10,770 --> 00:39:13,570
+مين F الـ Capital اللي أخدناها إيه إيه إيش Sigma
+
+401
+00:39:13,570 --> 00:39:19,630
+في Sigma of D حيث D بتجسم مين الـ N وهو المطلوب
+
+402
+00:39:19,630 --> 00:39:22,810
+نيجي
+
+403
+00:39:22,810 --> 00:39:31,070
+لآخر نظرية في ال sectionاللي هي اللي وعدناكم فيها
+
+404
+00:39:31,070 --> 00:39:38,210
+في الأول اللي قلنا انه لو كانت ال F multiplicative
+
+405
+00:39:38,210 --> 00:39:41,750
+بيصير .. احنا اللي أثبتناها قبل هيك ان لو كانت ال
+
+406
+00:39:41,750 --> 00:39:45,230
+F small multiplicative هتكون ال F أشمالها
+
+407
+00:39:45,230 --> 00:39:49,970
+multiplicative اللي بتحكيها ده النظرية انه لو كان
+
+408
+00:39:49,970 --> 00:39:53,810
+اللي هو ال F capital هي ال multiplicative هتكون
+
+409
+00:39:53,810 --> 00:39:57,050
+اللي جوا ال summation برضه أشمالهاmultiplicative
+
+410
+00:39:57,050 --> 00:40:02,550
+إذا كانت F F small multiplicative F capital
+
+411
+00:40:02,550 --> 00:40:06,770
+multiplicative F capital multiplicative F small
+
+412
+00:40:06,770 --> 00:40:13,390
+إيه شمالها multiplicative مظبوط يا محمد معانها خير
+
+413
+00:40:13,390 --> 00:40:18,610
+نستخدم
+
+414
+00:40:18,610 --> 00:40:20,610
+هذا عشان نخليها
+
+415
+00:40:27,650 --> 00:40:41,050
+فيرم تمانية تمانية الان if F is multiplicative and
+
+416
+00:40:41,050 --> 00:40:53,830
+F of N سم F of D دي بتجسم N then F برضه اشمالة is
+
+417
+00:40:53,830 --> 00:41:01,870
+multiplicative معايا يا شبابالغروف الغروف 6 8 غروف
+
+418
+00:41:01,870 --> 00:41:07,750
+عشان اثبت ان ال F small multiplicative ايش بيدقول
+
+419
+00:41:07,750 --> 00:41:13,830
+بيدقول let M و N element in Z positive such that
+
+420
+00:41:13,830 --> 00:41:17,490
+ال greatest common divisor بين ال M و ال N بساوة
+
+421
+00:41:17,490 --> 00:41:21,530
+واحد و اثبت لكم ان ال F small M في N بساوة F small
+
+422
+00:41:21,530 --> 00:41:23,390
+of M في F small of M
+
+423
+00:41:26,550 --> 00:41:35,130
+عندي f small of n في n بساوة الآن عشان أعرف أتحرك
+
+424
+00:41:35,130 --> 00:41:41,370
+بدي أحول اللي هو fmn نفسها على صورة main على صورة
+
+425
+00:41:41,370 --> 00:41:46,150
+summation الان الـ main اللي بده يحرك ليه يغير ليه
+
+426
+00:41:46,150 --> 00:41:54,190
+المبيوث inversion formula معايا؟ الآن عندي fnأف أن
+
+427
+00:41:54,190 --> 00:41:58,590
+إذا كانت أف أن على الصورة هذه فبتصير أف أن للي جوا
+
+428
+00:41:58,590 --> 00:42:04,430
+فاهمين عليها دي بتقسم أن أف أن بساوي ال summation
+
+429
+00:42:04,430 --> 00:42:10,750
+ميو of دي في أف أن على دي أو ميو of أن على دي أف
+
+430
+00:42:10,750 --> 00:42:14,630
+of دي اللي بديها باستخدامها فيساوي ال summation
+
+431
+00:42:14,630 --> 00:42:22,910
+للي ميو of ديالأن أف كويت الـ of مين؟ M فن على D
+
+432
+00:42:22,910 --> 00:42:28,630
+لأنه أنا بوجد لمين؟ للـ M فن حيث الـ D بتكسب مين؟
+
+433
+00:42:28,630 --> 00:42:33,230
+الـ M فن الآن الـ Great School Divisor بين الـ M و
+
+434
+00:42:33,230 --> 00:42:38,490
+الـ N أيش بيساوي؟ واحد هذا إذن هيساوي الـ
+
+435
+00:42:38,490 --> 00:42:48,370
+summation لـ Mu of الـ D بتكسب الـ M Nأه في
+
+436
+00:42:48,370 --> 00:42:52,930
+الشيبان هى مشترك الـ M و الـ N فبتصير عبارة عن D1
+
+437
+00:42:52,930 --> 00:42:58,770
+بتكسب الـ M و D2 بتكسب الـ M و الـ D أش بيساوي D1
+
+438
+00:42:58,770 --> 00:43:05,050
+في D2 و عملناها قبل هيك هذه اللى عبارة عن Mu D1 D2
+
+439
+00:43:05,050 --> 00:43:11,310
+في F capital of M N D1 D2
+
+440
+00:43:13,470 --> 00:43:17,790
+الـ F Multiplicative والـ Mu Multiplicative إذا
+
+441
+00:43:17,790 --> 00:43:20,810
+إيش هيساوي؟ لأن العام المشترك اللي على بين الـ D1
+
+442
+00:43:20,810 --> 00:43:23,910
+والـ D2 بيساوي واحد والعام المشترك اللي على بين
+
+443
+00:43:23,910 --> 00:43:27,170
+الـ M والـ N إيش ماله؟ بيساوي واحد إذا العام
+
+444
+00:43:27,170 --> 00:43:29,730
+المشترك اللي على بين هذه على هذه وهذه على هذه برضه
+
+445
+00:43:29,730 --> 00:43:37,810
+إيش فاهمين؟ إذا بيصير summation Mu of D1 Mu of D2
+
+446
+00:43:38,520 --> 00:43:47,320
+فى F M على D 1 فى F M على D 2 حيث دي واحد بتقسم ال
+
+447
+00:43:47,320 --> 00:43:55,180
+M دي اتنين بتقسم مين ال N هي نفسها بتساوي هذه
+
+448
+00:43:55,180 --> 00:44:00,740
+بتساوي summation summation واحد دي واحد بتقسم ال M
+
+449
+00:44:00,740 --> 00:44:10,260
+واحد دي اتنين بتقسم مين ال N MuF of D1 F of M على
+
+450
+00:44:10,260 --> 00:44:22,000
+D1 في ميو D2 F of M على D2 F of M على D2 F of M
+
+451
+00:44:22,000 --> 00:44:29,860
+على D2 F of M على D2 F of M على D2
+
+452
+00:44:29,940 --> 00:44:39,560
+of D1 F of M على D1 في الـ summation F of M على D2
+
+453
+00:44:39,560 --> 00:44:51,500
+ميو D2 D2 تجسم، هذه N طبعا تجسم الـ N وهذه D1
+
+454
+00:44:51,500 --> 00:44:57,820
+بتجسم الـ M الأولاني هو عبارة عن F of M F small of
+
+455
+00:44:57,820 --> 00:45:05,510
+Mوالتاني f of small of n صار عندي fmn سوى fm في fn
+
+456
+00:45:05,510 --> 00:45:09,990
+إذا صارت ال f إيش ما لها is a multiplicative
+
+457
+00:45:09,990 --> 00:45:15,290
+function والمرة الجاية إن شاء الله بنكمل بنبدأ في
+
+458
+00:45:15,290 --> 00:45:17,970
+chapter 7 إن شاء الله
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/83b4FEtBAAM.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/83b4FEtBAAM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..21f170af53d3022dc20e78a3e0c6695aa0702103
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/83b4FEtBAAM.srt
@@ -0,0 +1,1899 @@
+1
+00:00:19,350 --> 00:00:24,970
+بسم الله الرحمن الرحيم المحاضرة اليوم محاضرة رقم 
+
+2
+00:00:24,970 --> 00:00:29,970
+عشرين في مساق نظرية الأعداد لطلبة الجامعة
+
+3
+00:00:29,970 --> 00:00:39,390
+الإسلامية قسم رياضيات كلية التربية والعلوم هنكمل 
+
+4
+00:00:39,390 --> 00:00:42,930
+في chapter 6 اللي بدنا إياه اللي بتحدث عن number
+
+5
+00:00:42,930 --> 00:00:47,850
+theoretic functions بدأنا المرة الماضية في الـ
+
+6
+00:00:47,850 --> 00:00:51,270
+section الأول اللي هو the function sigma and tau
+
+7
+00:00:51,270 --> 00:00:57,810
+اللي هي عدد ال divisors ومجموع ال divisors عرفنا
+
+8
+00:00:57,810 --> 00:01:01,490
+شو معنى number theoretic function وقلنا هي اللي
+
+9
+00:01:01,490 --> 00:01:04,870
+عبارة عن function domainها بيكون the set of
+
+10
+00:01:04,870 --> 00:01:09,570
+positive integers وبعدين عرفنا اللي هو tau of n
+
+11
+00:01:10,230 --> 00:01:13,650
+تاو عبارة عن الـ function هنا من الـ z
+
+12
+00:01:13,650 --> 00:01:18,210
+positive وبتودّي على الـ z positive وهذا قلنا عنها
+
+13
+00:01:18,210 --> 00:01:22,770
+اللي هي the number of divisors tau of n اللي هي 
+
+14
+00:01:22,770 --> 00:01:29,390
+عبارة عن عدد قواسم العدد n وعرفنا أيضا برضه sigma من
+
+15
+00:01:29,390 --> 00:01:33,390
+z positive لz positive وقلنا عنها sigma of n هي
+
+16
+00:01:33,390 --> 00:01:38,530
+عبارة عن the sum of divisors أو مجموع قواسم العدد
+
+17
+00:01:40,150 --> 00:01:44,850
+أخذنا أمثلة المرة الماضية حسابية لإيجاد Sigma وTau
+
+18
+00:01:44,850 --> 00:01:49,530
+وقلنا إنه لو بدنا نوجد اللي هو Sigma أو Tau
+
+19
+00:01:49,530 --> 00:01:56,420
+للأعداد مثلًا 1800 أو Sigma of 1800 طبعًا بالطريقة
+
+20
+00:01:56,420 --> 00:02:00,560
+العادية إنه نوجد الـ divisors ونجمّعهم أو نوجد الـ
+
+21
+00:02:00,560 --> 00:02:03,760
+divisors ونعدّ من عددهم بالطريقة اللي حكيناها طبعًا
+
+22
+00:02:03,760 --> 00:02:07,920
+طريقة غير عملية وأكيد فيها غلب كثير فعشان هيك
+
+23
+00:02:07,920 --> 00:02:16,090
+بلزمنا ندرس خواص إضافية للـ Sigma والـ Tau اللي من
+
+24
+00:02:16,090 --> 00:02:22,310
+خلالها إن شاء الله هنقدر نحصل على طريقة سهلة أو
+
+25
+00:02:22,310 --> 00:02:26,270
+طرق سهلة لإيجاد sum of divisors و number of
+
+26
+00:02:26,270 --> 00:02:30,790
+divisors وأيضًا لدراسة خلاص sum of divisors و
+
+27
+00:02:30,790 --> 00:02:35,030
+number of divisors حكينا المرة الماضية برضه نظرية
+
+28
+00:02:35,030 --> 00:02:41,210
+6.1 قلنا لو كان عندي N أي عدد أكبر من عدد أكبر
+
+29
+00:02:41,210 --> 00:02:44,990
+من واحد أي عدد أكبر من واحد N أكيد الـ N الأكبر من
+
+30
+00:02:44,990 --> 00:02:48,750
+واحد في الـ unique factorization theorem بنقدر
+
+31
+00:02:48,750 --> 00:02:52,830
+نكتبه على صورة اللي هو bar of the primes اللي هي
+
+32
+00:02:52,830 --> 00:03:00,410
+P1 أُس K1 اللي عند P R أُس K R
+
+33
+00:03:00,410 --> 00:03:06,250
+P R إذا قلنا بالضبط Precisely the divisors of N
+
+34
+00:03:06,250 --> 00:03:13,610
+are those written as D بتساوي P1 أُس ألفا 1 اللي
+
+35
+00:03:13,610 --> 00:03:20,300
+عند P R أُس ألفا R حيث الالفا اي بين الصفر وبين الـ K
+
+36
+00:03:20,300 --> 00:03:25,140
+اي هذا اللي هي بالضبط اللي هي ال divisors اللي للـ N
+
+37
+00:03:25,140 --> 00:03:31,840
+اللي للـ N الآن الطريق للوصول لـ number of divisors و
+
+38
+00:03:31,840 --> 00:03:35,860
+sum of divisors هي عبر اللي هو كتابة الـ N على
+
+39
+00:03:35,860 --> 00:03:40,280
+صورة اللي هو ال canonical form أو ال form اللي
+
+40
+00:03:40,280 --> 00:03:44,720
+عندنا P1 أُس K1 و P R أُس K R ومن ثم حصر
+
+41
+00:03:44,720 --> 00:03:49,640
+مين هي ال divisors من خلال المعلومة اللي أمامنا أن
+
+42
+00:03:49,640 --> 00:03:54,780
+ال divisors هيشكلها بصير فيه إمكانية لحصر من ال
+
+43
+00:03:54,780 --> 00:04:01,410
+divisors اللي للعدد N الآن نجي لنظريتنا الأولى
+
+44
+00:04:01,410 --> 00:04:09,050
+نظريتنا
+
+45
+00:04:09,050 --> 00:04:15,050
+الأولى كبرت شوية اللي هي إن لو كانت N بتساوي P1 أُس K1
+
+46
+00:04:15,050 --> 00:04:19,410
+P2 أُس K2 لعند PR أُس KR is a prime factorization of N
+
+47
+00:04:19,410 --> 00:04:23,710
+أكبر من 1 يعني النظرية عشان نطبقها بدنا نجهز العدد
+
+48
+00:04:23,710 --> 00:04:27,170
+N على صورة إيش اللي هو ال prime factorization له
+
+49
+00:04:27,170 --> 00:04:32,970
+بتكون على طول Tau of N هي عبارة عن هنتعامل بس مع
+
+50
+00:04:32,970 --> 00:04:39,610
+الأسس اللي هي K1 زائد 1 في K2 زائد 1 لعند KR زائد 1
+
+51
+00:04:40,260 --> 00:04:43,280
+ماشي الحال حاصل ضرب هنا بيكون اللي هو number of
+
+52
+00:04:43,280 --> 00:04:47,880
+divisors الآن sum of divisors هو عبارة عن P1 أُس
+
+53
+00:04:47,880 --> 00:04:51,440
+K1 أُس 1 زائد 1 ناقص 1 على P1
+
+54
+00:04:51,440 --> 00:04:55,580
+ناقص 1 كله هنا بنفس الأسلوب لعن P R أُس KR زائد
+
+55
+00:04:55,580 --> 00:05:00,120
+1 ناقص 1 على P R ناقص 1 خلينا للرسول
+
+56
+00:05:00,120 --> 00:05:04,080
+للبرهان بخلينا بس نطلعنا على مثال هيك على جنب و
+
+57
+00:05:04,080 --> 00:05:09,170
+نشوف كيف بدنا نروح باتجاه البرهان لو جينا أخذنا
+
+58
+00:05:09,170 --> 00:05:17,370
+الأمر عبارة عن 2 أُس 2 في 5 أُس 3 مثلًا هي عندي هذا
+
+59
+00:05:17,370 --> 00:05:23,630
+بدي أشوف له الـ divisors تبعونه اتفقنا أن الـ
+
+60
+00:05:23,630 --> 00:05:32,170
+divisors دي هتكون على شكل 2 أُس ألفا 1 في 5 أُس
+
+61
+00:05:32,170 --> 00:05:36,530
+ألفا 2 حيث ألفا 1 أكبر أو يساوي صفر وأصغر أو
+
+62
+00:05:36,530 --> 00:05:41,450
+يساوي 2 وألفا 2 هتكون أكبر أو يساوي صفر
+
+63
+00:05:41,450 --> 00:05:45,490
+وأصغر أو يساوي مين 3 ماشي الحال هاي شكل ال
+
+64
+00:05:45,490 --> 00:05:48,610
+divisors اللي عندي بناء على هذه المعلومة على شكل
+
+65
+00:05:48,610 --> 00:05:53,040
+ال divisors خليني آجي أطلع على 2 تربيع 2
+
+66
+00:05:53,040 --> 00:05:58,300
+تربيع اللي هي عندي اللي هي قواسمها بناء على الحديث
+
+67
+00:05:58,300 --> 00:06:02,300
+هذا إنه القواسم هتكون على الصورة هذه وألفا 1
+
+68
+00:06:02,300 --> 00:06:06,220
+بين الصفر وبين الـ 2 هيكون عندي قواسم العدد هذا
+
+69
+00:06:06,220 --> 00:06:09,680
+اللي هي الطبيعية اللي هي 1 اللي هي 2 أُس صفر
+
+70
+00:06:09,680 --> 00:06:15,640
+و الثاني عبارة عن 2 أُس 1 والثالث عبارة عن
+
+71
+00:06:15,640 --> 00:06:21,920
+2 أُس 2 هذه قواسم العدد من 2 تربيع الآن
+
+72
+00:06:21,920 --> 00:06:27,500
+جنبه قواسم العدد الآخر اللي هي عبارة عن 1 و5
+
+73
+00:06:28,480 --> 00:06:36,220
+و5 تربيع و5 تكعيب هاي قواسم العدد الآخر طيب الآن
+
+74
+00:06:36,220 --> 00:06:40,980
+أنا بدي قواسم العدد N اللي هو ممزوج بين اللي هو
+
+75
+00:06:40,980 --> 00:06:47,100
+هذا في هذا إذا الأعداد اللي على الصورة 2 أُس ألفا 
+
+76
+00:06:47,100 --> 00:06:51,040
+1 في 5 أُس ألفا 2 هتكون هي الأعداد
+
+77
+00:06:51,040 --> 00:06:57,350
+التالي 1 مع الـ 1 هذه هاي أول واحد الثاني 1
+
+78
+00:06:57,350 --> 00:07:02,970
+مع مين؟ مع الـ 5 الثالث 1 مع مين؟ مع الـ 5
+
+79
+00:07:02,970 --> 00:07:09,750
+تربيع يعني الآن الـ 1 بيجيب وفي 1 في مين؟ في
+
+80
+00:07:09,750 --> 00:07:15,760
+الـ 5 تكعيب نفس الأشياء الآن هذا الـ 1 اللي هو
+
+81
+00:07:15,760 --> 00:07:22,660
+راح مع كل هدول يعني خيار الـ Alpha 1 Alpha 2 1 2
+
+82
+00:07:22,660 --> 00:07:29,860
+3 4 خيارات يعني خياره طلع Alpha 1 و2 زائد 1 مع
+
+83
+00:07:29,860 --> 00:07:34,120
+العدد الأول اللي هو الـ 1 مع التاني برضه نفس الشيء ماشي
+
+84
+00:07:34,120 --> 00:07:43,610
+2 الآن في 1 2 2 2 في 5 تكعيب
+
+85
+00:07:43,610 --> 00:07:53,060
+والعمود على 2 تربيع فيه 1 2 تربيع في
+
+86
+00:07:53,060 --> 00:07:58,620
+5 2 تربيع في 5 تربيع 2 تربيع في 5
+
+87
+00:07:58,620 --> 00:08:04,300
+تكعيب يعني الآن number of choices اللي هنا اللي هي
+
+88
+00:08:04,300 --> 00:08:08,460
+1 2 كلاته 4 مع تثبيت الأول إذا كل واحد
+
+89
+00:08:08,460 --> 00:08:13,820
+من هدول بيجيب عاملين 4 divisors الآن هذا مكرر
+
+90
+00:08:13,820 --> 00:08:18,840
+أكام مرة اللي هو 3 مرات، بصحيح؟ هاي 1، 2،
+
+91
+00:08:18,840 --> 00:08:23,000
+3، بصحيح؟ إذًا عدد الخيارات هنا عبارة عن 2
+
+92
+00:08:23,000 --> 00:08:25,960
+زائد 1 وعدد الخيارات هنا 3 زائد 1 يعني
+
+93
+00:08:25,960 --> 00:08:31,180
+4 يعني هيكون الـ divisors كلهم اللي هو 3
+
+94
+00:08:31,180 --> 00:08:36,320
+الخيارات اللي هنا مع الـ 4 ويساوي إيش 12
+
+95
+00:08:36,320 --> 00:08:40,260
+divisor هذا الـ mean اللي هو عدد ال divisors هذا
+
+96
+00:08:40,260 --> 00:08:47,040
+طلع عندي tau of N هذا الـ 3 عبارة عن إيش
+
+97
+00:08:47,040 --> 00:08:51,940
+في الواقع ألفا 1 زائد 1 هذه عبارة عن مين عن
+
+98
+00:08:51,940 --> 00:08:56,000
+ألفا 2 زائد 1 طيب
+
+99
+00:08:57,800 --> 00:09:01,140
+الآن هذا اللي هو number of divisors طب بدي أجيب
+
+100
+00:09:01,140 --> 00:09:07,480
+أنا مجموع ال divisors مجمّعين الآن مجمّعين كيف
+
+101
+00:09:07,480 --> 00:09:10,320
+احنا جبنا ال divisors الآن 1 مع حد و1 مع
+
+102
+00:09:10,320 --> 00:09:13,900
+حد و1 مع حد و1 مع حد طب عشان أجيب المجموع
+
+103
+00:09:13,900 --> 00:09:20,640
+بس أجمع لي هذول واضرب اليهم في إيش؟ في بعض بيصير حاصل
+
+104
+00:09:20,640 --> 00:09:25,680
+ضرب هذا مع حاصل ضرب هذا مع .. نضرب هذا في هذا
+
+105
+00:09:25,680 --> 00:09:31,340
+بيطلع اللي هو إيش ماله؟ مجموع الـ divisors in
+
+106
+00:09:31,340 --> 00:09:36,740
+general .. in general لو كان عندي الآن لو كان عندي
+
+107
+00:09:36,740 --> 00:09:40,440
+لو
+
+108
+00:09:40,440 --> 00:09:44,840
+كان عندي الآن N
+
+109
+00:09:46,120 --> 00:09:55,560
+بتساوي P1 أُس ألفا 1 P2 أُس ألفا 2 P
+
+110
+00:09:55,560 --> 00:10:06,940
+1 أُس
+
+111
+00:10:06,940 --> 00:10:13,560
+ألفا 1 P2 أُس ألفا 2 P1 أُس
+
+112
+00:10:13,560 --> 00:10:14,600
+ألفا 1 P2 أُس ألفا 2 P1 أُس 1 P2 أُس
+
+113
+00:10:14,600 --> 00:10:14,960
+2 ألفا 1 P1 2 ألفا 1 P1
+
+114
+00:10:14,960 --> 00:10:19,290
+2 زائد P2 لما أصل لعند P2 أُس ألفا 
+
+115
+00:10:19,290 --> 00:10:23,770
+2 الـ divisors الكلية لأن هي هذا مع هذول
+
+116
+00:10:23,770 --> 0:10:28,910
+كلهم ضرب وهذا مع هذول كلهم ضرب فبيصير اللي هو
+
+117
+00:10:28,910 --> 00:10:34,230
+هذا إيه أكبر choice ألفا 1 زائد 1 لأن هذول
+
+118
+00:10:34,230 --> 00:10:37,970
+أحدد هنا ألفا 1 وهذا اللي هو الصفر بيصير ألفا 1
+
+119
+00:10:37,970 --> 00:10:44,740
+زائد 1 وهذا الـ choices بتبعته قداش ألفا 2
+
+120
+00:10:44,740 --> 00:10:51,040
+زائد 1 فبيصير ال tau of N بتساوي ألفا 1 زائد 1
+
+121
+00:10:51,040 --> 00:10:55,780
+في ألفا 2 زائد 1 إذا لو في عندي كمان P3
+
+122
+00:10:55,780 --> 00:11:00,880
+أُس ألفا 3 لعند PR أُس ألفا R بيصير اللي هو
+
+123
+00:11:00,880 --> 00:11:09,300
+هذول ال divisors اللي كاتبين جنب بعض لما
+
+124
+00:11:09,300 --> 00:11:17,930
+أصل لآخر واحد اللي هو 1 لعند P R أُس ألفا R
+
+125
+00:11:17,930 --> 00:11:21,370
+الآخر
+
+126
+00:11:21,370 --> 00:11:29,070
+هذا اللي بيجيب لي tau of N عشان أوجد مجمّع بس بأجمّع
+
+127
+00:11:29,070 --> 00:11:36,650
+هدول وبضربهم في بعض بيطلع عندي اللي هو مجموع الـ
+
+128
+00:11:36,650 --> 00:11:39,690
+divisors طب كيف تكون مجموع ال divisors في هذه
+
+129
+00:11:39,690 --> 00:11:47,370
+الحالة Sigma of N بتساوي هذه اللي عبارة عن إيش
+
+130
+00:11:47,370 --> 00:11:54,690
+finite geometric series معايا إيش اللي هو قانونها
+
+131
+00:11:54,690 --> 00:12:02,650
+الأساس P1 أُس اللي هو عددهم عددهم إيش بيساوي
+
+132
+00:12:02,650 --> 00:12:08,610
+ألفا 1 زائد 1 ناقص 1 على P1 ناقص 1
+
+133
+00:12:08,610 --> 00:12:12,950
+على P1 ناقص 1 P1 اللي هو مين اللي هو الأساس
+
+134
+00:12:12,950 --> 00:12:18,150
+اللي هو الـ N اللي هو عدد مين الحدود واضح آه من
+
+135
+00:12:18,150 --> 00:12:23,690
+الحد الأول 1 على P1 ناقص 1 هذا اللي هو
+
+136
+00:12:23,690 --> 00:12:31,060
+المجموع هذا بس هذا المجموع ده مجموع ده ولا مضروب
+
+137
+00:12:31,060 --> 00:12:36,300
+في P2 أُس ألفا 2 زائد 1 ناقص 1 على P
+
+138
+00:12:36,300 --> 00:12:42,160
+2 ناقص 1 لما أصل لآخر واحد P R أُس ألفا R
+
+139
+00:12:42,160 --> 00:12:48,180
+زائد 1 ناقص 1 على P R ناقص 1 فبقول هذا
+
+140
+00:12:48,180 --> 00:12:53,460
+اللي هو Sigma of N ومجموع ال divisors إذن الآن صار عندي 
+
+141
+00:12:53,460 --> 00:12:57,040
+fn بتساوي
+
+142
+00:12:59,920 --> 00:13:08,080
+B1K1B2K2 ... B<sub>r</sub>K<sub>r </sub> Number of Divisors بس باعتمد على مين
+
+143
+00:13:08,080 --> 00:13:13,340
+على الأسس اللي هي K1 زيادة واحد في K2 زيادة واحد لـ K<sub>r</sub>
+
+144
+00:13:13,340 --> 00:13:17,580
+زيادة واحد مضروبات في بعض. الـ Sigma of N هو عبارة
+
+145
+00:13:17,580 --> 00:13:22,280
+عن مجموع مين اللي هو B1 K1 زيادة واحد ناقص واحد على
+
+146
+00:13:22,280 --> 00:13:26,080
+B1 ناقص واحد. لما أصل لآخر term فبكون هذا اللي هو 
+
+147
+00:13:26,080 --> 00:13:29,340
+عبارة عن Number of Divisors and the sum of
+
+148
+00:13:29,340 --> 00:13:35,200
+Divisors. اطلع لفوق، example هو البرنامج اللي قلت لك 
+
+149
+00:13:35,200 --> 00:13:35,400
+إيه
+
+150
+00:13:41,230 --> 00:13:47,510
+البرهان اللي حكيناه أنه عندي ألف واحد في α<sub>1</sub>
+
+151
+00:13:47,510 --> 00:13:52,030
+Choices لها ألف واحد زائد واحد. هذه لها α<sub>1</sub> Choices 
+
+152
+00:13:52,030 --> 00:13:55,350
+ألف اتنين زائد واحد. الـ Choice ده مبنية على إيه؟
+
+153
+00:13:55,350 --> 00:14:00,370
+مبنية على إن أنا اللي قلته إن الـ N هي و الـ Data
+
+154
+00:14:00,370 --> 00:14:08,530
+معها Divisors بالظبط من العصورة P<sub>1</sub><sup>K<sub>1</sub></sup> لعند P<sub>r</sub><sup>K<sub>r</sub></sup>
+
+155
+00:14:08,530 --> 00:14:14,050
+ماشي الحال. الآن الـ Divisors هذه، الـ K1 إيش الـ
+
+156
+00:14:14,050 --> 00:14:18,470
+Choices لها؟ من صفر لعند اللي هي α<sub>1</sub> يعني
+
+157
+00:14:18,470 --> 00:14:23,210
+عددها اللي هو الـ Choices α<sub>1</sub> زائد 1. التاني نفس
+
+158
+00:14:23,210 --> 00:14:26,010
+الأشياء، التالت نفس الأشياء، الأخر نفس الأشياء، إذا
+
+159
+00:14:26,010 --> 00:14:31,530
+عدد الـ Choices اللي هي حاصلة الضرب هي عبارة عن
+
+160
+00:14:31,530 --> 00:14:37,670
+حاصلة ضرب مين اللي هي K1 زائد 1 بناء على تثبيت
+
+161
+00:14:37,670 --> 00:14:40,390
+الـ Bag وتغيير واحدة، تثبيت الـ Bag وتغيير واحدة بيصير
+
+162
+00:14:40,390 --> 00:14:45,590
+الـ Choices K1 زائد 1 في K2 زائد واحد، لما أصل في K<sub>r</sub>
+
+163
+00:14:45,590 --> 00:14:51,170
+زائد واحد. واضح؟ اه. إيه السؤال فالليجي لـ Tao of Tao
+
+164
+00:14:51,170 --> 00:15:01,690
+of 180 و Sigma of 180 ناخد
+
+165
+00:15:01,690 --> 00:15:13,600
+أي رقم بدكم إياه. Tao of 180 عشان أوجده بساويه Sigma
+
+166
+00:15:13,600 --> 00:15:19,240
+of 180. عشان أوجده بلزم إيش؟ أول خطوة نوجدها إيش؟
+
+167
+00:15:19,240 --> 00:15:23,900
+الـ Prime Factorization. إذا أول حاجة عشان أوجد تاو
+
+168
+00:15:23,900 --> 00:15:28,720
+الـ سيجما بدي أكتب الـ 180 على صورة الـ Canonical Form
+
+169
+00:15:28,720 --> 00:15:36,380
+اللي هي في هذه الحالة 2 أقصى 2 في 3 أقصى 2 في 5
+
+170
+00:15:36,380 --> 00:15:46,250
+هيك صار سهل الأمر على طول. بساوي اتنين زائد واحد في
+
+171
+00:15:46,250 --> 00:15:51,510
+اتنين زائد واحد في واحد زائد واحد. صح؟ تلاتة في
+
+172
+00:15:51,510 --> 00:16:00,130
+تلاتة، تسعة، تسعة في اتنين في 18. واضح؟ اه. سيجما
+
+173
+00:16:00,130 --> 00:16:07,560
+of 180 إيش بيساوي؟ اللي هو عبارة عن القانون
+
+174
+00:16:07,560 --> 00:16:13,560
+2 أس 2 زائد 1 ناقص 1 على 2 ناقص
+
+175
+00:16:13,560 --> 00:16:19,800
+1 في 3 أس 2 زائد 1 ناقص 1 على
+
+176
+00:16:19,800 --> 00:16:25,400
+3 ناقص 1 في 5 أس 1 زائد 1 ناقص 1
+
+177
+00:16:25,400 --> 00:16:31,320
+على 5 ناقص 1. فاللحة هي تسعة ناقص 1، 8
+
+178
+00:16:31,320 --> 00:16:40,370
+8 مظبوط، 7 بالسيرة 7 صح. اللي بعدها 27 ناقص 1
+
+179
+00:16:40,370 --> 00:16:50,570
+26 على 2، 13 في 25 ناقص 1، 24 على 4، 6. بيطلع اللي هو
+
+180
+00:16:50,570 --> 00:16:58,930
+الرقم 546 وهكذا طيب
+
+181
+00:16:58,930 --> 00:17:02,170
+لاحظ
+
+182
+00:17:02,170 --> 00:17:04,910
+أنه
+
+183
+00:17:06,790 --> 00:17:15,790
+الآن الـ Number of Divisors طلع عندي 18 يعني زوجي
+
+184
+00:17:15,790 --> 00:17:19,590
+اه
+
+185
+00:17:19,590 --> 00:17:31,090
+لو جينا أخدنا العدد مثلا، ناخد إن بتساوي 2 أس
+
+186
+00:17:31,090 --> 00:17:32,730
+2 في 3
+
+187
+00:17:36,290 --> 00:17:46,270
+أقصى 2 مثلا بس. 3 أقصى 2 ال
+
+188
+00:17:46,270 --> 00:17:56,930
+Tao of N بساوي اللي هو 2 زائد 1 في 2
+
+189
+00:17:56,930 --> 00:18:04,670
+زائد 1 ويساوي كم؟ 9 معايا؟ إذا عدد ال
+
+190
+00:18:04,670 --> 00:18:12,580
+Divisors عدد الـ Divisors فردي الآن
+
+191
+00:18:12,580 --> 00:18:25,560
+عدد الـ Divisors فردي. لو أجيت أخدت N استوف N على 2
+
+192
+00:18:25,560 --> 00:18:30,960
+عدد
+
+193
+00:18:30,960 --> 00:18:40,110
+الـ Divisors فردي فيه معنى. ليش فيه إله معنى؟ ولما
+
+194
+00:18:40,110 --> 00:18:51,970
+كان برضه اللي فوق سمّيه M، M استوف M على 2 برضه إله
+
+195
+00:18:51,970 --> 00:19:00,970
+معنى طبعا M استوف M على 2 إله معنى هل؟ بديهي لعدد
+
+196
+00:19:00,970 --> 00:19:04,930
+الـ Divisors إيه شماله؟ اللي هو زوجي طلع جدش قبل
+
+197
+00:19:04,930 --> 00:19:12,390
+شوية؟ 18. يعني بيصير M اللي هي 180 أس 18 على 2
+
+198
+00:19:12,390 --> 00:19:21,090
+ويساوي 180 أس 9. يعني الآن M استوى في M على 2 لما
+
+199
+00:19:21,090 --> 00:19:27,540
+كانت زوجي بديهي إنها إلها معنى. برضه أنا بتدعي إن لو
+
+200
+00:19:27,540 --> 00:19:33,360
+كان الرقم اللي هو الآن عدد الـ Divisors له فردي
+
+201
+00:19:33,360 --> 00:19:38,180
+برضه أنه معنى. شوف هذا المثال وبعدين بعمل المثال
+
+202
+00:19:38,180 --> 00:19:46,730
+هذا إيش بقول لك؟ بساوي N أقص نص في Tao of N جدش أنها
+
+203
+00:19:46,730 --> 00:19:51,490
+9. شيل منها 1 اللي هو نص بيظل 8 على
+
+204
+00:19:51,490 --> 00:19:55,770
+2 اللي هي N أقص 4 مظبوط ولا لأ؟ N أقص
+
+205
+00:19:55,770 --> 00:20:01,150
+4. مش فيها مشكلة لإنه لها معنى لإنه N مرفوع
+
+206
+00:20:01,150 --> 00:20:04,630
+عالميا للعدد 4 وبتطلع Integer اللي معنى بمعنى
+
+207
+00:20:04,630 --> 00:20:08,010
+أنه احنا جاعدين وين؟ في Integers هي اللي بنقص ده
+
+208
+00:20:08,010 --> 00:20:16,220
+الآن N أقص نص. مدام طلع عندك Tau of N فردي غصب عنه
+
+209
+00:20:16,220 --> 00:20:25,360
+بتطلع إن مربع كامل غصب عنه. الآن إن بتساوي 2
+
+210
+00:20:25,360 --> 00:20:29,000
+أقصى 2 في 2 أقصى 4. فبتصير في هذه
+
+211
+00:20:29,000 --> 00:20:35,100
+الحالة إنقص نص الومين 2 في 3 مظبوط ولا لأ؟
+
+212
+00:20:35,740 --> 00:20:41,220
+إذا إيه المعنى؟ إذا في حالة الفردي برضه اللي هو
+
+213
+00:20:41,220 --> 00:20:44,840
+إيه المعنى؟ يعني بمعنى آخر اللي بقوله أنا اللي
+
+214
+00:20:44,840 --> 00:20:52,160
+بادعيه إن N استوف N على 2 is always an
+
+215
+00:20:52,160 --> 00:20:56,220
+Integer سواء
+
+216
+00:20:56,220 --> 00:21:01,160
+كان الـ Tau of N فردي أو الـ Tau of N شماله زوجي. الآن
+
+217
+00:21:01,160 --> 00:21:11,540
+الآن الـ Tau of N بساوي 2K زائد 1 فردي. طرد إنه الـ N
+
+218
+00:21:11,540 --> 00:21:20,340
+بتساوي P<sub>1</sub><sup>α<sub>1</sub></sup> ... P<sub>r</sub><sup>α<sub>r</sub></sup> الـ N عندي عدد
+
+219
+00:21:20,340 --> 00:21:27,380
+الـ Divisors مين هي؟ K α<sub>1</sub> Tau of N حسب
+
+220
+00:21:27,380 --> 00:21:31,480
+القانون. إيش بتساوي؟ ما ببرهنش، بس بقعد بوضح لكم
+
+221
+00:21:31,480 --> 00:21:34,840
+البرنامج. بتبرهنوا، بترتبوا لحالكم α<sub>1</sub> زائد 1
+
+222
+00:21:35,690 --> 00:21:44,110
+لما أصل عند α<sub>r</sub> زائد إيش؟ زائد واحد. ركز معايا الآن
+
+223
+00:21:44,110 --> 00:21:51,030
+مدام Tau of N فردي إذا غصب عن كل هذول الأعداد فردية
+
+224
+00:21:51,030 --> 00:21:55,170
+لأن لو كان واحد زوجي بيطلع إيش ماله؟ مدامة كل
+
+225
+00:21:55,170 --> 00:22:00,230
+الأعداد هذول الفردية المضربات في بعض، معناته الـ α<sub>i</sub>
+
+226
+00:22:00,230 --> 00:22:05,760
+اللي هي الـ α<sub>i</sub> زائد واحد زوجي .. فردي. الـ α<sub>i</sub> إيش
+
+227
+00:22:05,760 --> 00:22:14,040
+هتكون is even. إذا لما كانت Tau of N فردي طلعت غصب عن
+
+228
+00:22:14,040 --> 00:22:17,580
+الـ α<sub>i</sub> even. إيش معناه الـ α<sub>i</sub> even؟ معناته هذا
+
+229
+00:22:17,580 --> 00:22:21,740
+مربع كامل، وهذا مربع كامل يعني هذا عبارة عن عدد
+
+230
+00:22:21,740 --> 00:22:31,460
+تربيع. إذا always N استوف N على 2 has a
+
+231
+00:22:31,460 --> 00:22:35,860
+meaning. نقطة تانية بدي أحكيها كمان اللهم صلي على
+
+232
+00:22:35,860 --> 00:22:48,140
+سيدنا محمد بس مانسهاش. لاحظ لو أجينا إلى حالة اللي
+
+233
+00:22:48,140 --> 00:22:58,040
+هو الفردي، الحالة الفردي ناخد مثالا على مربع كامل
+
+234
+00:22:58,040 --> 00:23:03,120
+اللي أخدناه قبله شوية. N بساوي 2 تربيع في 5
+
+235
+00:23:03,120 --> 00:23:07,400
+تربيع. هذا مربع كامل اللي هو Tau of N له إيش ماله؟
+
+236
+00:23:07,400 --> 00:23:13,300
+فردي معايا؟ طيب هذا العدد N بساوي 2 تربيع في 5
+
+237
+00:23:13,300 --> 00:23:22,660
+تربيع. لو أجينا لقواسمه هنلاقي واحد من القواسم اللي
+
+238
+00:23:22,660 --> 00:23:25,860
+هو 2 في 5 صح؟ اللي هو العشرة
+
+239
+00:23:31,730 --> 00:23:36,870
+ما دام 2 في 5 في 10 عنده إذا 2 في
+
+240
+00:23:36,870 --> 00:23:41,930
+5 في 2 في إيش؟ في 5 لكي نضيع الفكرة عشان
+
+241
+00:23:41,930 --> 00:23:47,230
+الحسابات كمان مرة. الآن إن بيساوي 2 تربيع في
+
+242
+00:23:47,230 --> 00:23:51,730
+5 تربيع بيساوي 104
+
+243
+00:23:51,730 --> 00:23:57,630
+في 5، 4 في 25، 100
+
+244
+00:23:59,940 --> 00:24:04,080
+طيب 4 في 25 ماشي لحال. طيب صلوا على النبي عليه
+
+245
+00:24:04,080 --> 00:24:08,580
+الصلاة والسلام. الآن أنا كله تحت بند مين؟ تحت بند
+
+246
+00:24:08,580 --> 00:24:17,860
+Tau of N is إيش طلع عندي؟ هذا Odd معايا؟ بدي شغلة
+
+247
+00:24:17,860 --> 00:24:22,680
+أنا بعد شوية حلت شغلة فاهمة. الآن الـ N هذه في هذه
+
+248
+00:24:22,680 --> 00:24:28,680
+الحالة إن جسمت عبارة عن 10 في إيش؟ في 10. الـ
+
+249
+00:24:28,680 --> 00:24:33,940
+Divisor اللي وصل للـ N هو نفسه في حالة الفرد في
+
+250
+00:24:33,940 --> 00:24:39,400
+حالة الفرد بصورة عامة. N بساوي 2 Tau of N is Odd
+
+251
+00:24:39,400 --> 00:24:43,980
+معناته إنه مربع كامل. معناته P<sub>1</sub> أس 2 α<sub>1</sub>
+
+252
+00:24:43,980 --> 00:24:51,170
+فاهمين؟ زائر عن P<sub>r</sub> أس 2 α<sub>r</sub>
+
+253
+00:24:51,170 --> 00:24:57,430
+من الـ Divisors اللي هنا اللي هو P<sub>1</sub> α<sub>1</sub>
+
+254
+00:24:57,430 --> 00:25:04,370
+لعند P<sub>r</sub> α<sub>r</sub> هو نفسه P<sub>1</sub> α<sub>1</sub> لعند P
+
+255
+00:25:04,370 --> 00:25:10,950
+<sub>r</sub> α<sub>r</sub> الـ Divisors هذا هو نفسه اللي لو ضربناه
+
+256
+00:25:10,950 --> 00:25:15,770
+في حاله بيطلع مين؟ بيطلع N. ماشي؟ خليها دي في
+
+257
+00:25:15,770 --> 00:25:24,290
+الذاكرة للي بدي احكي دلوقتي. طيب الآن بدي أثبت لك
+
+258
+00:25:24,290 --> 00:25:32,570
+بدي أثبت لك معيا ليه؟ شوف
+
+259
+00:25:32,570 --> 00:25:35,630
+عندي
+
+260
+00:25:35,630 --> 00:25:47,670
+بدي أثبت لك If N أكبر من 1 Then N استواف N على
+
+261
+00:25:47,670 --> 00:25:55,690
+2 بساوي الـ Product دي بتكسبها حكينا
+
+262
+00:25:55,690 --> 00:26:00,230
+يا أبو يحيى عن الـ Number of Divisors وحكينا عن ال
+
+263
+00:26:00,230 --> 00:26:04,730
+Sum of Divisors. هل جيت بتدعي أوددلك كيف الـ Product
+
+264
+00:26:04,730 --> 00:26:09,990
+of Divisors. ماشي الحال؟ لو حاصل ضرب مين؟ الـ Divisors
+
+265
+00:26:09,990 --> 00:26:15,450
+الآن الادعاء هذه. الـ Remark بتقول لك لو كان أكبر من
+
+266
+00:26:15,450 --> 00:26:23,970
+1 بيكون حاصل ضرب الـ Divisors بساوي N أس عدد الـ
+
+267
+00:26:23,970 --> 00:26:29,250
+Divisors على مين؟ على 2. ماشي الحال؟ عدد ال
+
+268
+00:26:29,250 --> 00:26:33,390
+Divisors على 2. N أس عدد الـ Divisors على 2
+
+269
+00:26:33,390 --> 00:26:39,250
+الآن لو
+
+270
+00:26:39,250 --> 00:26:47,530
+أخدنا أي D، لو كانت D، لو قلنا ليه الـ D بتجسم N، الـ D
+
+271
+00:26:47,530 --> 00:26:48,190
+بتجسم N
+
+272
+00:26:51,260 --> 00:27:01,600
+Then there exist D Prime such that N إيش بتساوي؟ D
+
+273
+00:27:01,600 --> 00:27:06,400
+في D Prime معايا؟
+
+274
+00:27:06,400 --> 00:27:17,940
+هذا شو معناته؟ معناته إن الـ Divisors تحدث أزواجة
+
+275
+00:27:19,470 --> 00:27:24,930
+الـ Divisors تحدث إيش؟ إلا في حالة واحدة إن الآن
+
+276
+00:27:24,930 --> 00:27:34,030
+مربع كامل يعني الـ D تساوت D' كمان مرة. الآن فرضنا
+
+277
+00:27:34,030 --> 00:27:38,710
+أنه أخدنا الـ D أي إيش؟ أي Divisor، الـ D ماله؟ أي
+
+278
+00:27:38,710 --> 00:27:43,310
+Divisor. مدام الـ D Divisor إذا فيه D' بحيث الآن إيش
+
+279
+00:27:43,310 --> 00:27:50,290
+بتساوي D في مين؟ في D'. إذا الـ Divisors للـ N تحدث
+
+280
+00:27:50,290 --> 00:27:55,670
+كل تنتين مع بعض إلا في حالة واحدة لو كانت اللي هي 
+
+281
+00:27:55,670 --> 00:27:59,630
+الـ D بتساوي مين هذا في الحالة اللي هو المنبع الكامل
+
+282
+00:27:59,630 --> 00:28:05,510
+اللي حكينا عنه هنا ماشي الحال معناته أنا لما بدي 
+
+283
+00:28:05,510 --> 00:28:11,010
+أجي أضرب كل ال Divisors للـ N، ال Divisors للـ N لما
+
+284
+00:28:11,010 --> 00:28:15,870
+بدي أضربها في بعض by الـ D حيث الـ D بتجسم إيهاش الـ
+
+285
+00:28:15,870 --> 00:28:24,930
+N بكون ضلّبتهم كلهم، عددهم كلهم tau of n، مظبوط ولا
+
+286
+00:28:24,930 --> 00:28:32,330
+لأ؟ كل اثنتين بيجيبن n، ما هو مظبوط؟ إذا كانت فردية،
+
+287
+00:28:32,330 --> 00:28:37,210
+إذا كان زوجي، خلاص كل اثنتين بيجيبن مين؟ بيجيبن
+
+288
+00:28:37,210 --> 00:28:45,510
+إيش؟ n إذا فرضي كل اثنتين بيجيب الـ N مائدة واحدة
+
+289
+00:28:45,510 --> 00:28:51,190
+إيش مالها؟ مربّعة بيجيب مين؟ بيجيب الـ N معناته إنه
+
+290
+00:28:51,190 --> 00:28:57,030
+صار ال product للـ D هو عبارة عن الـ N اتكررت tau
+
+291
+00:28:57,030 --> 00:29:02,650
+of N على مين؟ أنه اتكررتها كم مرة؟ اتكررتها كم
+
+292
+00:29:02,650 --> 00:29:07,330
+مرة؟ اللي هو tau of N على مين؟ على 2
+
+293
+00:29:12,040 --> 00:29:20,520
+كمان مرة؟ أي سؤال؟ الزوجيات
+
+294
+00:29:20,520 --> 00:29:25,880
+مع بعض، مظبوط؟ زائد الواحد، بس هذا ما يطلع فيه إيش
+
+295
+00:29:25,880 --> 00:29:29,100
+لما يكون .. لما يكون فردي، ما يطلع أصول زائد ..
+
+296
+00:29:29,100 --> 00:29:38,420
+بيطلع نصف، لأنه بيطلع واحد لحاله، محسوب هو أنتم
+
+297
+00:29:38,420 --> 00:29:45,920
+.. أنتم .. أنتم .. أنتم ..الآن عندك الآن الـ
+
+298
+00:29:45,920 --> 00:29:54,960
+divisors tau of n عددها زوجي 2k زائد 1 ماشي الحال
+
+299
+00:29:54,960 --> 00:30:04,220
+الآن المفروض أن ال divisors دي واحد لعندي 2k هدول
+
+300
+00:30:04,220 --> 00:30:14,990
+اتفاجنت تحدث أزواجها ما عدا الـ D2Kز1 ده ده ده ده ده
+
+301
+00:30:14,990 --> 00:30:15,110
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+302
+00:30:15,110 --> 00:30:16,010
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+303
+00:30:16,010 --> 00:30:16,990
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+304
+00:30:16,990 --> 00:30:17,710
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+305
+00:30:17,710 --> 00:30:20,350
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+306
+00:30:20,350 --> 00:30:34,750
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده د
+
+307
+00:30:36,540 --> 00:30:40,420
+اللي هو إيش مقله؟ اللي هو الجذر التربيعي لـ N لأن
+
+308
+00:30:40,420 --> 00:30:45,340
+هو اللي .. اللي هو نفسه جاب N تربيعه بتجيب N
+
+309
+00:30:45,340 --> 00:30:54,060
+فاهمين؟ إذا زائد نصف أه؟ مظبوط؟
+
+310
+00:30:54,060 --> 00:30:57,480
+اللي هو الجذر لـ N، الـ N هذه عبارة عن إيش يا
+
+311
+00:30:57,480 --> 00:31:03,380
+جماعة؟ عبارة عن 2K زائد 1 اللي عددهم اللي هو توف N
+
+312
+00:31:03,380 --> 00:31:12,210
+على مين؟ على اثنين كم مرة يا عبد؟ عددين جديش في
+
+313
+00:31:12,210 --> 00:31:16,730
+دولة؟ اثنين K زياد واحد اللي هم طالعين يتجاوب إيه
+
+314
+00:31:16,730 --> 00:31:20,310
+أشماله؟ انقص K زياد نصف الـ K زياد نصف هداش عبارة
+
+315
+00:31:20,310 --> 00:31:25,070
+اثنين K زياد واحد على اثنين اللي هو التهوفن على
+
+316
+00:31:25,070 --> 00:31:28,270
+اثنين مش عددين تفجرن اثنين K زياد واحد؟
+
+317
+00:31:31,160 --> 00:31:36,080
+واضح ها؟ إذا صار عندي دائماً if n أكبر من واحد then
+
+318
+00:31:36,080 --> 00:31:39,940
+n أستوى if n على اثنين بيساوي ال product لديه، دي
+
+319
+00:31:39,940 --> 00:31:42,480
+بتكسب مين؟ دي بتكسب الآن
+
+320
+00:31:51,230 --> 00:31:54,430
+الآن ما قلنا دي تسمى الآن دي تسمى الآن دي تسمى
+
+321
+00:31:54,430 --> 00:31:55,830
+الآن دي تسمى الآن دي تسمى الآن دي تسمى الآن دي
+
+322
+00:31:55,830 --> 00:31:56,910
+تسمى الآن دي تسمى الآن دي تسمى الآن دي تسمى الآن
+
+323
+00:31:56,910 --> 00:31:58,290
+دي تسمى الآن دي تسمى الآن دي تسمى الآن دي تسمى
+
+324
+00:31:58,290 --> 00:32:01,890
+الآن دي تسمى الآن دي تسمى الآن دي تسمى الآن دي
+
+325
+00:32:01,890 --> 00:32:01,990
+تسمى الآن دي تسمى الآن دي تسمى الآن دي تسمى الآن
+
+326
+00:32:01,990 --> 00:32:05,430
+الآن دي تسمى الآن دي تسمى الآن دي تسمى الآن
+
+327
+00:32:05,430 --> 00:32:19,230
+دي تسمى الآن دي تسمى الآن دي تسمى الآن
+
+328
+00:32:19,230 --> 00:32:25,000
+د in each case, by the dxmn must be of the form n
+
+329
+00:32:25,000 --> 00:32:30,140
+أستوى of n على مين على اثنين شرحنا ليش الـ
+
+330
+00:32:30,140 --> 00:32:36,580
+Definition
+
+331
+00:32:36,580 --> 00:32:43,700
+طلع لفوق خلاص خلّيه مش مشكلة طلع بس في الفور اللي
+
+332
+00:32:43,700 --> 00:32:45,600
+أنا بدنا نعرف شو معناه
+
+333
+00:32:53,800 --> 00:33:01,760
+قبل ما نعرف خلينا بس شغلة لو جينا قلنا أو جيلي
+
+334
+00:33:01,760 --> 00:33:11,120
+tau of 2 في tau of 4 بساومة tau
+
+335
+00:33:11,120 --> 00:33:21,700
+of 2 جديش شفها بدّه يصير tau of 2 أقصد واحد هذه هذه
+
+336
+00:33:21,700 --> 00:33:26,580
+اللي هو واحد زائد واحد مظبوط؟ ليه اثنين؟ تاو في
+
+337
+00:33:26,580 --> 00:33:29,380
+أربعة اللي هي tau of اثنين تربيع اللي هو إيه
+
+338
+00:33:29,380 --> 00:33:37,380
+أشماله؟ ثلاثة اثنين في ثلاثة؟ بستة ميحك؟ طيب خد
+
+339
+00:33:37,380 --> 00:33:45,240
+الآن tau of اثنين في اثنين تربيع اللي هو .. مين هو
+
+340
+00:33:45,240 --> 00:33:50,820
+هذا؟ tau of اثنين أس ثلاثة صح؟ tau of اثنين أس
+
+341
+00:33:50,820 --> 00:33:57,820
+ثلاثة اش بساوي ثلاثة مالكم ثلاثة زي واحد واضح أنه إيش
+
+342
+00:33:57,820 --> 00:34:05,960
+بيساوي لا يساوي الستة يعني واضح أن تو of M في N
+
+343
+00:34:05,960 --> 00:34:17,420
+ليس شرطاً أنه يساوي تو of M في تو of N ليس شرطاً اه
+
+344
+00:34:17,420 --> 00:34:28,370
+اللي هو need not need notequal to of M for if need
+
+345
+00:34:28,370 --> 00:34:32,170
+not equal to of M to of M لكن الـ Sigma زيّه برضه
+
+346
+00:34:32,170 --> 00:34:40,210
+لو جيت كمان أخذت Sigma of 2 في Sigma of 2 تربيع
+
+347
+00:34:40,210 --> 00:34:44,930
+بساوية احسبوا معايا يا جماعة Sigma of 2 مين هي؟
+
+348
+00:34:44,930 --> 00:34:50,710
+اثنين أس اثنين ناقص واحد على اثنين ناقص واحد في
+
+349
+00:34:51,790 --> 00:34:58,870
+اثنين از تلاتة نقص واحد اثنين نقص واحد ويساوي هذه
+
+350
+00:34:58,870 --> 00:35:03,490
+عبارة عن أربعة نقص واحد ثلاثة ثلاثة وهذه عبارة عن
+
+351
+00:35:03,490 --> 00:35:08,390
+ثمانية نقص واحد سبعة ويساوي واحد وعشرين معايا يا
+
+352
+00:35:08,390 --> 00:35:15,670
+شباب اه مظبوط هيك اه سيجما of اثنين في اثنين تربيع
+
+353
+00:35:15,670 --> 00:35:20,280
+اللي هي سيجما of اثنين از تلاتة ماذا يساوي حسب
+
+354
+00:35:20,280 --> 00:35:24,140
+القانون؟ اثنين نقص أربعة نقص واحد على اثنين نقص
+
+355
+00:35:24,140 --> 00:35:28,040
+واحد ويساوي اثنين نقص أربعة كم؟ ستة عشر نقص واحد
+
+356
+00:35:28,040 --> 00:35:33,160
+ماذا يساوي؟ خمسة عشر ليس شرطاً أنه يساوي مين إذا
+
+357
+00:35:33,160 --> 00:35:43,140
+sigma of M في N need not equal sigma of M في sigma
+
+358
+00:35:43,140 --> 00:35:49,020
+of N but but if
+
+359
+00:35:50,400 --> 00:35:54,940
+إذا كان الـ greatest common divisor بين الـ M والـ
+
+360
+00:35:54,940 --> 00:36:00,940
+N بساوية واحد ثم يجب أن نحصل على Sigma of M في N
+
+361
+00:36:00,940 --> 00:36:07,000
+بساوية Sigma of M في Sigma of N وTau of M بساوية
+
+362
+00:36:07,000 --> 00:36:17,980
+Tau M بساوية Tau M في Tau of M معايا؟ واضح؟ طيب
+
+363
+00:36:20,010 --> 00:36:25,970
+وهذا بيعني في الجملة الأخيرة اللي تحت اللي كتبتها
+
+364
+00:36:25,970 --> 00:36:30,290
+أنه sigma and tau are multiplicative functions
+
+365
+00:36:30,290 --> 00:36:35,550
+multiplicative functions إذا الآن بدنا نعرف حاجة
+
+366
+00:36:35,550 --> 00:36:40,590
+اسمها multiplicative function a number theoretic
+
+367
+00:36:40,590 --> 00:36:45,430
+function f هذا بنحكي على number theoretic function
+
+368
+00:36:45,430 --> 00:36:51,380
+يعني f من z positive إلى z positive بنقول الـ
+
+369
+00:36:51,380 --> 00:36:57,520
+number theoretic function F is multiplicative if
+
+370
+00:36:57,520 --> 00:37:03,580
+اللي هو F of M في N بتساوي F of M في F of N for
+
+371
+00:37:03,580 --> 00:37:07,620
+every M و N with the greatest common divisor بين
+
+372
+00:37:07,620 --> 00:37:10,980
+الـ M و الـ N إيش بيساوي؟ بيساوي 1 لأنه احنا طبعاً
+
+373
+00:37:10,980 --> 00:37:14,260
+بنحكي على المعنى ال multiplicative هنا في number
+
+374
+00:37:14,260 --> 00:37:19,780
+theoretic function في أماكن أخرى ممكن نعرف اللي هو
+
+375
+00:37:19,780 --> 00:37:22,940
+الـ Real Value Function إنها عبارة عن
+
+376
+00:37:22,940 --> 00:37:27,120
+Multiplicative إذا بس بيتحقق F of X في Y بيساوي F
+
+377
+00:37:27,120 --> 00:37:32,520
+of X في مين في F of Y بس هنا إحنا بمعرفين a number
+
+378
+00:37:32,520 --> 00:37:35,760
+theoretic function F is said to be multiplicative
+
+379
+00:37:35,760 --> 00:37:40,460
+if F of M of N بيساوي F of M في F of N whenever الـ
+
+380
+00:37:40,460 --> 00:37:45,060
+Greatest common divisor بين M و N بيساوي 1
+
+381
+00:37:50,650 --> 00:37:57,210
+بعض الملاحظات على ذلك بعض الملاحظات على ذلك أول
+
+382
+00:37:57,210 --> 00:38:02,790
+حاجة الـ function f of n بتساوي واحد و الـ g of n
+
+383
+00:38:02,790 --> 00:38:06,690
+بيساوي n الدالة الثابتة واحد و ال identity
+
+384
+00:38:06,690 --> 00:38:12,570
+function g of n بيساوي n are then f and g are
+
+385
+00:38:12,570 --> 00:38:20,040
+multiplicative إثبات سهلة لو أخذنا fof n بساوية
+
+386
+00:38:20,040 --> 00:38:24,280
+واحد هي الدالة for every n element in z positive
+
+387
+00:38:24,280 --> 00:38:32,640
+multiplicative ليش let and prove let اللي هو m و n
+
+388
+00:38:32,640 --> 00:38:35,140
+element in z positive such that the greatest
+
+389
+00:38:35,140 --> 00:38:38,900
+common divisor بين ال m و ال n بساوية واحد then
+
+390
+00:38:41,240 --> 00:38:47,260
+f of m في n أي إن كانت هي دالة ثابتة بساوي واحد صح
+
+391
+00:38:47,260 --> 00:38:56,820
+ويساوي واحد في واحد صح ويساوي f of m في f of n
+
+392
+00:38:56,820 --> 00:39:03,340
+إذا صارت أشمالها f is multiplicative similarly
+
+393
+00:39:03,340 --> 00:39:13,570
+اللي هو هذا ذنب G of M فعلاً بيساوي الـ Identity
+
+394
+00:39:13,570 --> 00:39:16,970
+الماخدينها الـ G of M أيش بتساوي الـ M بثبت فيها
+
+395
+00:39:16,970 --> 00:39:21,890
+يعني إذا كانت بتساوي M، M ويساوي M اللي هي G of M
+
+396
+00:39:21,890 --> 00:39:26,690
+و الـ M في B من مين هي G of M إذا الـ Identity
+
+397
+00:39:26,690 --> 00:39:30,030
+function برضه أيش مالها is a multiplicative
+
+398
+00:39:30,030 --> 00:39:36,930
+function الشيء
+
+399
+00:39:36,930 --> 00:39:37,370
+اللي صحيح
+
+400
+00:39:40,540 --> 00:39:46,700
+هذولا اه طبعاً هذولا أصلاً are multiplicative in R
+
+401
+00:39:46,700 --> 00:39:53,540
+أنا اللي بقى نحكيه لأن بدنا نعرف ال number
+
+402
+00:39:53,540 --> 00:39:58,440
+theoretic function انها multiplicative إذا كان الـ
+
+403
+00:39:58,440 --> 00:40:01,020
+Greatest common divisor للـ M والـ N بساوية واحد
+
+404
+00:40:01,020 --> 00:40:06,720
+ثم F of M في N بساوية F of M في F مين في F of N
+
+405
+00:40:06,720 --> 00:40:12,000
+هذا فيه له هدف برضه أنه هيخدمني في أن تعريف هذا
+
+406
+00:40:12,000 --> 00:40:16,500
+هيخدمني أيضاً في أنه أثبت أن الـ Sigma والـ Tau
+
+407
+00:40:16,500 --> 00:40:21,460
+أشمالهم are multiplicative ماشي الحال؟
+
+408
+00:40:23,300 --> 00:40:28,540
+إذا كان الـ F مرتبطاً لـ N1,N2,NR، الوضع في الـ Z
+
+409
+00:40:28,540 --> 00:40:37,460
+يكون مرتبطاً لـ N1
+
+410
+00:40:37,460 --> 00:40:39,880
+,N2,NR، الوضع في الـ Z يكون مرتبط لـ N1,N2,NR،
+
+411
+00:40:39,880 --> 00:40:39,920
+الوضع في الـ Z يكون مرتبط لـ N1,N2,NR، الوضع في
+
+412
+00:40:39,920 --> 00:40:40,860
+الـ Z يكون مرتبط لـ N1,N2,NR، الوضع في الـ Z يكون
+
+413
+00:40:40,860 --> 00:40:41,420
+مرتبط لـ N1,N2,NR، الوضع في الـ Z يكون مرتبط لـ N1
+
+414
+00:40:41,420 --> 00:40:48,380
+,N2,NR، الوضع في الـ Z يكون مرتبط لـ N1,N2,NR،
+
+415
+00:40:48,380 --> 00:40:49,860
+الوضع في الـ Z يكون مرتبط لـ N1,N2,NR
+
+416
+00:40:53,900 --> 00:41:01,740
+ماخد أنا اللي هو ثلاثة بالنسبة اثنين الآن F is
+
+417
+00:41:01,740 --> 00:41:06,540
+multiplicative مادام F multiplicative F N واحد
+
+418
+00:41:06,540 --> 00:41:12,140
+لعند N R بساوي
+
+419
+00:41:12,140 --> 00:41:17,400
+الـ N واحد مع أي واحدة من ال relative ال prime إذا
+
+420
+00:41:17,400 --> 00:41:21,720
+الـ N واحد مع هدول مع بعض أشمالها relatively prime
+
+421
+00:41:21,720 --> 00:41:28,940
+و F مضروبة F of N واحد في F of N اتنين عند
+
+422
+00:41:28,940 --> 00:41:34,600
+مين NR نفس الشيء لأن اتنين شمالها relatively 
+
+423
+00:41:34,600 --> 00:41:38,320
+prime مع اللي باقي إذا بطبقها أي شمال مياه مرة
+
+424
+00:41:38,320 --> 00:41:46,060
+بيصير F of N واحد في F of N اتنين في F of N تلاتة
+
+425
+00:41:46,060 --> 00:41:52,450
+عند NRafter الهو finite number of steps حصل لإن f
+
+426
+00:41:52,450 --> 00:41:59,910
+of n واحد لعند f of n are طيب fn
+
+427
+00:42:01,290 --> 00:42:04,970
+بساوة بي واحد بي اتنين بي تلاتة مرفوعات لل ألف
+
+428
+00:42:04,970 --> 00:42:08,770
+واحد ألف اتنين ألف R is the canonical form of N
+
+429
+00:42:08,770 --> 00:42:12,310
+أكبر من واحدة أن F is multiplicative then F of N
+
+430
+00:42:12,310 --> 00:42:16,490
+إيش بيساوي F للأولى فF للتانية فالأف لمين للأخيرة
+
+431
+00:42:16,490 --> 00:42:23,330
+إذا كانت عندي F multiplicative وعندي ال N على صورة
+
+432
+00:42:23,330 --> 00:42:28,230
+ال canonical form بي واحد عند بي R ألف R بيكون ال
+
+433
+00:42:28,230 --> 00:42:38,820
+F of N بتساوي f of b1 α1 لعند f of br αr واضح ليش؟
+
+434
+00:42:38,820 --> 00:42:43,900
+f is multiplicative وكل هدولة مدن في ال canonical
+
+435
+00:42:43,900 --> 00:42:52,640
+form اذا distinct primes b1, b2 لعند br نطلع
+
+436
+00:42:52,640 --> 00:42:54,340
+لفوق اللي بعد يا أبو يحيى
+
+437
+00:43:00,280 --> 00:43:04,860
+if F is multiplicative and F لا تساوي صفر then F
+
+438
+00:43:04,860 --> 00:43:12,700
+of واحد ايش بيساوي واحد معايا معايا
+
+439
+00:43:12,700 --> 00:43:20,220
+شباب اثبتها هذه عندي F is multiplicative F is
+
+440
+00:43:20,220 --> 00:43:27,660
+multiplicative و F لا تساوي صفر then ال F هتنجل ال
+
+441
+00:43:27,660 --> 00:43:33,020
+واحد لمين للواحد الواحد لفحة English الواحد لمين
+
+442
+00:43:33,020 --> 00:43:44,780
+للواحد الآن عندي ال F of واحد بساوي F of واحد في
+
+443
+00:43:44,780 --> 00:43:52,940
+واحد صح أو ال F of واحد في
+
+444
+00:43:52,940 --> 00:43:59,480
+واحد Multiplicative هذا Multiplicative إذا أف في واحد
+
+445
+00:43:59,480 --> 00:44:06,860
+فأف في واحد صح ولا لأ؟ باضح أه؟ ليش أنا واحد ما
+
+446
+00:44:06,860 --> 00:44:13,960
+نقلت لسه؟ فاهمين أه؟ لأن أف في واحد في أف في واحد
+
+447
+00:44:13,960 --> 00:44:22,490
+بيساوي أف في واحد وبما أن ال F لا يساوي صفر فهو F
+
+448
+00:44:22,490 --> 00:44:26,790
+لا يساوي صفر فهو
+
+449
+00:44:26,790 --> 00:44:32,830
+F لا يساوي صفر فهو
+
+450
+00:44:32,830 --> 00:44:41,790
+F لا يساوي صفر فهو F لا يساوي صفر
+
+451
+00:44:47,810 --> 00:44:52,650
+عارفين ليش؟ هذه .. هذه .. هذه بعدين بتبتلكوا إياها
+
+452
+00:44:52,650 --> 00:44:58,970
+انت بغان ال F لا تساوي صفر لأ بتعطينا أن F of F of
+
+453
+00:44:58,970 --> 00:45:02,850
+واحد شمالها لا تساوي صفر ده استخدام هذه طب ليش
+
+454
+00:45:02,850 --> 00:45:06,150
+هذه؟
+
+455
+00:45:06,150 --> 00:45:14,450
+الآن F of N إيش بتساوي؟ F of N في واحد ويساوي F of
+
+456
+00:45:14,450 --> 00:45:22,120
+N في F of واحد لو كانت f of 1 صفر معايا، لو صارت
+
+457
+00:45:22,120 --> 00:45:25,860
+الـ f of n صفر و n arbitrarily، إذا الـ f مش
+
+458
+00:45:25,860 --> 00:45:31,800
+هتساوي صفر، contradiction فاهمين؟ إذا كانت الـ F
+
+459
+00:45:31,800 --> 00:45:37,160
+بتسويش صفر و F multiplicative إذا الـ F واحد
+
+460
+00:45:37,160 --> 00:45:41,700
+شمالها لاتساوي صفر كمان مرة المعلومة if F is
+
+461
+00:45:41,700 --> 00:45:46,000
+multiplicative and F is a non-zero function then F
+
+462
+00:45:46,000 --> 00:45:51,180
+of واحد لا يساوي صفر لأنه لو ساوى F واحد صفر هتطلع
+
+463
+00:45:51,180 --> 00:45:54,040
+للـ F of N automatically بتساوي صفر مع نتوا
+
+464
+00:45:54,040 --> 00:45:57,910
+contradiction طيب نيجي لقالنا بقى لسؤالنا بما أن F
+
+465
+00:45:57,910 --> 00:46:01,850
+لا تساوي صفر إذا الـ F في واحد لا تساوي صفر مدام
+
+466
+00:46:01,850 --> 00:46:04,550
+الـ F في واحد لا تساوي صفر إذا أنت تختصر هذه محطة
+
+467
+00:46:04,550 --> 00:46:09,390
+هذه بتطلع عندك الـ F في واحد إيش هتساوي واحد واضح
+
+468
+00:46:09,390 --> 00:46:18,290
+أه معانا يا شباب أخر نقطة قلنا Tau في عشرين لا
+
+469
+00:46:18,290 --> 00:46:25,200
+يساوي Tau في اتنين في Tau في عشرة and سيجما او
+
+470
+00:46:25,200 --> 00:46:28,020
+عشرين لا يساوي سيجما او اتنين في سيجما او عشرة
+
+471
+00:46:28,020 --> 00:46:31,880
+ماشي الحالة اعملنا اخدنا مثال قولنا تاو اف ام فان
+
+472
+00:46:31,880 --> 00:46:37,100
+need not equal تاو اف ام فتاو اف ام وسيجما اف ام
+
+473
+00:46:37,100 --> 00:46:41,660
+فان need not equal سيجما اف ام فسيجما اف ام ولكن
+
+474
+00:46:41,660 --> 00:46:46,380
+the functions تاو and سيجما are both
+
+475
+00:46:46,380 --> 00:46:48,020
+multiplicative functions
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/83b4FEtBAAM_postprocess.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/83b4FEtBAAM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..119818c9d13a53900e428a91e99b41748ce31f4e
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/83b4FEtBAAM_postprocess.srt
@@ -0,0 +1,1900 @@
+1
+00:00:19,350 --> 00:00:24,970
+بسم الله الرحمن الرحيم المحاضرة اليوم محاضرة رقم
+
+2
+00:00:24,970 --> 00:00:29,970
+عشرين في مساق نظرية الأعداد لطلبة الجامعة
+
+3
+00:00:29,970 --> 00:00:39,390
+الإسلامية قسم رياضيات كليتي التربية والعلوم هنكمل
+
+4
+00:00:39,390 --> 00:00:42,930
+في chapter 6 اللي بدناه اللي بتحدث عن number
+
+5
+00:00:42,930 --> 00:00:47,850
+theoretic functionsبدأنا المرة الماضية في الـ
+
+6
+00:00:47,850 --> 00:00:51,270
+section الأول اللي هو the function sigma and tau
+
+7
+00:00:51,270 --> 00:00:57,810
+اللي هي عدد ال divisors ومجموع ال divisors عرفنا
+
+8
+00:00:57,810 --> 00:01:01,490
+شو معناه number theoretic function وقلنا هي اللي
+
+9
+00:01:01,490 --> 00:01:04,870
+عبارة عن function domainها بيكون the set of
+
+10
+00:01:04,870 --> 00:01:09,570
+positive integers و بعدين عرفنا اللي هو tau of n
+
+11
+00:01:10,230 --> 00:01:13,650
+تاو عبارة عن function الـ function هنا من الـ z
+
+12
+00:01:13,650 --> 00:01:18,210
+positive و بتود على الـ z positive وهذا قلنا عنها
+
+13
+00:01:18,210 --> 00:01:22,770
+اللي هي the number of divisors tau of n اللي هي
+
+14
+00:01:22,770 --> 00:01:29,390
+عبارة عدب قواسم العدد n وعرفنا أيضا برضه sigma من
+
+15
+00:01:29,390 --> 00:01:33,390
+z positive لz positive وقلنا عنها sigma of n هي
+
+16
+00:01:33,390 --> 00:01:38,530
+عبارة عن the sum of divisors أو مجموع قواسم العدد
+
+17
+00:01:40,150 --> 00:01:44,850
+أخدنا أمثلة المرة الماضية حسابية لإيجاد Sigma وTau
+
+18
+00:01:44,850 --> 00:01:49,530
+وقلنا إنه لو بدنا نوجد اللي هو Sigma أو Tau
+
+19
+00:01:49,530 --> 00:01:56,420
+للأعداد مثلا 1800 أو Sigma of 1800 طبعابالطريقة
+
+20
+00:01:56,420 --> 00:02:00,560
+العادية إنه نوجد الـ divisors و نجمحهم أو نوجد الـ
+
+21
+00:02:00,560 --> 00:02:03,760
+divisors و نعدد من عدهم بالطريقة اللي حكيناها طبعا
+
+22
+00:02:03,760 --> 00:02:07,920
+طريقة غير عملية و أكيد فيها غلب كثير فعشان هيك
+
+23
+00:02:07,920 --> 00:02:16,090
+بلزمنا ندرس خواص إضافيةالـ Sigma والـ Tau اللي من
+
+24
+00:02:16,090 --> 00:02:22,310
+خلالها ان شاء الله هنقدر نحصل على طريقة سهلة أو
+
+25
+00:02:22,310 --> 00:02:26,270
+طرق سهلة لإيجاد sum of divisors و number of
+
+26
+00:02:26,270 --> 00:02:30,790
+divisors و أيضا لدراسة خلاص sum of divisors و
+
+27
+00:02:30,790 --> 00:02:35,030
+number of divisors حكينا المرة الماضية برضه نظرية
+
+28
+00:02:35,030 --> 00:02:41,210
+ستة واحد قلنالو كان عندي N أي عدد أكبر من عدد أكبر
+
+29
+00:02:41,210 --> 00:02:44,990
+من واحد أي عدد أكبر من واحد N أكيد الـ N الأكبر من
+
+30
+00:02:44,990 --> 00:02:48,750
+واحد في الـ unique factorization theorem بنقدر
+
+31
+00:02:48,750 --> 00:02:52,830
+نكتبه على صورة اللي هو bar of the brines اللي هي
+
+32
+00:02:52,830 --> 00:03:00,410
+B1اللي عند B ألفة أو K سمناها K واحد اللي عند B R
+
+33
+00:03:00,410 --> 00:03:06,250
+K R إذا قلنا بالظبط Precisely the divisors of M
+
+34
+00:03:06,250 --> 00:03:13,610
+are those written as D بتساوي B واحد ألف واحد اللي
+
+35
+00:03:13,610 --> 00:03:20,300
+عند B Rالفا ار حيث الالفا اي بين السفر وبين الكي
+
+36
+00:03:20,300 --> 00:03:25,140
+اي هذا اللي هي بالظبط اللي هي ال divisors اللي لمن
+
+37
+00:03:25,140 --> 00:03:31,840
+اللي لانالان الطريق للوصول لـ number of divisors و
+
+38
+00:03:31,840 --> 00:03:35,860
+some of divisors هي عبر اللي هو كتابة الان على
+
+39
+00:03:35,860 --> 00:03:40,280
+صورة اللي هو ال canonical form أو ال form اللي
+
+40
+00:03:40,280 --> 00:03:44,720
+عندنا بي واحد كي واحد و بي ار كي ار و من ثم حصر
+
+41
+00:03:44,720 --> 00:03:49,640
+مين هي ال divisors من خلال المعلومة اللي أمامنا ان
+
+42
+00:03:49,640 --> 00:03:54,780
+ال divisors هيشكلها بصير فيه إمكانية لحصر من ال
+
+43
+00:03:54,780 --> 00:04:01,410
+divisors اللي للعددالان نجي لنظريتنا الأولى
+
+44
+00:04:01,410 --> 00:04:09,050
+نظريتنا
+
+45
+00:04:09,050 --> 00:04:15,050
+الأولى كبر شويةاللي هي إن لو كانت N بيساوة P1 K1
+
+46
+00:04:15,050 --> 00:04:19,410
+P2 K2 لعند PR KR is a prime factorization of N
+
+47
+00:04:19,410 --> 00:04:23,710
+أكبر من 1 يعني النظرية عشان نطبقها بدنا نجهز العدد
+
+48
+00:04:23,710 --> 00:04:27,170
+N على صورة إيش اللي هو ال prime factorization له
+
+49
+00:04:27,170 --> 00:04:32,970
+بتكون على طول Tau of N هي عبارة عن هنتعامل بس مع
+
+50
+00:04:32,970 --> 00:04:39,610
+الأسس اللي هي K1 زائد 1 في K2 زائد 2 عند KR زائد 1
+
+51
+00:04:40,260 --> 00:04:43,280
+ماشي الحال حاصل ضرب هنا بيكون اللي هو number of
+
+52
+00:04:43,280 --> 00:04:47,880
+divisors الان sum of divisors هو عبارة عن بي واحد
+
+53
+00:04:47,880 --> 00:04:51,440
+كي واحد أس واحد زائد واحد ناقص واحد على بي واحد
+
+54
+00:04:51,440 --> 00:04:55,580
+ناقص R كله هنا بنفس الأسلوب لعن بي R كي R زائد
+
+55
+00:04:55,580 --> 00:05:00,120
+واحد ناقص واحد على بي R ناقص واحد خلينا للرسول
+
+56
+00:05:00,120 --> 00:05:04,080
+للبرهان بخلينا بس نطلعنا على مثال هيك على جنب و
+
+57
+00:05:04,080 --> 00:05:09,170
+نشوف كيف بدنا نروح باتجاه البرهانلو جينا أخدنا
+
+58
+00:05:09,170 --> 00:05:17,370
+الأمر عبارة عن 2 أُس 2 في 5 أُس 3 مثلا هي عندي هذا
+
+59
+00:05:17,370 --> 00:05:23,630
+بدي أشوف له الـ divisors تبعونه اتفجنا أن الـ
+
+60
+00:05:23,630 --> 00:05:32,170
+divisors دي هتكون على شكل 2 أُس 1000I 10001 في 5أس
+
+61
+00:05:32,170 --> 00:05:36,530
+الفا اتنين حيث الفا واحد أكبر أو سوى سفر و أصغر أو
+
+62
+00:05:36,530 --> 00:05:41,450
+سوى جديش اتنين و الفا اتنين هتكون أكبر أو سوى سفر
+
+63
+00:05:41,450 --> 00:05:45,490
+و أصغر أو سوى مين تلاتة ماشي الحال هاي شكل ال
+
+64
+00:05:45,490 --> 00:05:48,610
+divisors اللي عندي بناء على هذه المعلومة على شكل
+
+65
+00:05:48,610 --> 00:05:53,040
+ال divisors خليني اجي اطلع على اتنين تربيعأتنين
+
+66
+00:05:53,040 --> 00:05:58,300
+تربيع اللي هي عندي اللي هي قواسمها بناء على الحديث
+
+67
+00:05:58,300 --> 00:06:02,300
+هذا انه القواسم هتكون على الصورة هذه و ألف و واحد
+
+68
+00:06:02,300 --> 00:06:06,220
+بين السفر و بين التنين هيكون عندي قواسم العدد هذا
+
+69
+00:06:06,220 --> 00:06:09,680
+اللي هي طبيعية اللي هي واحد اللي هي اتنين أس سفر
+
+70
+00:06:09,680 --> 00:06:15,640
+والتاني عبارة عن اتنين أس واحد والتالت عبارة عن
+
+71
+00:06:15,640 --> 00:06:21,920
+اتنين أس اتنين هذه قواسم العدد من اتنين تربيعالان
+
+72
+00:06:21,920 --> 00:06:27,500
+جنبه قواسم العدد الآخر اللي هي عبارة عن واحد وخمسة
+
+73
+00:06:28,480 --> 00:06:36,220
+و 5 تربيع و 5 تكعيب هاي قواسم العدد الآخر طيب الآن
+
+74
+00:06:36,220 --> 00:06:40,980
+أنا بدي قواسم العدد N اللي هو ممزوج بين اللي هو
+
+75
+00:06:40,980 --> 00:06:47,100
+هذا في هذا إذا الأعداد اللي على الصورة 2 أس الف
+
+76
+00:06:47,100 --> 00:06:51,040
+واحد في خمس في خمسة أس الف اتنين هتكون هي الأعداد
+
+77
+00:06:51,040 --> 00:06:57,350
+التالية واحد مع الواحد هذي هاي أول واحدالثاني واحد
+
+78
+00:06:57,350 --> 00:07:02,970
+مع مين؟ مع الخمسة التالت واحد مع مين؟ مع الخمسة
+
+79
+00:07:02,970 --> 00:07:09,750
+تربيع يعني الآن الواحد بيجيب و في واحد في مين؟ في
+
+80
+00:07:09,750 --> 00:07:15,760
+الخمسة تكعيب نفس الأشياء الآن هذا الواحداللي هو
+
+81
+00:07:15,760 --> 00:07:22,660
+راح مع كل هدولة يعني خيار الـ Alpha 1 Alpha 2 1 2
+
+82
+00:07:22,660 --> 00:07:29,860
+3 4 خيارات يعني خياره طلع Alpha و 2 زائد 1 مع
+
+83
+00:07:29,860 --> 00:07:34,120
+العدد الأول اللي هو الواحد مع التاني برضه نفسي مشي
+
+84
+00:07:34,120 --> 00:07:43,610
+2 الان في واحد اتنين اتنينأتنين في خمسة تكعيب
+
+85
+00:07:43,610 --> 00:07:53,060
+والعمود على اتنين تربيعفيه واحد اتنين تربيع في
+
+86
+00:07:53,060 --> 00:07:58,620
+خمسة اتنين تربيع في خمسة تربيع اتنين تربيع في خمسة
+
+87
+00:07:58,620 --> 00:08:04,300
+تكعيب يعني الآن number of choices اللي هنا اللي هي
+
+88
+00:08:04,300 --> 00:08:08,460
+واحد اتنين كلاتة اربعة مع تثبيت الأول إذا كل واحد
+
+89
+00:08:08,460 --> 00:08:13,820
+من هدولة بيجيب أعاملين اربع divisorsالأن هذا مكرر
+
+90
+00:08:13,820 --> 00:08:18,840
+أكام مرة اللي هو تلت مرات، بصبوط؟ هاي واحد، تمين،
+
+91
+00:08:18,840 --> 00:08:23,000
+تلاتة، بصبوط؟ إذاً عدد الخيارات هنا عبارة عن اتنين
+
+92
+00:08:23,000 --> 00:08:25,960
+زائد واحد وعدد الخيارات هنا تلاتة زائد واحد يعني
+
+93
+00:08:25,960 --> 00:08:31,180
+أربعة يعني هيكون الـ divisors كلهم اللي هو تلاتة
+
+94
+00:08:31,180 --> 00:08:36,320
+الخيارات اللي هنا مع الأربعة ويساوي إيش اتناشر
+
+95
+00:08:36,320 --> 00:08:40,260
+divisor هذا الـ mean اللي هو عدد ال divisors هذا
+
+96
+00:08:40,260 --> 00:08:47,040
+طلع عندى tauof mean of un هذه التلاتة عبارة عن ايش
+
+97
+00:08:47,040 --> 00:08:51,940
+في الواقع الف واحد زائد واحد هذه عبارة عن مين عن
+
+98
+00:08:51,940 --> 00:08:56,000
+الف اتنين زائد واحد طيب
+
+99
+00:08:57,800 --> 00:09:01,140
+الان هذا اللي هو number of divisors طب بدي اجيب
+
+100
+00:09:01,140 --> 00:09:07,480
+انا مجموع ال divisors مجموحين الان مجموحين كيف
+
+101
+00:09:07,480 --> 00:09:10,320
+احنا جيبنا ال divisors الان واحد مع حد و واحد مع
+
+102
+00:09:10,320 --> 00:09:13,900
+حد و واحد مع حد و واحد مع حد طب عشان اجيب المجموع
+
+103
+00:09:13,900 --> 00:09:20,640
+بس اجمعلي هذولوضرب اليهن في إيش؟ في بعض بيصير حاصل
+
+104
+00:09:20,640 --> 00:09:25,680
+ضرب هذا مع حاصل ضرب هذا مع .. نضرب هذا في هذا
+
+105
+00:09:25,680 --> 00:09:31,340
+بيطلع اللي هو إيش ماله؟ مجموع الـ divisors in
+
+106
+00:09:31,340 --> 00:09:36,740
+general .. in general لو كان عندي الآن لو كان عندي
+
+107
+00:09:36,740 --> 00:09:40,440
+لو
+
+108
+00:09:40,440 --> 00:09:44,840
+كان عندي الآن أمن
+
+109
+00:09:46,120 --> 00:09:55,560
+بساوة بي واحد ألف واحد بي اتنين ألف اتنين بي
+
+110
+00:09:55,560 --> 00:10:06,940
+واحد
+
+111
+00:10:06,940 --> 00:10:13,560
+ألف واحد بي اتنين ألف اتنين بي واحد ألف
+
+112
+00:10:13,560 --> 00:10:14,600
+واحد بي اتنين ألف اتنين بي واحد ألف واحد بي واحد
+
+113
+00:10:14,600 --> 00:10:14,960
+أتنين ألف واحد بي واحد أتنين ألف واحد بي واحد
+
+114
+00:10:14,960 --> 00:10:19,290
+أتنزائد بي اتنين لما أصل لعين بي اتنين أس الف
+
+115
+00:10:19,290 --> 00:10:23,770
+اتنين الـ divisors الكلية لان هي هذا مع هذولا
+
+116
+00:10:23,770 --> 00:10:28,910
+كلهين ضرب وهذا مع هذولا كلهين ضرب فبصير اللي هو
+
+117
+00:10:28,910 --> 00:10:34,230
+هذا إيه أكبر choice ألف واحد زائد واحد لأن هذولا
+
+118
+00:10:34,230 --> 00:10:37,970
+أحدد هنا ألف واحد وهذا اللي هو الصفر بصير ألف واحد
+
+119
+00:10:37,970 --> 00:10:44,740
+زائد واحدوهذا الـ choices بتبعته قداش ألف اتنين
+
+120
+00:10:44,740 --> 00:10:51,040
+زائد واحد فبصير التوف أن بساوي ألف واحد زائد واحد
+
+121
+00:10:51,040 --> 00:10:55,780
+فألف اتنين زائد واحد إذا لو في عندي كمان بي تلاتة
+
+122
+00:10:55,780 --> 00:11:00,880
+أس ألف تلاتة لعند بي آر أس ألف آر بيصير اللي هو
+
+123
+00:11:00,880 --> 00:11:09,300
+هذوي ال devices اللي كتبان جنبات لما
+
+124
+00:11:09,300 --> 00:11:17,930
+أصل آخر واحداللي هو واحد لعند بي ألف ار بي ار
+
+125
+00:11:17,930 --> 00:11:21,370
+الاخر
+
+126
+00:11:21,370 --> 00:11:29,070
+هذا اللي بيجيب لي توفان عشان ايجد مجموح بس باجمح
+
+127
+00:11:29,070 --> 00:11:36,650
+هدول و بضربهم في بعضبطلع عندى اللى هو مجموع الـ
+
+128
+00:11:36,650 --> 00:11:39,690
+divisors طب كيف تكون مجموع ال divisors في هذه
+
+129
+00:11:39,690 --> 00:11:47,370
+الحالة سيجما of n بساوي هذه اللى عبارة عن ايش
+
+130
+00:11:47,370 --> 00:11:54,690
+finite geometric series معايا ايش اللى هو قانونها
+
+131
+00:11:54,690 --> 00:12:02,650
+الاساس بي واحدأُس اللي هو عددهن عددهن إيش بيساوي
+
+132
+00:12:02,650 --> 00:12:08,610
+ألف واحد زائد واحد ناقص واحد ره أسنون ناقص واحد
+
+133
+00:12:08,610 --> 00:12:12,950
+على ره ناقص واحد ره اللي هو مين اللي هو الأساس
+
+134
+00:12:12,950 --> 00:12:18,150
+اللي هو الون اللي هو عدد مين الحدود واضح أه من
+
+135
+00:12:18,150 --> 00:12:23,690
+الحد الأول واحد على بي واحد ناقص واحد هذا اللي هو
+
+136
+00:12:23,690 --> 00:12:31,060
+المجبوح هذابس هذا المجموعة ده مجموعة ده ولا مضروب
+
+137
+00:12:31,060 --> 00:12:36,300
+في بي اتنين الف اتنين زائد واحد ناقص واحد على بي
+
+138
+00:12:36,300 --> 00:12:42,160
+اتنين ناقص واحد لما أصل لآخر واحد بي ار الف ار
+
+139
+00:12:42,160 --> 00:12:48,180
+زائد واحد ناقص واحد على بي ار ناقص واحد فبقول هذا
+
+140
+00:12:48,180 --> 00:12:53,460
+اللي هو أشمال ومجموع ال divisors إذن الآن صار عندي
+
+141
+00:12:53,460 --> 00:12:57,040
+fn بتساوي
+
+142
+00:12:59,920 --> 00:13:08,080
+B1K1B2K2 VRKR NUMBER OF DIVISORSبس باعتمد على مين
+
+143
+00:13:08,080 --> 00:13:13,340
+على الأسس اللي هي K1 زياد واحد في K2 زياد واحد لKR
+
+144
+00:13:13,340 --> 00:13:17,580
+زياد واحد مضروبات في بعض الـ Sigma of N هو عبارة
+
+145
+00:13:17,580 --> 00:13:22,280
+عن مجموع مين اللي هو B1 K1 زياد واحد ناقص واحد على
+
+146
+00:13:22,280 --> 00:13:26,080
+B1 ناقص واحد لما أصل لآخر term فبكون هذا اللي هو
+
+147
+00:13:26,080 --> 00:13:29,340
+عبارة عن number of divisors and the sum of
+
+148
+00:13:29,340 --> 00:13:35,200
+divisors اطلع لفوق example هو البرنامج اللي قلتلك
+
+149
+00:13:35,200 --> 00:13:35,400
+إيه
+
+150
+00:13:41,230 --> 00:13:47,510
+البرهنجل اللي حكيناه انه عندي الألف واحد في أكمت
+
+151
+00:13:47,510 --> 00:13:52,030
+choice لها ألف واحد زائد واحد هذه لها أكمت choice
+
+152
+00:13:52,030 --> 00:13:55,350
+ألف اتنين زائد واحد ال choice ده مبنيه على أيه؟
+
+153
+00:13:55,350 --> 00:14:00,370
+مبنيه على ان انا اللي قلته انه الأن هي و ال data
+
+154
+00:14:00,370 --> 00:14:08,530
+معتها divisors بالظبط من العصورة P1K1 لعند PRKR
+
+155
+00:14:08,530 --> 00:14:14,050
+ماشي الحالالان الـ divisors هذه الـ K1 ايش الـ
+
+156
+00:14:14,050 --> 00:14:18,470
+choices لها؟من صفر لعينج اللي هي Alpha 1 يعني
+
+157
+00:14:18,470 --> 00:14:23,210
+عددها اللي هو الـChoices Alpha 1 زائد 1 التاني نفس
+
+158
+00:14:23,210 --> 00:14:26,010
+الأشياء التالت نفس الأشياء الأخر نفس الأشياء إذا
+
+159
+00:14:26,010 --> 00:14:31,530
+عدد الـChoices اللي هي حاصلة الضرب هي عبارة عن
+
+160
+00:14:31,530 --> 00:14:37,670
+حاصلة ضرب مين اللي هي K1 زائد 1 بناء على تثبيت
+
+161
+00:14:37,670 --> 00:14:40,390
+الباج وتغيير واحدة تثبيت الباج وتغيير واحدة بيصير
+
+162
+00:14:40,390 --> 00:14:45,590
+الـChoices K1 زائد 1فى K2 زائد واحد لما اصل فى KR
+
+163
+00:14:45,590 --> 00:14:51,170
+زائد واحد واضح اه ايه السؤال فالليجي ل Tao of Tao
+
+164
+00:14:51,170 --> 00:15:01,690
+of 180 و Sigma of 180 ناخد
+
+165
+00:15:01,690 --> 00:15:13,600
+اي رقم بدكمياه Tao of 180 عشان اوجده بساويو sigma
+
+166
+00:15:13,600 --> 00:15:19,240
+of 180 عشان اوجده بلزم اياش اول خطوة نوجدها اياش
+
+167
+00:15:19,240 --> 00:15:23,900
+ال prime factorization اذا اول حاجة عشان اوجد تاو
+
+168
+00:15:23,900 --> 00:15:28,720
+السيجما بدي اكتب ال 180 على صورة ال canonical form
+
+169
+00:15:28,720 --> 00:15:36,380
+اللي هي في هذه الحالة 2 اقصى 2 فى 3 اقصى 2 فى 5
+
+170
+00:15:36,380 --> 00:15:46,250
+هيك صار سهل الأمر على طولبساوي اتنين زائد واحد في
+
+171
+00:15:46,250 --> 00:15:51,510
+اتنين زائد واحد في واحد زائد واحد صح تلاتة في
+
+172
+00:15:51,510 --> 00:16:00,130
+تلاتة تسعة تسعة في اتنين في تمانتاش باضح اه سيجما
+
+173
+00:16:00,130 --> 00:16:07,560
+of مية و تمانين ايش بيساوي اللي هو عبارة عنالقانون
+
+174
+00:16:07,560 --> 00:16:13,560
+اتنين أس اتنين زائد واحد نقص واحد على اتنين نقص
+
+175
+00:16:13,560 --> 00:16:19,800
+واحد في تلاتة أس اتنين زائد واحد نقص واحد على
+
+176
+00:16:19,800 --> 00:16:25,400
+تلاتة نقص واحد في خمسة أس واحد زائد واحد نقص واحد
+
+177
+00:16:25,400 --> 00:16:31,320
+على خمسة نقص واحد فاللحة هي تسعة نقص واحد تمانية
+
+178
+00:16:31,320 --> 00:16:40,370
+تمانية مظبوط سبعة بالسيرة7 صح اللي بعدها 27 نقص 1
+
+179
+00:16:40,370 --> 00:16:50,570
+26 على 2 13 فى 25 نقص 1 24 على 4 6 بطلع اللي هو
+
+180
+00:16:50,570 --> 00:16:58,930
+الرقم 546 وهكذا طيب
+
+181
+00:16:58,930 --> 00:17:02,170
+لاحظ
+
+182
+00:17:02,170 --> 00:17:04,910
+انه
+
+183
+00:17:06,790 --> 00:17:15,790
+الان ال number of divisors طلع عندي 18 يعني زوجي
+
+184
+00:17:15,790 --> 00:17:19,590
+اه
+
+185
+00:17:19,590 --> 00:17:31,090
+لو جينا أخدنا العدد مثلا ناخد ان بتساوي اتنين أس
+
+186
+00:17:31,090 --> 00:17:32,730
+اتنين في تلاتة
+
+187
+00:17:36,290 --> 00:17:46,270
+قص اتين مثلا بس تلاتة قص اتنين ال
+
+188
+00:17:46,270 --> 00:17:56,930
+Tao of N بساوي اللي هو اتنين زائد واحد في اتنين
+
+189
+00:17:56,930 --> 00:18:04,670
+زائد واحد ويساوي كم؟ تسعة معايا؟ اذا عدد ال
+
+190
+00:18:04,670 --> 00:18:12,580
+divisorsعدد ال divisors فردي الآن
+
+191
+00:18:12,580 --> 00:18:25,560
+عدد ال divisors فردي لو أجيت أخدت N أستاوف N على 2
+
+192
+00:18:25,560 --> 00:18:30,960
+عدد
+
+193
+00:18:30,960 --> 00:18:40,110
+ال divisors فردي فيه معنىليش فيه إله معنى؟ ولمّا
+
+194
+00:18:40,110 --> 00:18:51,970
+كان برضه اللي فوق سمّيه M M أستوف M على 2 برضه إله
+
+195
+00:18:51,970 --> 00:19:00,970
+معنى طبعاً M أستوف M على 2 إله معنى هل؟بديهي لعدد
+
+196
+00:19:00,970 --> 00:19:04,930
+الـ divisors إيه شماله؟ اللي هو زوجي طلع جديش قبل
+
+197
+00:19:04,930 --> 00:19:12,390
+شوية؟ 18 يعني بيصير M اللي هي 180 أس 18 على 2
+
+198
+00:19:12,390 --> 00:19:21,090
+ويساوي 180 أس 9 يعني الآن M أستوى في M على 2 لما
+
+199
+00:19:21,090 --> 00:19:27,540
+كانت زوجي بديهي إنها إلها معنىبرضه انا بتدعي ان لو
+
+200
+00:19:27,540 --> 00:19:33,360
+كان الرقم اللي هو الان عدد ال divisors له فردي
+
+201
+00:19:33,360 --> 00:19:38,180
+برضه انه معنى شوف هذا المثال و بعدين بعمل المثال
+
+202
+00:19:38,180 --> 00:19:46,730
+هذا ايش بقولك بساوي N أص نص فيTau of N جدش أنها
+
+203
+00:19:46,730 --> 00:19:51,490
+تسعة شيل منها واحد اللي هو نص بيظل تمانية على
+
+204
+00:19:51,490 --> 00:19:55,770
+اتنين اللي هي N أقص أربعة مظبوط ولا لأ؟ N أقص
+
+205
+00:19:55,770 --> 00:20:01,150
+أربعة مش فيها مشكلة لإنه لها معنى لإنه N مرفوع
+
+206
+00:20:01,150 --> 00:20:04,630
+عالميا للعدد أربعة وبتطلع integer اللي معنى بمعنى
+
+207
+00:20:04,630 --> 00:20:08,010
+إنه احنا جاعدين وين في integers هي اللي بنقص ده
+
+208
+00:20:08,010 --> 00:20:16,220
+الان N أقص نصمدام طلع عندك توف أن فردي غصب عنه
+
+209
+00:20:16,220 --> 00:20:25,360
+بتطلع أن مربع كامل غصب عنه الآن أن بتساوي اتنين
+
+210
+00:20:25,360 --> 00:20:29,000
+اقصى اتنين في اتنين اقصى اربعة فبتصير في هذه
+
+211
+00:20:29,000 --> 00:20:35,100
+الحالة انقص نص الومين اتنين في تلاتة مظبوط ولا لأ؟
+
+212
+00:20:35,740 --> 00:20:41,220
+إذا إيه المعنى؟ إذا في حالة الفردي برضه اللي هو
+
+213
+00:20:41,220 --> 00:20:44,840
+إيه المعنى؟ يعني بمعنى آخر اللي بقوله أنا اللي
+
+214
+00:20:44,840 --> 00:20:52,160
+بادعيه أن أن أستاوف أن على اتنين is always an
+
+215
+00:20:52,160 --> 00:20:56,220
+integer سواء
+
+216
+00:20:56,220 --> 00:21:01,160
+كان التاوف أن فردي أو التاوف أن إشماله زوجي الان
+
+217
+00:21:01,160 --> 00:21:11,540
+الان التاوف أنبساوي 2K زائد 1 فردي طرد أنه الـ N
+
+218
+00:21:11,540 --> 00:21:20,340
+بتساوي P1 Alpha 1 لعين PR Alpha R الـ N عندي عدد
+
+219
+00:21:20,340 --> 00:21:27,380
+الـ divisors مين هي K Alpha 1 Tau of N حسب
+
+220
+00:21:27,380 --> 00:21:31,480
+القانون، إيش بتساوي؟ ماببرهنش، بس بقعد بوضح لكم
+
+221
+00:21:31,480 --> 00:21:34,840
+البرنامج بتبرهنوا، بترتبوا لحالكم Alpha 1 زائد 1
+
+222
+00:21:35,690 --> 00:21:44,110
+لما أصل عند αR زائد إيش؟ زائد واحد ركز معايا الآن
+
+223
+00:21:44,110 --> 00:21:51,030
+مدام توف أن فردي إذا غصب عن كل هذول الأعداد فردية
+
+224
+00:21:51,030 --> 00:21:55,170
+لأن لو كان واحد زودي بيطلع أيش ماله مدامة كل
+
+225
+00:21:55,170 --> 00:22:00,230
+الأعداد هذول الفردية المضربات في بعض معناته الـ αI
+
+226
+00:22:00,230 --> 00:22:05,760
+اللي هيالـ α I زائد واحد زوجي .. فردي الـ α I إيش
+
+227
+00:22:05,760 --> 00:22:14,040
+هتكون is even إذا لما كانت وفقان فردي طلعت غصب عن
+
+228
+00:22:14,040 --> 00:22:17,580
+الـ α I even إيش معناه الـ α I even معناته هذا
+
+229
+00:22:17,580 --> 00:22:21,740
+مربع كامل وهذا مربع كامل يعني هذا عبارة عن عدد
+
+230
+00:22:21,740 --> 00:22:31,460
+تربية إذا alwaysأن أستوف أن على اتنين has a
+
+231
+00:22:31,460 --> 00:22:35,860
+meaning نقطة تانية بدي أحكيها كمان اللهم صلي على
+
+232
+00:22:35,860 --> 00:22:48,140
+سيدنا محمد بس مانسهاش لاحظ لو أجينا إلى حالة اللي
+
+233
+00:22:48,140 --> 00:22:58,040
+هو الفردي الحالة الفردي ناخد مثالعلى مربع كامل
+
+234
+00:22:58,040 --> 00:23:03,120
+اللي أخدناه قبله شوية n بساوة 2 تربيع في خمسة
+
+235
+00:23:03,120 --> 00:23:07,400
+تربيع هذا مربع كامل اللي هو توف n له إيش ماله؟
+
+236
+00:23:07,400 --> 00:23:13,300
+فردي معايا؟ طيب هذا العدد n بساوة 2 تربيع في خمسة
+
+237
+00:23:13,300 --> 00:23:22,660
+تربيع لو أجينا لقواسمه هنلاقي واحد من القواسم اللي
+
+238
+00:23:22,660 --> 00:23:25,860
+هو 2 في 5 صح؟ اللي هو العشرة
+
+239
+00:23:31,730 --> 00:23:36,870
+ما دام اتنين في خمسة في عشرة عنده اذا اتنين في
+
+240
+00:23:36,870 --> 00:23:41,930
+خمسة في اتنين في اياش في خمسة لكي نضيع الفكرة عشان
+
+241
+00:23:41,930 --> 00:23:47,230
+الحسابات كمان مرة الان ان بيساوي اتنين تربيع في
+
+242
+00:23:47,230 --> 00:23:51,730
+خمسة تربيع بيساوي مية اربعة
+
+243
+00:23:51,730 --> 00:23:57,630
+في خمسة اربعة في خمسة عشرين مية
+
+244
+00:23:59,940 --> 00:24:04,080
+طيب 4 فى 25% ماشي لحال طيب صلوا على النبي عليه
+
+245
+00:24:04,080 --> 00:24:08,580
+الصلاة والسلام الان انا كله تحت band مين تحت band
+
+246
+00:24:08,580 --> 00:24:17,860
+tau of n is ايش طلع عندي هذا odd معايا؟ بدي شغلة
+
+247
+00:24:17,860 --> 00:24:22,680
+انا بعد شوية حلت شغلة فاهمة الان ال n هذهفي هذه
+
+248
+00:24:22,680 --> 00:24:28,680
+الحالة إن جسمت عبارة عن عشرة في إياش في عشرة الـ
+
+249
+00:24:28,680 --> 00:24:33,940
+Divisor اللي وصل للـ N هو نفسه في حالة الفرد في
+
+250
+00:24:33,940 --> 00:24:39,400
+حالة الفرد بصورة عامة N بساوة 2 تواف N is odd
+
+251
+00:24:39,400 --> 00:24:43,980
+معناته أنه مربع كامل معناته بي واحد أس اتنين ألف
+
+252
+00:24:43,980 --> 00:24:51,170
+واحد فاهمين؟ زائر عن بي ار أس اتنين ألف ارفي واحد
+
+253
+00:24:51,170 --> 00:24:57,430
+من الـ divisors اللي هنا اللي هو بي واحد الف واحد
+
+254
+00:24:57,430 --> 00:25:04,370
+لعند بي ار الف ار هو نفسه بي واحد الف واحد لعند بي
+
+255
+00:25:04,370 --> 00:25:10,950
+ار الف ار ال divisors هذا هو نفسه اللي لو ضربناه
+
+256
+00:25:10,950 --> 00:25:15,770
+في حاله بيطلع مين بيطلع ان ماشي خليها دي في
+
+257
+00:25:15,770 --> 00:25:24,290
+الذاكرة للي بدي احكي دلوقتي طيبالان بدي أثبت لك
+
+258
+00:25:24,290 --> 00:25:32,570
+بدي أثبت لك معيا ليه شوف
+
+259
+00:25:32,570 --> 00:25:35,630
+عندي
+
+260
+00:25:35,630 --> 00:25:47,670
+بدي أثبت لك if n أكبر من واحد then n أستواف n على
+
+261
+00:25:47,670 --> 00:25:55,690
+اتنين بساوي ال productدي بتكسبها حكينا
+
+262
+00:25:55,690 --> 00:26:00,230
+يا أبو يحيي عن ال number of divisors وحكينا عن ال
+
+263
+00:26:00,230 --> 00:26:04,730
+sum of divisors هل جيت بتدعي أوددلك كيف ال product
+
+264
+00:26:04,730 --> 00:26:09,990
+of divisors ماشي الحال لو حاصل ضرب مين ال divisors
+
+265
+00:26:09,990 --> 00:26:15,450
+الآن الادعاء هذه ال remark بتقولك لو كان أكبر من
+
+266
+00:26:15,450 --> 00:26:23,970
+واحد بيكون حاصل ضرب ال divisorsبساول N أُس عدد الـ
+
+267
+00:26:23,970 --> 00:26:29,250
+divisors على مين؟ على اتنين ماشي الحال عدد ال
+
+268
+00:26:29,250 --> 00:26:33,390
+divisors على اتنين N أُس عدد ال divisors على اتنين
+
+269
+00:26:33,390 --> 00:26:39,250
+الان لو
+
+270
+00:26:39,250 --> 00:26:47,530
+أخدنا أي D لو كانت D لو قلنا ليه ال D بتجسم N ال D
+
+271
+00:26:47,530 --> 00:26:48,190
+بتجسم N
+
+272
+00:26:51,260 --> 00:27:01,600
+then there exist D prime such that N ايش بتساوي D
+
+273
+00:27:01,600 --> 00:27:06,400
+في D prime معايا؟
+
+274
+00:27:06,400 --> 00:27:17,940
+هذا شو معناته؟ معناته ان ال divisors تحدث أزواجة
+
+275
+00:27:19,470 --> 00:27:24,930
+الـ Divisors تحدث إيش إلا في حالة واحدة أن الان
+
+276
+00:27:24,930 --> 00:27:34,030
+مربع كامل يعني الـDH تساوت D' كمان مرة الآن فرضنا
+
+277
+00:27:34,030 --> 00:27:38,710
+أنه أخدنا الـD أي إيش أي Divisor الـDH ماله أي
+
+278
+00:27:38,710 --> 00:27:43,310
+Divisor مدام الـD Divisor إذا فيه D' بحيث الان إيش
+
+279
+00:27:43,310 --> 00:27:50,290
+بتساوي D في مين في D'إذا الـ Divisors للـ N تحدث
+
+280
+00:27:50,290 --> 00:27:55,670
+كل تنتين مع بعض إلا في حالة واحدة لو كانت اللي هي
+
+281
+00:27:55,670 --> 00:27:59,630
+الـ D بتساومين هذا في الحالة اللي هو المنبع الكامل
+
+282
+00:27:59,630 --> 00:28:05,510
+اللي حكينا عنه هنا ماشي الحال معناته أنا لما بدي
+
+283
+00:28:05,510 --> 00:28:11,010
+أجي أضرب كل ال Divisors لل N ال Divisors لل N لما
+
+284
+00:28:11,010 --> 00:28:15,870
+بدي أضربها في بعض by ال D حيث ال D بتجسم إيهاش ال
+
+285
+00:28:15,870 --> 00:28:24,930
+Nبكون ضلبتهم كلهم، عددهم كلهم tau of n، مظبوط ولا
+
+286
+00:28:24,930 --> 00:28:32,330
+لأ؟ كل تنتين بيجيبن n، ما هو مظبوط؟ إذا كانت فرد،
+
+287
+00:28:32,330 --> 00:28:37,210
+إذا كان زوجي، خلاص كل تنتين بيجيبن مين؟ بيجيبن
+
+288
+00:28:37,210 --> 00:28:45,510
+إيش؟ nإذا فرضي كل تنتين بيجيب الـ N مائدة واحدة
+
+289
+00:28:45,510 --> 00:28:51,190
+إيش مالها؟ مربحة بيجيب مين؟ بيجيب الـ N معناته إنه
+
+290
+00:28:51,190 --> 00:28:57,030
+صار ال product للـ D هو عبارة عن الـ N اتكررت tau
+
+291
+00:28:57,030 --> 00:29:02,650
+of N على مين؟ انه اتكررتها كم مرة؟ اتكررتها كم
+
+292
+00:29:02,650 --> 00:29:07,330
+مرة؟ اللي هو tau of N على مين؟ على 2
+
+293
+00:29:12,040 --> 00:29:20,520
+كمان مرة؟ أي سؤال؟ الزوجيات
+
+294
+00:29:20,520 --> 00:29:25,880
+مع بعض، مظبوط؟ زائد الواحد، بس هذا ماحيطلع فيه إيش
+
+295
+00:29:25,880 --> 00:29:29,100
+لما يكون .. لما يكون فردي، ماحيطلع أصول زائد ..
+
+296
+00:29:29,100 --> 00:29:38,420
+بيطلع نص، لأنه بيطلع واحد لحاله، محسوب هو انتم
+
+297
+00:29:38,420 --> 00:29:45,920
+.. انتم .. انتم .. انتم ..الان عندك الان ال
+
+298
+00:29:45,920 --> 00:29:54,960
+divisors tau of n عددها فرضي 2k زائد 1 ماشي الحال
+
+299
+00:29:54,960 --> 00:30:04,220
+الان المفروض ان ال divisors دي واحد لعندي 2k هدول
+
+300
+00:30:04,220 --> 00:30:14,990
+اتفاجنة تحدث أزواجةما عدى الـ D2Kز1 ده ده ده ده ده
+
+301
+00:30:14,990 --> 00:30:15,110
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+302
+00:30:15,110 --> 00:30:16,010
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+303
+00:30:16,010 --> 00:30:16,990
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+304
+00:30:16,990 --> 00:30:17,710
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+305
+00:30:17,710 --> 00:30:20,350
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده
+
+306
+00:30:20,350 --> 00:30:34,750
+ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده د
+
+307
+00:30:36,540 --> 00:30:40,420
+اللي هو إيش مقله؟ اللي هو الجدر التربيعي لـ N لأن
+
+308
+00:30:40,420 --> 00:30:45,340
+هو اللي .. اللي هو نفسه جاب N تربيعه بتجيب N
+
+309
+00:30:45,340 --> 00:30:54,060
+فاهمين؟ إذا زائد نص أه؟ مظبوط؟
+
+310
+00:30:54,060 --> 00:30:57,480
+اللي هو الجدر لـ N الـ N هذه عبارة عن إيش يا
+
+311
+00:30:57,480 --> 00:31:03,380
+جماعة؟ عبارة عن 2K زائد 1 اللي عددهم اللي هو توف N
+
+312
+00:31:03,380 --> 00:31:12,210
+على مين؟على اتنين كم مرة يا عبد؟ عددين جديش في
+
+313
+00:31:12,210 --> 00:31:16,730
+دولة؟ اتنين K زياد واحد اللي هم طالعين يتجاوب ايه
+
+314
+00:31:16,730 --> 00:31:20,310
+اشماله؟ انقص K زياد نص الكي زياد نص هداش عبارة
+
+315
+00:31:20,310 --> 00:31:25,070
+اتنين K زياد واحد على اتنين اللي هو التهوفن على
+
+316
+00:31:25,070 --> 00:31:28,270
+اتنين مش عددين اتفجرن اتنين K زياد واحد؟
+
+317
+00:31:31,160 --> 00:31:36,080
+واضح ها؟ إذا صار عندي دائما if n أكبر من واحد then
+
+318
+00:31:36,080 --> 00:31:39,940
+n أستوى if n على اتنين بيساوي ال product لديه، دي
+
+319
+00:31:39,940 --> 00:31:42,480
+بتكسب مين؟ دي بتكسب الان
+
+320
+00:31:51,230 --> 00:31:54,430
+الأن ما قلنا دي تسمى الان دي تسمى الان دي تسمى
+
+321
+00:31:54,430 --> 00:31:55,830
+الان دي تسمى الان دي تسمى الان دي تسمى الان دي
+
+322
+00:31:55,830 --> 00:31:56,910
+تسمى الان دي تسمى الان دي تسمى الان دي تسمى الان
+
+323
+00:31:56,910 --> 00:31:58,290
+دي تسمى الان دي تسمى الان دي تسمى الان دي تسمى
+
+324
+00:31:58,290 --> 00:32:01,890
+الان دي تسمى الان دي تسمى الان دي تسمى الان دي
+
+325
+00:32:01,890 --> 00:32:01,990
+تسمى الان دي تسمى الان دي تسمى الان دي تسمى الان
+
+326
+00:32:01,990 --> 00:32:05,430
+الان دي تسمى الان دي تسمى الان دي تسمى الان
+
+327
+00:32:05,430 --> 00:32:19,230
+دي تسمى الان دي تسمى الان دي تسمى الان
+
+328
+00:32:19,230 --> 00:32:25,000
+دin each case, by the dxmn must be of the form n
+
+329
+00:32:25,000 --> 00:32:30,140
+أستوى of n على مين على اتنين شرحنا ليش الـ
+
+330
+00:32:30,140 --> 00:32:36,580
+Definition
+
+331
+00:32:36,580 --> 00:32:43,700
+طلع لفوق خلاص خلّيه مش مشكلة طلع بس فى الفور اللي
+
+332
+00:32:43,700 --> 00:32:45,600
+انا بدنا نعرف شو معناته
+
+333
+00:32:53,800 --> 00:33:01,760
+قبل ما نعرف خلّينا بس شغلة لو جينا قولنا او جيلي
+
+334
+00:33:01,760 --> 00:33:11,120
+tau of 2 في tau of 4 بساومة tau
+
+335
+00:33:11,120 --> 00:33:21,700
+of 2 جديش شفها بده يصير tau of 2 أقصد واحد هذه هذه
+
+336
+00:33:21,700 --> 00:33:26,580
+اللي هو واحد زائد واحدمظبوط؟ ليه اتنين؟ تاو في
+
+337
+00:33:26,580 --> 00:33:29,380
+اربعة اللي هي تاو of اتنين تربيع اللي هو ايه
+
+338
+00:33:29,380 --> 00:33:37,380
+اشماله؟ تلاتة اتنين في تلاتة؟ بستة ميحك؟ طيب خد
+
+339
+00:33:37,380 --> 00:33:45,240
+الآن تاو of اتنين في اتنين تربيع اللي هو .. مين هو
+
+340
+00:33:45,240 --> 00:33:50,820
+هذا؟ تاو of اتنين أس تلاتة صح؟ تاو of اتنين أس
+
+341
+00:33:50,820 --> 00:33:57,820
+تلاتاش بساويثلاثة مالكم ثلاثة زي واحد واضح انه ايش
+
+342
+00:33:57,820 --> 00:34:05,960
+بيساوي لا يساوي الستة يعني واضح ان تو of M في N
+
+343
+00:34:05,960 --> 00:34:17,420
+ليس شرطا انه يساوي تو of M في تو of N ليس شرطا اه
+
+344
+00:34:17,420 --> 00:34:28,370
+اللي هو need not need notequal to of M for if need
+
+345
+00:34:28,370 --> 00:34:32,170
+not equal to of M to of M لكن الـ Sigma زيه برضه
+
+346
+00:34:32,170 --> 00:34:40,210
+لو جيت كمان أخدت Sigma of 2 في Sigma of 2 تربية
+
+347
+00:34:40,210 --> 00:34:44,930
+بساوية احسبوا معايا يا جماعة Sigma of 2 مين هي؟
+
+348
+00:34:44,930 --> 00:34:50,710
+اتنين أس اتنين ماقص واحد على اتنين ماقص واحد في
+
+349
+00:34:51,790 --> 00:34:58,870
+تنين از تلاتة نقص واحد اتنين نقص واحد ويساوي هذه
+
+350
+00:34:58,870 --> 00:35:03,490
+عبارة عن اربعة نقص واحد تلاتة تلاتة وهذه عبارة عن
+
+351
+00:35:03,490 --> 00:35:08,390
+تمانية نقص واحد سبعة ويساوي واحد وعشرين معايا يا
+
+352
+00:35:08,390 --> 00:35:15,670
+شباب اه مظبوط هيك اه سيجما of اتنين في اتنين تربيع
+
+353
+00:35:15,670 --> 00:35:20,280
+اللي هي سيجما of اتنين از تلاتةماذا يساوي حسب
+
+354
+00:35:20,280 --> 00:35:24,140
+القانون؟ اتنين نقص اربعة نقص واحد على اتنين نقص
+
+355
+00:35:24,140 --> 00:35:28,040
+واحد ويساوي اتنين نقص اربعة كم؟ ستة عشر نقص واحد
+
+356
+00:35:28,040 --> 00:35:33,160
+ماذا يساوي؟ خمس عشر ليس شرطا انه يساوي مين اذا
+
+357
+00:35:33,160 --> 00:35:43,140
+sigma of M في N need not equal sigma of M في sigma
+
+358
+00:35:43,140 --> 00:35:49,020
+of N but but if
+
+359
+00:35:50,400 --> 00:35:54,940
+إذا كان الـ greatest common divisor بين الـ M والـ
+
+360
+00:35:54,940 --> 00:36:00,940
+N بساوية واحدة ثم يجب أن نحصل على Sigma of M في N
+
+361
+00:36:00,940 --> 00:36:07,000
+بساوية Sigma of M في Sigma of N وTau of M بساوية
+
+362
+00:36:07,000 --> 00:36:17,980
+Tau M بساوية Tau M في Tau of M معايا؟ واضح؟ طيب
+
+363
+00:36:20,010 --> 00:36:25,970
+وهذا بنعنى في الجملة الأخيرة اللى تحت اللى كتبتها
+
+364
+00:36:25,970 --> 00:36:30,290
+انه sigma and tau are multiplicative functions
+
+365
+00:36:30,290 --> 00:36:35,550
+multiplicative functions اذا الان بدنا نعرف حاجة
+
+366
+00:36:35,550 --> 00:36:40,590
+اسمها multiplicative function a number theoretic
+
+367
+00:36:40,590 --> 00:36:45,430
+function f هذا بنحكي على number theoretic function
+
+368
+00:36:45,430 --> 00:36:51,380
+يعني f من z positive إلى z positiveبنقول الـ
+
+369
+00:36:51,380 --> 00:36:57,520
+number theoretic function F is multiplicative if
+
+370
+00:36:57,520 --> 00:37:03,580
+اللي هو F of M في N بتساوي F of M في F of N for
+
+371
+00:37:03,580 --> 00:37:07,620
+every M و N with the greatest common divisor بين
+
+372
+00:37:07,620 --> 00:37:10,980
+الـ M و الـ N إيش بيساوي؟ بيساوي 1 لإنه احنا طبعا
+
+373
+00:37:10,980 --> 00:37:14,260
+بنحكي على المعنى ال multiplicative هنا في number
+
+374
+00:37:14,260 --> 00:37:19,780
+theoretic functionفي أماكن أخرى ممكن نعرف اللي هو
+
+375
+00:37:19,780 --> 00:37:22,940
+الـ Real Value Function إنها عبارة عن
+
+376
+00:37:22,940 --> 00:37:27,120
+Multiplicative إذا بس بيتحقق F of X في Y بيسوا F
+
+377
+00:37:27,120 --> 00:37:32,520
+of X في مين في F of Y بس هنا إحنا امعرفين a number
+
+378
+00:37:32,520 --> 00:37:35,760
+theoretic function F is said to be multiplicative
+
+379
+00:37:35,760 --> 00:37:40,460
+if F of M of N بيسوا F of M في F of N whenever ال
+
+380
+00:37:40,460 --> 00:37:45,060
+Greatest common divisor بين M و N بيسوا 1
+
+381
+00:37:50,650 --> 00:37:57,210
+بعض الملاحظات على ذلك بعض الملاحظات على ذلك أول
+
+382
+00:37:57,210 --> 00:38:02,790
+حاجة الـ function f of n بتساوي واحد و الـ g of n
+
+383
+00:38:02,790 --> 00:38:06,690
+بيساوي n الدالة الثابتة واحد و ال identity
+
+384
+00:38:06,690 --> 00:38:12,570
+function g of n بيساوي n are then f and g are
+
+385
+00:38:12,570 --> 00:38:20,040
+multiplicative أثبات سهلة لو أخدنا fof n بساوة
+
+386
+00:38:20,040 --> 00:38:24,280
+واحد هي الدالة for every n element in z positive
+
+387
+00:38:24,280 --> 00:38:32,640
+multiplicative ليش let and prove let اللي هو m و n
+
+388
+00:38:32,640 --> 00:38:35,140
+element in z positive such that the greatest
+
+389
+00:38:35,140 --> 00:38:38,900
+common divisor بين ال m و ال n بساوة واحد then
+
+390
+00:38:41,240 --> 00:38:47,260
+of n في n أي إن كانت هي دالة ثابتة بساوي واحد صح
+
+391
+00:38:47,260 --> 00:38:56,820
+ويساوي واحد في واحد صح ويساوي f of n في half of n
+
+392
+00:38:56,820 --> 00:39:03,340
+إذا صارت أشمالها f is multiplicative similarly
+
+393
+00:39:03,340 --> 00:39:13,570
+اللي هو هذا ذنبG of M فعلاً بيساوي الـ Identity
+
+394
+00:39:13,570 --> 00:39:16,970
+الماخدينها الـ G of M أيش بتساوي الـ M بثبت فيها
+
+395
+00:39:16,970 --> 00:39:21,890
+يعني إذا كانت بتساوي M، M ويساوي M اللي هي G of M
+
+396
+00:39:21,890 --> 00:39:26,690
+والـ M في B من مين هي G of M إذا الـ Identity
+
+397
+00:39:26,690 --> 00:39:30,030
+function برضه أيش مالها is a multiplicative
+
+398
+00:39:30,030 --> 00:39:36,930
+function الشيء
+
+399
+00:39:36,930 --> 00:39:37,370
+اللي صحيح
+
+400
+00:39:40,540 --> 00:39:46,700
+هذولا اه طبعا هذولا اصلا are multiplicative in R
+
+401
+00:39:46,700 --> 00:39:53,540
+انا اللي بقى نحكيه لان بدنا نعرف ال number
+
+402
+00:39:53,540 --> 00:39:58,440
+theoretic function انها multiplicativeإذا كان الـ
+
+403
+00:39:58,440 --> 00:40:01,020
+Greatest common divisor للـ M والـ N بساوية واحد
+
+404
+00:40:01,020 --> 00:40:06,720
+ثم F of M في N بساوية F of M في F مين في F of N
+
+405
+00:40:06,720 --> 00:40:12,000
+هذا فيه له هدف برضه انه هيخدمني في ان تعريف هذا
+
+406
+00:40:12,000 --> 00:40:16,500
+هيخدمني ايضا في انه اثبت ان الـ Sigma والـ Tau
+
+407
+00:40:16,500 --> 00:40:21,460
+أشمالهم are multiplicative ماشي الحال؟
+
+408
+00:40:23,300 --> 00:40:28,540
+إذا كان الـ F مرتبطًا لـ N1,N2,NR، الوضع في الـ Z
+
+409
+00:40:28,540 --> 00:40:37,460
+يكون مرتبطًا لـ N1
+
+410
+00:40:37,460 --> 00:40:39,880
+,N2,NR، الوضع في الـ Z يكون مرتبط لـ N1,N2,NR،
+
+411
+00:40:39,880 --> 00:40:39,920
+الوضع في الـ Z يكون مرتبط لـ N1,N2,NR، الوضع في
+
+412
+00:40:39,920 --> 00:40:40,860
+الـ Z يكون مرتبط لـ N1,N2,NR، الوضع في الـ Z يكون
+
+413
+00:40:40,860 --> 00:40:41,420
+مرتبط لـ N1,N2,NR، الوضع في الـ Z يكون مرتبط لـ N1
+
+414
+00:40:41,420 --> 00:40:48,380
+,N2,NR، الوضع في الـ Z يكون مرتبط لـ N1,N2,NR،
+
+415
+00:40:48,380 --> 00:40:49,860
+الوضع في الـ Z يكون مرتبط لـ N1,N2,NR
+
+416
+00:40:53,900 --> 00:41:01,740
+ماخد انا اللي هو تلاتة بالنسبة اتنين الان F is
+
+417
+00:41:01,740 --> 00:41:06,540
+multiplicative مادام F multiplicative F N واحد
+
+418
+00:41:06,540 --> 00:41:12,140
+لعند N R بساوي
+
+419
+00:41:12,140 --> 00:41:17,400
+ال N واحد مع اي واحدة من ال relative ال prime اذا
+
+420
+00:41:17,400 --> 00:41:21,720
+ال N واحد مع هدولة مع بعض اشمالهاrelatively prime
+
+421
+00:41:21,720 --> 00:41:28,940
+و F multiplicative F of N واحد في F of N اتنين عند
+
+422
+00:41:28,940 --> 00:41:34,600
+مين NR نفس الشيء لأن اتنين اشمالها relatively
+
+423
+00:41:34,600 --> 00:41:38,320
+prime مع اللي باقي اذا بطبقها اي اشمال مياه مرة
+
+424
+00:41:38,320 --> 00:41:46,060
+بيصير F of N واحد في F of N اتنين في F of N تلاتة
+
+425
+00:41:46,060 --> 00:41:52,450
+عند NRafter الهو finite number of steps حصل لإن f
+
+426
+00:41:52,450 --> 00:41:59,910
+of n واحد لعند f of n are طيب fn
+
+427
+00:42:01,290 --> 00:42:04,970
+بساوة بي واحد بي اتنين بي تلاتة مرفوعات لل ألف
+
+428
+00:42:04,970 --> 00:42:08,770
+واحد ألف اتنين ألف R is the canonical form of N
+
+429
+00:42:08,770 --> 00:42:12,310
+أكبر من واحدة أن F is multiplicative then F of N
+
+430
+00:42:12,310 --> 00:42:16,490
+إيش بيساوي F للأولى فF للتانية فالأف لمين للأخيرة
+
+431
+00:42:16,490 --> 00:42:23,330
+إذا كانت عندي F multiplicative وعندي ال N على صورة
+
+432
+00:42:23,330 --> 00:42:28,230
+ال canonical form بي واحد عند بي R ألف R بيكون ال
+
+433
+00:42:28,230 --> 00:42:38,820
+F of Nبتساوي f of b1 α1 لعند f of br αr واضح ليش؟
+
+434
+00:42:38,820 --> 00:42:43,900
+f is multiplicative وكل هدولة مدن في ال canonical
+
+435
+00:42:43,900 --> 00:42:52,640
+form اذا distinct primes b1, b2 لعند br نطلع
+
+436
+00:42:52,640 --> 00:42:54,340
+لفوق اللي بعد يا أبو يحيى
+
+437
+00:43:00,280 --> 00:43:04,860
+if F is multiplicative and F لا تساوي سفر then F
+
+438
+00:43:04,860 --> 00:43:12,700
+of واحد ايش بيساوي واحد معايا معايا
+
+439
+00:43:12,700 --> 00:43:20,220
+شباب اثبتها هذه عندي F is multiplicative F is
+
+440
+00:43:20,220 --> 00:43:27,660
+multiplicative و F لا تساوي سفر then ال F هتنجل ال
+
+441
+00:43:27,660 --> 00:43:33,020
+واحد لمينللواحد الواحد لفحة English الواحد لمين
+
+442
+00:43:33,020 --> 00:43:44,780
+للواحد الان عندي ال F of واحد بساوي F of واحد في
+
+443
+00:43:44,780 --> 00:43:52,940
+واحد صح او ال F of واحد في
+
+444
+00:43:52,940 --> 00:43:59,480
+واحدMultiplicator هذا Multiplicator إذا أف في واحد
+
+445
+00:43:59,480 --> 00:44:06,860
+فأف في واحد صح ولا لأ؟ باضح أه؟ ليش أنا واحد ما
+
+446
+00:44:06,860 --> 00:44:13,960
+نقلت لسه؟ فاهمين أه؟ لأن أف في واحد في أف في واحد
+
+447
+00:44:13,960 --> 00:44:22,490
+بيساوي أف في واحدوبما ان ال F لا يساوي صفر فهو F
+
+448
+00:44:22,490 --> 00:44:26,790
+لا يساوي صفر فهو
+
+449
+00:44:26,790 --> 00:44:32,830
+F لا يساوي صفر فهو
+
+450
+00:44:32,830 --> 00:44:41,790
+F لا يساوي صفر فهو F لا يساوي صفر
+
+451
+00:44:47,810 --> 00:44:52,650
+عارفين ليش؟ هذه .. هذه .. هذه بعدين بتبتلكوا إياها
+
+452
+00:44:52,650 --> 00:44:58,970
+انت بغان ال F لا تساوي سفر لأ بتعطينا أن F of F of
+
+453
+00:44:58,970 --> 00:45:02,850
+واحد أشمالها لا تساوي سفر ده استخدام هذه طب ليش
+
+454
+00:45:02,850 --> 00:45:06,150
+هذه؟
+
+455
+00:45:06,150 --> 00:45:14,450
+الآن F of N إيش بتساوي؟ F of N في واحد ويساوي F of
+
+456
+00:45:14,450 --> 00:45:22,120
+N في F of واحدلو كانت f of 1 صفر معايا، لو صارت
+
+457
+00:45:22,120 --> 00:45:25,860
+الـ f of n صفر و n arbitrarily، إذا الـ f مش
+
+458
+00:45:25,860 --> 00:45:31,800
+هتساوي، صفر، contradictionفاهمين؟ إذا كانت الـ F
+
+459
+00:45:31,800 --> 00:45:37,160
+بتسويش صفر و F multiplicative إذا الـ F واحد
+
+460
+00:45:37,160 --> 00:45:41,700
+أشمالها لاتساوي صفر كمان مرة المعلومة if F is
+
+461
+00:45:41,700 --> 00:45:46,000
+multiplicative and F is a non-zero function then F
+
+462
+00:45:46,000 --> 00:45:51,180
+of واحد لا يساوي صفر لأنه لو ساول F واحد صفر هتطلع
+
+463
+00:45:51,180 --> 00:45:54,040
+للـ F of N automatic بتساوي صفر مع نتوا
+
+464
+00:45:54,040 --> 00:45:57,910
+contradiction طيب نيجي لقالنا بقى لسؤالنابما أن F
+
+465
+00:45:57,910 --> 00:46:01,850
+لا تساوي سفر إذا الـ F في واحد لا تساوي سفر مدام
+
+466
+00:46:01,850 --> 00:46:04,550
+الـ F في واحد لا تساوي سفر إذا أنت تختصر هذه محطة
+
+467
+00:46:04,550 --> 00:46:09,390
+هذه بتطلع عندك الـ F في واحد إيش هتساوي واحد واضح
+
+468
+00:46:09,390 --> 00:46:18,290
+أه معانا يا شباب أخر نقطة قلنا Tau في عشرين لا
+
+469
+00:46:18,290 --> 00:46:25,200
+يساوي Tau في اتنين في Tau في عشرة andسيجما او
+
+470
+00:46:25,200 --> 00:46:28,020
+عشرين لا يساوي سيجما او اتنين في سيجما او عشرة
+
+471
+00:46:28,020 --> 00:46:31,880
+ماشي الحالة اعملنا اخدنا مثال قولنا تاو اف ام فان
+
+472
+00:46:31,880 --> 00:46:37,100
+need not equal تاو اف ام فتاو اف ام وسيجما اف ام
+
+473
+00:46:37,100 --> 00:46:41,660
+فان need not equal سيجما اف ام فسيجما اف ام ولكن
+
+474
+00:46:41,660 --> 00:46:46,380
+the functions تاو and سيجما are both
+
+475
+00:46:46,380 --> 00:46:48,020
+multiplicative functions
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/8V_OrbONO3g_postprocess.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/8V_OrbONO3g_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c230f0b478d5b79716d099496957112b076b0005
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/8V_OrbONO3g_postprocess.srt
@@ -0,0 +1,1772 @@
+1
+00:00:20,740 --> 00:00:25,820
+بسم الله الرحمن الرحيم محاضرة رقم 34 في مساق نظرية
+
+2
+00:00:25,820 --> 00:00:31,020
+الاعداد لطلاب الجامعة الإسلامية قسم رياضيات
+
+3
+00:00:31,020 --> 00:00:37,060
+كولياتية العلوم والتربية اليوم هنتحدث عن اخر موضوع
+
+4
+00:00:37,060 --> 00:00:43,520
+بدنا نتحدث عنه في المساق اللي هو هنحكي عن ال
+
+5
+00:00:43,520 --> 00:00:49,900
+primitive roots for primes هنتحدث عن اللي هو
+
+6
+00:00:52,350 --> 00:01:00,830
+معلومات في النهاية نصل من خلالها إنه اللي هو فيه
+
+7
+00:01:00,830 --> 00:01:05,910
+إمكانية أو يُقع نثبت وجود اللي هو primitive roots
+
+8
+00:01:05,910 --> 00:01:13,070
+for abrahams قبل ما نتحدث عن primitive roots for
+
+9
+00:01:13,070 --> 00:01:18,980
+abrahams نحكي عن نظرية LagrangeTheorem 8.5 اللي
+
+10
+00:01:18,980 --> 00:01:25,320
+بتقول ما يلي نظرية مهمة بالنسبة إلينا حتى في حد
+
+11
+00:01:25,320 --> 00:01:36,520
+ذاتها غير إنها مهمة كمقدمة تثبت من أجل إثبات ما
+
+12
+00:01:36,520 --> 00:01:48,590
+بعدها Lagrange theorem بتقول if B is primeأن F of
+
+13
+00:01:48,590 --> 00:01:56,590
+X بسوء A0 زائد A1 X زائد A N X أُس N is a
+
+14
+00:01:56,590 --> 00:02:00,850
+polynomial of degree N of integral coefficients
+
+15
+00:02:00,850 --> 00:02:04,990
+يعني الـ A0 والـ A1 والـ A N كلها انتجار
+
+16
+00:02:06,730 --> 00:02:13,710
+الـ An لا تطابق السفر modulo B يعني الـ B لا تقسم
+
+17
+00:02:13,710 --> 00:02:17,190
+من الـ An يعني اللي هو العامل المشترك الأعلى بين
+
+18
+00:02:17,190 --> 00:02:25,890
+الـ An والـ B بساوية واحدة ثم زي ما قلنا if B is a
+
+19
+00:02:25,890 --> 00:02:30,350
+prime and F of X is a polynomial of integral
+
+20
+00:02:30,350 --> 00:02:37,700
+coefficients and An لا تطابق السفر modulo Bعندي
+
+21
+00:02:37,700 --> 00:02:46,820
+اللي هو الـ F of X تطابق الـ Zero modulo B has at
+
+22
+00:02:46,820 --> 00:02:53,940
+most M اللي هي درجة اللي هي polynomial M
+
+23
+00:02:53,940 --> 00:02:59,960
+incongruent solutions
+
+24
+00:02:59,960 --> 00:03:05,800
+modulo B modulo B
+
+25
+00:03:08,610 --> 00:03:13,770
+كمان مرة، النظرية بتقول إذا كان B is a prime and F
+
+26
+00:03:13,770 --> 00:03:18,350
+of X is a polynomial of degree N أكبر سواء واحد
+
+27
+00:03:18,350 --> 00:03:23,250
+وليه N طبعا لا تطابق السفر modulo B with integral
+
+28
+00:03:23,250 --> 00:03:26,410
+coefficients, then the congruence F of X تطابق
+
+29
+00:03:26,410 --> 00:03:31,850
+الـ0 modulo B has at most an incongruent solutions
+
+30
+00:03:31,850 --> 00:03:37,230
+modulo Bبدنا نثبت على و أكثر في NDA ايش ماله
+
+31
+00:03:37,230 --> 00:03:50,250
+Unincongruent Solutions Model بيه ال proof شوف
+
+32
+00:03:50,250 --> 00:03:54,330
+بصلى النبي عليه الصلاة والسلام بده بالهم اللي هي
+
+33
+00:03:54,330 --> 00:03:59,270
+النظرية by induction
+
+34
+00:04:01,500 --> 00:04:09,010
+on and اللي يعني درجة بولنوبيالبدأ أثبت لكم الآن
+
+35
+00:04:09,010 --> 00:04:14,390
+إنها صحيحة للبولنوميال لل degree اللي هي واحد يعني
+
+36
+00:04:14,390 --> 00:04:20,730
+for n بتساوي واحد وبعدين أفترض صحة اللي هو النظرية
+
+37
+00:04:20,730 --> 00:04:26,230
+للبولنوميال of degree k minus واحد ومنها أصل إنها
+
+38
+00:04:26,230 --> 00:04:31,350
+صحيحة للبولنوميال of degree h بساوي k بناء على كل
+
+39
+00:04:31,350 --> 00:04:35,870
+ذلك بيكون اللي هي صحيحة النظرية لكل بولنوميال
+
+40
+00:04:38,900 --> 00:04:51,580
+الان فرقان بتساوي واحد اول polynomial بيقوم
+
+41
+00:04:51,580 --> 00:04:57,140
+بتسيي البلوميال تبعتنا الآن من هي f of x بساوي a
+
+42
+00:04:57,140 --> 00:05:07,200
+mod زائد a1 x وال a1لاتطابق السفر Modulo B لأن
+
+43
+00:05:07,200 --> 00:05:11,260
+عشان أثبت صحة النظرية للـ polynomials of N بتساوي
+
+44
+00:05:11,260 --> 00:05:16,260
+A1 لازم أثبت أن هذه الـ polynomial الـ F of X
+
+45
+00:05:16,260 --> 00:05:23,700
+تطابق السفر Modulo B has at most one solution بما
+
+46
+00:05:23,700 --> 00:05:29,880
+أن الـ A1 لا تتطابق السفر Modulo B إذا أكيد الـ B
+
+47
+00:05:29,880 --> 00:05:34,670
+لا تقسم الـ A1لأن لو قسمته هتصير الـ A1 وتعريق
+
+48
+00:05:34,670 --> 00:05:38,910
+الصفر مضرو بي لأن بما أن الـ B لا تقسم الـ A1 إذا
+
+49
+00:05:38,910 --> 00:05:42,890
+أكيد الـ Greatest Common Divisor بين الـ B والـ A1
+
+50
+00:05:42,890 --> 00:05:51,040
+أيش بيساوي صفر .. بيساوي واحد، مظبوط؟ما دام العامل
+
+51
+00:05:51,040 --> 00:05:55,860
+المشترك الأعلى بين الـ B و الـ A واحد بيساوي واحد
+
+52
+00:05:55,860 --> 00:05:59,620
+إذا ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+53
+00:05:59,620 --> 00:06:02,080
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+54
+00:06:02,080 --> 00:06:02,900
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+55
+00:06:02,900 --> 00:06:03,240
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+56
+00:06:03,240 --> 00:06:03,800
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+57
+00:06:03,800 --> 00:06:07,820
+ال .. ال .. ال .. ال .. ال ..
+
+58
+00:06:07,820 --> 00:06:18,960
+ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+59
+00:06:20,280 --> 00:06:24,660
+Solution يعني ايش one solution exactly one
+
+60
+00:06:24,660 --> 00:06:31,320
+solution اذا او that is وهذا معناته ان F of X اللي
+
+61
+00:06:31,320 --> 00:06:40,780
+هي بالساوية A1 X زائد A0 بالطبق من الصفر Modulo B
+
+62
+00:06:40,780 --> 00:06:46,920
+has a unique solution
+
+63
+00:06:48,760 --> 00:06:52,980
+وهذا طبعا يؤدي إلى أنه اللي هي في حالة اللي هي
+
+64
+00:06:52,980 --> 00:06:57,380
+Polynomials of degree one اللي هو في عندنا at most
+
+65
+00:06:57,380 --> 00:07:01,380
+one solution وفي الواقع أحصلها الأكتر من ذلك اللي
+
+66
+00:07:01,380 --> 00:07:05,060
+هو exactly إيش one solution إذا صارت عندي then
+
+67
+00:07:05,060 --> 00:07:12,620
+اللي هو it is true for un بتساوي واحد يعني النظرية
+
+68
+00:07:12,620 --> 00:07:18,980
+صحيحة for polynomials of degree one أي سؤال؟الأن
+
+69
+00:07:18,980 --> 00:07:27,380
+suppose that .. ركزوا معايا .. suppose that
+
+70
+00:07:27,380 --> 00:07:32,620
+theorem
+
+71
+00:07:32,620 --> 00:07:42,900
+is true for
+
+72
+00:07:42,900 --> 00:07:51,400
+polynomials of degreeكي ماينس واحد ايش معناه هذا
+
+73
+00:07:51,400 --> 00:08:04,040
+يعني that is any polynomial of degree k minus واحد
+
+74
+00:08:04,040 --> 00:08:12,700
+with a k minus واحد لايطابق السفر modulo b has at
+
+75
+00:08:12,700 --> 00:08:20,260
+mostجد ياش تاني واحد من ال solutions اللي أشملهم
+
+76
+00:08:20,260 --> 00:08:29,670
+in congruent كم مرة؟لأن ايش بفترض؟ بفترض انه عندي
+
+77
+00:08:29,670 --> 00:08:34,650
+اللي هو اي polynomial of degree k minus واحد has
+
+78
+00:08:34,650 --> 00:08:39,010
+at most ايش مالها؟ k minus واحد من مين؟ من ال
+
+79
+00:08:39,010 --> 00:08:43,790
+incongruent solutions بدي اثبت الآن اخدوا لكم اي F
+
+80
+00:08:43,790 --> 00:08:49,510
+of X of degree k و اثبتوا لكم انها برضه ايش مالها؟
+
+81
+00:08:49,510 --> 00:08:56,850
+at mostK من الـ incongruent solutions واضح؟ طيب
+
+82
+00:08:56,850 --> 00:09:08,470
+وهذه سمونيها اللي هو واحد الان let let f of x be
+
+83
+00:09:08,470 --> 00:09:22,270
+any polynomial of degree K withA K لأ تطابق السفر
+
+84
+00:09:22,270 --> 00:09:26,350
+Modulo B Modulo A Modulo B Modulo B Modulo A
+
+85
+00:09:26,350 --> 00:09:27,810
+Modulo B Modulo A Modulo B Modulo A Modulo B
+
+86
+00:09:27,810 --> 00:09:28,350
+Modulo A Modulo B Modulo A Modulo A Modulo A
+
+87
+00:09:28,350 --> 00:09:30,990
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+88
+00:09:30,990 --> 00:09:31,010
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+89
+00:09:31,010 --> 00:09:31,050
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+90
+00:09:31,050 --> 00:09:36,030
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+91
+00:09:36,030 --> 00:09:36,490
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+92
+00:09:36,490 --> 00:09:36,530
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+93
+00:09:36,530 --> 00:09:36,550
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+94
+00:09:36,550 --> 00:09:36,570
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+95
+00:09:36,570 --> 00:09:37,690
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+96
+00:09:37,690 --> 00:09:37,890
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+97
+00:09:37,890 --> 00:09:37,910
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+98
+00:09:37,910 --> 00:09:44,800
+Modulo Aالآن عندي الـ F of X بتساوي سفر تطابق سفر
+
+99
+00:09:44,800 --> 00:09:50,440
+Modulo B لا احتمالين يا إلها solution يا مافيش
+
+100
+00:09:50,440 --> 00:09:54,060
+إلها solution إذا انقسمت العالم تبعي الآن إلى
+
+101
+00:09:54,060 --> 00:10:02,600
+قسمين case واحد أن F of X تطابق السفر Modulo B has
+
+102
+00:10:02,600 --> 00:10:11,640
+no solution ال case التانيf of x بطاقة الصفر
+
+103
+00:10:11,640 --> 00:10:17,700
+modulo b has a solution يا إلا solution يا إياش
+
+104
+00:10:17,700 --> 00:10:22,640
+مالهاش solution في حالة تكون مالهاش solution إذاً
+
+105
+00:10:22,640 --> 00:10:27,360
+هي at most اللي ده مالها zero solutions إذاً هي at
+
+106
+00:10:27,360 --> 00:10:36,020
+most كي من ال solutions تتحقق إذاً then it has at
+
+107
+00:10:36,020 --> 00:10:43,820
+mostK solutions هي في الواقع بالظبط في إيها إيهاش
+
+108
+00:10:43,820 --> 00:10:47,680
+Zero solutions فش solutions يعني No solutions إذا
+
+109
+00:10:47,680 --> 00:10:51,760
+it has at most K من ال solutions دي جي لحالة ثانية
+
+110
+00:10:51,760 --> 00:10:56,000
+أن F of X تطابق Zero بدون بيهاش إيهاش a solution
+
+111
+00:10:56,000 --> 00:11:07,350
+say خلينا نقول say A is a solutionof F of X تطابق
+
+112
+00:11:07,350 --> 00:11:12,690
+الـ Zero مدنبيين مدنبيين نفترض إن F of X إيش ما
+
+113
+00:11:12,690 --> 00:11:22,090
+لها؟ لها solution اسمه إيه مدنبي طبعا ال solution
+
+114
+00:11:34,590 --> 00:11:39,990
+معايا يا شباب إذا اللي بقوله الحالة التانية أن F
+
+115
+00:11:39,990 --> 00:11:43,830
+of X يطابق الـ 0 modulo B has a solution نفترض أن
+
+116
+00:11:43,830 --> 00:11:48,270
+هذا ال solution A ماشي الحال مادام A solution هي F
+
+117
+00:11:48,270 --> 00:11:53,870
+of X يطابق الـ 0 modulo B then هيكون F of X اللي
+
+118
+00:11:53,870 --> 00:11:59,410
+هو F of A يطابق الـ 0 modulo A modulo B فانه ايه
+
+119
+00:11:59,410 --> 00:12:02,990
+ال solution مادام solution تحقق رفاية المتطابقة
+
+120
+00:12:02,990 --> 00:12:10,500
+معايا؟طيب الآن صار
+
+121
+00:12:10,500 --> 00:12:18,240
+عندي f of a تطابق السفر modulo b لو أجيت عندي ال
+
+122
+00:12:18,240 --> 00:12:21,200
+polynomial f of x ال degree تبعته إيش بيساوي
+
+123
+00:12:21,200 --> 00:12:27,480
+بيساوي كيه؟ بدي أجسم اللي هو ال polynomial f of x
+
+124
+00:12:27,480 --> 00:12:33,930
+بدي أجسمها عالميا على x minus aأه بدك اسمها على x
+
+125
+00:12:33,930 --> 00:12:40,490
+minus a لأن هذه degree هي ايش بتساوي kفرضينا إيهاش
+
+126
+00:12:40,490 --> 00:12:45,710
+K وده ال degree اللي لابساه واحد إذا لما نأجسمها
+
+127
+00:12:45,710 --> 00:12:50,610
+على بعض ال F of X هيساوي اللي هو هيطلع ناتج قسمة
+
+128
+00:12:50,610 --> 00:12:55,650
+ومتبقي للقسمة الناتج القسمة اللي هو عبارة عن Q of
+
+129
+00:12:55,650 --> 00:13:00,910
+X في X minus A زائد remainder اللي هو R ال
+
+130
+00:13:00,910 --> 00:13:05,250
+remainder R هو عبارة عن integer عبارة عن integer
+
+131
+00:13:05,950 --> 00:13:10,950
+الان عندى polynomial هذه صارت من degree جديش في
+
+132
+00:13:10,950 --> 00:13:15,250
+نقص واحد وهذه من degree واحد وهذا remainder عبارة
+
+133
+00:13:15,250 --> 00:13:19,130
+عن constant اذا صارت اللى هى F of X بساوة Q of X
+
+134
+00:13:19,130 --> 00:13:22,850
+فى X minus A زايد مين زايد R بتفلتلك ان ال R
+
+135
+00:13:22,850 --> 00:13:27,310
+remainder هيتلعاش بساوة سفر هيتلع بساوة سفر مضلوا
+
+136
+00:13:27,310 --> 00:13:33,920
+B او من مضاعفات من ال B شوف كيفقسمنا الـ
+
+137
+00:13:33,920 --> 00:13:37,480
+polynomial f of x على x minus a طلع عند المقدار
+
+138
+00:13:37,480 --> 00:13:42,020
+هذا الآن
+
+139
+00:13:42,020 --> 00:13:50,000
+أحسب دي f of a للجهتين بيصير اللي هو q of a في a
+
+140
+00:13:50,000 --> 00:13:57,720
+minus a زائد r بساوي f of a صح ولا لأ؟ معايا أه؟
+
+141
+00:13:57,720 --> 00:14:07,460
+وهذا ال f of a أشمالهيطابق السفر مدلو B لأن A is a
+
+142
+00:14:07,460 --> 00:14:13,340
+solution لـF of X تطابق الـ0 مدلو B وهذه سفر إذا
+
+143
+00:14:13,340 --> 00:14:17,840
+إيش متساوي هذه؟ R إذا صارت الـR تطابق الـ0 مدلو
+
+144
+00:14:17,840 --> 00:14:24,980
+100 مدلو B إذا صارت عند الـF of X تبعتنا then F of
+
+145
+00:14:24,980 --> 00:14:35,410
+X صارت تطابق لـQ of X في X minus A مدلوB شوفوا
+
+146
+00:14:35,410 --> 00:14:45,110
+الآن إيش اللي بدي أعمله الآن بدي أقول لك let B لا
+
+147
+00:14:45,110 --> 00:14:57,450
+تطابق الـ A modulo B بـ any other solution of F of
+
+148
+00:14:57,450 --> 00:15:05,630
+X تطابق السفرmodulo B معايا يا جماعة؟ الآن فرضت أن
+
+149
+00:15:05,630 --> 00:15:11,530
+بي أي solution آخر لل F of X وطابق الـ 0 modulo B
+
+150
+00:15:11,530 --> 00:15:18,090
+يختلف عن مين in congruent لمين للـ A معايا؟ طيب،
+
+151
+00:15:18,090 --> 00:15:24,990
+مدام الـ B solution إذا أكيد هيكون عندي then F of
+
+152
+00:15:24,990 --> 00:15:33,050
+B على طابق السفر modulo مين؟ modulo Bمن جهة أخرى
+
+153
+00:15:33,050 --> 00:15:37,970
+الـ F of B إيش هتساوي؟ من جهة أخرى الـ F of B
+
+154
+00:15:37,970 --> 00:15:49,690
+بالطابق لـ Q of B في B minus A modulo B معايا؟
+
+155
+00:15:49,690 --> 00:15:55,790
+أي سؤال؟ الآن عندي F of B إيش بالطابق؟ السفر إذا
+
+156
+00:15:55,790 --> 00:15:59,510
+برضه هذي هيصير A شمال هي بالطابق بالسفريعني هيصير
+
+157
+00:15:59,510 --> 00:16:04,630
+عندك Q of B في B minus A تطابق الصفر Modulo B
+
+158
+00:16:04,630 --> 00:16:11,190
+Modulo B الان انت فيه عندك ال B مالها لا تطابق ال
+
+159
+00:16:11,190 --> 00:16:16,790
+A مدام ال B لا تطابق ال A يعني معناته ال B لا تقسم
+
+160
+00:16:16,790 --> 00:16:23,190
+ال B minus A مظبوط؟ما دام الـ B لا تطابق الـ A،
+
+161
+00:16:23,190 --> 00:16:25,730
+إذا الـ B minus A لا تطابق السفر، يعني الـ B لا
+
+162
+00:16:25,730 --> 00:16:29,990
+تقسم الـ B minus A، مظبوط؟ الـ B لا تقسم الـ B
+
+163
+00:16:29,990 --> 00:16:33,250
+minus A طيب ما هي الـ B prime؟ ما دام الـ B لا
+
+164
+00:16:33,250 --> 00:16:35,650
+تقسم الـ B minus A، ده الـ greatest common divisor
+
+165
+00:16:35,650 --> 00:16:41,200
+بين الـ B و الـ B minus A، إيش مساوى؟ واحدما دام
+
+166
+00:16:41,200 --> 00:16:44,980
+هذه وهذه اللي هو العالم الشركي الأعلى بين الواحد
+
+167
+00:16:44,980 --> 00:16:51,500
+إذا بقدر أختصر هذه إذا بيصير عندي then اللي هو لـQ
+
+168
+00:16:51,500 --> 00:17:01,140
+of B تطابق الـ0 مضلمين مضلمين واضح؟ طيب إذا الآن
+
+169
+00:17:01,140 --> 00:17:07,620
+إيش اللي وصلنا له؟وصلنا إن الـ B عبارة عن solution
+
+170
+00:17:07,620 --> 00:17:14,520
+لمين لـ Q X تطابق الـ 0 مدل بيه؟ إيش اللي وصلنا؟
+
+171
+00:17:14,520 --> 00:17:20,240
+اللي وصلنا إلى ما هي ليه؟ إن أي solution أخدنا
+
+172
+00:17:20,240 --> 00:17:29,780
+إحنا بدأنا إن B أي solution للـ F X تطابق الـ 0
+
+173
+00:17:29,780 --> 00:17:36,640
+مدل بيه؟ووصلنا إن الـ B solution لمين لـ Q لـ Q of
+
+174
+00:17:36,640 --> 00:17:41,060
+X تطابق الـ 0 modulo B إذن اللي وصلنا له ما يالي
+
+175
+00:17:41,060 --> 00:17:46,720
+بعيد و أكرر إنه أي solution للـ F of X تطابق الـ 0
+
+176
+00:17:46,720 --> 00:17:54,900
+modulo B غير A بيعطيني إنه إنه هو solution لـ Q X
+
+177
+00:17:54,900 --> 00:18:01,140
+modulo B ماشي الحال ركز الآنالان Q of X درجتها
+
+178
+00:18:01,140 --> 00:18:08,620
+كده؟ K-1 و احنا
+
+179
+00:18:08,620 --> 00:18:14,000
+مفترضين من واحد ان النظرية الصحيحة لها يعني الـ Q
+
+180
+00:18:14,000 --> 00:18:21,090
+of X هزأت نص تقاش K-1 من ال solutionsالآن لاحظ هذا
+
+181
+00:18:21,090 --> 00:18:25,790
+على الأكتر فيه لـK-1 من ال solutions واحنا بنقول
+
+182
+00:18:25,790 --> 00:18:29,610
+أي solution ها لسolution ها يعني ماتحلمش أنه إيش
+
+183
+00:18:29,610 --> 00:18:34,630
+يكون مش solutions لهذه يكون solution لهذه إذا على
+
+184
+00:18:34,630 --> 00:18:38,910
+الأكتر على الأكتر غير هذه كده إيش لها solutions ال
+
+185
+00:18:38,910 --> 00:18:42,690
+solutions دول اللي هي K-1 وفي عندي واحد في الأصل
+
+186
+00:18:42,690 --> 00:18:47,750
+إذا على الأكتر إيش ماله F of X has at most K من ال
+
+187
+00:18:47,750 --> 00:18:53,640
+solutionsكمان مرة اللي قلته ما هي ليه أن أي
+
+188
+00:18:53,640 --> 00:18:59,040
+solution هنا غير الـA هيكون solution هنا هذه كل ال
+
+189
+00:18:59,040 --> 00:19:04,420
+solutions تبعتها K- واحد من ال solutions إذاً هذه
+
+190
+00:19:04,420 --> 00:19:10,280
+هيكون أكتر إشي لغير الـA برضه K- واحد من ال
+
+191
+00:19:10,280 --> 00:19:14,560
+solutions ليش؟ لأن مش solution هنا مش solution هنا
+
+192
+00:19:15,430 --> 00:19:19,650
+إذن الخيارات لهذه بس من ال solutions اللي ليانا
+
+193
+00:19:19,650 --> 00:19:24,330
+بالإضافة لل A إذا ال QF of X وطبقه Zero مدله B has
+
+194
+00:19:24,330 --> 00:19:28,550
+at most K minus واحد زائد واحد ويساوي K solutions
+
+195
+00:19:28,550 --> 00:19:33,150
+إذا النظرية سارت true for any N بتساوي K من كل
+
+196
+00:19:33,150 --> 00:19:38,130
+معمضة بيصير النظرية true for any N أكبر أو يساوي
+
+197
+00:19:38,130 --> 00:19:41,190
+واحد أي سؤال
+
+198
+00:19:51,790 --> 00:19:57,710
+باز إبراهيم باز
+
+199
+00:19:57,710 --> 00:19:58,590
+إبراهيم
+
+200
+00:20:26,370 --> 00:20:33,670
+معايا يا شباب عند B is prime وعندي
+
+201
+00:20:33,670 --> 00:20:40,070
+D بتقسم ال B minus واحد ال D بتقسم ال B minus واحد
+
+202
+00:20:40,070 --> 00:20:52,550
+then X to the D تطابق الواحد modulo B has exactly
+
+203
+00:21:02,650 --> 00:21:05,890
+معايا النظرية بتقول الميالي او الكورلر بتقول
+
+204
+00:21:05,890 --> 00:21:11,410
+الميالي اذا كانت بي برايم وكان دي قاسم من قاسم ال
+
+205
+00:21:11,410 --> 00:21:14,990
+بي ماينس واحد بيكون اكس تو دالي تطابق الواحد مدلوا
+
+206
+00:21:14,990 --> 00:21:19,530
+بي إلى بالظبط جدياش دي من ال incongruent solutions
+
+207
+00:21:20,860 --> 00:21:24,440
+لاحظوا احنا في الـ .. في الـ .. في الـ polynomials
+
+208
+00:21:24,440 --> 00:21:27,820
+اللي .. او في ال .. الـ congruences ال degree اللي
+
+209
+00:21:27,820 --> 00:21:33,240
+لها اتنين او اكثر احنا ماتطرقناش إلى الحلول الا في
+
+210
+00:21:33,240 --> 00:21:36,120
+حال .. الا في الحالة .. حالة الـ X سر بيها تطابق
+
+211
+00:21:36,120 --> 00:21:40,720
+ناقص واحد حالة الـ B على صورة 4K زي التلاتة،
+
+212
+00:21:40,720 --> 00:21:44,120
+مظبوط؟ وهي هذه الحالة التانية، لأن احنا ماتدخلناش
+
+213
+00:21:44,120 --> 00:21:47,400
+لشرطة تسعة اللي بتتكلم عن تفاصيل اللي هو الـ
+
+214
+00:21:47,400 --> 00:21:51,370
+quadratic congruencesالان هذه تطبيقات على النظريات
+
+215
+00:21:51,370 --> 00:21:58,270
+اللي احنا درسناها في الـ Chapter 8 و Chapter 7
+
+216
+00:21:58,270 --> 00:22:04,920
+سابقاً شوف الان دي is prime و دي تقسم الـP-1إذاً X
+
+217
+00:22:04,920 --> 00:22:08,600
+تطابق الواحد مضروبيها is exactly incongruent دي
+
+218
+00:22:08,600 --> 00:22:11,840
+incongruent solutions يعني مثال باخدلك مثال عددي
+
+219
+00:22:11,840 --> 00:22:17,460
+example لو جيت أخدت انت ال X أُس خمسة تطابق الواحد
+
+220
+00:22:17,460 --> 00:22:24,770
+مضلوا مثلا واحد وتلاتين زي ما هو باخدهاالآن هذه
+
+221
+00:22:24,770 --> 00:22:30,550
+فيها أكم solution بنقدر نعرف بناء على هذه
+
+222
+00:22:30,550 --> 00:22:34,810
+الكورولاري إيش الكورولاري بتقول الخمسة بناء أن
+
+223
+00:22:34,810 --> 00:22:37,270
+الخمسة بتكسب من الواحد و تلاتين مع صواعد هو
+
+224
+00:22:37,270 --> 00:22:43,610
+التلاتين then it has five incongruent solutions
+
+225
+00:22:43,610 --> 00:22:46,450
+five incongruent solutions بس هي المعلومة اللي
+
+226
+00:22:46,450 --> 00:22:48,770
+عندنا اللي بدنا نحكي فيها اللي بعده
+
+227
+00:22:56,630 --> 00:23:06,050
+النظرية و الـ Corollary بتقدي في برهان نظرية 8.6
+
+228
+00:23:06,050 --> 00:23:13,650
+التي بتقول أن if B is a prime and D تكسب B-1 then
+
+229
+00:23:13,650 --> 00:23:18,750
+there are exactly 5 of D incongruent integers have
+
+230
+00:23:18,750 --> 00:23:21,850
+ordered D modulo B
+
+231
+00:23:31,120 --> 00:23:43,080
+النظرية تقول معيالي theorem if B is prime وD تقسم
+
+232
+00:23:43,080 --> 00:23:50,100
+ال B-1 وD تقسم ال B-1
+
+233
+00:23:50,100 --> 00:24:03,520
+معيا وD تقسم ال B-1 then they areأو تقريبًا فاي اف
+
+234
+00:24:03,520 --> 00:24:14,000
+دي فاي اف دي غير متجر غير متجر غير متجر غير متجر
+
+235
+00:24:14,000 --> 00:24:15,780
+غير متجر غير متجر غير متجر غير متجر غير متجر غير
+
+236
+00:24:15,780 --> 00:24:21,180
+متجر غير متجر غير متجر
+
+237
+00:24:28,480 --> 00:24:31,280
+بتقول لو كانت عندي بي برايم و D بتكسيب ال بي و
+
+238
+00:24:31,280 --> 00:24:37,240
+ماينس واحد بقول في عندي بالظبط five of D من ال
+
+239
+00:24:37,240 --> 00:24:42,360
+incongruent integers having order A شماله D modulo
+
+240
+00:24:42,360 --> 00:24:46,060
+B الأن
+
+241
+00:24:46,060 --> 00:24:53,480
+example find
+
+242
+00:24:53,480 --> 00:24:57,160
+the
+
+243
+00:24:57,160 --> 00:24:57,640
+number
+
+244
+00:25:02,470 --> 00:25:09,130
+of incongruent integers
+
+245
+00:25:09,130 --> 00:25:24,390
+having واحد اللي هو order two modulo اللي هو مثلا
+
+246
+00:25:24,390 --> 00:25:39,470
+سبعة اتنين orderthree modulo سبعة ثلاثة order ستة
+
+247
+00:25:39,470 --> 00:25:47,130
+modulo سبعة حسب
+
+248
+00:25:47,130 --> 00:25:55,960
+اللي هي النظرية عندي اللي هو ال بيه متساوي سبعةإذن
+
+249
+00:25:55,960 --> 00:26:00,920
+أكيد اللي هو الـ 2 بيقسم الـ B-1 الـ 6 إذا الـ 2
+
+250
+00:26:00,920 --> 00:26:04,960
+بتقسم ال 6 طبعا انا اختارتهم اللي هو الـ 2 بتقسم
+
+251
+00:26:04,960 --> 00:26:11,520
+ال 6 و 3 بتقسم ال 6 و 6 بتقسم ال 6 إذا الجواب
+
+252
+00:26:11,520 --> 00:26:18,890
+اللي هو أشمالهأيش بيساوي حسب النظرية فايل of mean
+
+253
+00:26:18,890 --> 00:26:23,250
+دي دي ايش بتساوي اتنين فايل اتنين ايش بتساوي واحد
+
+254
+00:26:23,250 --> 00:26:29,770
+اذا في عندي بس one integer اللي هو ال order له
+
+255
+00:26:29,770 --> 00:26:33,950
+يعني في a واحد there exist a واحد such that ال
+
+256
+00:26:33,950 --> 00:26:41,170
+order لل a واحد modulo سبعة بيساوي قداش اتنين في
+
+257
+00:26:41,170 --> 00:26:47,460
+واحد بسالأن ال order له تلاتة modulo سبعة اللي هو
+
+258
+00:26:47,460 --> 00:26:52,880
+جدش بيكون five of تلاتة اللي هو جدش بيساوي اتنين
+
+259
+00:26:52,880 --> 00:26:58,120
+يعني there exist a واحد و a اتنين incongruent غير
+
+260
+00:26:58,120 --> 00:27:03,380
+متطابقين modulo سبعة such that ال order لل a واحد
+
+261
+00:27:03,380 --> 00:27:10,850
+بيساوي ال order لل a اتنين بيساوي جدش تلاتةمدلوا
+
+262
+00:27:10,850 --> 00:27:16,170
+مين طبعا مدلوا سبعة فاهمين علي ايش بقول الان ها
+
+263
+00:27:16,170 --> 00:27:22,110
+انا جدش فيه اللي هو في عندي five of ستة اللي هو
+
+264
+00:27:22,110 --> 00:27:28,150
+برضه جداش اتنينأتنين من الـ incongruent solutions
+
+265
+00:27:28,150 --> 00:27:35,650
+يعني من الـ incongruent integers احد لايطابق اتنين
+
+266
+00:27:35,650 --> 00:27:41,510
+modulo بي أو modulo سبعة فاهمين such that ال order
+
+267
+00:27:41,510 --> 00:27:47,070
+للأحد modulo سبعة بسوء ال order للأتنين modulo
+
+268
+00:27:47,070 --> 00:27:49,950
+سبعة بسوء قداش ستة
+
+269
+00:27:52,590 --> 00:27:58,230
+طيب نيجي لا اللي هو مثال اللي بيعطينا إياه بقول
+
+270
+00:27:58,230 --> 00:28:01,690
+find the number of incongruent integers having
+
+271
+00:28:01,690 --> 00:28:05,790
+order خمسة مدن ومين مدن واحد تلاتين من نفس الطريقة
+
+272
+00:28:05,790 --> 00:28:10,960
+الخمسة بتكسب تلاتينذن في عند ال order اللي هو قداش
+
+273
+00:28:10,960 --> 00:28:15,500
+عدد العناصر لل orderها خمسة مضلوا واحد و تلاتين
+
+274
+00:28:15,500 --> 00:28:18,840
+اللي هو five خمسة مش بيساوي بيساوي أربعة يعني في
+
+275
+00:28:18,840 --> 00:28:23,040
+أربع عدد ا واحد و اتنين و اتلت او اربعة بقيت ان ال
+
+276
+00:28:23,040 --> 00:28:27,780
+order لكل واحد مضلوا واحد و تلاتين يساوي أربعة
+
+277
+00:28:27,780 --> 00:28:36,360
+يساوي خمسة آسف كونوا لغايةالآن بناءً على اللي هو
+
+278
+00:28:36,360 --> 00:28:40,840
+النظرية اللي هي اللي عندي اللي فوق هذه الـ
+
+279
+00:28:40,840 --> 00:28:47,760
+Corollary بتعددلي بالظبط لـ Primitive Roots اما هو
+
+280
+00:28:47,760 --> 00:28:52,840
+الـ Primitive Roots هو عبارة عن عدد order بسوء 5
+
+281
+00:28:52,840 --> 00:28:59,100
+of B الـ B-1 الـ
+
+282
+00:28:59,100 --> 00:29:05,330
+R بيكون Primitive Rootsمدل و N إذا كان order ال R
+
+283
+00:29:05,330 --> 00:29:10,290
+مدل و N بيساوي Phi of N ماشي الحالة إذا اللي حالة
+
+284
+00:29:10,290 --> 00:29:14,450
+خاصة من مين من النظرية اللي فوق إذا بتقولك بالظبط
+
+285
+00:29:14,450 --> 00:29:18,370
+if B is a prime then there are exactly إيش ماله
+
+286
+00:29:18,370 --> 00:29:25,430
+Phi of B minus واحد incongruent primitive roots of
+
+287
+00:29:25,430 --> 00:29:31,170
+مين؟ of Bواضح على طول إذن اللي هي B-1 بتقسم الـ B
+
+288
+00:29:31,170 --> 00:29:35,750
+-1 إذا فيها Default of B-1 من ال integers اللي
+
+289
+00:29:35,750 --> 00:29:55,510
+orderedها B-1 واضح خليني أقولها نضحها بشكل نقول
+
+290
+00:29:55,510 --> 00:29:56,110
+corollary
+
+291
+00:30:05,170 --> 00:30:17,130
+إذا كان بي برامج فهناك
+
+292
+00:30:17,130 --> 00:30:27,790
+تقريبًا فاي اف بي ماينس واحد ساوي فاي اف فاي اف بي
+
+293
+00:30:37,520 --> 00:30:42,160
+primitive roots of
+
+294
+00:30:42,160 --> 00:30:50,780
+B من وين جبناها دي الان في النظرية اللي جابلها من
+
+295
+00:30:50,780 --> 00:30:53,680
+النظرية اللي جابلها بما ان الـ B minus واحد اللي
+
+296
+00:30:53,680 --> 00:30:57,460
+هو D بيكون الـ B minus واحد اللي هي D في هذه
+
+297
+00:30:57,460 --> 00:31:00,820
+الحالة B minus واحد تكسب الـ B minus واحد إذا في
+
+298
+00:31:00,820 --> 00:31:06,730
+عندياللي هو Phi of B minus واحد من ال integers
+
+299
+00:31:06,730 --> 00:31:10,810
+اللي incongruent اللي orderedها بساوي B minus واحد
+
+300
+00:31:10,810 --> 00:31:15,350
+يعني اللي orderedها بساوي Phi of B يعني صار في
+
+301
+00:31:15,350 --> 00:31:20,710
+عندي Phi of B minus واحد من ال primitive roots لأن
+
+302
+00:31:20,710 --> 00:31:26,290
+اللي هو اللي orderedه بساوي Phi of B هو عبارة عن
+
+303
+00:31:26,290 --> 00:31:28,490
+مين ال primitive root
+
+304
+00:31:30,220 --> 00:31:34,020
+إذا صار عندي Phi of B minus واحد من ال primitive
+
+305
+00:31:34,020 --> 00:31:41,960
+roots وإيه شمالهم كلهم in congruent modulo B أي
+
+306
+00:31:41,960 --> 00:31:50,540
+سؤال نجي لمثالنا أخد مثال اللي هو find the number
+
+307
+00:31:50,540 --> 00:31:54,700
+of primitive roots find the number of primitive
+
+308
+00:31:54,700 --> 00:32:00,560
+roots of الواحد وتلاتينThe number of primitive
+
+309
+00:32:00,560 --> 00:32:06,840
+roots للـ 31 هي 5 من 100 من 30 5 من 30 أشهر تطلع
+
+310
+00:32:06,840 --> 00:32:10,840
+لتساوية تمانية إذا في عندي تمانية من ال
+
+311
+00:32:10,840 --> 00:32:19,240
+incongruent ال primitive roots of 31 أي سؤال؟
+
+312
+00:32:19,240 --> 00:32:23,780
+اطلعينا على الأسئلة خليني أحللكم نجينا السؤال
+
+313
+00:32:23,780 --> 00:32:33,960
+الأول if B then of the primeسؤال أول ايه؟ be an
+
+314
+00:32:33,960 --> 00:32:39,200
+odd prime
+
+315
+00:32:39,200 --> 00:32:44,940
+then the only incongruent solutions of x تربيع
+
+316
+00:32:44,940 --> 00:32:52,140
+find all incongruent
+
+317
+00:32:52,140 --> 00:32:55,440
+solutions
+
+318
+00:32:56,800 --> 00:33:08,780
+of x تربية تطابق الواحد modulo b proof بيقول
+
+319
+00:33:08,780 --> 00:33:13,980
+لي بي إذا نقدّهاش إبراهيم بيقول لي أودد كل ال
+
+320
+00:33:13,980 --> 00:33:20,260
+solutions لل x تربية تطابق الواحد مدلو مين مدلو بي
+
+321
+00:33:20,260 --> 00:33:25,430
+معايالأن P is odd prime مدان P is odd prime إذا
+
+322
+00:33:25,430 --> 00:33:36,210
+أكيد since P is odd then الاتنين تقسم ال P minus
+
+323
+00:33:36,210 --> 00:33:42,610
+واحد لأن ال P minus واحد صارت even then
+
+324
+00:33:42,610 --> 00:33:51,550
+by كرولر اللي جاب اللي بشوية X تربيعتطابق الواحد
+
+325
+00:33:51,550 --> 00:34:01,310
+مضلوا بي has exactly .. كده ايش؟ two solutions
+
+326
+00:34:01,310 --> 00:34:10,650
+طبعاً incongruent معايا؟
+
+327
+00:34:10,650 --> 00:34:15,590
+لأنه .. لأنه بتقسم الـ P minus واحد إذن هذه اللي
+
+328
+00:34:15,590 --> 00:34:22,590
+هي exactly two solutions واضحإن الواحد since
+
+329
+00:34:22,590 --> 00:34:29,370
+الواحد تربيعي وطابق الواحد model of B then واحد is
+
+330
+00:34:29,370 --> 00:34:36,690
+a solution ماشي دائما
+
+331
+00:34:36,690 --> 00:34:40,250
+أبحث عن solutions من عند الواحد لعند ال B- واحد
+
+332
+00:34:40,250 --> 00:34:43,190
+لأن اللي بعد هي انك لو بديكون solutions بديكون
+
+333
+00:34:43,190 --> 00:34:47,490
+congruent للأولانيات لأن الواحد لعند ال B- واحد is
+
+334
+00:34:47,490 --> 00:34:51,260
+a complete residue systemعند الـ B حتى if I
+
+335
+00:34:51,260 --> 00:34:55,340
+complete residue system فاهمين؟ أي شيء براهن
+
+336
+00:34:55,340 --> 00:35:00,840
+مايكون أشمال وزاية اللي جوا إذا واحد تربيع تطرق
+
+337
+00:35:00,840 --> 00:35:04,120
+الواحد مدنه بيه الآن برضه لو جيت لل بيه ماينس واحد
+
+338
+00:35:04,120 --> 00:35:09,560
+لكل تربيع إيش هيساوي؟ اللي هو بيه تربيع ناقص اتنين
+
+339
+00:35:09,560 --> 00:35:16,400
+بيه زاد واحد مدنه بيه هذا سفر وهذا سفر إذا إيش هذا
+
+340
+00:35:16,400 --> 00:35:22,930
+بطابق؟ الواحد مدنهب فاهمين إذا صراحة دي X تربيع
+
+341
+00:35:22,930 --> 00:35:26,430
+تطابق الواحد مضله بي في حالة ال X ايش بتساوي بي
+
+342
+00:35:26,430 --> 00:35:35,530
+minus واحد إذا since كذا thenB-1 is the another
+
+343
+00:35:35,530 --> 00:35:40,630
+solution و أنا مرتاح أصلا عارف أن الـ B-1 أشمال A
+
+344
+00:35:40,630 --> 00:35:45,750
+لاتطابق من الـ 1 لأن هما عبارة عن عناصر من عناصر
+
+345
+00:35:45,750 --> 00:35:48,930
+الـ Complete Residue System Modulo B وهي أنصرين في
+
+346
+00:35:48,930 --> 00:35:51,370
+الـ Complete Residue System Modulo B أشمال الـ R
+
+347
+00:35:51,370 --> 00:35:55,410
+Incongruent و معروف أن الـ B-1 لاتطابق الـ 1
+
+348
+00:35:55,410 --> 00:36:05,340
+Modulo B أي سؤال؟ طيبسؤال 6 نشوف ايش سؤال 6 بيقول
+
+349
+00:36:05,340 --> 00:36:19,640
+بيقوللي سؤال 6 if R is a primitive root
+
+350
+00:36:19,640 --> 00:36:28,960
+of the odd prime B approve A
+
+351
+00:36:31,080 --> 00:36:40,000
+Proof A بتساوي اللي هي The congruence A
+
+352
+00:36:40,000 --> 00:36:43,740
+to the B minus واحد على اتنين تطابق نقص واحد
+
+353
+00:36:43,740 --> 00:36:49,020
+modulo B holds Proof
+
+354
+00:36:56,650 --> 00:37:01,130
+معايا يا شباب؟ طيب صلى على النبي عليه الصلاة
+
+355
+00:37:01,130 --> 00:37:07,030
+والسلام اللي هم بيقوللي R primitive root of B to
+
+356
+00:37:07,030 --> 00:37:10,890
+prove that the congruence R to the B minus واحد
+
+357
+00:37:10,890 --> 00:37:14,350
+على اتنين التطابق التطابق نقص واحد بدل بيه هولس
+
+358
+00:37:14,350 --> 00:37:20,150
+يعني تتحقق يعني صحيح شوفوا اول حاجة شو معناه R is
+
+359
+00:37:20,150 --> 00:37:25,520
+primitive root؟معناته الـ order للـ R modulo B
+
+360
+00:37:25,520 --> 00:37:34,660
+بساوة B-1 اللي هو 5B، مظبوط؟ يعني بمعنى أخر أنه ال
+
+361
+00:37:34,660 --> 00:37:39,620
+order زي ما قلنا للـ R modulo B بساوة B-1 هذا
+
+362
+00:37:39,620 --> 00:37:43,600
+معناته R the primitive root of B وهذا يعني شغلتين
+
+363
+00:37:43,600 --> 00:37:48,800
+الشغل الأول زي ما قلنا أن R to the B-1 تطابق
+
+364
+00:37:48,800 --> 00:37:56,630
+الواحد modulo Bوالشغل الثاني أن R أُس T لا يطابق
+
+365
+00:37:56,630 --> 00:38:03,070
+الواحد modulo B لكل T أكبر من ال .. أكبر يساوي
+
+366
+00:38:03,070 --> 00:38:14,050
+واحد و أصغر منين من ال B minus واحد واضح؟
+
+367
+00:38:14,050 --> 00:38:25,130
+وش هي أصغر R أُس Phi of Bأصغر اللي هو أُس بتخلّي R
+
+368
+00:38:25,130 --> 00:38:31,150
+أُس اللي هي اللي عندي K يطابق الواحد مضروبيه مافيش
+
+369
+00:38:31,150 --> 00:38:37,290
+ولا K قبلها خلّيني بتذكر اللي واحد بتستخدمه لأن
+
+370
+00:38:37,290 --> 00:38:46,210
+since R is a primitive root
+
+371
+00:38:46,210 --> 00:38:57,160
+of B thenR to the 5 of B يطابق الواحد modulo B
+
+372
+00:38:57,160 --> 00:39:03,460
+وهذا IE معناته أن R أقصى B minus واحد تطابق الواحد
+
+373
+00:39:03,460 --> 00:39:10,560
+modulo B معيش يا جماعة لكن B معطينيها إيه أشمالها
+
+374
+00:39:10,560 --> 00:39:15,820
+is an odd ببراية،
+
+375
+00:39:15,820 --> 00:39:23,140
+مظبوط؟ معطينيها B في السؤالB is an odd prime مدام
+
+376
+00:39:23,140 --> 00:39:28,960
+odd prime مدام B is an odd prime إذا الـ B-1 إيش
+
+377
+00:39:28,960 --> 00:39:36,800
+ماله is even ماشي مدام even إذا R B-1 ناقص واحد
+
+378
+00:39:36,800 --> 00:39:41,420
+تطابق السفر modulo B صارت اللي هي فرق بين المربعين
+
+379
+00:39:41,420 --> 00:39:48,710
+لأن هذا مربع كامل بيصير B-1 evenإذا بقدر أحللها
+
+380
+00:39:48,710 --> 00:39:56,110
+لفرق بين المربعين هذي تعني هذي و B odd بي minus
+
+381
+00:39:56,110 --> 00:40:00,790
+واحد evil إذا هذا صار فرق بين المربعين إذا بمعنى
+
+382
+00:40:00,790 --> 00:40:05,190
+آخر بقدر أقول R بي minus واحد على اتنين ناقص واحد
+
+383
+00:40:05,190 --> 00:40:10,870
+في R بي minus واحد على اتنين زائد واحد تطابق السفر
+
+384
+00:40:10,870 --> 00:40:19,290
+modulo B معاشر باباحللت هذا على فرق بين مربعين
+
+385
+00:40:19,290 --> 00:40:23,710
+مجلد
+
+386
+00:40:23,710 --> 00:40:28,110
+الواحد هنا r بي minus واحد ناقص واحد معايا يا شباب
+
+387
+00:40:28,110 --> 00:40:34,270
+إذا صار عندي الآن then ال بي هتجسم ال r بي minus
+
+388
+00:40:34,270 --> 00:40:39,490
+واحد على اتنين ناقص واحد في r بي minus واحد على
+
+389
+00:40:39,490 --> 00:40:43,630
+اتنين زائد واحد و ال بي is Zebral إذا يا بي بتجسم
+
+390
+00:40:43,630 --> 00:40:48,480
+الأولى و يا ابنى بتجسم الميال التانية thenand so
+
+391
+00:40:48,480 --> 00:40:59,100
+الـ R بتقسم الـ B بتقسم الـ R أُس B minus واحد على
+
+392
+00:40:59,100 --> 00:41:07,000
+اتنين ناقص واحد or الـ B بتقسم الـ R أُس B minus
+
+393
+00:41:07,000 --> 00:41:15,080
+واحد على اتنين زائد واحد، مظبوط؟ الآن هذه مستحيلة
+
+394
+00:41:15,950 --> 00:41:20,230
+ليش هذه مستحيلة؟ لأن هذه بتعني أن ر بي ماينوس واحد
+
+395
+00:41:20,230 --> 00:41:28,070
+على اتنين تطابق الواحد وهذا بناقض أن ال order للر
+
+396
+00:41:28,070 --> 00:41:32,250
+هو بي ماينوس واحد لأن ر is a primitive root إذن
+
+397
+00:41:32,250 --> 00:41:35,850
+هذه ليست واحدة إذن بتبقى هذه ما هو المطلوب كمان
+
+398
+00:41:35,850 --> 00:41:43,310
+مرة خليني أكتب هنا أكمل
+
+399
+00:41:43,310 --> 00:41:43,710
+فوق
+
+400
+00:41:47,240 --> 00:41:53,940
+هوضح اللي حكيته قبله شوية اذا صار عندي then اللي
+
+401
+00:41:53,940 --> 00:42:03,940
+هو ال R بي minus واحد ناقص واحد تطابق السفر modulo
+
+402
+00:42:03,940 --> 00:42:15,980
+B or R على اتنين R معايا او R بي ناقص واحد على
+
+403
+00:42:15,980 --> 00:42:24,970
+اتنينزائد واحد تطابق السفر modulo بي واضح IE وهذا
+
+404
+00:42:24,970 --> 00:42:29,570
+معنى أن R أقص بي minus واحد على اتنين تطابق الواحد
+
+405
+00:42:29,570 --> 00:42:35,890
+modulo بي or R أقص بي minus واحد على اتنين يطابق
+
+406
+00:42:35,890 --> 00:42:40,950
+الناقص واحد modulo مين modulo بي الأول هو مستحيل
+
+407
+00:42:40,950 --> 00:42:45,890
+هذا مستحيل
+
+408
+00:42:48,480 --> 00:42:56,120
+because ال order لل R modulo B بيساوي B minus واحد
+
+409
+00:42:56,120 --> 00:43:03,020
+وهذا أكبر من مين؟ أكبر من B ناقص واحد على اتنين
+
+410
+00:43:03,020 --> 00:43:09,460
+وهذا بناقض مين أنه مافيش ولا T بين ال B minus واحد
+
+411
+00:43:09,460 --> 00:43:15,240
+حيث أن R وت T تطابق ال واحد مدلوق إذا دل عندي مين
+
+412
+00:43:15,240 --> 00:43:17,000
+بس therefore
+
+413
+00:43:18,830 --> 00:43:28,470
+RB-1 على 2 تطابق الناقص 1 modulo B وهو المطلوب أي
+
+414
+00:43:28,470 --> 00:43:31,630
+سؤال؟
+
+415
+00:43:31,630 --> 00:43:40,610
+نجي الآن أنحل
+
+416
+00:43:40,610 --> 00:43:44,970
+B إذن
+
+417
+00:43:44,970 --> 00:43:49,470
+الله أثبتنا إنه لما كانت الـR primitive rootللـ B
+
+418
+00:43:49,470 --> 00:43:56,510
+فلعندي هذا التطابق أي شمالها صحيحة الان
+
+419
+00:43:56,510 --> 00:44:01,010
+بي بي
+
+420
+00:44:01,010 --> 00:44:07,750
+بي بتقولنا يلي بي
+
+421
+00:44:07,750 --> 00:44:18,010
+if R and R prime are primitive roots
+
+422
+00:44:18,980 --> 00:44:31,120
+of B then R' is not a primitive root
+
+423
+00:44:31,120 --> 00:44:34,340
+of
+
+424
+00:44:34,340 --> 00:44:41,340
+B غروف إذا
+
+425
+00:44:41,340 --> 00:44:46,730
+كانت B زي نقطة برايم إذا حاصل درباللي هو two
+
+426
+00:44:46,730 --> 00:44:52,190
+primitive roots اللي هي مش primitive root معايا يا
+
+427
+00:44:52,190 --> 00:44:58,410
+شباب ده نشوف كيف since
+
+428
+00:44:58,410 --> 00:45:08,490
+R and R' are primitive roots
+
+429
+00:45:08,490 --> 00:45:18,400
+of B then by A اللي أثبتناهااللي هو R أس بي ماينس
+
+430
+00:45:18,400 --> 00:45:26,320
+واحد على اتنين تطابق ناقص واحد modulo بي and R
+
+431
+00:45:26,320 --> 00:45:31,140
+prime أس بي ماينس واحد على اتنين برضه الشمالها
+
+432
+00:45:31,140 --> 00:45:39,460
+تطابق ناقص واحد modulo بي together دروبهم
+
+433
+00:45:39,460 --> 00:45:47,310
+مع بعضأضرب التلتين بيصير R في R' أُس P مالنس واحد
+
+434
+00:45:47,310 --> 00:45:51,650
+على اتنين تطابق الناقص واحد في الناقص واحد اللي هو
+
+435
+00:45:51,650 --> 00:46:04,410
+واحد modulo P إذا صار عندي but أو hence hence
+
+436
+00:46:05,590 --> 00:46:13,790
+هيكون الـ order للـ R فـ R' modulo B أصغر أو يساوي
+
+437
+00:46:13,790 --> 00:46:17,050
+B-1 على 2
+
+438
+00:46:20,710 --> 00:46:25,630
+وهذا طبعا strictly أصغر من مين من ال B-1 اللي هو
+
+439
+00:46:25,630 --> 00:46:31,410
+Phi of B-1 يعني صار ال order لل R في R' modulo B
+
+440
+00:46:31,410 --> 00:46:40,970
+لا يساوي ال Phi of B-1 وهذا يعني hence R في R' is
+
+441
+00:46:40,970 --> 00:46:43,770
+not a primitive
+
+442
+00:46:47,770 --> 00:47:00,650
+Root modulo of B is not primitive root of B و إلى
+
+443
+00:47:00,650 --> 00:47:01,810
+لقاء آخر
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/8V_OrbONO3g_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/8V_OrbONO3g_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3589ef956f56eda332cc01d89370277b63c7943f
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/8V_OrbONO3g_raw.srt
@@ -0,0 +1,1792 @@
+1
+00:00:20,740 --> 00:00:25,820
+بسم الله الرحمن الرحيم محاضرة رقم 34 في مساق نظرية
+
+2
+00:00:25,820 --> 00:00:31,020
+الاعداد لطلاب الجامعة الإسلامية قسم رياضيات
+
+3
+00:00:31,020 --> 00:00:37,060
+كولياتية العلوم والتربية اليوم هنتحدث عن اخر موضوع
+
+4
+00:00:37,060 --> 00:00:43,520
+بدنا نتحدث عنه في المساق اللي هو هنحكي عن ال
+
+5
+00:00:43,520 --> 00:00:49,900
+primitive roots for primes هنتحدث عن اللي هو
+
+6
+00:00:52,350 --> 00:01:00,830
+معلومات في النهاية نصل من خلالها إنه اللي هو فيه
+
+7
+00:01:00,830 --> 00:01:05,910
+إمكانية أو يُقع نثبت وجود اللي هو primitive roots
+
+8
+00:01:05,910 --> 00:01:13,070
+for abrahams قبل ما نتحدث عن primitive roots for
+
+9
+00:01:13,070 --> 00:01:18,980
+abrahams نحكي عن نظرية LagrangeTheorem 8.5 اللي
+
+10
+00:01:18,980 --> 00:01:25,320
+بتقول ما يلي نظرية مهمة بالنسبة إلينا حتى في حد
+
+11
+00:01:25,320 --> 00:01:36,520
+ذاتها غير إنها مهمة كمقدمة تثبت من أجل إثبات ما
+
+12
+00:01:36,520 --> 00:01:48,590
+بعدها Lagrange theorem بتقول if B is primeأن F of
+
+13
+00:01:48,590 --> 00:01:56,590
+X بسوء A0 زائد A1 X زائد A N X أُس N is a
+
+14
+00:01:56,590 --> 00:02:00,850
+polynomial of degree N of integral coefficients
+
+15
+00:02:00,850 --> 00:02:04,990
+يعني الـ A0 والـ A1 والـ A N كلها انتجار
+
+16
+00:02:06,730 --> 00:02:13,710
+الـ An لا تطابق السفر modulo B يعني الـ B لا تقسم
+
+17
+00:02:13,710 --> 00:02:17,190
+من الـ An يعني اللي هو العامل المشترك الأعلى بين
+
+18
+00:02:17,190 --> 00:02:25,890
+الـ An والـ B بساوية واحدة ثم زي ما قلنا if B is a
+
+19
+00:02:25,890 --> 00:02:30,350
+prime and F of X is a polynomial of integral
+
+20
+00:02:30,350 --> 00:02:37,700
+coefficients and An لا تطابق السفر modulo Bعندي
+
+21
+00:02:37,700 --> 00:02:46,820
+اللي هو الـ F of X تطابق الـ Zero modulo B has at
+
+22
+00:02:46,820 --> 00:02:53,940
+most M اللي هي درجة اللي هي polynomial M
+
+23
+00:02:53,940 --> 00:02:59,960
+incongruent solutions
+
+24
+00:02:59,960 --> 00:03:05,800
+modulo B modulo B
+
+25
+00:03:08,610 --> 00:03:13,770
+كمان مرة، النظرية بتقول إذا كان B is a prime and F
+
+26
+00:03:13,770 --> 00:03:18,350
+of X is a polynomial of degree N أكبر سواء واحد
+
+27
+00:03:18,350 --> 00:03:23,250
+وليه N طبعا لا تطابق السفر modulo B with integral
+
+28
+00:03:23,250 --> 00:03:26,410
+coefficients, then the congruence F of X تطابق
+
+29
+00:03:26,410 --> 00:03:31,850
+الـ0 modulo B has at most an incongruent solutions
+
+30
+00:03:31,850 --> 00:03:37,230
+modulo Bبدنا نثبت على و أكثر في NDA ايش ماله
+
+31
+00:03:37,230 --> 00:03:50,250
+Unincongruent Solutions Model بيه ال proof شوف
+
+32
+00:03:50,250 --> 00:03:54,330
+بصلى النبي عليه الصلاة والسلام بده بالهم اللي هي
+
+33
+00:03:54,330 --> 00:03:59,270
+النظرية by induction
+
+34
+00:04:01,500 --> 00:04:09,010
+on and اللي يعني درجة بولنوبيالبدأ أثبت لكم الآن
+
+35
+00:04:09,010 --> 00:04:14,390
+إنها صحيحة للبولنوميال لل degree اللي هي واحد يعني
+
+36
+00:04:14,390 --> 00:04:20,730
+for n بتساوي واحد وبعدين أفترض صحة اللي هو النظرية
+
+37
+00:04:20,730 --> 00:04:26,230
+للبولنوميال of degree k minus واحد ومنها أصل إنها
+
+38
+00:04:26,230 --> 00:04:31,350
+صحيحة للبولنوميال of degree h بساوي k بناء على كل
+
+39
+00:04:31,350 --> 00:04:35,870
+ذلك بيكون اللي هي صحيحة النظرية لكل بولنوميال
+
+40
+00:04:38,900 --> 00:04:51,580
+الان فرقان بتساوي واحد اول polynomial بيقوم
+
+41
+00:04:51,580 --> 00:04:57,140
+بتسيي البلوميال تبعتنا الآن من هي f of x بساوي a
+
+42
+00:04:57,140 --> 00:05:07,200
+mod زائد a1 x وال a1لاتطابق السفر Modulo B لأن
+
+43
+00:05:07,200 --> 00:05:11,260
+عشان أثبت صحة النظرية للـ polynomials of N بتساوي
+
+44
+00:05:11,260 --> 00:05:16,260
+A1 لازم أثبت أن هذه الـ polynomial الـ F of X
+
+45
+00:05:16,260 --> 00:05:23,700
+تطابق السفر Modulo B has at most one solution بما
+
+46
+00:05:23,700 --> 00:05:29,880
+أن الـ A1 لا تتطابق السفر Modulo B إذا أكيد الـ B
+
+47
+00:05:29,880 --> 00:05:34,670
+لا تقسم الـ A1لأن لو قسمته هتصير الـ A1 وتعريق
+
+48
+00:05:34,670 --> 00:05:38,910
+الصفر مضرو بي لأن بما أن الـ B لا تقسم الـ A1 إذا
+
+49
+00:05:38,910 --> 00:05:42,890
+أكيد الـ Greatest Common Divisor بين الـ B والـ A1
+
+50
+00:05:42,890 --> 00:05:51,040
+أيش بيساوي صفر .. بيساوي واحد، مظبوط؟ما دام العامل
+
+51
+00:05:51,040 --> 00:05:55,860
+المشترك الأعلى بين الـ B و الـ A واحد بيساوي واحد
+
+52
+00:05:55,860 --> 00:05:59,620
+إذا ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+53
+00:05:59,620 --> 00:06:02,080
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+54
+00:06:02,080 --> 00:06:02,080
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+55
+00:06:02,080 --> 00:06:02,900
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+56
+00:06:02,900 --> 00:06:03,240
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+57
+00:06:03,240 --> 00:06:03,800
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+58
+00:06:03,800 --> 00:06:07,820
+ال .. ال .. ال .. ال .. ال ..
+
+59
+00:06:07,820 --> 00:06:07,820
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+60
+00:06:07,820 --> 00:06:07,820
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+61
+00:06:07,820 --> 00:06:07,820
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+62
+00:06:07,820 --> 00:06:07,820
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+63
+00:06:07,820 --> 00:06:18,960
+ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+64
+00:06:20,280 --> 00:06:24,660
+Solution يعني ايش one solution exactly one
+
+65
+00:06:24,660 --> 00:06:31,320
+solution اذا او that is وهذا معناته ان F of X اللي
+
+66
+00:06:31,320 --> 00:06:40,780
+هي بالساوية A1 X زائد A0 بالطبق من الصفر Modulo B
+
+67
+00:06:40,780 --> 00:06:46,920
+has a unique solution
+
+68
+00:06:48,760 --> 00:06:52,980
+وهذا طبعا يؤدي إلى أنه اللي هي في حالة اللي هي
+
+69
+00:06:52,980 --> 00:06:57,380
+Polynomials of degree one اللي هو في عندنا at most
+
+70
+00:06:57,380 --> 00:07:01,380
+one solution وفي الواقع أحصلها الأكتر من ذلك اللي
+
+71
+00:07:01,380 --> 00:07:05,060
+هو exactly إيش one solution إذا صارت عندي then
+
+72
+00:07:05,060 --> 00:07:12,620
+اللي هو it is true for un بتساوي واحد يعني النظرية
+
+73
+00:07:12,620 --> 00:07:18,980
+صحيحة for polynomials of degree one أي سؤال؟الأن
+
+74
+00:07:18,980 --> 00:07:27,380
+suppose that .. ركزوا معايا .. suppose that
+
+75
+00:07:27,380 --> 00:07:32,620
+theorem
+
+76
+00:07:32,620 --> 00:07:42,900
+is true for
+
+77
+00:07:42,900 --> 00:07:51,400
+polynomials of degreeكي ماينس واحد ايش معناه هذا
+
+78
+00:07:51,400 --> 00:08:04,040
+يعني that is any polynomial of degree k minus واحد
+
+79
+00:08:04,040 --> 00:08:12,700
+with a k minus واحد لايطابق السفر modulo b has at
+
+80
+00:08:12,700 --> 00:08:20,260
+mostجد ياش تاني واحد من ال solutions اللي أشملهم
+
+81
+00:08:20,260 --> 00:08:29,670
+in congruent كم مرة؟لأن ايش بفترض؟ بفترض انه عندي
+
+82
+00:08:29,670 --> 00:08:34,650
+اللي هو اي polynomial of degree k minus واحد has
+
+83
+00:08:34,650 --> 00:08:39,010
+at most ايش مالها؟ k minus واحد من مين؟ من ال
+
+84
+00:08:39,010 --> 00:08:43,790
+incongruent solutions بدي اثبت الآن اخدوا لكم اي F
+
+85
+00:08:43,790 --> 00:08:49,510
+of X of degree k و اثبتوا لكم انها برضه ايش مالها؟
+
+86
+00:08:49,510 --> 00:08:56,850
+at mostK من الـ incongruent solutions واضح؟ طيب
+
+87
+00:08:56,850 --> 00:09:08,470
+وهذه سمونيها اللي هو واحد الان let let f of x be
+
+88
+00:09:08,470 --> 00:09:22,270
+any polynomial of degree K withA K لأ تطابق السفر
+
+89
+00:09:22,270 --> 00:09:26,350
+Modulo B Modulo A Modulo B Modulo B Modulo A
+
+90
+00:09:26,350 --> 00:09:27,810
+Modulo B Modulo A Modulo B Modulo A Modulo B
+
+91
+00:09:27,810 --> 00:09:28,350
+Modulo A Modulo B Modulo A Modulo A Modulo A
+
+92
+00:09:28,350 --> 00:09:30,990
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+93
+00:09:30,990 --> 00:09:31,010
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+94
+00:09:31,010 --> 00:09:31,050
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+95
+00:09:31,050 --> 00:09:36,030
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+96
+00:09:36,030 --> 00:09:36,490
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+97
+00:09:36,490 --> 00:09:36,530
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+98
+00:09:36,530 --> 00:09:36,550
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+99
+00:09:36,550 --> 00:09:36,570
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+100
+00:09:36,570 --> 00:09:37,690
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+101
+00:09:37,690 --> 00:09:37,890
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+102
+00:09:37,890 --> 00:09:37,910
+Modulo A Modulo A Modulo A Modulo A Modulo A
+
+103
+00:09:37,910 --> 00:09:44,800
+Modulo Aالآن عندي الـ F of X بتساوي سفر تطابق سفر
+
+104
+00:09:44,800 --> 00:09:50,440
+Modulo B لا احتمالين يا إلها solution يا مافيش
+
+105
+00:09:50,440 --> 00:09:54,060
+إلها solution إذا انقسمت العالم تبعي الآن إلى
+
+106
+00:09:54,060 --> 00:10:02,600
+قسمين case واحد أن F of X تطابق السفر Modulo B has
+
+107
+00:10:02,600 --> 00:10:11,640
+no solution ال case التانيf of x بطاقة الصفر
+
+108
+00:10:11,640 --> 00:10:17,700
+modulo b has a solution يا إلا solution يا إياش
+
+109
+00:10:17,700 --> 00:10:22,640
+مالهاش solution في حالة تكون مالهاش solution إذاً
+
+110
+00:10:22,640 --> 00:10:27,360
+هي at most اللي ده مالها zero solutions إذاً هي at
+
+111
+00:10:27,360 --> 00:10:36,020
+most كي من ال solutions تتحقق إذاً then it has at
+
+112
+00:10:36,020 --> 00:10:43,820
+mostK solutions هي في الواقع بالظبط في إيها إيهاش
+
+113
+00:10:43,820 --> 00:10:47,680
+Zero solutions فش solutions يعني No solutions إذا
+
+114
+00:10:47,680 --> 00:10:51,760
+it has at most K من ال solutions دي جي لحالة ثانية
+
+115
+00:10:51,760 --> 00:10:56,000
+أن F of X تطابق Zero بدون بيهاش إيهاش a solution
+
+116
+00:10:56,000 --> 00:11:07,350
+say خلينا نقول say A is a solutionof F of X تطابق
+
+117
+00:11:07,350 --> 00:11:12,690
+الـ Zero مدنبيين مدنبيين نفترض إن F of X إيش ما
+
+118
+00:11:12,690 --> 00:11:22,090
+لها؟ لها solution اسمه إيه مدنبي طبعا ال solution
+
+119
+00:11:34,590 --> 00:11:39,990
+معايا يا شباب إذا اللي بقوله الحالة التانية أن F
+
+120
+00:11:39,990 --> 00:11:43,830
+of X يطابق الـ 0 modulo B has a solution نفترض أن
+
+121
+00:11:43,830 --> 00:11:48,270
+هذا ال solution A ماشي الحال مادام A solution هي F
+
+122
+00:11:48,270 --> 00:11:53,870
+of X يطابق الـ 0 modulo B then هيكون F of X اللي
+
+123
+00:11:53,870 --> 00:11:59,410
+هو F of A يطابق الـ 0 modulo A modulo B فانه ايه
+
+124
+00:11:59,410 --> 00:12:02,990
+ال solution مادام solution تحقق رفاية المتطابقة
+
+125
+00:12:02,990 --> 00:12:10,500
+معايا؟طيب الآن صار
+
+126
+00:12:10,500 --> 00:12:18,240
+عندي f of a تطابق السفر modulo b لو أجيت عندي ال
+
+127
+00:12:18,240 --> 00:12:21,200
+polynomial f of x ال degree تبعته إيش بيساوي
+
+128
+00:12:21,200 --> 00:12:27,480
+بيساوي كيه؟ بدي أجسم اللي هو ال polynomial f of x
+
+129
+00:12:27,480 --> 00:12:33,930
+بدي أجسمها عالميا على x minus aأه بدك اسمها على x
+
+130
+00:12:33,930 --> 00:12:40,490
+minus a لأن هذه degree هي ايش بتساوي kفرضينا إيهاش
+
+131
+00:12:40,490 --> 00:12:45,710
+K وده ال degree اللي لابساه واحد إذا لما نأجسمها
+
+132
+00:12:45,710 --> 00:12:50,610
+على بعض ال F of X هيساوي اللي هو هيطلع ناتج قسمة
+
+133
+00:12:50,610 --> 00:12:55,650
+ومتبقي للقسمة الناتج القسمة اللي هو عبارة عن Q of
+
+134
+00:12:55,650 --> 00:13:00,910
+X في X minus A زائد remainder اللي هو R ال
+
+135
+00:13:00,910 --> 00:13:05,250
+remainder R هو عبارة عن integer عبارة عن integer
+
+136
+00:13:05,950 --> 00:13:10,950
+الان عندى polynomial هذه صارت من degree جديش في
+
+137
+00:13:10,950 --> 00:13:15,250
+نقص واحد وهذه من degree واحد وهذا remainder عبارة
+
+138
+00:13:15,250 --> 00:13:19,130
+عن constant اذا صارت اللى هى F of X بساوة Q of X
+
+139
+00:13:19,130 --> 00:13:22,850
+فى X minus A زايد مين زايد R بتفلتلك ان ال R
+
+140
+00:13:22,850 --> 00:13:27,310
+remainder هيتلعاش بساوة سفر هيتلع بساوة سفر مضلوا
+
+141
+00:13:27,310 --> 00:13:33,920
+B او من مضاعفات من ال B شوف كيفقسمنا الـ
+
+142
+00:13:33,920 --> 00:13:37,480
+polynomial f of x على x minus a طلع عند المقدار
+
+143
+00:13:37,480 --> 00:13:42,020
+هذا الآن
+
+144
+00:13:42,020 --> 00:13:50,000
+أحسب دي f of a للجهتين بيصير اللي هو q of a في a
+
+145
+00:13:50,000 --> 00:13:57,720
+minus a زائد r بساوي f of a صح ولا لأ؟ معايا أه؟
+
+146
+00:13:57,720 --> 00:14:07,460
+وهذا ال f of a أشمالهيطابق السفر مدلو B لأن A is a
+
+147
+00:14:07,460 --> 00:14:13,340
+solution لـF of X تطابق الـ0 مدلو B وهذه سفر إذا
+
+148
+00:14:13,340 --> 00:14:17,840
+إيش متساوي هذه؟ R إذا صارت الـR تطابق الـ0 مدلو
+
+149
+00:14:17,840 --> 00:14:24,980
+100 مدلو B إذا صارت عند الـF of X تبعتنا then F of
+
+150
+00:14:24,980 --> 00:14:35,410
+X صارت تطابق لـQ of X في X minus A مدلوB شوفوا
+
+151
+00:14:35,410 --> 00:14:45,110
+الآن إيش اللي بدي أعمله الآن بدي أقول لك let B لا
+
+152
+00:14:45,110 --> 00:14:57,450
+تطابق الـ A modulo B بـ any other solution of F of
+
+153
+00:14:57,450 --> 00:15:05,630
+X تطابق السفرmodulo B معايا يا جماعة؟ الآن فرضت أن
+
+154
+00:15:05,630 --> 00:15:11,530
+بي أي solution آخر لل F of X وطابق الـ 0 modulo B
+
+155
+00:15:11,530 --> 00:15:18,090
+يختلف عن مين in congruent لمين للـ A معايا؟ طيب،
+
+156
+00:15:18,090 --> 00:15:24,990
+مدام الـ B solution إذا أكيد هيكون عندي then F of
+
+157
+00:15:24,990 --> 00:15:33,050
+B على طابق السفر modulo مين؟ modulo Bمن جهة أخرى
+
+158
+00:15:33,050 --> 00:15:37,970
+الـ F of B إيش هتساوي؟ من جهة أخرى الـ F of B
+
+159
+00:15:37,970 --> 00:15:49,690
+بالطابق لـ Q of B في B minus A modulo B معايا؟
+
+160
+00:15:49,690 --> 00:15:55,790
+أي سؤال؟ الآن عندي F of B إيش بالطابق؟ السفر إذا
+
+161
+00:15:55,790 --> 00:15:59,510
+برضه هذي هيصير A شمال هي بالطابق بالسفريعني هيصير
+
+162
+00:15:59,510 --> 00:16:04,630
+عندك Q of B في B minus A تطابق الصفر Modulo B
+
+163
+00:16:04,630 --> 00:16:11,190
+Modulo B الان انت فيه عندك ال B مالها لا تطابق ال
+
+164
+00:16:11,190 --> 00:16:16,790
+A مدام ال B لا تطابق ال A يعني معناته ال B لا تقسم
+
+165
+00:16:16,790 --> 00:16:23,190
+ال B minus A مظبوط؟ما دام الـ B لا تطابق الـ A،
+
+166
+00:16:23,190 --> 00:16:25,730
+إذا الـ B minus A لا تطابق السفر، يعني الـ B لا
+
+167
+00:16:25,730 --> 00:16:29,990
+تقسم الـ B minus A، مظبوط؟ الـ B لا تقسم الـ B
+
+168
+00:16:29,990 --> 00:16:33,250
+minus A طيب ما هي الـ B prime؟ ما دام الـ B لا
+
+169
+00:16:33,250 --> 00:16:35,650
+تقسم الـ B minus A، ده الـ greatest common divisor
+
+170
+00:16:35,650 --> 00:16:41,200
+بين الـ B و الـ B minus A، إيش مساوى؟ واحدما دام
+
+171
+00:16:41,200 --> 00:16:44,980
+هذه وهذه اللي هو العالم الشركي الأعلى بين الواحد
+
+172
+00:16:44,980 --> 00:16:51,500
+إذا بقدر أختصر هذه إذا بيصير عندي then اللي هو لـQ
+
+173
+00:16:51,500 --> 00:17:01,140
+of B تطابق الـ0 مضلمين مضلمين واضح؟ طيب إذا الآن
+
+174
+00:17:01,140 --> 00:17:07,620
+إيش اللي وصلنا له؟وصلنا إن الـ B عبارة عن solution
+
+175
+00:17:07,620 --> 00:17:14,520
+لمين لـ Q X تطابق الـ 0 مدل بيه؟ إيش اللي وصلنا؟
+
+176
+00:17:14,520 --> 00:17:20,240
+اللي وصلنا إلى ما هي ليه؟ إن أي solution أخدنا
+
+177
+00:17:20,240 --> 00:17:29,780
+إحنا بدأنا إن B أي solution للـ F X تطابق الـ 0
+
+178
+00:17:29,780 --> 00:17:36,640
+مدل بيه؟ووصلنا إن الـ B solution لمين لـ Q لـ Q of
+
+179
+00:17:36,640 --> 00:17:41,060
+X تطابق الـ 0 modulo B إذن اللي وصلنا له ما يالي
+
+180
+00:17:41,060 --> 00:17:46,720
+بعيد و أكرر إنه أي solution للـ F of X تطابق الـ 0
+
+181
+00:17:46,720 --> 00:17:54,900
+modulo B غير A بيعطيني إنه إنه هو solution لـ Q X
+
+182
+00:17:54,900 --> 00:18:01,140
+modulo B ماشي الحال ركز الآنالان Q of X درجتها
+
+183
+00:18:01,140 --> 00:18:08,620
+كده؟ K-1 و احنا
+
+184
+00:18:08,620 --> 00:18:14,000
+مفترضين من واحد ان النظرية الصحيحة لها يعني الـ Q
+
+185
+00:18:14,000 --> 00:18:21,090
+of X هزأت نص تقاش K-1 من ال solutionsالآن لاحظ هذا
+
+186
+00:18:21,090 --> 00:18:25,790
+على الأكتر فيه لـK-1 من ال solutions واحنا بنقول
+
+187
+00:18:25,790 --> 00:18:29,610
+أي solution ها لسolution ها يعني ماتحلمش أنه إيش
+
+188
+00:18:29,610 --> 00:18:34,630
+يكون مش solutions لهذه يكون solution لهذه إذا على
+
+189
+00:18:34,630 --> 00:18:38,910
+الأكتر على الأكتر غير هذه كده إيش لها solutions ال
+
+190
+00:18:38,910 --> 00:18:42,690
+solutions دول اللي هي K-1 وفي عندي واحد في الأصل
+
+191
+00:18:42,690 --> 00:18:47,750
+إذا على الأكتر إيش ماله F of X has at most K من ال
+
+192
+00:18:47,750 --> 00:18:53,640
+solutionsكمان مرة اللي قلته ما هي ليه أن أي
+
+193
+00:18:53,640 --> 00:18:59,040
+solution هنا غير الـA هيكون solution هنا هذه كل ال
+
+194
+00:18:59,040 --> 00:19:04,420
+solutions تبعتها K- واحد من ال solutions إذاً هذه
+
+195
+00:19:04,420 --> 00:19:10,280
+هيكون أكتر إشي لغير الـA برضه K- واحد من ال
+
+196
+00:19:10,280 --> 00:19:14,560
+solutions ليش؟ لأن مش solution هنا مش solution هنا
+
+197
+00:19:15,430 --> 00:19:19,650
+إذن الخيارات لهذه بس من ال solutions اللي ليانا
+
+198
+00:19:19,650 --> 00:19:24,330
+بالإضافة لل A إذا ال QF of X وطبقه Zero مدله B has
+
+199
+00:19:24,330 --> 00:19:28,550
+at most K minus واحد زائد واحد ويساوي K solutions
+
+200
+00:19:28,550 --> 00:19:33,150
+إذا النظرية سارت true for any N بتساوي K من كل
+
+201
+00:19:33,150 --> 00:19:38,130
+معمضة بيصير النظرية true for any N أكبر أو يساوي
+
+202
+00:19:38,130 --> 00:19:41,190
+واحد أي سؤال
+
+203
+00:19:51,790 --> 00:19:57,710
+باز إبراهيم باز
+
+204
+00:19:57,710 --> 00:19:58,590
+إبراهيم
+
+205
+00:20:26,370 --> 00:20:33,670
+معايا يا شباب عند B is prime وعندي
+
+206
+00:20:33,670 --> 00:20:40,070
+D بتقسم ال B minus واحد ال D بتقسم ال B minus واحد
+
+207
+00:20:40,070 --> 00:20:52,550
+then X to the D تطابق الواحد modulo B has exactly
+
+208
+00:21:02,650 --> 00:21:05,890
+معايا النظرية بتقول الميالي او الكورلر بتقول
+
+209
+00:21:05,890 --> 00:21:11,410
+الميالي اذا كانت بي برايم وكان دي قاسم من قاسم ال
+
+210
+00:21:11,410 --> 00:21:14,990
+بي ماينس واحد بيكون اكس تو دالي تطابق الواحد مدلوا
+
+211
+00:21:14,990 --> 00:21:19,530
+بي إلى بالظبط جدياش دي من ال incongruent solutions
+
+212
+00:21:20,860 --> 00:21:24,440
+لاحظوا احنا في الـ .. في الـ .. في الـ polynomials
+
+213
+00:21:24,440 --> 00:21:27,820
+اللي .. او في ال .. الـ congruences ال degree اللي
+
+214
+00:21:27,820 --> 00:21:33,240
+لها اتنين او اكثر احنا ماتطرقناش إلى الحلول الا في
+
+215
+00:21:33,240 --> 00:21:36,120
+حال .. الا في الحالة .. حالة الـ X سر بيها تطابق
+
+216
+00:21:36,120 --> 00:21:40,720
+ناقص واحد حالة الـ B على صورة 4K زي التلاتة،
+
+217
+00:21:40,720 --> 00:21:44,120
+مظبوط؟ وهي هذه الحالة التانية، لأن احنا ماتدخلناش
+
+218
+00:21:44,120 --> 00:21:47,400
+لشرطة تسعة اللي بتتكلم عن تفاصيل اللي هو الـ
+
+219
+00:21:47,400 --> 00:21:51,370
+quadratic congruencesالان هذه تطبيقات على النظريات
+
+220
+00:21:51,370 --> 00:21:58,270
+اللي احنا درسناها في الـ Chapter 8 و Chapter 7
+
+221
+00:21:58,270 --> 00:22:04,920
+سابقاً شوف الان دي is prime و دي تقسم الـP-1إذاً X
+
+222
+00:22:04,920 --> 00:22:08,600
+تطابق الواحد مضروبيها is exactly incongruent دي
+
+223
+00:22:08,600 --> 00:22:11,840
+incongruent solutions يعني مثال باخدلك مثال عددي
+
+224
+00:22:11,840 --> 00:22:17,460
+example لو جيت أخدت انت ال X أُس خمسة تطابق الواحد
+
+225
+00:22:17,460 --> 00:22:24,770
+مضلوا مثلا واحد وتلاتين زي ما هو باخدهاالآن هذه
+
+226
+00:22:24,770 --> 00:22:30,550
+فيها أكم solution بنقدر نعرف بناء على هذه
+
+227
+00:22:30,550 --> 00:22:34,810
+الكورولاري إيش الكورولاري بتقول الخمسة بناء أن
+
+228
+00:22:34,810 --> 00:22:37,270
+الخمسة بتكسب من الواحد و تلاتين مع صواعد هو
+
+229
+00:22:37,270 --> 00:22:43,610
+التلاتين then it has five incongruent solutions
+
+230
+00:22:43,610 --> 00:22:46,450
+five incongruent solutions بس هي المعلومة اللي
+
+231
+00:22:46,450 --> 00:22:48,770
+عندنا اللي بدنا نحكي فيها اللي بعده
+
+232
+00:22:56,630 --> 00:23:06,050
+النظرية و الـ Corollary بتقدي في برهان نظرية 8.6
+
+233
+00:23:06,050 --> 00:23:13,650
+التي بتقول أن if B is a prime and D تكسب B-1 then
+
+234
+00:23:13,650 --> 00:23:18,750
+there are exactly 5 of D incongruent integers have
+
+235
+00:23:18,750 --> 00:23:21,850
+ordered D modulo B
+
+236
+00:23:31,120 --> 00:23:43,080
+النظرية تقول معيالي theorem if B is prime وD تقسم
+
+237
+00:23:43,080 --> 00:23:50,100
+ال B-1 وD تقسم ال B-1
+
+238
+00:23:50,100 --> 00:24:03,520
+معيا وD تقسم ال B-1 then they areأو تقريبًا فاي اف
+
+239
+00:24:03,520 --> 00:24:14,000
+دي فاي اف دي غير متجر غير متجر غير متجر غير متجر
+
+240
+00:24:14,000 --> 00:24:15,780
+غير متجر غير متجر غير متجر غير متجر غير متجر غير
+
+241
+00:24:15,780 --> 00:24:21,180
+متجر غير متجر غير متجر
+
+242
+00:24:28,480 --> 00:24:31,280
+بتقول لو كانت عندي بي برايم و D بتكسيب ال بي و
+
+243
+00:24:31,280 --> 00:24:37,240
+ماينس واحد بقول في عندي بالظبط five of D من ال
+
+244
+00:24:37,240 --> 00:24:42,360
+incongruent integers having order A شماله D modulo
+
+245
+00:24:42,360 --> 00:24:46,060
+B الأن
+
+246
+00:24:46,060 --> 00:24:53,480
+example find
+
+247
+00:24:53,480 --> 00:24:57,160
+the
+
+248
+00:24:57,160 --> 00:24:57,640
+number
+
+249
+00:25:02,470 --> 00:25:09,130
+of incongruent integers
+
+250
+00:25:09,130 --> 00:25:24,390
+having واحد اللي هو order two modulo اللي هو مثلا
+
+251
+00:25:24,390 --> 00:25:39,470
+سبعة اتنين orderthree modulo سبعة ثلاثة order ستة
+
+252
+00:25:39,470 --> 00:25:47,130
+modulo سبعة حسب
+
+253
+00:25:47,130 --> 00:25:55,960
+اللي هي النظرية عندي اللي هو ال بيه متساوي سبعةإذن
+
+254
+00:25:55,960 --> 00:26:00,920
+أكيد اللي هو الـ 2 بيقسم الـ B-1 الـ 6 إذا الـ 2
+
+255
+00:26:00,920 --> 00:26:04,960
+بتقسم ال 6 طبعا انا اختارتهم اللي هو الـ 2 بتقسم
+
+256
+00:26:04,960 --> 00:26:11,520
+ال 6 و 3 بتقسم ال 6 و 6 بتقسم ال 6 إذا الجواب
+
+257
+00:26:11,520 --> 00:26:18,890
+اللي هو أشمالهأيش بيساوي حسب النظرية فايل of mean
+
+258
+00:26:18,890 --> 00:26:23,250
+دي دي ايش بتساوي اتنين فايل اتنين ايش بتساوي واحد
+
+259
+00:26:23,250 --> 00:26:29,770
+اذا في عندي بس one integer اللي هو ال order له
+
+260
+00:26:29,770 --> 00:26:33,950
+يعني في a واحد there exist a واحد such that ال
+
+261
+00:26:33,950 --> 00:26:41,170
+order لل a واحد modulo سبعة بيساوي قداش اتنين في
+
+262
+00:26:41,170 --> 00:26:47,460
+واحد بسالأن ال order له تلاتة modulo سبعة اللي هو
+
+263
+00:26:47,460 --> 00:26:52,880
+جدش بيكون five of تلاتة اللي هو جدش بيساوي اتنين
+
+264
+00:26:52,880 --> 00:26:58,120
+يعني there exist a واحد و a اتنين incongruent غير
+
+265
+00:26:58,120 --> 00:27:03,380
+متطابقين modulo سبعة such that ال order لل a واحد
+
+266
+00:27:03,380 --> 00:27:10,850
+بيساوي ال order لل a اتنين بيساوي جدش تلاتةمدلوا
+
+267
+00:27:10,850 --> 00:27:16,170
+مين طبعا مدلوا سبعة فاهمين علي ايش بقول الان ها
+
+268
+00:27:16,170 --> 00:27:22,110
+انا جدش فيه اللي هو في عندي five of ستة اللي هو
+
+269
+00:27:22,110 --> 00:27:28,150
+برضه جداش اتنينأتنين من الـ incongruent solutions
+
+270
+00:27:28,150 --> 00:27:35,650
+يعني من الـ incongruent integers احد لايطابق اتنين
+
+271
+00:27:35,650 --> 00:27:41,510
+modulo بي أو modulo سبعة فاهمين such that ال order
+
+272
+00:27:41,510 --> 00:27:47,070
+للأحد modulo سبعة بسوء ال order للأتنين modulo
+
+273
+00:27:47,070 --> 00:27:49,950
+سبعة بسوء قداش ستة
+
+274
+00:27:52,590 --> 00:27:58,230
+طيب نيجي لا اللي هو مثال اللي بيعطينا إياه بقول
+
+275
+00:27:58,230 --> 00:28:01,690
+find the number of incongruent integers having
+
+276
+00:28:01,690 --> 00:28:05,790
+order خمسة مدن ومين مدن واحد تلاتين من نفس الطريقة
+
+277
+00:28:05,790 --> 00:28:10,960
+الخمسة بتكسب تلاتينذن في عند ال order اللي هو قداش
+
+278
+00:28:10,960 --> 00:28:15,500
+عدد العناصر لل orderها خمسة مضلوا واحد و تلاتين
+
+279
+00:28:15,500 --> 00:28:18,840
+اللي هو five خمسة مش بيساوي بيساوي أربعة يعني في
+
+280
+00:28:18,840 --> 00:28:23,040
+أربع عدد ا واحد و اتنين و اتلت او اربعة بقيت ان ال
+
+281
+00:28:23,040 --> 00:28:27,780
+order لكل واحد مضلوا واحد و تلاتين يساوي أربعة
+
+282
+00:28:27,780 --> 00:28:36,360
+يساوي خمسة آسف كونوا لغايةالآن بناءً على اللي هو
+
+283
+00:28:36,360 --> 00:28:40,840
+النظرية اللي هي اللي عندي اللي فوق هذه الـ
+
+284
+00:28:40,840 --> 00:28:47,760
+Corollary بتعددلي بالظبط لـ Primitive Roots اما هو
+
+285
+00:28:47,760 --> 00:28:52,840
+الـ Primitive Roots هو عبارة عن عدد order بسوء 5
+
+286
+00:28:52,840 --> 00:28:59,100
+of B الـ B-1 الـ
+
+287
+00:28:59,100 --> 00:29:05,330
+R بيكون Primitive Rootsمدل و N إذا كان order ال R
+
+288
+00:29:05,330 --> 00:29:10,290
+مدل و N بيساوي Phi of N ماشي الحالة إذا اللي حالة
+
+289
+00:29:10,290 --> 00:29:14,450
+خاصة من مين من النظرية اللي فوق إذا بتقولك بالظبط
+
+290
+00:29:14,450 --> 00:29:18,370
+if B is a prime then there are exactly إيش ماله
+
+291
+00:29:18,370 --> 00:29:25,430
+Phi of B minus واحد incongruent primitive roots of
+
+292
+00:29:25,430 --> 00:29:31,170
+مين؟ of Bواضح على طول إذن اللي هي B-1 بتقسم الـ B
+
+293
+00:29:31,170 --> 00:29:35,750
+-1 إذا فيها Default of B-1 من ال integers اللي
+
+294
+00:29:35,750 --> 00:29:55,510
+orderedها B-1 واضح خليني أقولها نضحها بشكل نقول
+
+295
+00:29:55,510 --> 00:29:56,110
+corollary
+
+296
+00:30:05,170 --> 00:30:17,130
+إذا كان بي برامج فهناك
+
+297
+00:30:17,130 --> 00:30:27,790
+تقريبًا فاي اف بي ماينس واحد ساوي فاي اف فاي اف بي
+
+298
+00:30:37,520 --> 00:30:42,160
+primitive roots of
+
+299
+00:30:42,160 --> 00:30:50,780
+B من وين جبناها دي الان في النظرية اللي جابلها من
+
+300
+00:30:50,780 --> 00:30:53,680
+النظرية اللي جابلها بما ان الـ B minus واحد اللي
+
+301
+00:30:53,680 --> 00:30:57,460
+هو D بيكون الـ B minus واحد اللي هي D في هذه
+
+302
+00:30:57,460 --> 00:31:00,820
+الحالة B minus واحد تكسب الـ B minus واحد إذا في
+
+303
+00:31:00,820 --> 00:31:06,730
+عندياللي هو Phi of B minus واحد من ال integers
+
+304
+00:31:06,730 --> 00:31:10,810
+اللي incongruent اللي orderedها بساوي B minus واحد
+
+305
+00:31:10,810 --> 00:31:15,350
+يعني اللي orderedها بساوي Phi of B يعني صار في
+
+306
+00:31:15,350 --> 00:31:20,710
+عندي Phi of B minus واحد من ال primitive roots لأن
+
+307
+00:31:20,710 --> 00:31:26,290
+اللي هو اللي orderedه بساوي Phi of B هو عبارة عن
+
+308
+00:31:26,290 --> 00:31:28,490
+مين ال primitive root
+
+309
+00:31:30,220 --> 00:31:34,020
+إذا صار عندي Phi of B minus واحد من ال primitive
+
+310
+00:31:34,020 --> 00:31:41,960
+roots وإيه شمالهم كلهم in congruent modulo B أي
+
+311
+00:31:41,960 --> 00:31:50,540
+سؤال نجي لمثالنا أخد مثال اللي هو find the number
+
+312
+00:31:50,540 --> 00:31:54,700
+of primitive roots find the number of primitive
+
+313
+00:31:54,700 --> 00:32:00,560
+roots of الواحد وتلاتينThe number of primitive
+
+314
+00:32:00,560 --> 00:32:06,840
+roots للـ 31 هي 5 من 100 من 30 5 من 30 أشهر تطلع
+
+315
+00:32:06,840 --> 00:32:10,840
+لتساوية تمانية إذا في عندي تمانية من ال
+
+316
+00:32:10,840 --> 00:32:19,240
+incongruent ال primitive roots of 31 أي سؤال؟
+
+317
+00:32:19,240 --> 00:32:23,780
+اطلعينا على الأسئلة خليني أحللكم نجينا السؤال
+
+318
+00:32:23,780 --> 00:32:33,960
+الأول if B then of the primeسؤال أول ايه؟ be an
+
+319
+00:32:33,960 --> 00:32:39,200
+odd prime
+
+320
+00:32:39,200 --> 00:32:44,940
+then the only incongruent solutions of x تربيع
+
+321
+00:32:44,940 --> 00:32:52,140
+find all incongruent
+
+322
+00:32:52,140 --> 00:32:55,440
+solutions
+
+323
+00:32:56,800 --> 00:33:08,780
+of x تربية تطابق الواحد modulo b proof بيقول
+
+324
+00:33:08,780 --> 00:33:13,980
+لي بي إذا نقدّهاش إبراهيم بيقول لي أودد كل ال
+
+325
+00:33:13,980 --> 00:33:20,260
+solutions لل x تربية تطابق الواحد مدلو مين مدلو بي
+
+326
+00:33:20,260 --> 00:33:25,430
+معايالأن P is odd prime مدان P is odd prime إذا
+
+327
+00:33:25,430 --> 00:33:36,210
+أكيد since P is odd then الاتنين تقسم ال P minus
+
+328
+00:33:36,210 --> 00:33:42,610
+واحد لأن ال P minus واحد صارت even then
+
+329
+00:33:42,610 --> 00:33:51,550
+by كرولر اللي جاب اللي بشوية X تربيعتطابق الواحد
+
+330
+00:33:51,550 --> 00:34:01,310
+مضلوا بي has exactly .. كده ايش؟ two solutions
+
+331
+00:34:01,310 --> 00:34:10,650
+طبعاً incongruent معايا؟
+
+332
+00:34:10,650 --> 00:34:15,590
+لأنه .. لأنه بتقسم الـ P minus واحد إذن هذه اللي
+
+333
+00:34:15,590 --> 00:34:22,590
+هي exactly two solutions واضحإن الواحد since
+
+334
+00:34:22,590 --> 00:34:29,370
+الواحد تربيعي وطابق الواحد model of B then واحد is
+
+335
+00:34:29,370 --> 00:34:36,690
+a solution ماشي دائما
+
+336
+00:34:36,690 --> 00:34:40,250
+أبحث عن solutions من عند الواحد لعند ال B- واحد
+
+337
+00:34:40,250 --> 00:34:43,190
+لأن اللي بعد هي انك لو بديكون solutions بديكون
+
+338
+00:34:43,190 --> 00:34:47,490
+congruent للأولانيات لأن الواحد لعند ال B- واحد is
+
+339
+00:34:47,490 --> 00:34:51,260
+a complete residue systemعند الـ B حتى if I
+
+340
+00:34:51,260 --> 00:34:55,340
+complete residue system فاهمين؟ أي شيء براهن
+
+341
+00:34:55,340 --> 00:35:00,840
+مايكون أشمال وزاية اللي جوا إذا واحد تربيع تطرق
+
+342
+00:35:00,840 --> 00:35:04,120
+الواحد مدنه بيه الآن برضه لو جيت لل بيه ماينس واحد
+
+343
+00:35:04,120 --> 00:35:09,560
+لكل تربيع إيش هيساوي؟ اللي هو بيه تربيع ناقص اتنين
+
+344
+00:35:09,560 --> 00:35:16,400
+بيه زاد واحد مدنه بيه هذا سفر وهذا سفر إذا إيش هذا
+
+345
+00:35:16,400 --> 00:35:22,930
+بطابق؟ الواحد مدنهب فاهمين إذا صراحة دي X تربيع
+
+346
+00:35:22,930 --> 00:35:26,430
+تطابق الواحد مضله بي في حالة ال X ايش بتساوي بي
+
+347
+00:35:26,430 --> 00:35:35,530
+minus واحد إذا since كذا thenB-1 is the another
+
+348
+00:35:35,530 --> 00:35:40,630
+solution و أنا مرتاح أصلا عارف أن الـ B-1 أشمال A
+
+349
+00:35:40,630 --> 00:35:45,750
+لاتطابق من الـ 1 لأن هما عبارة عن عناصر من عناصر
+
+350
+00:35:45,750 --> 00:35:48,930
+الـ Complete Residue System Modulo B وهي أنصرين في
+
+351
+00:35:48,930 --> 00:35:51,370
+الـ Complete Residue System Modulo B أشمال الـ R
+
+352
+00:35:51,370 --> 00:35:55,410
+Incongruent و معروف أن الـ B-1 لاتطابق الـ 1
+
+353
+00:35:55,410 --> 00:36:05,340
+Modulo B أي سؤال؟ طيبسؤال 6 نشوف ايش سؤال 6 بيقول
+
+354
+00:36:05,340 --> 00:36:19,640
+بيقوللي سؤال 6 if R is a primitive root
+
+355
+00:36:19,640 --> 00:36:28,960
+of the odd prime B approve A
+
+356
+00:36:31,080 --> 00:36:40,000
+Proof A بتساوي اللي هي The congruence A
+
+357
+00:36:40,000 --> 00:36:43,740
+to the B minus واحد على اتنين تطابق نقص واحد
+
+358
+00:36:43,740 --> 00:36:49,020
+modulo B holds Proof
+
+359
+00:36:56,650 --> 00:37:01,130
+معايا يا شباب؟ طيب صلى على النبي عليه الصلاة
+
+360
+00:37:01,130 --> 00:37:07,030
+والسلام اللي هم بيقوللي R primitive root of B to
+
+361
+00:37:07,030 --> 00:37:10,890
+prove that the congruence R to the B minus واحد
+
+362
+00:37:10,890 --> 00:37:14,350
+على اتنين التطابق التطابق نقص واحد بدل بيه هولس
+
+363
+00:37:14,350 --> 00:37:20,150
+يعني تتحقق يعني صحيح شوفوا اول حاجة شو معناه R is
+
+364
+00:37:20,150 --> 00:37:25,520
+primitive root؟معناته الـ order للـ R modulo B
+
+365
+00:37:25,520 --> 00:37:34,660
+بساوة B-1 اللي هو 5B، مظبوط؟ يعني بمعنى أخر أنه ال
+
+366
+00:37:34,660 --> 00:37:39,620
+order زي ما قلنا للـ R modulo B بساوة B-1 هذا
+
+367
+00:37:39,620 --> 00:37:43,600
+معناته R the primitive root of B وهذا يعني شغلتين
+
+368
+00:37:43,600 --> 00:37:48,800
+الشغل الأول زي ما قلنا أن R to the B-1 تطابق
+
+369
+00:37:48,800 --> 00:37:56,630
+الواحد modulo Bوالشغل الثاني أن R أُس T لا يطابق
+
+370
+00:37:56,630 --> 00:38:03,070
+الواحد modulo B لكل T أكبر من ال .. أكبر يساوي
+
+371
+00:38:03,070 --> 00:38:14,050
+واحد و أصغر منين من ال B minus واحد واضح؟
+
+372
+00:38:14,050 --> 00:38:25,130
+وش هي أصغر R أُس Phi of Bأصغر اللي هو أُس بتخلّي R
+
+373
+00:38:25,130 --> 00:38:31,150
+أُس اللي هي اللي عندي K يطابق الواحد مضروبيه مافيش
+
+374
+00:38:31,150 --> 00:38:37,290
+ولا K قبلها خلّيني بتذكر اللي واحد بتستخدمه لأن
+
+375
+00:38:37,290 --> 00:38:46,210
+since R is a primitive root
+
+376
+00:38:46,210 --> 00:38:57,160
+of B thenR to the 5 of B يطابق الواحد modulo B
+
+377
+00:38:57,160 --> 00:39:03,460
+وهذا IE معناته أن R أقصى B minus واحد تطابق الواحد
+
+378
+00:39:03,460 --> 00:39:10,560
+modulo B معيش يا جماعة لكن B معطينيها إيه أشمالها
+
+379
+00:39:10,560 --> 00:39:15,820
+is an odd ببراية،
+
+380
+00:39:15,820 --> 00:39:23,140
+مظبوط؟ معطينيها B في السؤالB is an odd prime مدام
+
+381
+00:39:23,140 --> 00:39:28,960
+odd prime مدام B is an odd prime إذا الـ B-1 إيش
+
+382
+00:39:28,960 --> 00:39:36,800
+ماله is even ماشي مدام even إذا R B-1 ناقص واحد
+
+383
+00:39:36,800 --> 00:39:41,420
+تطابق السفر modulo B صارت اللي هي فرق بين المربعين
+
+384
+00:39:41,420 --> 00:39:48,710
+لأن هذا مربع كامل بيصير B-1 evenإذا بقدر أحللها
+
+385
+00:39:48,710 --> 00:39:56,110
+لفرق بين المربعين هذي تعني هذي و B odd بي minus
+
+386
+00:39:56,110 --> 00:40:00,790
+واحد evil إذا هذا صار فرق بين المربعين إذا بمعنى
+
+387
+00:40:00,790 --> 00:40:05,190
+آخر بقدر أقول R بي minus واحد على اتنين ناقص واحد
+
+388
+00:40:05,190 --> 00:40:10,870
+في R بي minus واحد على اتنين زائد واحد تطابق السفر
+
+389
+00:40:10,870 --> 00:40:19,290
+modulo B معاشر باباحللت هذا على فرق بين مربعين
+
+390
+00:40:19,290 --> 00:40:23,710
+مجلد
+
+391
+00:40:23,710 --> 00:40:28,110
+الواحد هنا r بي minus واحد ناقص واحد معايا يا شباب
+
+392
+00:40:28,110 --> 00:40:34,270
+إذا صار عندي الآن then ال بي هتجسم ال r بي minus
+
+393
+00:40:34,270 --> 00:40:39,490
+واحد على اتنين ناقص واحد في r بي minus واحد على
+
+394
+00:40:39,490 --> 00:40:43,630
+اتنين زائد واحد و ال بي is Zebral إذا يا بي بتجسم
+
+395
+00:40:43,630 --> 00:40:48,480
+الأولى و يا ابنى بتجسم الميال التانية thenand so
+
+396
+00:40:48,480 --> 00:40:59,100
+الـ R بتقسم الـ B بتقسم الـ R أُس B minus واحد على
+
+397
+00:40:59,100 --> 00:41:07,000
+اتنين ناقص واحد or الـ B بتقسم الـ R أُس B minus
+
+398
+00:41:07,000 --> 00:41:15,080
+واحد على اتنين زائد واحد، مظبوط؟ الآن هذه مستحيلة
+
+399
+00:41:15,950 --> 00:41:20,230
+ليش هذه مستحيلة؟ لأن هذه بتعني أن ر بي ماينوس واحد
+
+400
+00:41:20,230 --> 00:41:28,070
+على اتنين تطابق الواحد وهذا بناقض أن ال order للر
+
+401
+00:41:28,070 --> 00:41:32,250
+هو بي ماينوس واحد لأن ر is a primitive root إذن
+
+402
+00:41:32,250 --> 00:41:35,850
+هذه ليست واحدة إذن بتبقى هذه ما هو المطلوب كمان
+
+403
+00:41:35,850 --> 00:41:43,310
+مرة خليني أكتب هنا أكمل
+
+404
+00:41:43,310 --> 00:41:43,710
+فوق
+
+405
+00:41:47,240 --> 00:41:53,940
+هوضح اللي حكيته قبله شوية اذا صار عندي then اللي
+
+406
+00:41:53,940 --> 00:42:03,940
+هو ال R بي minus واحد ناقص واحد تطابق السفر modulo
+
+407
+00:42:03,940 --> 00:42:15,980
+B or R على اتنين R معايا او R بي ناقص واحد على
+
+408
+00:42:15,980 --> 00:42:24,970
+اتنينزائد واحد تطابق السفر modulo بي واضح IE وهذا
+
+409
+00:42:24,970 --> 00:42:29,570
+معنى أن R أقص بي minus واحد على اتنين تطابق الواحد
+
+410
+00:42:29,570 --> 00:42:35,890
+modulo بي or R أقص بي minus واحد على اتنين يطابق
+
+411
+00:42:35,890 --> 00:42:40,950
+الناقص واحد modulo مين modulo بي الأول هو مستحيل
+
+412
+00:42:40,950 --> 00:42:45,890
+هذا مستحيل
+
+413
+00:42:48,480 --> 00:42:56,120
+because ال order لل R modulo B بيساوي B minus واحد
+
+414
+00:42:56,120 --> 00:43:03,020
+وهذا أكبر من مين؟ أكبر من B ناقص واحد على اتنين
+
+415
+00:43:03,020 --> 00:43:09,460
+وهذا بناقض مين أنه مافيش ولا T بين ال B minus واحد
+
+416
+00:43:09,460 --> 00:43:15,240
+حيث أن R وت T تطابق ال واحد مدلوق إذا دل عندي مين
+
+417
+00:43:15,240 --> 00:43:17,000
+بس therefore
+
+418
+00:43:18,830 --> 00:43:28,470
+RB-1 على 2 تطابق الناقص 1 modulo B وهو المطلوب أي
+
+419
+00:43:28,470 --> 00:43:31,630
+سؤال؟
+
+420
+00:43:31,630 --> 00:43:40,610
+نجي الآن أنحل
+
+421
+00:43:40,610 --> 00:43:44,970
+B إذن
+
+422
+00:43:44,970 --> 00:43:49,470
+الله أثبتنا إنه لما كانت الـR primitive rootللـ B
+
+423
+00:43:49,470 --> 00:43:56,510
+فلعندي هذا التطابق أي شمالها صحيحة الان
+
+424
+00:43:56,510 --> 00:44:01,010
+بي بي
+
+425
+00:44:01,010 --> 00:44:07,750
+بي بتقولنا يلي بي
+
+426
+00:44:07,750 --> 00:44:18,010
+if R and R prime are primitive roots
+
+427
+00:44:18,980 --> 00:44:31,120
+of B then R' is not a primitive root
+
+428
+00:44:31,120 --> 00:44:34,340
+of
+
+429
+00:44:34,340 --> 00:44:41,340
+B غروف إذا
+
+430
+00:44:41,340 --> 00:44:46,730
+كانت B زي نقطة برايم إذا حاصل درباللي هو two
+
+431
+00:44:46,730 --> 00:44:52,190
+primitive roots اللي هي مش primitive root معايا يا
+
+432
+00:44:52,190 --> 00:44:58,410
+شباب ده نشوف كيف since
+
+433
+00:44:58,410 --> 00:45:08,490
+R and R' are primitive roots
+
+434
+00:45:08,490 --> 00:45:18,400
+of B then by A اللي أثبتناهااللي هو R أس بي ماينس
+
+435
+00:45:18,400 --> 00:45:26,320
+واحد على اتنين تطابق ناقص واحد modulo بي and R
+
+436
+00:45:26,320 --> 00:45:31,140
+prime أس بي ماينس واحد على اتنين برضه الشمالها
+
+437
+00:45:31,140 --> 00:45:39,460
+تطابق ناقص واحد modulo بي together دروبهم
+
+438
+00:45:39,460 --> 00:45:47,310
+مع بعضأضرب التلتين بيصير R في R' أُس P مالنس واحد
+
+439
+00:45:47,310 --> 00:45:51,650
+على اتنين تطابق الناقص واحد في الناقص واحد اللي هو
+
+440
+00:45:51,650 --> 00:46:04,410
+واحد modulo P إذا صار عندي but أو hence hence
+
+441
+00:46:05,590 --> 00:46:13,790
+هيكون الـ order للـ R فـ R' modulo B أصغر أو يساوي
+
+442
+00:46:13,790 --> 00:46:17,050
+B-1 على 2
+
+443
+00:46:20,710 --> 00:46:25,630
+وهذا طبعا strictly أصغر من مين من ال B-1 اللي هو
+
+444
+00:46:25,630 --> 00:46:31,410
+Phi of B-1 يعني صار ال order لل R في R' modulo B
+
+445
+00:46:31,410 --> 00:46:40,970
+لا يساوي ال Phi of B-1 وهذا يعني hence R في R' is
+
+446
+00:46:40,970 --> 00:46:43,770
+not a primitive
+
+447
+00:46:47,770 --> 00:47:00,650
+Root modulo of B is not primitive root of B و إلى
+
+448
+00:47:00,650 --> 00:47:01,810
+لقاء آخر
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BjST7SecAl4_postprocess.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BjST7SecAl4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..540797ed1137ad47266a3f34c0467f3f0e9cccfa
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BjST7SecAl4_postprocess.srt
@@ -0,0 +1,1780 @@
+1
+00:00:19,300 --> 00:00:24,480
+بسم الله الرحمن الرحيم المساق هو مساق نظرية
+
+2
+00:00:24,480 --> 00:00:31,640
+الإعداد number theory math 4342 ال course outline
+
+3
+00:00:31,640 --> 00:00:36,340
+textbook elementary number theory لديفيد بيرتون
+
+4
+00:00:36,340 --> 00:00:44,860
+اللي هو الطبعة السادسة ال
+
+5
+00:00:44,860 --> 00:00:49,770
+course outline هو عبارة عن التاليهنبدأ اللي هو في
+
+6
+00:00:49,770 --> 00:00:54,670
+الـDivision Algorithm خورزمية القسمة الـGreatest
+
+7
+00:00:54,670 --> 00:00:59,890
+Common Divisor الـEuclidean Algorithm الـEuclidean
+
+8
+00:00:59,890 --> 00:01:03,730
+Equation إحدى صور الـEuclidean Equation اللي
+
+9
+00:01:03,730 --> 00:01:09,050
+أمامنا هنحاول ناخد بعض حلولها هذا اللي هو الشبطر
+
+10
+00:01:09,050 --> 00:01:14,050
+الثاني في الكتاب هو من ثم الشبطر الثاني The
+
+11
+00:01:14,050 --> 00:01:17,510
+Fundamental Theorem of ArithmeticSum of properties
+
+12
+00:01:17,510 --> 00:01:22,490
+of a prime numbers والشبطر الثالث هو عبارة عن
+
+13
+00:01:22,490 --> 00:01:27,850
+يتحدث عن الـ primes بعض أو يتحدث عن ال
+
+14
+00:01:27,850 --> 00:01:31,410
+concurrences والتطابقات ال binary and decimal
+
+15
+00:01:31,410 --> 00:01:35,450
+representations of integers اللي بتقودنا لنظام
+
+16
+00:01:35,450 --> 00:01:41,320
+العد الثنائي ونظام العد العشري المعروفينالنظرية
+
+17
+00:01:41,320 --> 00:01:43,760
+المشهورة Linear Concurrences and Chinese Remainder
+
+18
+00:01:43,760 --> 00:01:45,900
+Theorem الناظرية المشهورة Chinese Remainder
+
+19
+00:01:45,900 --> 00:01:54,000
+Theorem هنتحدث عنها خلال الشبطر الرابع ويكون عندنا
+
+20
+00:01:54,000 --> 00:01:57,400
+ال first exam بعد اللي هو شبطر اتنين وشبطر تلاتة
+
+21
+00:01:57,400 --> 00:02:03,260
+وشبطر اربعة من ثم اللي هو هنصل لشبطر خمسة ل
+
+22
+00:02:03,260 --> 00:02:08,020
+Fermat's Little Theorem أو بسيدو برايمز وويلسونز
+
+23
+00:02:08,020 --> 00:02:13,960
+Theoremالشبتر السادس اللي هو the sum and number of
+
+24
+00:02:13,960 --> 00:02:23,460
+divisors مجموع وأعداد القواسم للعدد الصحيح ومن ثم
+
+25
+00:02:23,460 --> 00:02:26,560
+هناخد formula تخدم الموضوع اللي هو Mobius
+
+26
+00:02:26,560 --> 00:02:33,960
+inversion formula وبقول أن هنا الشبتر السادس ومن
+
+27
+00:02:33,960 --> 00:02:38,200
+ثم الشبتر السابع اللي هنتحدث عن الalors phi
+
+28
+00:02:38,200 --> 00:02:45,760
+functionوعن خواصها و هنتحدث عن Euler's theorem ال
+
+29
+00:02:45,760 --> 00:02:49,580
+second exam بيكون بعد ال chapter الخامس والسادس
+
+30
+00:02:49,580 --> 00:02:56,560
+والسابع و من ثم اللي هو هنتحدث عن ال perfect
+
+31
+00:02:56,560 --> 00:03:05,940
+numbers عن المرسيني برايمز و عن فيرمات number و عن
+
+32
+00:03:05,940 --> 00:03:12,630
+خواص هذه الاعداد في حينه ان شاء اللهالشبتر الثامن
+
+33
+00:03:12,630 --> 00:03:17,870
+اللي هو هنتحدث عن ال primitive roots أو مقدمة عن
+
+34
+00:03:17,870 --> 00:03:20,730
+ال primitive roots هناخد في البداية ال order of n
+
+35
+00:03:20,730 --> 00:03:25,610
+integer modulo n ونتحدث عن ال primitive roots of
+
+36
+00:03:25,610 --> 00:03:31,950
+our primes ومن ثم نتحدث إذا سمح الوقت عن مقدمة في
+
+37
+00:03:31,950 --> 00:03:36,260
+علم التشفيروبكون في عندي الآن في النهاية ال final
+
+38
+00:03:36,260 --> 00:03:41,800
+exam إذا ال grading هيكون معتمد على شغلتين عندنا
+
+39
+00:03:41,800 --> 00:03:47,200
+الشغلة الأولى اللي هو two hour exams خمسين في
+
+40
+00:03:47,200 --> 00:03:51,700
+المية وعلى طريقة الحصفة ان شاء الله بنتفج و ال
+
+41
+00:03:51,700 --> 00:03:57,330
+final خمسين في الميةاللي هيكون فيه انه homeworks
+
+42
+00:03:57,330 --> 00:04:01,190
+ال homeworks طبعا هعطيكم homeworks تحلوها في البيت
+
+43
+00:04:01,190 --> 00:04:05,050
+و الأسئلة اللي بتعرفوش تحلوها بتيجوا انها ان شاء
+
+44
+00:04:05,050 --> 00:04:09,510
+الله بنعمل discussion و بنحل هذه الأسئلة اي سؤال
+
+45
+00:04:09,510 --> 00:04:17,050
+اي استفسار حول ما تحدثنا به حول ال course outline
+
+46
+00:04:17,050 --> 00:04:23,570
+او خطة المساقة اه بصين طيب
+
+47
+00:04:26,180 --> 00:04:30,780
+الصلاة على النبي عليه الصلاة والسلام هنبدأ اليوم
+
+48
+00:04:30,780 --> 00:04:39,740
+إن شاء الله في المحاضرة الأولى في نظرية الأعداد أو
+
+49
+00:04:39,740 --> 00:04:44,040
+في مسافة نظرية الأعداد في قسم الرياضيات بالجامعة
+
+50
+00:04:44,040 --> 00:04:51,300
+الإسلامية هنبدأ حسب ال course outline اللي اتحدثنا
+
+51
+00:04:51,300 --> 00:04:59,420
+فيها قبل قليلالشبتر التاني بذوه عنوان Divisibility
+
+52
+00:04:59,420 --> 00:05:03,120
+Theory in the Integers فارساله عن النبي عليه
+
+53
+00:05:03,120 --> 00:05:06,080
+الصلاة والسلام الشبتر التاني Divisibility Theory
+
+54
+00:05:06,080 --> 00:05:11,660
+in the Integers أو نظرية القسمة على الأعداب
+
+55
+00:05:11,660 --> 00:05:16,520
+الصحيحةالـ section الثاني 222 the division
+
+56
+00:05:16,520 --> 00:05:19,400
+algorithm الـ section الأول عبارة عن مقدمة الـ
+
+57
+00:05:19,400 --> 00:05:22,820
+section الثاني the division algorithm أو خوارزمية
+
+58
+00:05:22,820 --> 00:05:27,440
+القسمة خوارزمية القسمة هنبدأ الآن ان شاء الله في
+
+59
+00:05:27,440 --> 00:05:31,920
+أول نظرية في هذا ال section وفي هذا ال course اللي
+
+60
+00:05:31,920 --> 00:05:38,320
+هي تتحدث عن خوارزمية القسمة باختصار ما تتحدث به
+
+61
+00:05:38,320 --> 00:05:44,190
+النظريةلو كان في عندي given integers a و b و b
+
+62
+00:05:44,190 --> 00:05:49,950
+أكبر من 0 عندي أي عددين صحيحين a و b و ال b أكبر
+
+63
+00:05:49,950 --> 00:05:54,870
+من 0 ال b طبعا غطى اللي يساوي سفر بدنا ناخد الحالة
+
+64
+00:05:54,870 --> 00:05:57,950
+الان بي أكبر من سفر و بعد شوية هيكون أصغر من سفر
+
+65
+00:05:57,950 --> 00:06:02,330
+في نظرية أخرى هتكون corollary لها أما الآن هنتحدث
+
+66
+00:06:02,330 --> 00:06:06,990
+عن هذا هيكون بمثابة المقسوم عليه الآن باختصار
+
+67
+00:06:06,990 --> 00:06:11,400
+النظرية بتقولك لو كان في عندي aوB integers ودينا
+
+68
+00:06:11,400 --> 00:06:17,680
+قولنا A على B هيطلع ناتج للقسمة ومتبقي هذا المتبقي
+
+69
+00:06:17,680 --> 00:06:21,360
+وهذا الناتج لو أنا قسمته وانت قسمته وهو قسمته
+
+70
+00:06:21,360 --> 00:06:26,140
+هيطلع اللي هو ناتج القسمة واحد والمتوقع واحد في
+
+71
+00:06:26,140 --> 00:06:31,060
+ضوء انه ناتج القسم اللي هو المتبقي R بين الـ0 و
+
+72
+00:06:31,060 --> 00:06:34,720
+بين الـB هذه هي النظرية باختصار نيجي الآن للتفاصيل
+
+73
+00:06:34,720 --> 00:06:39,910
+given integers A and B with B أكبر من 0There exist
+
+74
+00:06:39,910 --> 00:06:45,830
+unique integers Q and R satisfying A بساوية B في Q
+
+75
+00:06:45,830 --> 00:06:50,490
+زاية R حيث R أكبر بساوية سفر وأصغر من مين من B
+
+76
+00:06:50,490 --> 00:06:57,350
+الان الـ Q هو عبارة عن ناتج القسمة والـ R هو عبارة
+
+77
+00:06:57,350 --> 00:07:05,030
+عن المتبقيإذا الانتجار Q وR يُسمى بالتعريف الـ
+
+78
+00:07:05,030 --> 00:07:10,190
+quotient و الـ remainder في الـ division of A بـ B
+
+79
+00:07:10,190 --> 00:07:15,570
+للتذكير
+
+80
+00:07:16,930 --> 00:07:19,850
+الشبطر التاني divisibility theory in the integers
+
+81
+00:07:19,850 --> 00:07:26,270
+أو نظرية القسمة في الأعداد الصحيحة أو للأعداد
+
+82
+00:07:26,270 --> 00:07:29,190
+الصحيحة ال section اللي بدأنا فيه اللي هو the
+
+83
+00:07:29,190 --> 00:07:32,470
+division algorithm خارزمية القسمةالنظرية اللي
+
+84
+00:07:32,470 --> 00:07:35,570
+بدأنا فيها اللي هي division algorithm لو كان في
+
+85
+00:07:35,570 --> 00:07:40,450
+عندي أي two integers a و b وكان b أكبر من 0 و
+
+86
+00:07:40,450 --> 00:07:45,170
+أردنا نقسم نقول a على b لما نقسم a على b معناته
+
+87
+00:07:45,170 --> 00:07:49,930
+هيكون في عندي ناتج قسمة ومتبقى قسمة الناتج هيكون
+
+88
+00:07:49,930 --> 00:07:56,350
+وحيد والمتبقى وحيدقلنا إنه هيكون الـ A هتصير على
+
+89
+00:07:56,350 --> 00:08:00,950
+صورة Q بـ B زائد R حيث الـ R أكبر سواء 0 وأصغر من
+
+90
+00:08:00,950 --> 00:08:05,390
+B هذا المتبقي من القسمة و الـ Q اللي هو ناتج
+
+91
+00:08:05,390 --> 00:08:11,710
+القسمة و Q and R اللي هما هم إنتجارات مختلفة The
+
+92
+00:08:11,710 --> 00:08:15,850
+first one Q is called the quotient The second one
+
+93
+00:08:15,850 --> 00:08:21,270
+R is called the remainder in the division of A by
+
+94
+00:08:21,270 --> 00:08:28,740
+Bلان نجي لبرهان النظرية برهان النظرية هستقل برهان
+
+95
+00:08:28,740 --> 00:08:36,220
+من المعطيات أو المطلوب من النظرية الان عندي اللي
+
+96
+00:08:36,220 --> 00:08:45,380
+هو A بتساوي Q في B زائد R عندي R اللي هو المتبقى
+
+97
+00:08:45,380 --> 00:08:53,500
+من القسمة بتساوي A ناقص Q في Bالآن بدي أكوّن set
+
+98
+00:08:53,500 --> 00:08:58,720
+هذه ال set هي المنطلق للوصول إلى النتيجة ال set
+
+99
+00:08:58,720 --> 00:09:07,940
+بتساوي عبارة عن كل الأعداد اللي عصورت a ناقص x في
+
+100
+00:09:07,940 --> 00:09:18,880
+b حيث ال x عبارة عن integer element in zوالعدد a-x
+
+101
+00:09:18,880 --> 00:09:25,440
+بb هيكون أكبر أو يساوي سفر طبعا أنا مطمعا ال a و
+
+102
+00:09:25,440 --> 00:09:30,740
+ال b و المتغير x فانا بدي أسي عبارة عن كل الأعداد
+
+103
+00:09:30,740 --> 00:09:37,420
+الممكنة اللي عصورة a-x بb حيث x في z و a-x بb أكبر
+
+104
+00:09:37,420 --> 00:09:41,980
+أو يساوي إياش أكبر أو يساوي سفر الآن بدي أثبتلك
+
+105
+00:09:41,980 --> 00:09:44,080
+شغلتين
+
+106
+00:09:45,290 --> 00:09:50,350
+الشغلة الأولى أن S is non-empty الشغلة الثانية
+
+107
+00:09:50,350 --> 00:09:55,550
+اللى هي واضحة أن الأعداد اللى بتتكون منها S اللى
+
+108
+00:09:55,550 --> 00:10:00,010
+هي A نقص 6B ماخدها A شمالها أكبر أو يساوي سفر يعني
+
+109
+00:10:00,010 --> 00:10:06,630
+بمعنى آخر S حصل عبارة عن non-empty set of non
+
+110
+00:10:06,630 --> 00:10:10,790
+-negative integersإذا حسب الـ Will Ordering
+
+111
+00:10:10,790 --> 00:10:13,890
+Principle إيش الـ Will Ordering Principle بتقول
+
+112
+00:10:13,890 --> 00:10:20,790
+أنه any non-empty set of non-negative integers has
+
+113
+00:10:20,790 --> 00:10:27,290
+a least element معايا؟ إذا .. إذا ال .. ال .. ال
+
+114
+00:10:27,290 --> 00:10:30,680
+Will Ordering Principle أخدناها في المبادئبتقول
+
+115
+00:10:30,680 --> 00:10:37,320
+كما يالي إنه أي مجموعة جزئية من الأعداد الصحيحة
+
+116
+00:10:37,320 --> 00:10:43,380
+الغير سالبة دائما لها عنصر أقل اللي هو بنسميه إيش
+
+117
+00:10:43,380 --> 00:10:47,760
+ماله least element اللي هو لو وصلت للأس إنه non
+
+118
+00:10:47,760 --> 00:10:49,760
+-intersect of positive of non-negative integers
+
+119
+00:10:49,760 --> 00:10:53,140
+معناته وصلت إنها إيش مالها إلها least element ال
+
+120
+00:10:53,140 --> 00:10:56,640
+least element أنا بتدعي اللي هو اللي على الصورة
+
+121
+00:10:56,640 --> 00:11:02,230
+هذه ده سميه Rفبتكون R هي هذه الـ R اللي إحنا بدنا
+
+122
+00:11:02,230 --> 00:11:06,710
+إياها وفي نفس الوقت قيمة X المقابلة هي الـ Q
+
+123
+00:11:06,710 --> 00:11:11,250
+المطلوبة وحنثبت لكم إن الـ R و الـ Q إيه شمالهم؟
+
+124
+00:11:11,250 --> 00:11:17,210
+واحدات نيجي الآن، اتوكل على الله، شوفوا عند الآن
+
+125
+00:11:17,210 --> 00:11:21,130
+consider the set S بتساوي A نقص X بي X limited Z A
+
+126
+00:11:21,130 --> 00:11:25,690
+minus X بيه أكبر أو يساوي سفرواضح إنها عبارة عن
+
+127
+00:11:25,690 --> 00:11:29,090
+set of positive integers أو non-negative integers
+
+128
+00:11:29,090 --> 00:11:39,510
+إذن S is a set of non-negative integers هذي الأول
+
+129
+00:11:39,510 --> 00:11:44,710
+لأن اتنين بيدثبتلك إن S non-empty يعني بيدجيب لك
+
+130
+00:11:44,710 --> 00:11:50,440
+concrete exampleبقيمة X بحيث يكون A-X في B و A
+
+131
+00:11:50,440 --> 00:11:57,480
+موجود فاس يعني أكبر يساوي إيهاش؟ سفر شوف عندي عندي
+
+132
+00:11:57,480 --> 00:12:04,600
+أنا معطيني في النظرية أن الـB أشماله أكبر من سفر و
+
+133
+00:12:04,600 --> 00:12:10,020
+B integer مزام أكبر من سفر إذا حيكون الـB عند نفسه
+
+134
+00:12:10,020 --> 00:12:16,020
+أشماله أكبر أو يساوي واحدصح ولا لأ؟ إذا من واحد
+
+135
+00:12:16,020 --> 00:12:21,240
+وطالع طيب اضربن الجهتين في ال absolute value للـA
+
+136
+00:12:21,240 --> 00:12:26,580
+في بصير ال absolute value للـA في ال B أكبر أو
+
+137
+00:12:26,580 --> 00:12:31,180
+يساوي ال absolute value لمين؟ مصبوط ولا لا؟ أكيد
+
+138
+00:12:31,180 --> 00:12:38,330
+صح طيبالان ضيف للجهتين a فبصير a زي ال absolute
+
+139
+00:12:38,330 --> 00:12:42,010
+value لل a أكبر أو ساوي ال absolute value لل a زي
+
+140
+00:12:42,010 --> 00:12:47,630
+المين زي ال a لاحظ الان ال absolute value لل a لها
+
+141
+00:12:47,630 --> 00:12:54,860
+حلقتين يا a موجبةY سالبة في حالة الـ A مُجّبة الـ
+
+142
+00:12:54,860 --> 00:12:58,900
+absolute value لـ A هي الـ A فبصير A زياد A اتنين
+
+143
+00:12:58,900 --> 00:13:04,000
+A أكيد أكبر أو يساوي إيهاش سفر طيب في حالة الـ A
+
+144
+00:13:04,000 --> 00:13:07,500
+سالبة بصير ال absolute value لـ A مقصه يعني أنه
+
+145
+00:13:07,500 --> 00:13:11,780
+مقص A زياد A مش بيساوي سفر إذا في كل الأحوال هيكون
+
+146
+00:13:11,780 --> 00:13:17,200
+هذا المقدار أكبر أو يساوي إيهاش سفرإذا الأن لو أنت
+
+147
+00:13:17,200 --> 00:13:22,380
+أخدت ال X هذا هو مين هذا نفسه عبارة عن A ناقص ال
+
+148
+00:13:22,380 --> 00:13:27,420
+absolute value ل A بالسالب في B مظبوط؟ هذا أكبر أو
+
+149
+00:13:27,420 --> 00:13:33,220
+ساوي سفر ال X خدها هذه و integer هذا فبصير عندي
+
+150
+00:13:33,220 --> 00:13:37,460
+حسب الحكي اللي هنا أن هذا المقدار و ال A بين دي
+
+151
+00:13:37,460 --> 00:13:41,520
+طبعا إذا صار عندي هذا المقدار موجود في S إذا صارت
+
+152
+00:13:41,520 --> 00:13:49,010
+Sلا تساوي فاهم من الجهتين صار في عندي S is a non
+
+153
+00:13:49,010 --> 00:13:53,010
+-empty set of non-negative integers معناه يا بابا
+
+154
+00:13:53,010 --> 00:13:59,030
+ويحيى فاهم اه ايه السؤال طيب صار عندنا S is a non
+
+155
+00:13:59,030 --> 00:14:03,050
+-empty set of positive integers او non-negative
+
+156
+00:14:03,050 --> 00:14:14,410
+integers اذا S اذا S has a least elementCall it
+
+157
+00:14:14,410 --> 00:14:21,750
+سمّيه R مش الحال اثبتنا انه خلاص R موجود لان R كيف
+
+158
+00:14:21,750 --> 00:14:28,030
+صورته؟ R بساوي A نقص X في B هذا اللي نجيته انا
+
+159
+00:14:28,030 --> 00:14:33,010
+اللي وجدته سمي ال X المقابلة إيه وإيش اسمها؟ Q
+
+160
+00:14:33,010 --> 00:14:38,470
+أكيد هذا من التعريف اللي فوق R أكبر يساوي إيش؟
+
+161
+00:14:38,470 --> 00:14:45,490
+سفر، إذا أول حاجةالان اكبر او يساوي سفر بدي اثبت
+
+162
+00:14:45,490 --> 00:14:51,230
+لك الان ان ال R أصغر من B معايا؟ الان ايش بدي
+
+163
+00:14:51,230 --> 00:14:55,750
+اثبتلك؟ اذا اثبتت R أصغر من B معناته انا لجيت R و
+
+164
+00:14:55,750 --> 00:15:00,430
+Q بحيث ان R بيساوي A نغسط Q في B وR بين السفر و
+
+165
+00:15:00,430 --> 00:15:07,090
+بين ال B بيظل علي اثبت ال uniqueness لل R و Q واضح
+
+166
+00:15:07,090 --> 00:15:18,990
+أه؟ طيبالآن نحن سنثبّر أن R أقل من B سببوز Not بدا
+
+167
+00:15:18,990 --> 00:15:23,170
+افترض العكس وصل الـ Contradiction الان بدا افترض
+
+168
+00:15:23,170 --> 00:15:28,750
+Not يعني بمعنى اخر ايش بدا افترض بدا افترض ان R
+
+169
+00:15:28,750 --> 00:15:35,260
+أكبر او يساوي Bطيب خدلك الحسبة البسيطة مدام R أكبر
+
+170
+00:15:35,260 --> 00:15:41,200
+أو سوى B معناته R ناقص B أكبر أو سوى إيش؟ سفر واضح
+
+171
+00:15:41,200 --> 00:15:46,740
+أه؟ R ناقص B أكبر أو سوى سفر R إيش قيمتها؟ هيها
+
+172
+00:15:46,740 --> 00:15:55,860
+اللي هو A ناقص U في B ناقص الـB صح ولا لا؟ هي لا
+
+173
+00:15:55,860 --> 00:16:03,390
+طيب الآن خد الـB أعمل مشتركبصير عندى هذا المقدار
+
+174
+00:16:03,390 --> 00:16:09,750
+عبارة عن a ناقص في u زائد واحد في b صح ولا لا هذا
+
+175
+00:16:09,750 --> 00:16:15,570
+هيصير بساوى هذا اللى هو أكبر أو يساوى من صفر إذا
+
+176
+00:16:15,570 --> 00:16:22,910
+صار هذا المقدار وين موجود لأن هى زي ال X تبعته صار
+
+177
+00:16:22,910 --> 00:16:28,860
+هذا موجود في Sإذا صار عند الـ r-b اللي بيثوي صار r
+
+178
+00:16:28,860 --> 00:16:34,760
+ناقص b element من مين enough لكن احنا بنعرف ان الـ
+
+179
+00:16:34,760 --> 00:16:39,500
+r ناقص b أكيد أصغر من مين من r وهذا contradiction
+
+180
+00:16:39,500 --> 00:16:45,510
+لأن ايش ما لها r is the least such elementما دام R
+
+181
+00:16:45,510 --> 00:16:49,410
+is the least element in S ولاقيت R نقص بيه element
+
+182
+00:16:49,410 --> 00:16:52,570
+in S إذا صار في عندي contradiction إذا الفرضية
+
+183
+00:16:52,570 --> 00:16:57,090
+اللي فرضتها اللي هي هذه خطأ إذا لازم تكون الـ R
+
+184
+00:16:57,090 --> 00:17:02,470
+أصغر من مين إذا صار عندي الآن النتيجة النهائية صار
+
+185
+00:17:02,470 --> 00:17:14,230
+عندي أنا وجدت أن في R و QElement in Z such that R
+
+186
+00:17:14,230 --> 00:17:22,090
+بتساوي A ناقص Q في B حيث R أكبر أو تساوي سفر وأصغر
+
+187
+00:17:22,090 --> 00:17:27,930
+من مين من B الآن بلى عليا أثبت أن الـ R و الـ Q
+
+188
+00:17:27,930 --> 00:17:33,290
+are unique يعني R is unique و Q is unique نفترض
+
+189
+00:17:33,290 --> 00:17:42,770
+الآن أنه لأ مش وحداتنفترض إنه في R' وفي Q' يحقق
+
+190
+00:17:42,770 --> 00:17:47,390
+نفس الشيء يعني بدأ افترض إنه في عندي برضه في عندي
+
+191
+00:17:47,390 --> 00:17:55,150
+there exist R وR' وQ وQ' such that نفترض إنه في R'
+
+192
+00:17:55,590 --> 00:18:07,550
+وR وQ وQ' بحيث اللي هو R R بتساوي A نقص Q في BوR'
+
+193
+00:18:08,070 --> 00:18:15,850
+بيساوي A ناقص U' في B حيث اللي هو R أكبر بيساوي
+
+194
+00:18:15,850 --> 00:18:21,770
+سفر وأصغر من B وR' أكبر بيساوي سفر وأصغر من مين من
+
+195
+00:18:21,770 --> 00:18:28,430
+B مظبوط اللي بيكتبه صحيح؟ طيب احسبني الأن R ناقص
+
+196
+00:18:28,430 --> 00:18:38,020
+R' R ناقص R' إيش هتساوي؟اللي هو سالب Q' نقص Q في B
+
+197
+00:18:38,020 --> 00:18:42,560
+صح ولا لا؟ راح نعمل معاها خد ال absolute value
+
+198
+00:18:42,560 --> 00:18:46,560
+الجهتين بطلع عندك ال absolute value لهذا ساو ال
+
+199
+00:18:46,560 --> 00:18:50,200
+absolute value لهذا في ال absolute value لل B و ال
+
+200
+00:18:50,200 --> 00:18:55,180
+B موجرة إيه دلوقتي نفسها، مظبوط؟ هذه سميليها 1،
+
+201
+00:18:55,180 --> 00:19:00,170
+هنرجع إليهابتثبت لكم الآن هذا المقدار سفر و من فمه
+
+202
+00:19:00,170 --> 00:19:03,390
+احصل على هذا سفر او هذا سفر احصل على هذا سفر و
+
+203
+00:19:03,390 --> 00:19:06,990
+بكون خلصت معايا؟ شوفوا طالع ال inequalities اللي
+
+204
+00:19:06,990 --> 00:19:13,350
+فوق هذول ننطلق من هنا ال inequalities اللي فوق
+
+205
+00:19:13,350 --> 00:19:18,850
+عندك ضروب اللي اتحت في سالب مثلا بصير عند R او
+
+206
+00:19:18,850 --> 00:19:22,090
+اطرحها من بعض او اطرحها من بعض R أكبر سواء سفر و
+
+207
+00:19:22,090 --> 00:19:28,170
+اصغر من B وعندي سالب R primeاللي هو مظبوط أصغر أو
+
+208
+00:19:28,170 --> 00:19:32,290
+يساوي صفر وأكبر أو يساوي سالب B مظبوط اللي عملناه،
+
+209
+00:19:32,290 --> 00:19:37,810
+صح؟
+
+210
+00:19:37,810 --> 00:19:42,630
+أه، بزول يساوي، صحيح، كلام صحيح، اجبحنا بعضنا
+
+211
+00:19:42,630 --> 00:19:49,050
+خلاص، بس أنا عندي R ناقص، R prime اللي هو أصغر أو
+
+212
+00:19:49,050 --> 00:19:54,970
+يساوي B وأكبر أو يساوي سالب Bهذا شو معناته؟ هذا ما
+
+213
+00:19:54,970 --> 00:19:58,410
+فوق الـ absolute value هذا معناته الـ absolute
+
+214
+00:19:58,410 --> 00:20:04,610
+value لـ R نقص R prime أصغر من مين؟ من B أصغر
+
+215
+00:20:04,610 --> 00:20:08,090
+strictly حتى لأن هذا أصغر strictly و هذا أصغر ساوي
+
+216
+00:20:08,090 --> 00:20:12,430
+التنتين مع بعض أصغر strictly واضح، و هذا نفس الشيء
+
+217
+00:20:12,430 --> 00:20:17,570
+أصغر strictly إذا صار عندي هذا أصغر strictly من
+
+218
+00:20:17,570 --> 00:20:26,080
+مين؟ من B معايا نرجع للي فوقما دام هذا أصغر من B،
+
+219
+00:20:26,080 --> 00:20:31,940
+إذاً هذا صار إيه أشماله؟ إذاً صار عندي Q ناقص، Q
+
+220
+00:20:31,940 --> 00:20:35,460
+prime absolute value في الـB أصغر الـcircuit من
+
+221
+00:20:35,460 --> 00:20:40,680
+مين؟ من B أكيد أه، دسم على B لأنه B لاتشهر سفر،
+
+222
+00:20:40,680 --> 00:20:46,360
+إذاً صار عندي Q prime ناقص Q أصغر من 1، ما هي
+
+223
+00:20:46,360 --> 00:20:50,840
+absolute value هذه؟ إذاً أكيد أكبر شهر مين؟ سفر
+
+224
+00:20:51,530 --> 00:20:56,470
+الأن أبشرله جاله أكبر أشهر و أصغر من واحد و هذا
+
+225
+00:20:56,470 --> 00:21:00,430
+أدت صحيح و هذا أدت صحيح فهذا أدت صحيح العدد الصحيح
+
+226
+00:21:00,430 --> 00:21:04,890
+اللي أكبر أشهر و أصغر من واحد مين هو؟ السفر بس
+
+227
+00:21:04,890 --> 00:21:11,150
+مدام هذا عدد صحيح و أكبر أشهر و أصغر من واحد قطعا
+
+228
+00:21:11,150 --> 00:21:19,950
+لازم يكون عندى Q' ناقص Q بساوي سفر ومن ثم Q' تساوي
+
+229
+00:21:19,950 --> 00:21:28,380
+Qرد وانعوض في واحد هذه سفر إذا صارت هذه سفر إذا
+
+230
+00:21:28,380 --> 00:21:37,300
+صار R إيش بتساوي؟ R إبراهيم إذا اللي سوناه أثبتنا
+
+231
+00:21:37,300 --> 00:21:44,510
+وجود R وQ في Zبحيث أن R بتساوي A نقص Q في B وR
+
+232
+00:21:44,510 --> 00:21:48,250
+أكبر تساوي 0 أصغر من B وR وQ اللي لاجيناه هنا إيه
+
+233
+00:21:48,250 --> 00:21:52,510
+شمال هنا واحدات وهذا بعزز الكلام اللي احنا من
+
+234
+00:21:52,510 --> 00:21:56,950
+الاصل عارفينه أو اتعلمناه في الإعداد أو كده إنه لو
+
+235
+00:21:56,950 --> 00:22:01,090
+جينا قسمنا عددين على بعض لو بدنا نقسم اللي هو 24
+
+236
+00:22:01,090 --> 00:22:02,090
+على 7
+
+237
+00:22:05,100 --> 00:22:09,800
+كلنا جوابنا واحد أن خارجنا ناتج القسمة تلاتة
+
+238
+00:22:09,800 --> 00:22:14,460
+والباقي تلاتة على اعتبار أن الباقي أكبر يساوي سفر
+
+239
+00:22:14,460 --> 00:22:19,760
+وأصغر من المقسوم عليه فهذا اللي هو بتكون اللي هي
+
+240
+00:22:19,760 --> 00:22:27,800
+احنا أثبتنا اللي هي خوارزميت القسمة اللي هي نظرية
+
+241
+00:22:27,800 --> 00:22:28,980
+2.1
+
+242
+00:22:32,450 --> 00:22:37,690
+لأن لاحظوا هنا أنا أخدت اللي هو الـ B أشماله أكبر
+
+243
+00:22:37,690 --> 00:22:43,110
+من 0 لأن حتى لو كانت الـ B أصغر من 0 هتطلع اللي هي
+
+244
+00:22:43,110 --> 00:22:48,650
+النظرية صحيحة ولكن مع شوية modification بسيطة اللي
+
+245
+00:22:48,650 --> 00:22:55,630
+هي الـ Corollary اللي عندنا اللي هو Corollary if A
+
+246
+00:22:55,630 --> 00:23:02,580
+and B are integers with الآن أشمالهاB لا تساوي سفر
+
+247
+00:23:02,580 --> 00:23:06,900
+شملنا الحالة التالية اللي هو الـ B أصغر من مين من
+
+248
+00:23:06,900 --> 00:23:13,700
+سفر then there exist unique integers Q and R such
+
+249
+00:23:13,700 --> 00:23:17,320
+that A بيساوي Q في B زايد R والـ R أكبر يساوي سفر
+
+250
+00:23:17,320 --> 00:23:21,060
+وأصغر من مين الآن من ال absolute value الـ B يعني
+
+251
+00:23:21,060 --> 00:23:25,240
+الآن صارت النظرية in general لو
+
+252
+00:23:34,520 --> 00:23:41,780
+أجينا لو أجينا كان عندنا أي عددين صحيحين A وB لا
+
+253
+00:23:41,780 --> 00:23:47,320
+تساوي سفر عشان بتقسم على الـB معايا؟بقدر اللي هو
+
+254
+00:23:47,320 --> 00:23:51,680
+على طول قسمة الـ A على الـ B بيصير عند A بيساوي B
+
+255
+00:23:51,680 --> 00:23:56,360
+في Q زائد اللي هو الـ remainder R الـ Q نتيجي
+
+256
+00:23:56,360 --> 00:24:01,680
+القسمة والـ R اللي هو المتبقى لان المتبقى R أكبر
+
+257
+00:24:01,680 --> 00:24:06,240
+يساوي سفر وأصغر من مين؟ من الـ absolute value
+
+258
+00:24:06,240 --> 00:24:12,500
+لمين؟ للـ B ال absolute value للـ B معايا؟ وحيكون
+
+259
+00:24:12,500 --> 00:24:18,780
+الـ R و الـ Q واحداتفي حالة الـ B أكبر من 0 اللي
+
+260
+00:24:18,780 --> 00:24:23,520
+هي النظرية في الأصل ماشي الحالة إذا الان إذا طبيعي
+
+261
+00:24:23,520 --> 00:24:27,880
+it is enough to consider the case in which B is a
+
+262
+00:24:27,880 --> 00:24:31,900
+negative معايا؟ مدام الـ B negative أكيد ال
+
+263
+00:24:31,900 --> 00:24:34,960
+absolute value اللي هي أشمالها أكبر من 0 الآن
+
+264
+00:24:34,960 --> 00:24:38,960
+بنطبق النظرية على مين؟ على absolute value ماشي؟
+
+265
+00:24:38,960 --> 00:24:43,020
+مدام بنطبق النظرية على absolute value إذا صار عند
+
+266
+00:24:43,020 --> 00:24:48,490
+الـ Aالـ A معايا يا شباب إذا طبّج النظرية اللي
+
+267
+00:24:48,490 --> 00:24:50,830
+جابله مش هو الـ Division Algorithm على الـ
+
+268
+00:24:50,830 --> 00:24:53,190
+Absolute Value يعني بتدبّث مع الـ Absolute Value
+
+269
+00:24:53,190 --> 00:24:57,550
+للـ A إذا بالساوية الـ Absolute Value للـ B في الـ
+
+270
+00:24:57,550 --> 00:25:04,950
+Q زائد R Q' بسميها النظرية اللي جابله بما إنه كيف
+
+271
+00:25:04,950 --> 00:25:09,870
+طبّجنا النظرية الآن A Integer والـ Absolute Value
+
+272
+00:25:09,870 --> 00:25:15,080
+للـ B أكبر من 0 Integer إذا there exist uniqueاللي
+
+273
+00:25:15,080 --> 00:25:21,440
+هو R و Q' such that معايا؟ ايه بيساوي الـ Absolute
+
+274
+00:25:21,440 --> 00:25:25,140
+value الـ B في Q' زي الـ R حيث و R أكبر أو يساوي
+
+275
+00:25:25,140 --> 00:25:29,000
+سفر و أصغر من مين Absolute value الـ B بدت تظهر
+
+276
+00:25:29,000 --> 00:25:33,060
+النتيجة اللي بديها اه؟ ضل الان هتبديش يهيأك اللي
+
+277
+00:25:33,060 --> 00:25:37,580
+بديها يهيأش على صورة B ماشي سهل اللي هو عندك الـ
+
+278
+00:25:37,580 --> 00:25:39,220
+Absolute value الـ B negative ما احنا خدناها حالة
+
+279
+00:25:39,220 --> 00:25:44,530
+الـ Negative اذا بيصير A بساوياللي هو عبارة عن الـ
+
+280
+00:25:44,530 --> 00:25:47,790
+absolute value للـ B اللي هو عبارة عن مين هي سلبي
+
+281
+00:25:47,790 --> 00:25:55,370
+في B في ناقص Q' زي دار هذا هي اللي فوقالان الناقص
+
+282
+00:25:55,370 --> 00:26:00,050
+الـ Q' هي الدسمية مين الـ Q وبما ان الـ Q' كانت
+
+283
+00:26:00,050 --> 00:26:04,730
+وحيدة إذا النقص هياش وحيد إذا صار عندي النتيجة
+
+284
+00:26:04,730 --> 00:26:09,710
+النهائية واضحة إذا there exists unique arrow Q
+
+285
+00:26:09,710 --> 00:26:15,920
+بحيث أن A بساوي الـ Bفي الـ Q اللي عندى زيادة الـ
+
+286
+00:26:15,920 --> 00:26:22,720
+R R أكبر يساوي صفر أخر absolute value لمن؟ لـ B أي
+
+287
+00:26:22,720 --> 00:26:29,100
+سؤال؟ أي استفسار؟ قولوا إذا كان فيه إشي يعني بدنا
+
+288
+00:26:29,100 --> 00:26:36,580
+نعيده واضح أه؟ طيب بعض الملاحظات على النظرية يعني
+
+289
+00:26:36,580 --> 00:26:40,820
+كيف بدنا نستخدم نوظف النظرية لاستخداماتنا في
+
+290
+00:26:40,820 --> 00:26:49,130
+الأسئلة أو حلول الأسئلةالان بناء على خوارزمية
+
+291
+00:26:49,130 --> 00:26:56,830
+القسم اللى حكينا عنها الان لو كان في عندى الـ AI
+
+292
+00:26:56,830 --> 00:27:01,050
+integer القسم
+
+293
+00:27:01,050 --> 00:27:05,010
+على 2 هتعملّي
+
+294
+00:27:05,010 --> 00:27:12,570
+classifications للأعداد الصحيحةإنه حاجتين يا إما
+
+295
+00:27:12,570 --> 00:27:18,910
+على صورة اللي هو المتبقي سفر يا واحد من أين جبته؟
+
+296
+00:27:18,910 --> 00:27:24,670
+خلّيني أشوف إذن الآن من قابلية القسمة على اتنين
+
+297
+00:27:24,670 --> 00:27:31,250
+اللي هي النظرية قبل شوية بس بتطبقها A انتجر والـ B
+
+298
+00:27:31,250 --> 00:27:38,370
+بتساوي اتنين إذن there exists unique ROQ such that
+
+299
+00:27:38,370 --> 00:27:47,060
+Aبتساوي B في Q اللي هي 2 Q زائد R حيث R أكبر أو
+
+300
+00:27:47,060 --> 00:27:54,710
+سوى 0 وأصغر من 100 من 2 إذا نقرنها عن الـ RHas two
+
+301
+00:27:54,710 --> 00:28:00,530
+cases only one or zero إذا .. إذا صار في عند
+
+302
+00:28:00,530 --> 00:28:05,670
+الأعداد اللي في الدنيا الصحيحة إما هتكون A على
+
+303
+00:28:05,670 --> 00:28:11,770
+صورة 2Q في حالة الأرض سفر أو A بساوة 2Q زائد 1
+
+304
+00:28:11,770 --> 00:28:18,410
+Similarly .. Similarly لو أجينا قولنا A ان انتجار
+
+305
+00:28:18,410 --> 00:28:26,060
+و اللي هو الـ B بتساوي تلاتةبرضه بخوارزمية القسمة
+
+306
+00:28:26,060 --> 00:28:33,900
+يوجد الـ Q وR واحدات حيث ايه؟ A بتسوى B في Q A
+
+307
+00:28:33,900 --> 00:28:43,540
+زائد R A في Q زائد R A بتسوى B في Q زائد R والـ R
+
+308
+00:28:43,540 --> 00:28:49,600
+أكبر بسوية سفر وأصغر من 3 اذا في عندي three cases
+
+309
+00:28:49,600 --> 00:28:56,650
+أو three forms عشان هيك بنقولالإنتجر A لديه إحدى
+
+310
+00:28:56,650 --> 00:28:58,490
+الانتجر A لديه إحدى الانتجر A لديه إحدى الانتجر A
+
+311
+00:28:58,490 --> 00:28:58,690
+لديه إحدى الانتجر A لديه إحدى الانتجر A لديه إحدى
+
+312
+00:28:58,690 --> 00:28:59,230
+الانتجر A لديه إحدى الانتجر A لديه إحدى الانتجر A
+
+313
+00:28:59,230 --> 00:29:00,750
+لديه إحدى الانتجر A لديه إحدى الانتجر A لديه إحدى
+
+314
+00:29:00,750 --> 00:29:01,130
+الانتجر A لديه إحدى الانتجر A لديه إحدى الانتجر A
+
+315
+00:29:01,130 --> 00:29:06,950
+لديه إحدى الانتجر A لديه إحدى الانتجر A لديه إحدى
+
+316
+00:29:06,950 --> 00:29:11,630
+الانتجر A لديه إحدى الانتجر A لديه إحدى الانتجر A
+
+317
+00:29:11,630 --> 00:29:12,430
+لدي
+
+318
+00:29:14,710 --> 00:29:21,770
+3 forms for the integer A is equal to 3Q A بيساوي
+
+319
+00:29:21,770 --> 00:29:30,450
+3Q plus 1 او A بيساوي 3Q plus 2 يعني
+
+320
+00:29:30,450 --> 00:29:39,070
+بمعنى آخر احنا بخوارزمية القسمة بنستطيع ان الاعداد
+
+321
+00:29:39,070 --> 00:29:44,110
+ال integers اي عدد integer في الدنياانخليه في
+
+322
+00:29:44,110 --> 00:29:49,810
+finite number of terms بحسب ما يخدمنا في السؤال
+
+323
+00:29:49,810 --> 00:29:53,850
+يعني يمكن يخدمني خمسة، يمكن يخدمني ستة، يمكن
+
+324
+00:29:53,850 --> 00:29:57,530
+يخدمني سبعة، يمكن يخدمني تمانية، إذا بالقسم على
+
+325
+00:29:57,530 --> 00:30:04,140
+اتنين، في عندي two formsبالقسم على ثلاثة بيساوي Q
+
+326
+00:30:04,140 --> 00:30:07,460
+ثلاثة Q ثلاثة Q زاد واحد ثلاثة Q ثلاثة U زاد اثنين
+
+327
+00:30:07,460 --> 00:30:10,800
+بالقسم على أربعة بيساوي 4Q ثلاثة 4Q زاد واحد ثلاثة
+
+328
+00:30:10,800 --> 00:30:14,240
+4Q زاد اثنين ثلاثة 4Q زاد ثلاثة 3 بالقسم على خمسة
+
+329
+00:30:14,240 --> 00:30:21,060
+و هكذا أي سؤال؟ اه صحيح
+
+330
+00:30:27,580 --> 00:30:31,140
+نعم تبدو كـ Odd الـ Odd بيكون على صورة اتنين Q
+
+331
+00:30:31,140 --> 00:30:38,170
+زائد واحد الـ Q انتجرلهو الـ Zero طبعا قطعا اللي
+
+332
+00:30:38,170 --> 00:30:43,430
+هو even مش الحاجة الـ Zero في بعض الكتب لكن قليلة
+
+333
+00:30:43,430 --> 00:30:47,930
+بتصنفه ك natural number وكثير من الكتب أو معظم
+
+334
+00:30:47,930 --> 00:30:52,550
+الكتب بتصنفه انه خارج ال natural number يعني هو
+
+335
+00:30:52,550 --> 00:30:56,370
+بقسم الأعداد هذي اصطلاحا يعني بقسم الأعداد إلى
+
+336
+00:30:56,370 --> 00:31:01,150
+صحيحة موجبة وصحيحة سالبةوالـ 0 اللي هو العدد اللي
+
+337
+00:31:01,150 --> 00:31:03,130
+هو الـ neutral بين الجهتي اللي هو الـ identity
+
+338
+00:31:03,130 --> 00:31:06,550
+بالعب لعبة الـ identity بالنسبة للجامع وها تمام
+
+339
+00:31:06,550 --> 00:31:10,890
+أما even لأ هو even يعني لأ الصورة 2Q يعني لا يمكن
+
+340
+00:31:10,890 --> 00:31:14,530
+كتابة الـ 0 0 لو فرضنا واحد جالب أقدر أكتب عليه 2Q
+
+341
+00:31:14,530 --> 00:31:18,750
+وزيد واحد و بعدين 2Q بس هو ناقص واحد لأ بصير الـ Q
+
+342
+00:31:18,750 --> 00:31:23,550
+is not انتجار واضح
+
+343
+00:31:23,550 --> 00:31:28,810
+أه؟ إذا أكيد اللي هو even numberبتصور انت بتقصد
+
+344
+00:31:28,810 --> 00:31:34,390
+انه zero natural او مش natural احنا
+
+345
+00:31:34,390 --> 00:31:39,650
+قولنا استلاحا استلاحا خلينا نقول المعظم الكتب
+
+346
+00:31:39,650 --> 00:31:43,530
+بتعتبر اللي هو ال zero is not a natural number
+
+347
+00:31:44,850 --> 00:31:48,270
+واللي هو بعض الكتب ما اتذكر انه في كتب عنا في
+
+348
+00:31:48,270 --> 00:31:50,510
+الاعدادية او في الكذا كانوا يعتبروه natural حاليا
+
+349
+00:31:50,510 --> 00:31:54,590
+لا اه حاليا لا يعني هذا أمر اصطلاحي يعني لكن لكن
+
+350
+00:31:54,590 --> 00:31:59,030
+الأنسب للاستعمال هو انه ما يعتبروش natural لإنها
+
+351
+00:31:59,030 --> 00:32:02,650
+تستثنى انتظرك تستثنى تحط أن الصار ليش فلس أنه فلس
+
+352
+00:32:02,650 --> 00:32:06,470
+فلع النبي عليه الصلاة والسلام الله الآن
+
+353
+00:32:08,810 --> 00:32:13,170
+قلنا الملاحظة الأولى الملاحظة الثانية the square
+
+354
+00:32:13,170 --> 00:32:19,010
+of any integer has the form 4k زائد او 4k زائد 1
+
+355
+00:32:19,010 --> 00:32:24,710
+الان بدنا نوظف معرفتنا يعني و كأنه الان بقولك show
+
+356
+00:32:24,710 --> 00:32:35,350
+that افترض ان اقول show that a تربيع has أو letbe
+
+357
+00:32:35,350 --> 00:32:45,050
+an integer show that a تربيع has one of the two
+
+358
+00:32:45,050 --> 00:32:53,730
+forms a أربع a أربع k او أربع k زائد واحد ماشي
+
+359
+00:32:53,730 --> 00:32:56,470
+الحاجة اللي أنا زي بقولها قبل و شوية بخبرزمية
+
+360
+00:32:56,470 --> 00:33:02,970
+القسمة by division algorithm by division algorithm
+
+361
+00:33:04,040 --> 00:33:12,180
+A لديه واحد من اتنين
+
+362
+00:33:12,180 --> 00:33:21,140
+كيوات او اتنين كيوات اكتر من واحد ثم ايه
+
+363
+00:33:21,140 --> 00:33:27,060
+تربيع بيساوي اتنين كيوات تربيع بيساوي اربعة كيوات
+
+364
+00:33:27,060 --> 00:33:30,480
+تربيع بيساوي اربعة كيف او some كيف يساوي كيوة
+
+365
+00:33:30,480 --> 00:33:36,770
+تربيع في هذه الحالةA تربيع يسوى 2Q plus 1 تربيع
+
+366
+00:33:36,770 --> 00:33:45,150
+يسوى 4Q تربيع زاد 4Q زاد 1 يسوى 4Q تربيع زاد Q زاد
+
+367
+00:33:45,150 --> 00:33:50,010
+1 يسوى 4K زاد 1 for some K في هذه الحالة Q تربيع
+
+368
+00:33:50,010 --> 00:33:54,750
+زاد K الـ
+
+369
+00:33:54,750 --> 00:34:00,250
+K هي عبارة عن صورة 4 في integer سميت ال integer Q
+
+370
+00:34:00,250 --> 00:34:04,480
+تربيع في هذه الحالة Kإذا قدرت أكتب ال .. ال .. ال
+
+371
+00:34:04,480 --> 00:34:08,180
+.. ال a تربيع على صورة أربعة في some integer وفي
+
+372
+00:34:08,180 --> 00:34:11,560
+الحالة الثانية أربعة في some integer زائد واحد
+
+373
+00:34:11,560 --> 00:34:16,260
+يعني in any case a تربيع has one of the two forms
+
+374
+00:34:16,260 --> 00:34:20,800
+يا يعني بمعنى أخر يا بيقبل القسم على أربعة يا إما
+
+375
+00:34:20,800 --> 00:34:25,960
+المتبقي من القسم على أربعة واحد واضح أه example
+
+376
+00:34:25,960 --> 00:34:34,880
+show that the square of n of anyodd integer is of
+
+377
+00:34:34,880 --> 00:34:43,700
+the form 8k زي 1 بدنا نثبت أنه اللي هو مربع أي odd
+
+378
+00:34:43,700 --> 00:34:51,300
+integer على صورة إيه شماله 8k زي 1 لو جينا ربعنا ل
+
+379
+00:34:51,300 --> 00:34:58,960
+2k زي 1 مش هيخدمنا الآن 8k زي 1 لو ربعنا اللي هو
+
+380
+00:34:58,960 --> 00:35:03,530
+القسم A3مش هيخدمنا لإن مبقى هو بيصير تسعة .. تسعة
+
+381
+00:35:03,530 --> 00:35:07,530
+.. تسعة .. تسعة كيو تربيع إذا .. إذا .. إت ..
+
+382
+00:35:07,530 --> 00:35:10,770
+إتنين مظبطش هيجيب التمانية لإن محدش يجيب التمانية
+
+383
+00:35:10,770 --> 00:35:15,530
+التلاتة مش هتجيب التمانية إذا مين؟ الأربعة طبعا في
+
+384
+00:35:15,530 --> 00:35:18,070
+مقارين بتجيب التمانية بتجيب التمانية لكن بديش ..
+
+385
+00:35:18,070 --> 00:35:21,050
+بديش أعلي ليش أفضل حالات كتيرة و أنا بقدر أفضل
+
+386
+00:35:21,050 --> 00:35:25,550
+حالات الأجل معايا يا شباب إذا الآن بواسطة
+
+387
+00:35:25,550 --> 00:35:30,740
+الـDivision Algorithm أيضا أي عدد في الدنياأي عدد
+
+388
+00:35:30,740 --> 00:35:37,180
+في الدنيا على صورة اربعة Q اربعة Q زائد واحد اربعة
+
+389
+00:35:37,180 --> 00:35:41,980
+Q زائد اتنين او اربعة Q زائد تلاتة لكن هو ايش بده
+
+390
+00:35:41,980 --> 00:35:51,460
+الود مزام A by differential algorithmThe odd A has
+
+391
+00:35:51,460 --> 00:35:56,860
+one of the forms ياك يو زياد واحد، ياك يو زياد
+
+392
+00:35:56,860 --> 00:36:01,780
+تلاتة، خلاص بس لإنه odd بده ياك إذا أنا بده ربحان،
+
+393
+00:36:01,780 --> 00:36:05,220
+بيصير التربيه إذا صارت الفكرة سهلة إذا أنا صار
+
+394
+00:36:05,220 --> 00:36:10,770
+عندي الـA تربيه في الحالة الأولىاربع Q زائد واحد
+
+395
+00:36:10,770 --> 00:36:15,530
+لكل تربيع ويساوي ستة عشر Q تربيع زائد تمانية Q
+
+396
+00:36:15,530 --> 00:36:20,470
+زائد واحد صح؟ ويساوي .. خد التمانية عام المشترك
+
+397
+00:36:20,470 --> 00:36:25,470
+تصبح تمانية في اتنين Q تربيع زائد Q زائد واحد
+
+398
+00:36:25,470 --> 00:36:28,990
+ويساوي تمانية K زائد واحد for some K هذا اللي هو
+
+399
+00:36:28,990 --> 00:36:32,810
+الـ K في هذا الحالة الآن الـ A تربيع في الحالة
+
+400
+00:36:32,810 --> 00:36:40,340
+التانية اربع Qزاد 3 لكل تربيع ويساوي 16 Q تربيع
+
+401
+00:36:40,340 --> 00:36:53,240
+زاد 24 Q زاد 9 ويساوي 16 Q تربيع زاد 24 Q زاد 8
+
+402
+00:36:53,240 --> 00:36:58,940
+زاد 1 صح ولا لأ؟فصلت اللي فيه تمانيات مع بعض
+
+403
+00:36:58,940 --> 00:37:06,320
+ويساوي تمانية في اتنين Q تربيع ثلاثة Q زائد واحد
+
+404
+00:37:06,320 --> 00:37:11,160
+الكل زائد واحد هذا كله سمي K بيصير تمانية K زائد
+
+405
+00:37:11,160 --> 00:37:18,020
+واحد any odd او the square of any odd integer has
+
+406
+00:37:18,020 --> 00:37:25,410
+the form تمانية K زائد واحد تمانية K زائد واحدواضح
+
+407
+00:37:25,410 --> 00:37:35,270
+أه؟ أي سؤال؟ قولوا محمد رسول الله الان prove that
+
+408
+00:37:35,270 --> 00:37:42,920
+a في a تربيع زاد اتنين على تلاتةis an integer for
+
+409
+00:37:42,920 --> 00:37:46,840
+انا ايه اكبر او ساوي ايش بساوي واحد واضح انه في
+
+410
+00:37:46,840 --> 00:37:50,020
+قسم معاه تلاتة مادام في قسم معاه تلاتة اكتر اللي
+
+411
+00:37:50,020 --> 00:37:52,820
+انا بشجعني طب انا مش هاروح للتنين اكيد اذا انا
+
+412
+00:37:52,820 --> 00:37:58,840
+هاروح لمين الواحد مش هيظبط الواحد مش هيسعفني اذا
+
+413
+00:37:58,840 --> 00:38:03,190
+انا هاروح لمين للتلاتةالقسم على واحد هو بيطلع نفس
+
+414
+00:38:03,190 --> 00:38:08,210
+العدد مش هيصيفني الان اللي هيصيفني مازال بده طالب
+
+415
+00:38:08,210 --> 00:38:11,510
+انه اثبت اشي مقسوم على تلاتة اذا انا هروح على طول
+
+416
+00:38:11,510 --> 00:38:16,110
+باتجاه مين التلاتة اذا في عندي three cases اللي هو
+
+417
+00:38:16,110 --> 00:38:22,270
+تلاتة Q by definition algorithm تلاتة Q تلاتة Q
+
+418
+00:38:22,270 --> 00:38:28,970
+زاد واحد تلاتة Q زاد اتنين وهي خط وهي خط وهي الخط
+
+419
+00:38:28,970 --> 00:38:37,110
+الثالثالآن في كل حالة بدي أحسب اللي هو الـ A الـ A
+
+420
+00:38:37,110 --> 00:38:45,610
+في الـ A تربيع زاد 2 على 3 ويساوي، هذه واضحة 3Q في
+
+421
+00:38:45,610 --> 00:38:54,950
+9Q تربيع زاد 2 على 3 3 مع 3 ويساوي Q في 9Q تربيع
+
+422
+00:38:54,950 --> 00:39:07,420
+زاد 2 is an integerمعايا هنا نفس الشيء بيصير تلاتة
+
+423
+00:39:07,420 --> 00:39:18,180
+Q زائد واحد في تلاتة Q زائد واحد تربيع زائد اتنين
+
+424
+00:39:18,180 --> 00:39:23,740
+على تلاتة ويساوي مضطر اتربي حد من هنا بيساوي تلاتة
+
+425
+00:39:23,740 --> 00:39:31,310
+Q زائد واحد اكيد هلاجيلي تلاتة اكيد فيتسعة Q تربيع
+
+426
+00:39:31,310 --> 00:39:37,810
+ستة Q زائد واحد زائد اتنين لجأت التلاتة اه هي عند
+
+427
+00:39:37,810 --> 00:39:42,370
+اتنين واحد زائد تلاتة وهذه فيها ستة Q وهذه تسعة Q
+
+428
+00:39:42,370 --> 00:39:46,910
+إذا هذه ستساوي هذه مع بعض تلاتة وهي ساوي باخد
+
+429
+00:39:46,910 --> 00:39:50,010
+التلاتة من هذول عامل مشترك بسمها محدد بطلع عنده
+
+430
+00:39:50,010 --> 00:39:55,430
+تلاتة Q زائد واحد في تلاتة Q تربيع زائد اتنين Q
+
+431
+00:39:55,430 --> 00:40:01,420
+زائد واحد الله يفتح عليكم وهذه ازعان انتجةأخيرا
+
+432
+00:40:04,080 --> 00:40:12,500
+نجي ا في تربيع زاد اتنين على تلاتة سوى تلاتة Q زاد
+
+433
+00:40:12,500 --> 00:40:19,000
+اتنين في تلاتة Q زاد اتنين لكل تربيع زاد اتنين على
+
+434
+00:40:19,000 --> 00:40:23,780
+تلاتة و قطعا هتلاقي فهذه تلاتة هي سوى تلاتة Q زاد
+
+435
+00:40:23,780 --> 00:40:29,520
+اتنين معايا يا جماعة في تسعة Q تربيع زاد اتناشر Q
+
+436
+00:40:29,520 --> 00:40:36,340
+زاد اربعة زاد اتنين على تلاتةهدولة فين ستة إذا نخد
+
+437
+00:40:36,340 --> 00:40:39,800
+التلاتة على المشترك ويصير عبارة عن تلاتة Q زاد
+
+438
+00:40:39,800 --> 00:40:49,180
+اتنين في تلاتة Q تربية زائد اربعة Q زائد اتنين ال
+
+439
+00:40:49,180 --> 00:40:55,660
+integer وهيك نكون خلصنا ال section اتنين اتنين
+
+440
+00:40:55,660 --> 00:41:02,220
+نكون معنا homework اللي هو اتنين خمسة اتنين خمسة
+
+441
+00:41:02,670 --> 00:41:05,350
+اللي هو من اتنين لعند خمسة يعني سؤال اتنين و تلتة
+
+442
+00:41:05,350 --> 00:41:12,270
+واربعة وخمسة طيب شوف عليها لان المرة الجاية بكون
+
+443
+00:41:12,270 --> 00:41:17,030
+عندى ان هنتحدث عن ال greatest common divisor ال
+
+444
+00:41:17,030 --> 00:41:20,390
+greatest common divisor ان شاء الله و الله يعطيكوا
+
+445
+00:41:20,390 --> 00:41:20,810
+العافية
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BjST7SecAl4_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BjST7SecAl4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..b6916d6eb003fbec3a5c89586b7e13d6e999459f
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BjST7SecAl4_raw.json
@@ -0,0 +1 @@
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"word": " وR", "probability": 0.762939453125}, {"start": 422.07, "end": 423.41, "word": " يُسمى", "probability": 0.4604034423828125}, {"start": 423.41, "end": 424.27, "word": " بالتعريف", "probability": 0.4102294921875}, {"start": 424.27, "end": 425.03, "word": " الـ", "probability": 0.42864990234375}, {"start": 425.03, "end": 425.73, "word": " quotient", "probability": 0.7744140625}, {"start": 425.73, "end": 426.23, "word": " و", "probability": 0.54541015625}, {"start": 426.23, "end": 426.67, "word": " الـ", "probability": 0.173797607421875}, {"start": 426.67, "end": 427.07, "word": " remainder", "probability": 0.87646484375}, {"start": 427.07, "end": 427.61, "word": " في", "probability": 0.79345703125}, {"start": 427.61, "end": 427.71, "word": " الـ", "probability": 0.24920654296875}, {"start": 427.71, "end": 428.09, "word": " division", "probability": 0.615234375}, {"start": 428.09, "end": 428.33, "word": " of", "probability": 0.4765625}, {"start": 428.33, "end": 428.71, "word": " A", "probability": 0.841796875}, {"start": 428.71, "end": 429.91, "word": " بـ", "probability": 0.3172607421875}, {"start": 429.91, "end": 430.19, "word": " B", "probability": 0.56787109375}, {"start": 430.19, "end": 435.57, "word": " للتذكير", "probability": 0.89072265625}], "temperature": 1.0}, {"id": 17, "seek": 45121, "start": 436.93, "end": 451.21, "text": "الشبطر التاني divisibility theory in the integers أو نظرية القسمة في الأعداد الصحيحة أو للأعداد الصحيحة ال section اللي بدأنا فيه اللي هو the division algorithm خارزمية القسمة", "tokens": [6027, 8592, 3555, 9566, 2288, 16712, 7649, 1829, 25974, 2841, 5261, 294, 264, 41674, 34051, 8717, 19913, 2288, 10632, 25062, 38251, 3660, 8978, 16247, 22488, 18513, 31767, 5016, 1829, 5016, 3660, 34051, 24976, 10721, 22488, 18513, 31767, 5016, 1829, 5016, 3660, 2423, 3541, 13672, 1829, 47525, 10721, 8315, 8978, 3224, 13672, 1829, 31439, 264, 10044, 9284, 16490, 9640, 11622, 2304, 10632, 25062, 38251, 3660], "avg_logprob": -0.1719951923076923, "compression_ratio": 1.5588235294117647, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 436.93, "end": 437.57, "word": "الشبطر", "probability": 0.74599609375}, {"start": 437.57, "end": 437.91, "word": " التاني", "probability": 0.9410807291666666}, {"start": 437.91, "end": 438.49, "word": " divisibility", "probability": 0.58062744140625}, {"start": 438.49, "end": 438.85, "word": " theory", "probability": 0.82373046875}, {"start": 438.85, "end": 439.13, "word": " in", "probability": 0.90673828125}, {"start": 439.13, "end": 439.29, "word": " the", "probability": 0.6865234375}, {"start": 439.29, "end": 439.85, "word": " integers", "probability": 0.93701171875}, {"start": 439.85, "end": 440.89, "word": " أو", "probability": 0.67333984375}, {"start": 440.89, "end": 441.57, "word": " نظرية", "probability": 0.942626953125}, {"start": 441.57, "end": 443.45, "word": " القسمة", "probability": 0.9861653645833334}, {"start": 443.45, "end": 444.15, "word": " في", "probability": 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وكان", "probability": 0.86279296875}, {"start": 458.53, "end": 458.71, "word": " b", "probability": 0.896484375}, {"start": 458.71, "end": 459.03, "word": " أكبر", "probability": 0.9501953125}, {"start": 459.03, "end": 459.19, "word": " من", "probability": 0.98291015625}, {"start": 459.19, "end": 459.51, "word": " 0", "probability": 0.6962890625}, {"start": 459.51, "end": 460.45, "word": " و", "probability": 0.74267578125}, {"start": 460.45, "end": 460.87, "word": " أردنا", "probability": 0.788818359375}, {"start": 460.87, "end": 461.39, "word": " نقسم", "probability": 0.9674479166666666}, {"start": 461.39, "end": 461.89, "word": " نقول", "probability": 0.709716796875}, {"start": 461.89, "end": 462.13, "word": " a", "probability": 0.9384765625}, {"start": 462.13, "end": 462.31, "word": " على", "probability": 0.6708984375}, {"start": 462.31, "end": 462.63, "word": " b", "probability": 0.9833984375}, {"start": 462.63, "end": 463.55, "word": " لما", "probability": 0.939208984375}, 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{"start": 468.73, "end": 469.61, "word": " الناتج", "probability": 0.85595703125}, {"start": 469.61, "end": 469.93, "word": " هيكون", "probability": 0.962158203125}, {"start": 469.93, "end": 470.41, "word": " وحيد", "probability": 0.9070638020833334}, {"start": 470.41, "end": 471.47, "word": " والمتبقى", "probability": 0.91650390625}, {"start": 471.47, "end": 472.07, "word": " وحيد", "probability": 0.9622395833333334}], "temperature": 1.0}, {"id": 19, "seek": 50175, "start": 472.57, "end": 501.75, "text": "قلنا إنه هيكون الـ A هتصير على صورة Q بـ B زائد R حيث الـ R أكبر سواء 0 وأصغر من B هذا المتبقي من القسمة و الـ Q اللي هو ناتج القسمة و Q and R اللي هما هم إنتجارات مختلفة The first one Q is called the quotient The second one R is called the remainder in the division of A by B", "tokens": [4587, 1211, 8315, 36145, 3224, 8032, 1829, 30544, 2423, 39184, 316, 8032, 2655, 9381, 13546, 15844, 20328, 13063, 3660, 1249, 4724, 39184, 363, 30767, 16373, 3215, 497, 11331, 1829, 12984, 2423, 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{"start": 523.36, "end": 524.7, "word": " اللي", "probability": 0.982177734375}, {"start": 524.7, "end": 524.8, "word": " هو", "probability": 0.97705078125}, {"start": 524.8, "end": 525.38, "word": " المتبقى", "probability": 0.9412109375}, {"start": 525.38, "end": 525.58, "word": " من", "probability": 0.59033203125}, {"start": 525.58, "end": 526.14, "word": " القسمة", "probability": 0.9801432291666666}, {"start": 526.14, "end": 526.56, "word": " بتساوي", "probability": 0.9334716796875}, {"start": 526.56, "end": 526.98, "word": " A", "probability": 0.919921875}, {"start": 526.98, "end": 528.22, "word": " ناقص", "probability": 0.805908203125}, {"start": 528.22, "end": 528.58, "word": " Q", "probability": 0.88916015625}, {"start": 528.58, "end": 529.3, "word": " في", "probability": 0.96728515625}, {"start": 529.3, "end": 529.52, "word": " B", "probability": 0.98681640625}], "temperature": 1.0}, {"id": 21, "seek": 55524, "start": 530.78, "end": 555.24, "text": "الآن بدي أكوّن set هذه ال set هي المنطلق للوصول إلى النتيجة ال set بتساوي عبارة عن كل الأعداد اللي عصورت a ناقص x في b حيث ال x عبارة عن integer element in z", "tokens": [6027, 148, 48506, 4724, 16254, 5551, 4117, 2407, 11703, 1863, 992, 29538, 2423, 992, 39896, 9673, 1863, 9566, 1211, 4587, 24976, 2407, 9381, 12610, 30731, 28239, 31371, 7435, 3660, 2423, 992, 39894, 3794, 995, 45865, 6225, 3555, 9640, 3660, 18871, 28242, 16247, 22488, 18513, 13672, 1829, 6225, 9381, 13063, 2655, 257, 8717, 995, 4587, 9381, 2031, 8978, 272, 11331, 1829, 12984, 2423, 2031, 6225, 3555, 9640, 3660, 18871, 24922, 4478, 294, 710], "avg_logprob": -0.1930650668601467, "compression_ratio": 1.4970059880239521, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 530.78, "end": 531.38, "word": "الآن", "probability": 0.68408203125}, {"start": 531.38, "end": 532.38, "word": " بدي", "probability": 0.763671875}, {"start": 532.38, "end": 533.0, "word": " أكوّن", "probability": 0.77333984375}, {"start": 533.0, "end": 533.5, "word": " 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{"start": 541.26, "end": 541.54, "word": " عن", "probability": 0.9970703125}, {"start": 541.54, "end": 541.88, "word": " كل", "probability": 0.95751953125}, {"start": 541.88, "end": 542.48, "word": " الأعداد", "probability": 0.9383138020833334}, {"start": 542.48, "end": 542.62, "word": " اللي", "probability": 0.88720703125}, {"start": 542.62, "end": 543.32, "word": " عصورت", "probability": 0.923583984375}, {"start": 543.32, "end": 544.3, "word": " a", "probability": 0.41943359375}, {"start": 544.3, "end": 545.98, "word": " ناقص", "probability": 0.780120849609375}, {"start": 545.98, "end": 547.2, "word": " x", "probability": 0.79150390625}, {"start": 547.2, "end": 547.94, "word": " في", "probability": 0.67578125}, {"start": 547.94, "end": 548.26, "word": " b", "probability": 0.81787109375}, {"start": 548.26, "end": 550.48, "word": " حيث", "probability": 0.9827473958333334}, {"start": 550.48, "end": 552.36, "word": " ال", "probability": 0.91455078125}, {"start": 552.36, "end": 552.9, 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657.58, "end": 657.84, "word": " R", "probability": 0.6640625}], "temperature": 1.0}, {"id": 26, "seek": 68343, "start": 658.73, "end": 683.43, "text": "فبتكون R هي هذه الـ R اللي إحنا بدنا إياها وفي نفس الوقت قيمة X المقابلة هي الـ Q المطلوبة وحنثبت لكم إن الـ R و الـ Q إيه شمالهم؟ واحدات نيجي الآن، اتوكل على الله، شوفوا عند الآن consider the set S بتساوي A نقص X بي X limited Z A minus X بيه أكبر أو يساوي سفر", "tokens": [5172, 3555, 2655, 30544, 497, 39896, 29538, 2423, 39184, 497, 13672, 1829, 11933, 5016, 8315, 47525, 8315, 11933, 25528, 11296, 4032, 41185, 8717, 36178, 2423, 30543, 2655, 12174, 32640, 3660, 1783, 9673, 4587, 16758, 37977, 39896, 2423, 39184, 1249, 9673, 9566, 1211, 37746, 3660, 4032, 5016, 1863, 12984, 3555, 2655, 5296, 24793, 36145, 2423, 39184, 497, 4032, 2423, 39184, 1249, 11933, 1829, 3224, 13412, 2304, 6027, 16095, 22807, 36764, 24401, 9307, 8717, 1829, 7435, 1829, 6024, 48506, 12399, 1975, 2655, 2407, 28820, 15844, 21984, 12399, 13412, 38688, 14407, 43242, 6024, 48506, 1949, 264, 992, 318, 39894, 3794, 995, 45865, 316, 8717, 4587, 9381, 1783, 4724, 1829, 1783, 5567, 1176, 316, 3175, 1783, 4724, 1829, 3224, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.2504921165976937, "compression_ratio": 1.626923076923077, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 658.73, "end": 659.29, "word": "فبتكون", "probability": 0.8033447265625}, {"start": 659.29, "end": 659.61, "word": " R", "probability": 0.591796875}, {"start": 659.61, "end": 659.93, "word": " هي", "probability": 0.93505859375}, {"start": 659.93, "end": 660.49, "word": " هذه", "probability": 0.8056640625}, {"start": 660.49, "end": 661.29, "word": " الـ", "probability": 0.94189453125}, {"start": 661.29, "end": 661.51, "word": " R", "probability": 0.439453125}, {"start": 661.51, "end": 661.69, "word": " اللي", "probability": 0.9423828125}, {"start": 661.69, "end": 661.95, "word": " إحنا", "probability": 0.7577311197916666}, {"start": 661.95, "end": 662.23, "word": " بدنا", "probability": 0.948486328125}, {"start": 662.23, "end": 662.73, "word": " إياها", "probability": 0.8658854166666666}, {"start": 662.73, "end": 663.41, "word": " وفي", "probability": 0.87548828125}, {"start": 663.41, "end": 663.81, "word": " نفس", "probability": 0.998779296875}, {"start": 663.81, "end": 664.41, "word": " الوقت", "probability": 0.9933268229166666}, {"start": 664.41, "end": 665.07, "word": " قيمة", "probability": 0.9920247395833334}, {"start": 665.07, "end": 665.29, "word": " X", "probability": 0.88671875}, {"start": 665.29, "end": 666.01, "word": " المقابلة", "probability": 0.9920654296875}, {"start": 666.01, "end": 666.23, "word": " هي", "probability": 0.974609375}, {"start": 666.23, "end": 666.45, "word": " الـ", "probability": 0.829345703125}, {"start": 666.45, "end": 666.71, "word": " Q", "probability": 0.806640625}, {"start": 666.71, "end": 668.09, "word": " المطلوبة", "probability": 0.984375}, {"start": 668.09, "end": 669.33, "word": " وحنثبت", "probability": 0.8306477864583334}, {"start": 669.33, "end": 669.49, "word": " لكم", "probability": 0.8388671875}, {"start": 669.49, "end": 669.65, "word": " إن", "probability": 0.71826171875}, {"start": 669.65, "end": 669.79, "word": " الـ", "probability": 0.85498046875}, {"start": 669.79, "end": 669.91, "word": " R", "probability": 0.8515625}, {"start": 669.91, "end": 670.03, "word": " و", "probability": 0.7109375}, {"start": 670.03, "end": 670.13, "word": " الـ", "probability": 0.718994140625}, {"start": 670.13, "end": 670.25, "word": " Q", "probability": 0.8515625}, {"start": 670.25, "end": 670.41, "word": " إيه", "probability": 0.7561848958333334}, {"start": 670.41, "end": 671.25, "word": " شمالهم؟", "probability": 0.667236328125}, {"start": 671.25, "end": 671.77, "word": " واحدات", "probability": 0.8408203125}, {"start": 671.77, "end": 672.43, "word": " نيجي", "probability": 0.89111328125}, {"start": 672.43, "end": 672.75, "word": " الآن،", "probability": 0.7073567708333334}, {"start": 672.75, "end": 672.95, "word": " اتوكل", "probability": 0.668701171875}, {"start": 672.95, "end": 673.09, "word": " على", "probability": 0.54541015625}, {"start": 673.09, "end": 673.93, "word": " الله،", "probability": 0.769775390625}, {"start": 673.93, "end": 674.79, "word": " شوفوا", "probability": 0.982421875}, {"start": 674.79, "end": 676.81, "word": " عند", "probability": 0.841796875}, {"start": 676.81, "end": 677.21, "word": " الآن", "probability": 0.743408203125}, {"start": 677.21, "end": 677.71, "word": " consider", "probability": 0.5947265625}, {"start": 677.71, "end": 677.95, "word": " the", "probability": 0.438232421875}, {"start": 677.95, "end": 678.21, "word": " set", "probability": 0.85693359375}, {"start": 678.21, "end": 678.41, "word": " S", "probability": 0.87744140625}, {"start": 678.41, "end": 678.79, "word": " بتساوي", "probability": 0.71881103515625}, {"start": 678.79, "end": 678.99, "word": " A", "probability": 0.2247314453125}, {"start": 678.99, "end": 679.27, "word": " نقص", "probability": 0.750244140625}, {"start": 679.27, "end": 679.49, "word": " X", "probability": 0.904296875}, {"start": 679.49, "end": 679.81, "word": " بي", "probability": 0.33837890625}, {"start": 679.81, "end": 680.23, "word": " X", "probability": 0.82373046875}, {"start": 680.23, "end": 680.49, "word": " limited", "probability": 0.1060791015625}, {"start": 680.49, "end": 680.89, "word": " Z", "probability": 0.417236328125}, {"start": 680.89, "end": 681.13, "word": " A", "probability": 0.82080078125}, {"start": 681.13, "end": 681.41, "word": " minus", "probability": 0.64208984375}, {"start": 681.41, "end": 681.85, "word": " X", "probability": 0.99560546875}, {"start": 681.85, "end": 682.33, "word": " بيه", "probability": 0.7262369791666666}, {"start": 682.33, "end": 682.59, "word": " أكبر", "probability": 0.9778645833333334}, {"start": 682.59, "end": 682.77, "word": " أو", "probability": 0.9833984375}, {"start": 682.77, "end": 683.05, "word": " يساوي", "probability": 0.838134765625}, {"start": 683.05, "end": 683.43, "word": " سفر", "probability": 0.7315266927083334}], "temperature": 1.0}, {"id": 27, "seek": 70607, "start": 684.09, "end": 706.07, "text": "واضح إنها عبارة عن set of positive integers أو non-negative integers إذن S is a set of non-negative integers هذي الأول لأن اتنين بيدثبتلك إن S non-empty يعني بيدجيب لك concrete example", "tokens": [2407, 46958, 5016, 36145, 11296, 6225, 3555, 9640, 3660, 18871, 992, 295, 3353, 41674, 34051, 2107, 12, 28561, 1166, 41674, 11933, 8848, 1863, 318, 307, 257, 992, 295, 2107, 12, 28561, 1166, 41674, 8032, 8848, 1829, 16247, 12610, 5296, 33456, 1975, 2655, 1863, 9957, 4724, 25708, 12984, 3555, 2655, 23275, 36145, 318, 2107, 12, 4543, 88, 37495, 22653, 4724, 25708, 7435, 1829, 3555, 5296, 4117, 9859, 1365], "avg_logprob": -0.2571231582585503, "compression_ratio": 1.4404761904761905, "no_speech_prob": 0.0, "words": [{"start": 684.09, "end": 684.73, "word": "واضح", "probability": 0.9850260416666666}, {"start": 684.73, "end": 685.03, "word": " إنها", "probability": 0.720458984375}, {"start": 685.03, "end": 685.43, "word": " عبارة", "probability": 0.99609375}, {"start": 685.43, "end": 685.69, "word": " عن", "probability": 0.9970703125}, {"start": 685.69, "end": 685.95, "word": " set", "probability": 0.6064453125}, {"start": 685.95, "end": 686.17, "word": " of", "probability": 0.953125}, {"start": 686.17, "end": 686.87, "word": " positive", "probability": 0.8955078125}, {"start": 686.87, "end": 687.71, "word": " integers", "probability": 0.95263671875}, {"start": 687.71, "end": 688.17, "word": " أو", "probability": 0.71435546875}, {"start": 688.17, "end": 688.33, "word": " non", "probability": 0.54736328125}, {"start": 688.33, "end": 688.65, "word": "-negative", "probability": 0.80810546875}, {"start": 688.65, "end": 689.09, "word": " integers", "probability": 0.91943359375}, {"start": 689.09, "end": 689.45, "word": " إذن", "probability": 0.614013671875}, {"start": 689.45, "end": 689.83, "word": " S", "probability": 0.72607421875}, {"start": 689.83, "end": 690.75, "word": " is", "probability": 0.7451171875}, {"start": 690.75, "end": 691.47, "word": " a", "probability": 0.966796875}, {"start": 691.47, "end": 692.07, "word": " set", "probability": 0.94775390625}, {"start": 692.07, "end": 693.11, "word": " of", "probability": 0.97265625}, {"start": 693.11, "end": 694.13, "word": " non", "probability": 0.93896484375}, {"start": 694.13, "end": 695.87, "word": "-negative", "probability": 0.900390625}, {"start": 695.87, "end": 697.89, "word": " integers", "probability": 0.951171875}, {"start": 697.89, "end": 699.13, "word": " هذي", "probability": 0.5305989583333334}, {"start": 699.13, "end": 699.51, "word": " الأول", "probability": 0.988525390625}, {"start": 699.51, "end": 700.63, "word": " لأن", "probability": 0.767822265625}, {"start": 700.63, "end": 701.09, "word": " اتنين", "probability": 0.796356201171875}, {"start": 701.09, "end": 701.91, "word": " بيدثبتلك", "probability": 0.72869873046875}, {"start": 701.91, "end": 702.11, "word": " إن", "probability": 0.568359375}, {"start": 702.11, "end": 702.43, "word": " S", "probability": 0.845703125}, {"start": 702.43, "end": 702.75, "word": " non", "probability": 0.456787109375}, {"start": 702.75, "end": 703.49, "word": "-empty", "probability": 0.9246419270833334}, {"start": 703.49, "end": 704.03, "word": " يعني", "probability": 0.93798828125}, {"start": 704.03, "end": 704.53, "word": " بيدجيب", "probability": 0.8484375}, {"start": 704.53, "end": 704.71, "word": " لك", "probability": 0.66796875}, {"start": 704.71, "end": 705.23, "word": " concrete", "probability": 0.59619140625}, {"start": 705.23, "end": 706.07, "word": " example", "probability": 0.9658203125}], "temperature": 1.0}, {"id": 28, "seek": 73300, "start": 706.96, "end": 733.0, "text": "بقيمة X بحيث يكون A-X في B و A موجود فاس يعني أكبر يساوي إيهاش؟ سفر شوف عندي عندي أنا معطيني في النظرية أن الـB أشماله أكبر من سفر و B integer مزام أكبر من سفر إذا حيكون الـB عند نفسه أشماله أكبر أو يساوي واحد", "tokens": [3555, 4587, 32640, 3660, 1783, 4724, 5016, 1829, 12984, 7251, 30544, 316, 12, 55, 8978, 363, 4032, 316, 3714, 29245, 23328, 6156, 32277, 37495, 22653, 5551, 4117, 26890, 7251, 3794, 995, 45865, 11933, 1829, 3224, 33599, 22807, 8608, 5172, 2288, 13412, 38688, 18871, 16254, 18871, 16254, 41850, 20449, 9566, 9957, 1829, 8978, 28239, 19913, 2288, 10632, 14739, 2423, 39184, 33, 5551, 8592, 2304, 6027, 3224, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 4032, 363, 24922, 3714, 11622, 10943, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 11933, 15730, 11331, 1829, 30544, 2423, 39184, 33, 43242, 8717, 36178, 3224, 5551, 8592, 2304, 6027, 3224, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 36764, 24401], "avg_logprob": -0.24419248420580297, "compression_ratio": 1.75, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 706.96, "end": 708.0, "word": "بقيمة", "probability": 0.71875}, {"start": 708.0, "end": 708.34, "word": " X", "probability": 0.5390625}, {"start": 708.34, "end": 708.74, "word": " بحيث", "probability": 0.83837890625}, {"start": 708.74, "end": 709.02, "word": " يكون", "probability": 0.56591796875}, {"start": 709.02, "end": 709.32, "word": " A", "probability": 0.412353515625}, {"start": 709.32, "end": 709.9, "word": "-X", "probability": 0.4842529296875}, {"start": 709.9, "end": 710.1, "word": " في", "probability": 0.2734375}, {"start": 710.1, "end": 710.26, "word": " B", "probability": 0.3173828125}, {"start": 710.26, "end": 710.36, "word": " و", "probability": 0.33154296875}, {"start": 710.36, "end": 710.44, "word": " A", "probability": 0.49169921875}, {"start": 710.44, "end": 711.08, "word": " موجود", "probability": 0.9576822916666666}, {"start": 711.08, "end": 711.9, "word": " فاس", "probability": 0.692138671875}, {"start": 711.9, "end": 712.14, "word": " يعني", "probability": 0.88916015625}, {"start": 712.14, "end": 712.42, "word": " أكبر", "probability": 0.94482421875}, {"start": 712.42, "end": 712.8, "word": " يساوي", "probability": 0.947998046875}, {"start": 712.8, "end": 713.34, "word": " إيهاش؟", "probability": 0.5787109375}, {"start": 713.34, "end": 714.1, "word": " سفر", "probability": 0.8611653645833334}, {"start": 714.1, "end": 715.22, "word": " شوف", "probability": 0.7021484375}, {"start": 715.22, "end": 715.56, "word": " عندي", "probability": 0.7147216796875}, {"start": 715.56, "end": 717.48, "word": " عندي", "probability": 0.796875}, {"start": 717.48, "end": 718.14, "word": " أنا", "probability": 0.869140625}, {"start": 718.14, "end": 719.36, "word": " معطيني", "probability": 0.81298828125}, {"start": 719.36, "end": 719.44, "word": " في", "probability": 0.9716796875}, {"start": 719.44, "end": 720.2, "word": " النظرية", "probability": 0.969482421875}, {"start": 720.2, "end": 721.2, "word": " أن", "probability": 0.465576171875}, {"start": 721.2, "end": 721.66, "word": " الـB", "probability": 0.75390625}, {"start": 721.66, "end": 722.5, "word": " أشماله", "probability": 0.90615234375}, {"start": 722.5, "end": 723.44, "word": " أكبر", "probability": 0.9835611979166666}, {"start": 723.44, "end": 723.62, "word": " من", "probability": 0.99755859375}, {"start": 723.62, "end": 724.06, "word": " سفر", "probability": 0.9676106770833334}, {"start": 724.06, "end": 724.6, "word": " و", "probability": 0.5830078125}, {"start": 724.6, "end": 724.74, "word": " B", "probability": 0.51953125}, {"start": 724.74, "end": 725.24, "word": " integer", "probability": 0.56103515625}, {"start": 725.24, "end": 725.96, "word": " مزام", "probability": 0.643798828125}, {"start": 725.96, "end": 726.32, "word": " أكبر", "probability": 0.9837239583333334}, {"start": 726.32, "end": 726.5, "word": " من", "probability": 0.99658203125}, {"start": 726.5, "end": 726.94, "word": " سفر", "probability": 0.9908854166666666}, {"start": 726.94, "end": 727.5, "word": " إذا", "probability": 0.794921875}, {"start": 727.5, "end": 728.06, "word": " حيكون", "probability": 0.7308756510416666}, {"start": 728.06, "end": 728.48, "word": " الـB", "probability": 0.9664713541666666}, {"start": 728.48, "end": 728.82, "word": " عند", "probability": 0.54541015625}, {"start": 728.82, "end": 730.02, "word": " نفسه", "probability": 0.9833984375}, {"start": 730.02, "end": 731.04, "word": " أشماله", "probability": 0.97783203125}, {"start": 731.04, "end": 731.66, "word": " أكبر", "probability": 0.9803059895833334}, {"start": 731.66, "end": 731.86, "word": " أو", "probability": 0.93212890625}, {"start": 731.86, "end": 732.36, "word": " يساوي", "probability": 0.9864501953125}, {"start": 732.36, "end": 733.0, "word": " واحد", "probability": 0.8359375}], "temperature": 1.0}, {"id": 29, "seek": 75252, "start": 733.74, "end": 752.52, "text": "صح ولا لأ؟ إذا من واحد وطالع طيب اضربن الجهتين في ال absolute value للـA في بصير ال absolute value للـA في ال B أكبر أو يساوي ال absolute value لمين؟ مصبوط ولا لا؟ أكيد صح طيب", "tokens": [9381, 5016, 49429, 5296, 10721, 22807, 11933, 15730, 9154, 36764, 24401, 4032, 9566, 6027, 3615, 23032, 1829, 3555, 1975, 11242, 25513, 1863, 25724, 3224, 2655, 9957, 8978, 2423, 8236, 2158, 24976, 39184, 32, 8978, 4724, 9381, 13546, 2423, 8236, 2158, 24976, 39184, 32, 8978, 2423, 363, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 2423, 8236, 2158, 5296, 2304, 9957, 22807, 3714, 9381, 3555, 2407, 9566, 49429, 20193, 22807, 5551, 4117, 25708, 20328, 5016, 23032, 1829, 3555], "avg_logprob": -0.25240384080471134, "compression_ratio": 1.6790123456790123, "no_speech_prob": 4.76837158203125e-06, "words": [{"start": 733.74, "end": 734.04, "word": "صح", "probability": 0.900390625}, {"start": 734.04, "end": 734.2, "word": " ولا", "probability": 0.89208984375}, {"start": 734.2, "end": 735.1, "word": " لأ؟", "probability": 0.7111002604166666}, {"start": 735.1, "end": 735.5, "word": " إذا", "probability": 0.740234375}, {"start": 735.5, "end": 735.68, "word": " من", 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بساوة 2Q زائد 1 Similarly .. 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"probability": 0.801025390625}, {"start": 2465.35, "end": 2465.95, "word": " واربعة", "probability": 0.74322509765625}, {"start": 2465.95, "end": 2467.21, "word": " وخمسة", "probability": 0.95654296875}, {"start": 2467.21, "end": 2467.59, "word": " طيب", "probability": 0.8904622395833334}, {"start": 2467.59, "end": 2467.85, "word": " شوف", "probability": 0.9599609375}, {"start": 2467.85, "end": 2468.37, "word": " عليها", "probability": 0.5555419921875}, {"start": 2468.37, "end": 2468.93, "word": " لان", "probability": 0.42987060546875}, {"start": 2468.93, "end": 2469.67, "word": " المرة", "probability": 0.96142578125}, {"start": 2469.67, "end": 2471.05, "word": " الجاية", "probability": 0.8738606770833334}, {"start": 2471.05, "end": 2472.27, "word": " بكون", "probability": 0.906005859375}, {"start": 2472.27, "end": 2472.83, "word": " عندى", "probability": 0.694580078125}, {"start": 2472.83, "end": 2473.09, "word": " ان", "probability": 0.2763671875}, {"start": 2473.09, "end": 2473.81, "word": " هنتحدث", "probability": 0.862060546875}, {"start": 2473.81, "end": 2474.03, "word": " عن", "probability": 0.97607421875}, {"start": 2474.03, "end": 2474.19, "word": " ال", "probability": 0.61962890625}, {"start": 2474.19, "end": 2474.75, "word": " greatest", "probability": 0.480224609375}, {"start": 2474.75, "end": 2475.99, "word": " common", "probability": 0.9052734375}, {"start": 2475.99, "end": 2476.81, "word": " divisor", "probability": 0.967041015625}, {"start": 2476.81, "end": 2477.03, "word": " ال", "probability": 0.414794921875}, {"start": 2477.03, "end": 2477.29, "word": " greatest", "probability": 0.7705078125}, {"start": 2477.29, "end": 2477.53, "word": " common", "probability": 0.951171875}, {"start": 2477.53, "end": 2478.29, "word": " divisor", "probability": 0.9736328125}, {"start": 2478.29, "end": 2479.05, "word": " ان", "probability": 0.8056640625}, {"start": 2479.05, "end": 2479.31, "word": " شاء", "probability": 0.964599609375}, {"start": 2479.31, "end": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BjST7SecAl4_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BjST7SecAl4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..540797ed1137ad47266a3f34c0467f3f0e9cccfa
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BjST7SecAl4_raw.srt
@@ -0,0 +1,1780 @@
+1
+00:00:19,300 --> 00:00:24,480
+بسم الله الرحمن الرحيم المساق هو مساق نظرية
+
+2
+00:00:24,480 --> 00:00:31,640
+الإعداد number theory math 4342 ال course outline
+
+3
+00:00:31,640 --> 00:00:36,340
+textbook elementary number theory لديفيد بيرتون
+
+4
+00:00:36,340 --> 00:00:44,860
+اللي هو الطبعة السادسة ال
+
+5
+00:00:44,860 --> 00:00:49,770
+course outline هو عبارة عن التاليهنبدأ اللي هو في
+
+6
+00:00:49,770 --> 00:00:54,670
+الـDivision Algorithm خورزمية القسمة الـGreatest
+
+7
+00:00:54,670 --> 00:00:59,890
+Common Divisor الـEuclidean Algorithm الـEuclidean
+
+8
+00:00:59,890 --> 00:01:03,730
+Equation إحدى صور الـEuclidean Equation اللي
+
+9
+00:01:03,730 --> 00:01:09,050
+أمامنا هنحاول ناخد بعض حلولها هذا اللي هو الشبطر
+
+10
+00:01:09,050 --> 00:01:14,050
+الثاني في الكتاب هو من ثم الشبطر الثاني The
+
+11
+00:01:14,050 --> 00:01:17,510
+Fundamental Theorem of ArithmeticSum of properties
+
+12
+00:01:17,510 --> 00:01:22,490
+of a prime numbers والشبطر الثالث هو عبارة عن
+
+13
+00:01:22,490 --> 00:01:27,850
+يتحدث عن الـ primes بعض أو يتحدث عن ال
+
+14
+00:01:27,850 --> 00:01:31,410
+concurrences والتطابقات ال binary and decimal
+
+15
+00:01:31,410 --> 00:01:35,450
+representations of integers اللي بتقودنا لنظام
+
+16
+00:01:35,450 --> 00:01:41,320
+العد الثنائي ونظام العد العشري المعروفينالنظرية
+
+17
+00:01:41,320 --> 00:01:43,760
+المشهورة Linear Concurrences and Chinese Remainder
+
+18
+00:01:43,760 --> 00:01:45,900
+Theorem الناظرية المشهورة Chinese Remainder
+
+19
+00:01:45,900 --> 00:01:54,000
+Theorem هنتحدث عنها خلال الشبطر الرابع ويكون عندنا
+
+20
+00:01:54,000 --> 00:01:57,400
+ال first exam بعد اللي هو شبطر اتنين وشبطر تلاتة
+
+21
+00:01:57,400 --> 00:02:03,260
+وشبطر اربعة من ثم اللي هو هنصل لشبطر خمسة ل
+
+22
+00:02:03,260 --> 00:02:08,020
+Fermat's Little Theorem أو بسيدو برايمز وويلسونز
+
+23
+00:02:08,020 --> 00:02:13,960
+Theoremالشبتر السادس اللي هو the sum and number of
+
+24
+00:02:13,960 --> 00:02:23,460
+divisors مجموع وأعداد القواسم للعدد الصحيح ومن ثم
+
+25
+00:02:23,460 --> 00:02:26,560
+هناخد formula تخدم الموضوع اللي هو Mobius
+
+26
+00:02:26,560 --> 00:02:33,960
+inversion formula وبقول أن هنا الشبتر السادس ومن
+
+27
+00:02:33,960 --> 00:02:38,200
+ثم الشبتر السابع اللي هنتحدث عن الalors phi
+
+28
+00:02:38,200 --> 00:02:45,760
+functionوعن خواصها و هنتحدث عن Euler's theorem ال
+
+29
+00:02:45,760 --> 00:02:49,580
+second exam بيكون بعد ال chapter الخامس والسادس
+
+30
+00:02:49,580 --> 00:02:56,560
+والسابع و من ثم اللي هو هنتحدث عن ال perfect
+
+31
+00:02:56,560 --> 00:03:05,940
+numbers عن المرسيني برايمز و عن فيرمات number و عن
+
+32
+00:03:05,940 --> 00:03:12,630
+خواص هذه الاعداد في حينه ان شاء اللهالشبتر الثامن
+
+33
+00:03:12,630 --> 00:03:17,870
+اللي هو هنتحدث عن ال primitive roots أو مقدمة عن
+
+34
+00:03:17,870 --> 00:03:20,730
+ال primitive roots هناخد في البداية ال order of n
+
+35
+00:03:20,730 --> 00:03:25,610
+integer modulo n ونتحدث عن ال primitive roots of
+
+36
+00:03:25,610 --> 00:03:31,950
+our primes ومن ثم نتحدث إذا سمح الوقت عن مقدمة في
+
+37
+00:03:31,950 --> 00:03:36,260
+علم التشفيروبكون في عندي الآن في النهاية ال final
+
+38
+00:03:36,260 --> 00:03:41,800
+exam إذا ال grading هيكون معتمد على شغلتين عندنا
+
+39
+00:03:41,800 --> 00:03:47,200
+الشغلة الأولى اللي هو two hour exams خمسين في
+
+40
+00:03:47,200 --> 00:03:51,700
+المية وعلى طريقة الحصفة ان شاء الله بنتفج و ال
+
+41
+00:03:51,700 --> 00:03:57,330
+final خمسين في الميةاللي هيكون فيه انه homeworks
+
+42
+00:03:57,330 --> 00:04:01,190
+ال homeworks طبعا هعطيكم homeworks تحلوها في البيت
+
+43
+00:04:01,190 --> 00:04:05,050
+و الأسئلة اللي بتعرفوش تحلوها بتيجوا انها ان شاء
+
+44
+00:04:05,050 --> 00:04:09,510
+الله بنعمل discussion و بنحل هذه الأسئلة اي سؤال
+
+45
+00:04:09,510 --> 00:04:17,050
+اي استفسار حول ما تحدثنا به حول ال course outline
+
+46
+00:04:17,050 --> 00:04:23,570
+او خطة المساقة اه بصين طيب
+
+47
+00:04:26,180 --> 00:04:30,780
+الصلاة على النبي عليه الصلاة والسلام هنبدأ اليوم
+
+48
+00:04:30,780 --> 00:04:39,740
+إن شاء الله في المحاضرة الأولى في نظرية الأعداد أو
+
+49
+00:04:39,740 --> 00:04:44,040
+في مسافة نظرية الأعداد في قسم الرياضيات بالجامعة
+
+50
+00:04:44,040 --> 00:04:51,300
+الإسلامية هنبدأ حسب ال course outline اللي اتحدثنا
+
+51
+00:04:51,300 --> 00:04:59,420
+فيها قبل قليلالشبتر التاني بذوه عنوان Divisibility
+
+52
+00:04:59,420 --> 00:05:03,120
+Theory in the Integers فارساله عن النبي عليه
+
+53
+00:05:03,120 --> 00:05:06,080
+الصلاة والسلام الشبتر التاني Divisibility Theory
+
+54
+00:05:06,080 --> 00:05:11,660
+in the Integers أو نظرية القسمة على الأعداب
+
+55
+00:05:11,660 --> 00:05:16,520
+الصحيحةالـ section الثاني 222 the division
+
+56
+00:05:16,520 --> 00:05:19,400
+algorithm الـ section الأول عبارة عن مقدمة الـ
+
+57
+00:05:19,400 --> 00:05:22,820
+section الثاني the division algorithm أو خوارزمية
+
+58
+00:05:22,820 --> 00:05:27,440
+القسمة خوارزمية القسمة هنبدأ الآن ان شاء الله في
+
+59
+00:05:27,440 --> 00:05:31,920
+أول نظرية في هذا ال section وفي هذا ال course اللي
+
+60
+00:05:31,920 --> 00:05:38,320
+هي تتحدث عن خوارزمية القسمة باختصار ما تتحدث به
+
+61
+00:05:38,320 --> 00:05:44,190
+النظريةلو كان في عندي given integers a و b و b
+
+62
+00:05:44,190 --> 00:05:49,950
+أكبر من 0 عندي أي عددين صحيحين a و b و ال b أكبر
+
+63
+00:05:49,950 --> 00:05:54,870
+من 0 ال b طبعا غطى اللي يساوي سفر بدنا ناخد الحالة
+
+64
+00:05:54,870 --> 00:05:57,950
+الان بي أكبر من سفر و بعد شوية هيكون أصغر من سفر
+
+65
+00:05:57,950 --> 00:06:02,330
+في نظرية أخرى هتكون corollary لها أما الآن هنتحدث
+
+66
+00:06:02,330 --> 00:06:06,990
+عن هذا هيكون بمثابة المقسوم عليه الآن باختصار
+
+67
+00:06:06,990 --> 00:06:11,400
+النظرية بتقولك لو كان في عندي aوB integers ودينا
+
+68
+00:06:11,400 --> 00:06:17,680
+قولنا A على B هيطلع ناتج للقسمة ومتبقي هذا المتبقي
+
+69
+00:06:17,680 --> 00:06:21,360
+وهذا الناتج لو أنا قسمته وانت قسمته وهو قسمته
+
+70
+00:06:21,360 --> 00:06:26,140
+هيطلع اللي هو ناتج القسمة واحد والمتوقع واحد في
+
+71
+00:06:26,140 --> 00:06:31,060
+ضوء انه ناتج القسم اللي هو المتبقي R بين الـ0 و
+
+72
+00:06:31,060 --> 00:06:34,720
+بين الـB هذه هي النظرية باختصار نيجي الآن للتفاصيل
+
+73
+00:06:34,720 --> 00:06:39,910
+given integers A and B with B أكبر من 0There exist
+
+74
+00:06:39,910 --> 00:06:45,830
+unique integers Q and R satisfying A بساوية B في Q
+
+75
+00:06:45,830 --> 00:06:50,490
+زاية R حيث R أكبر بساوية سفر وأصغر من مين من B
+
+76
+00:06:50,490 --> 00:06:57,350
+الان الـ Q هو عبارة عن ناتج القسمة والـ R هو عبارة
+
+77
+00:06:57,350 --> 00:07:05,030
+عن المتبقيإذا الانتجار Q وR يُسمى بالتعريف الـ
+
+78
+00:07:05,030 --> 00:07:10,190
+quotient و الـ remainder في الـ division of A بـ B
+
+79
+00:07:10,190 --> 00:07:15,570
+للتذكير
+
+80
+00:07:16,930 --> 00:07:19,850
+الشبطر التاني divisibility theory in the integers
+
+81
+00:07:19,850 --> 00:07:26,270
+أو نظرية القسمة في الأعداد الصحيحة أو للأعداد
+
+82
+00:07:26,270 --> 00:07:29,190
+الصحيحة ال section اللي بدأنا فيه اللي هو the
+
+83
+00:07:29,190 --> 00:07:32,470
+division algorithm خارزمية القسمةالنظرية اللي
+
+84
+00:07:32,470 --> 00:07:35,570
+بدأنا فيها اللي هي division algorithm لو كان في
+
+85
+00:07:35,570 --> 00:07:40,450
+عندي أي two integers a و b وكان b أكبر من 0 و
+
+86
+00:07:40,450 --> 00:07:45,170
+أردنا نقسم نقول a على b لما نقسم a على b معناته
+
+87
+00:07:45,170 --> 00:07:49,930
+هيكون في عندي ناتج قسمة ومتبقى قسمة الناتج هيكون
+
+88
+00:07:49,930 --> 00:07:56,350
+وحيد والمتبقى وحيدقلنا إنه هيكون الـ A هتصير على
+
+89
+00:07:56,350 --> 00:08:00,950
+صورة Q بـ B زائد R حيث الـ R أكبر سواء 0 وأصغر من
+
+90
+00:08:00,950 --> 00:08:05,390
+B هذا المتبقي من القسمة و الـ Q اللي هو ناتج
+
+91
+00:08:05,390 --> 00:08:11,710
+القسمة و Q and R اللي هما هم إنتجارات مختلفة The
+
+92
+00:08:11,710 --> 00:08:15,850
+first one Q is called the quotient The second one
+
+93
+00:08:15,850 --> 00:08:21,270
+R is called the remainder in the division of A by
+
+94
+00:08:21,270 --> 00:08:28,740
+Bلان نجي لبرهان النظرية برهان النظرية هستقل برهان
+
+95
+00:08:28,740 --> 00:08:36,220
+من المعطيات أو المطلوب من النظرية الان عندي اللي
+
+96
+00:08:36,220 --> 00:08:45,380
+هو A بتساوي Q في B زائد R عندي R اللي هو المتبقى
+
+97
+00:08:45,380 --> 00:08:53,500
+من القسمة بتساوي A ناقص Q في Bالآن بدي أكوّن set
+
+98
+00:08:53,500 --> 00:08:58,720
+هذه ال set هي المنطلق للوصول إلى النتيجة ال set
+
+99
+00:08:58,720 --> 00:09:07,940
+بتساوي عبارة عن كل الأعداد اللي عصورت a ناقص x في
+
+100
+00:09:07,940 --> 00:09:18,880
+b حيث ال x عبارة عن integer element in zوالعدد a-x
+
+101
+00:09:18,880 --> 00:09:25,440
+بb هيكون أكبر أو يساوي سفر طبعا أنا مطمعا ال a و
+
+102
+00:09:25,440 --> 00:09:30,740
+ال b و المتغير x فانا بدي أسي عبارة عن كل الأعداد
+
+103
+00:09:30,740 --> 00:09:37,420
+الممكنة اللي عصورة a-x بb حيث x في z و a-x بb أكبر
+
+104
+00:09:37,420 --> 00:09:41,980
+أو يساوي إياش أكبر أو يساوي سفر الآن بدي أثبتلك
+
+105
+00:09:41,980 --> 00:09:44,080
+شغلتين
+
+106
+00:09:45,290 --> 00:09:50,350
+الشغلة الأولى أن S is non-empty الشغلة الثانية
+
+107
+00:09:50,350 --> 00:09:55,550
+اللى هي واضحة أن الأعداد اللى بتتكون منها S اللى
+
+108
+00:09:55,550 --> 00:10:00,010
+هي A نقص 6B ماخدها A شمالها أكبر أو يساوي سفر يعني
+
+109
+00:10:00,010 --> 00:10:06,630
+بمعنى آخر S حصل عبارة عن non-empty set of non
+
+110
+00:10:06,630 --> 00:10:10,790
+-negative integersإذا حسب الـ Will Ordering
+
+111
+00:10:10,790 --> 00:10:13,890
+Principle إيش الـ Will Ordering Principle بتقول
+
+112
+00:10:13,890 --> 00:10:20,790
+أنه any non-empty set of non-negative integers has
+
+113
+00:10:20,790 --> 00:10:27,290
+a least element معايا؟ إذا .. إذا ال .. ال .. ال
+
+114
+00:10:27,290 --> 00:10:30,680
+Will Ordering Principle أخدناها في المبادئبتقول
+
+115
+00:10:30,680 --> 00:10:37,320
+كما يالي إنه أي مجموعة جزئية من الأعداد الصحيحة
+
+116
+00:10:37,320 --> 00:10:43,380
+الغير سالبة دائما لها عنصر أقل اللي هو بنسميه إيش
+
+117
+00:10:43,380 --> 00:10:47,760
+ماله least element اللي هو لو وصلت للأس إنه non
+
+118
+00:10:47,760 --> 00:10:49,760
+-intersect of positive of non-negative integers
+
+119
+00:10:49,760 --> 00:10:53,140
+معناته وصلت إنها إيش مالها إلها least element ال
+
+120
+00:10:53,140 --> 00:10:56,640
+least element أنا بتدعي اللي هو اللي على الصورة
+
+121
+00:10:56,640 --> 00:11:02,230
+هذه ده سميه Rفبتكون R هي هذه الـ R اللي إحنا بدنا
+
+122
+00:11:02,230 --> 00:11:06,710
+إياها وفي نفس الوقت قيمة X المقابلة هي الـ Q
+
+123
+00:11:06,710 --> 00:11:11,250
+المطلوبة وحنثبت لكم إن الـ R و الـ Q إيه شمالهم؟
+
+124
+00:11:11,250 --> 00:11:17,210
+واحدات نيجي الآن، اتوكل على الله، شوفوا عند الآن
+
+125
+00:11:17,210 --> 00:11:21,130
+consider the set S بتساوي A نقص X بي X limited Z A
+
+126
+00:11:21,130 --> 00:11:25,690
+minus X بيه أكبر أو يساوي سفرواضح إنها عبارة عن
+
+127
+00:11:25,690 --> 00:11:29,090
+set of positive integers أو non-negative integers
+
+128
+00:11:29,090 --> 00:11:39,510
+إذن S is a set of non-negative integers هذي الأول
+
+129
+00:11:39,510 --> 00:11:44,710
+لأن اتنين بيدثبتلك إن S non-empty يعني بيدجيب لك
+
+130
+00:11:44,710 --> 00:11:50,440
+concrete exampleبقيمة X بحيث يكون A-X في B و A
+
+131
+00:11:50,440 --> 00:11:57,480
+موجود فاس يعني أكبر يساوي إيهاش؟ سفر شوف عندي عندي
+
+132
+00:11:57,480 --> 00:12:04,600
+أنا معطيني في النظرية أن الـB أشماله أكبر من سفر و
+
+133
+00:12:04,600 --> 00:12:10,020
+B integer مزام أكبر من سفر إذا حيكون الـB عند نفسه
+
+134
+00:12:10,020 --> 00:12:16,020
+أشماله أكبر أو يساوي واحدصح ولا لأ؟ إذا من واحد
+
+135
+00:12:16,020 --> 00:12:21,240
+وطالع طيب اضربن الجهتين في ال absolute value للـA
+
+136
+00:12:21,240 --> 00:12:26,580
+في بصير ال absolute value للـA في ال B أكبر أو
+
+137
+00:12:26,580 --> 00:12:31,180
+يساوي ال absolute value لمين؟ مصبوط ولا لا؟ أكيد
+
+138
+00:12:31,180 --> 00:12:38,330
+صح طيبالان ضيف للجهتين a فبصير a زي ال absolute
+
+139
+00:12:38,330 --> 00:12:42,010
+value لل a أكبر أو ساوي ال absolute value لل a زي
+
+140
+00:12:42,010 --> 00:12:47,630
+المين زي ال a لاحظ الان ال absolute value لل a لها
+
+141
+00:12:47,630 --> 00:12:54,860
+حلقتين يا a موجبةY سالبة في حالة الـ A مُجّبة الـ
+
+142
+00:12:54,860 --> 00:12:58,900
+absolute value لـ A هي الـ A فبصير A زياد A اتنين
+
+143
+00:12:58,900 --> 00:13:04,000
+A أكيد أكبر أو يساوي إيهاش سفر طيب في حالة الـ A
+
+144
+00:13:04,000 --> 00:13:07,500
+سالبة بصير ال absolute value لـ A مقصه يعني أنه
+
+145
+00:13:07,500 --> 00:13:11,780
+مقص A زياد A مش بيساوي سفر إذا في كل الأحوال هيكون
+
+146
+00:13:11,780 --> 00:13:17,200
+هذا المقدار أكبر أو يساوي إيهاش سفرإذا الأن لو أنت
+
+147
+00:13:17,200 --> 00:13:22,380
+أخدت ال X هذا هو مين هذا نفسه عبارة عن A ناقص ال
+
+148
+00:13:22,380 --> 00:13:27,420
+absolute value ل A بالسالب في B مظبوط؟ هذا أكبر أو
+
+149
+00:13:27,420 --> 00:13:33,220
+ساوي سفر ال X خدها هذه و integer هذا فبصير عندي
+
+150
+00:13:33,220 --> 00:13:37,460
+حسب الحكي اللي هنا أن هذا المقدار و ال A بين دي
+
+151
+00:13:37,460 --> 00:13:41,520
+طبعا إذا صار عندي هذا المقدار موجود في S إذا صارت
+
+152
+00:13:41,520 --> 00:13:49,010
+Sلا تساوي فاهم من الجهتين صار في عندي S is a non
+
+153
+00:13:49,010 --> 00:13:53,010
+-empty set of non-negative integers معناه يا بابا
+
+154
+00:13:53,010 --> 00:13:59,030
+ويحيى فاهم اه ايه السؤال طيب صار عندنا S is a non
+
+155
+00:13:59,030 --> 00:14:03,050
+-empty set of positive integers او non-negative
+
+156
+00:14:03,050 --> 00:14:14,410
+integers اذا S اذا S has a least elementCall it
+
+157
+00:14:14,410 --> 00:14:21,750
+سمّيه R مش الحال اثبتنا انه خلاص R موجود لان R كيف
+
+158
+00:14:21,750 --> 00:14:28,030
+صورته؟ R بساوي A نقص X في B هذا اللي نجيته انا
+
+159
+00:14:28,030 --> 00:14:33,010
+اللي وجدته سمي ال X المقابلة إيه وإيش اسمها؟ Q
+
+160
+00:14:33,010 --> 00:14:38,470
+أكيد هذا من التعريف اللي فوق R أكبر يساوي إيش؟
+
+161
+00:14:38,470 --> 00:14:45,490
+سفر، إذا أول حاجةالان اكبر او يساوي سفر بدي اثبت
+
+162
+00:14:45,490 --> 00:14:51,230
+لك الان ان ال R أصغر من B معايا؟ الان ايش بدي
+
+163
+00:14:51,230 --> 00:14:55,750
+اثبتلك؟ اذا اثبتت R أصغر من B معناته انا لجيت R و
+
+164
+00:14:55,750 --> 00:15:00,430
+Q بحيث ان R بيساوي A نغسط Q في B وR بين السفر و
+
+165
+00:15:00,430 --> 00:15:07,090
+بين ال B بيظل علي اثبت ال uniqueness لل R و Q واضح
+
+166
+00:15:07,090 --> 00:15:18,990
+أه؟ طيبالآن نحن سنثبّر أن R أقل من B سببوز Not بدا
+
+167
+00:15:18,990 --> 00:15:23,170
+افترض العكس وصل الـ Contradiction الان بدا افترض
+
+168
+00:15:23,170 --> 00:15:28,750
+Not يعني بمعنى اخر ايش بدا افترض بدا افترض ان R
+
+169
+00:15:28,750 --> 00:15:35,260
+أكبر او يساوي Bطيب خدلك الحسبة البسيطة مدام R أكبر
+
+170
+00:15:35,260 --> 00:15:41,200
+أو سوى B معناته R ناقص B أكبر أو سوى إيش؟ سفر واضح
+
+171
+00:15:41,200 --> 00:15:46,740
+أه؟ R ناقص B أكبر أو سوى سفر R إيش قيمتها؟ هيها
+
+172
+00:15:46,740 --> 00:15:55,860
+اللي هو A ناقص U في B ناقص الـB صح ولا لا؟ هي لا
+
+173
+00:15:55,860 --> 00:16:03,390
+طيب الآن خد الـB أعمل مشتركبصير عندى هذا المقدار
+
+174
+00:16:03,390 --> 00:16:09,750
+عبارة عن a ناقص في u زائد واحد في b صح ولا لا هذا
+
+175
+00:16:09,750 --> 00:16:15,570
+هيصير بساوى هذا اللى هو أكبر أو يساوى من صفر إذا
+
+176
+00:16:15,570 --> 00:16:22,910
+صار هذا المقدار وين موجود لأن هى زي ال X تبعته صار
+
+177
+00:16:22,910 --> 00:16:28,860
+هذا موجود في Sإذا صار عند الـ r-b اللي بيثوي صار r
+
+178
+00:16:28,860 --> 00:16:34,760
+ناقص b element من مين enough لكن احنا بنعرف ان الـ
+
+179
+00:16:34,760 --> 00:16:39,500
+r ناقص b أكيد أصغر من مين من r وهذا contradiction
+
+180
+00:16:39,500 --> 00:16:45,510
+لأن ايش ما لها r is the least such elementما دام R
+
+181
+00:16:45,510 --> 00:16:49,410
+is the least element in S ولاقيت R نقص بيه element
+
+182
+00:16:49,410 --> 00:16:52,570
+in S إذا صار في عندي contradiction إذا الفرضية
+
+183
+00:16:52,570 --> 00:16:57,090
+اللي فرضتها اللي هي هذه خطأ إذا لازم تكون الـ R
+
+184
+00:16:57,090 --> 00:17:02,470
+أصغر من مين إذا صار عندي الآن النتيجة النهائية صار
+
+185
+00:17:02,470 --> 00:17:14,230
+عندي أنا وجدت أن في R و QElement in Z such that R
+
+186
+00:17:14,230 --> 00:17:22,090
+بتساوي A ناقص Q في B حيث R أكبر أو تساوي سفر وأصغر
+
+187
+00:17:22,090 --> 00:17:27,930
+من مين من B الآن بلى عليا أثبت أن الـ R و الـ Q
+
+188
+00:17:27,930 --> 00:17:33,290
+are unique يعني R is unique و Q is unique نفترض
+
+189
+00:17:33,290 --> 00:17:42,770
+الآن أنه لأ مش وحداتنفترض إنه في R' وفي Q' يحقق
+
+190
+00:17:42,770 --> 00:17:47,390
+نفس الشيء يعني بدأ افترض إنه في عندي برضه في عندي
+
+191
+00:17:47,390 --> 00:17:55,150
+there exist R وR' وQ وQ' such that نفترض إنه في R'
+
+192
+00:17:55,590 --> 00:18:07,550
+وR وQ وQ' بحيث اللي هو R R بتساوي A نقص Q في BوR'
+
+193
+00:18:08,070 --> 00:18:15,850
+بيساوي A ناقص U' في B حيث اللي هو R أكبر بيساوي
+
+194
+00:18:15,850 --> 00:18:21,770
+سفر وأصغر من B وR' أكبر بيساوي سفر وأصغر من مين من
+
+195
+00:18:21,770 --> 00:18:28,430
+B مظبوط اللي بيكتبه صحيح؟ طيب احسبني الأن R ناقص
+
+196
+00:18:28,430 --> 00:18:38,020
+R' R ناقص R' إيش هتساوي؟اللي هو سالب Q' نقص Q في B
+
+197
+00:18:38,020 --> 00:18:42,560
+صح ولا لا؟ راح نعمل معاها خد ال absolute value
+
+198
+00:18:42,560 --> 00:18:46,560
+الجهتين بطلع عندك ال absolute value لهذا ساو ال
+
+199
+00:18:46,560 --> 00:18:50,200
+absolute value لهذا في ال absolute value لل B و ال
+
+200
+00:18:50,200 --> 00:18:55,180
+B موجرة إيه دلوقتي نفسها، مظبوط؟ هذه سميليها 1،
+
+201
+00:18:55,180 --> 00:19:00,170
+هنرجع إليهابتثبت لكم الآن هذا المقدار سفر و من فمه
+
+202
+00:19:00,170 --> 00:19:03,390
+احصل على هذا سفر او هذا سفر احصل على هذا سفر و
+
+203
+00:19:03,390 --> 00:19:06,990
+بكون خلصت معايا؟ شوفوا طالع ال inequalities اللي
+
+204
+00:19:06,990 --> 00:19:13,350
+فوق هذول ننطلق من هنا ال inequalities اللي فوق
+
+205
+00:19:13,350 --> 00:19:18,850
+عندك ضروب اللي اتحت في سالب مثلا بصير عند R او
+
+206
+00:19:18,850 --> 00:19:22,090
+اطرحها من بعض او اطرحها من بعض R أكبر سواء سفر و
+
+207
+00:19:22,090 --> 00:19:28,170
+اصغر من B وعندي سالب R primeاللي هو مظبوط أصغر أو
+
+208
+00:19:28,170 --> 00:19:32,290
+يساوي صفر وأكبر أو يساوي سالب B مظبوط اللي عملناه،
+
+209
+00:19:32,290 --> 00:19:37,810
+صح؟
+
+210
+00:19:37,810 --> 00:19:42,630
+أه، بزول يساوي، صحيح، كلام صحيح، اجبحنا بعضنا
+
+211
+00:19:42,630 --> 00:19:49,050
+خلاص، بس أنا عندي R ناقص، R prime اللي هو أصغر أو
+
+212
+00:19:49,050 --> 00:19:54,970
+يساوي B وأكبر أو يساوي سالب Bهذا شو معناته؟ هذا ما
+
+213
+00:19:54,970 --> 00:19:58,410
+فوق الـ absolute value هذا معناته الـ absolute
+
+214
+00:19:58,410 --> 00:20:04,610
+value لـ R نقص R prime أصغر من مين؟ من B أصغر
+
+215
+00:20:04,610 --> 00:20:08,090
+strictly حتى لأن هذا أصغر strictly و هذا أصغر ساوي
+
+216
+00:20:08,090 --> 00:20:12,430
+التنتين مع بعض أصغر strictly واضح، و هذا نفس الشيء
+
+217
+00:20:12,430 --> 00:20:17,570
+أصغر strictly إذا صار عندي هذا أصغر strictly من
+
+218
+00:20:17,570 --> 00:20:26,080
+مين؟ من B معايا نرجع للي فوقما دام هذا أصغر من B،
+
+219
+00:20:26,080 --> 00:20:31,940
+إذاً هذا صار إيه أشماله؟ إذاً صار عندي Q ناقص، Q
+
+220
+00:20:31,940 --> 00:20:35,460
+prime absolute value في الـB أصغر الـcircuit من
+
+221
+00:20:35,460 --> 00:20:40,680
+مين؟ من B أكيد أه، دسم على B لأنه B لاتشهر سفر،
+
+222
+00:20:40,680 --> 00:20:46,360
+إذاً صار عندي Q prime ناقص Q أصغر من 1، ما هي
+
+223
+00:20:46,360 --> 00:20:50,840
+absolute value هذه؟ إذاً أكيد أكبر شهر مين؟ سفر
+
+224
+00:20:51,530 --> 00:20:56,470
+الأن أبشرله جاله أكبر أشهر و أصغر من واحد و هذا
+
+225
+00:20:56,470 --> 00:21:00,430
+أدت صحيح و هذا أدت صحيح فهذا أدت صحيح العدد الصحيح
+
+226
+00:21:00,430 --> 00:21:04,890
+اللي أكبر أشهر و أصغر من واحد مين هو؟ السفر بس
+
+227
+00:21:04,890 --> 00:21:11,150
+مدام هذا عدد صحيح و أكبر أشهر و أصغر من واحد قطعا
+
+228
+00:21:11,150 --> 00:21:19,950
+لازم يكون عندى Q' ناقص Q بساوي سفر ومن ثم Q' تساوي
+
+229
+00:21:19,950 --> 00:21:28,380
+Qرد وانعوض في واحد هذه سفر إذا صارت هذه سفر إذا
+
+230
+00:21:28,380 --> 00:21:37,300
+صار R إيش بتساوي؟ R إبراهيم إذا اللي سوناه أثبتنا
+
+231
+00:21:37,300 --> 00:21:44,510
+وجود R وQ في Zبحيث أن R بتساوي A نقص Q في B وR
+
+232
+00:21:44,510 --> 00:21:48,250
+أكبر تساوي 0 أصغر من B وR وQ اللي لاجيناه هنا إيه
+
+233
+00:21:48,250 --> 00:21:52,510
+شمال هنا واحدات وهذا بعزز الكلام اللي احنا من
+
+234
+00:21:52,510 --> 00:21:56,950
+الاصل عارفينه أو اتعلمناه في الإعداد أو كده إنه لو
+
+235
+00:21:56,950 --> 00:22:01,090
+جينا قسمنا عددين على بعض لو بدنا نقسم اللي هو 24
+
+236
+00:22:01,090 --> 00:22:02,090
+على 7
+
+237
+00:22:05,100 --> 00:22:09,800
+كلنا جوابنا واحد أن خارجنا ناتج القسمة تلاتة
+
+238
+00:22:09,800 --> 00:22:14,460
+والباقي تلاتة على اعتبار أن الباقي أكبر يساوي سفر
+
+239
+00:22:14,460 --> 00:22:19,760
+وأصغر من المقسوم عليه فهذا اللي هو بتكون اللي هي
+
+240
+00:22:19,760 --> 00:22:27,800
+احنا أثبتنا اللي هي خوارزميت القسمة اللي هي نظرية
+
+241
+00:22:27,800 --> 00:22:28,980
+2.1
+
+242
+00:22:32,450 --> 00:22:37,690
+لأن لاحظوا هنا أنا أخدت اللي هو الـ B أشماله أكبر
+
+243
+00:22:37,690 --> 00:22:43,110
+من 0 لأن حتى لو كانت الـ B أصغر من 0 هتطلع اللي هي
+
+244
+00:22:43,110 --> 00:22:48,650
+النظرية صحيحة ولكن مع شوية modification بسيطة اللي
+
+245
+00:22:48,650 --> 00:22:55,630
+هي الـ Corollary اللي عندنا اللي هو Corollary if A
+
+246
+00:22:55,630 --> 00:23:02,580
+and B are integers with الآن أشمالهاB لا تساوي سفر
+
+247
+00:23:02,580 --> 00:23:06,900
+شملنا الحالة التالية اللي هو الـ B أصغر من مين من
+
+248
+00:23:06,900 --> 00:23:13,700
+سفر then there exist unique integers Q and R such
+
+249
+00:23:13,700 --> 00:23:17,320
+that A بيساوي Q في B زايد R والـ R أكبر يساوي سفر
+
+250
+00:23:17,320 --> 00:23:21,060
+وأصغر من مين الآن من ال absolute value الـ B يعني
+
+251
+00:23:21,060 --> 00:23:25,240
+الآن صارت النظرية in general لو
+
+252
+00:23:34,520 --> 00:23:41,780
+أجينا لو أجينا كان عندنا أي عددين صحيحين A وB لا
+
+253
+00:23:41,780 --> 00:23:47,320
+تساوي سفر عشان بتقسم على الـB معايا؟بقدر اللي هو
+
+254
+00:23:47,320 --> 00:23:51,680
+على طول قسمة الـ A على الـ B بيصير عند A بيساوي B
+
+255
+00:23:51,680 --> 00:23:56,360
+في Q زائد اللي هو الـ remainder R الـ Q نتيجي
+
+256
+00:23:56,360 --> 00:24:01,680
+القسمة والـ R اللي هو المتبقى لان المتبقى R أكبر
+
+257
+00:24:01,680 --> 00:24:06,240
+يساوي سفر وأصغر من مين؟ من الـ absolute value
+
+258
+00:24:06,240 --> 00:24:12,500
+لمين؟ للـ B ال absolute value للـ B معايا؟ وحيكون
+
+259
+00:24:12,500 --> 00:24:18,780
+الـ R و الـ Q واحداتفي حالة الـ B أكبر من 0 اللي
+
+260
+00:24:18,780 --> 00:24:23,520
+هي النظرية في الأصل ماشي الحالة إذا الان إذا طبيعي
+
+261
+00:24:23,520 --> 00:24:27,880
+it is enough to consider the case in which B is a
+
+262
+00:24:27,880 --> 00:24:31,900
+negative معايا؟ مدام الـ B negative أكيد ال
+
+263
+00:24:31,900 --> 00:24:34,960
+absolute value اللي هي أشمالها أكبر من 0 الآن
+
+264
+00:24:34,960 --> 00:24:38,960
+بنطبق النظرية على مين؟ على absolute value ماشي؟
+
+265
+00:24:38,960 --> 00:24:43,020
+مدام بنطبق النظرية على absolute value إذا صار عند
+
+266
+00:24:43,020 --> 00:24:48,490
+الـ Aالـ A معايا يا شباب إذا طبّج النظرية اللي
+
+267
+00:24:48,490 --> 00:24:50,830
+جابله مش هو الـ Division Algorithm على الـ
+
+268
+00:24:50,830 --> 00:24:53,190
+Absolute Value يعني بتدبّث مع الـ Absolute Value
+
+269
+00:24:53,190 --> 00:24:57,550
+للـ A إذا بالساوية الـ Absolute Value للـ B في الـ
+
+270
+00:24:57,550 --> 00:25:04,950
+Q زائد R Q' بسميها النظرية اللي جابله بما إنه كيف
+
+271
+00:25:04,950 --> 00:25:09,870
+طبّجنا النظرية الآن A Integer والـ Absolute Value
+
+272
+00:25:09,870 --> 00:25:15,080
+للـ B أكبر من 0 Integer إذا there exist uniqueاللي
+
+273
+00:25:15,080 --> 00:25:21,440
+هو R و Q' such that معايا؟ ايه بيساوي الـ Absolute
+
+274
+00:25:21,440 --> 00:25:25,140
+value الـ B في Q' زي الـ R حيث و R أكبر أو يساوي
+
+275
+00:25:25,140 --> 00:25:29,000
+سفر و أصغر من مين Absolute value الـ B بدت تظهر
+
+276
+00:25:29,000 --> 00:25:33,060
+النتيجة اللي بديها اه؟ ضل الان هتبديش يهيأك اللي
+
+277
+00:25:33,060 --> 00:25:37,580
+بديها يهيأش على صورة B ماشي سهل اللي هو عندك الـ
+
+278
+00:25:37,580 --> 00:25:39,220
+Absolute value الـ B negative ما احنا خدناها حالة
+
+279
+00:25:39,220 --> 00:25:44,530
+الـ Negative اذا بيصير A بساوياللي هو عبارة عن الـ
+
+280
+00:25:44,530 --> 00:25:47,790
+absolute value للـ B اللي هو عبارة عن مين هي سلبي
+
+281
+00:25:47,790 --> 00:25:55,370
+في B في ناقص Q' زي دار هذا هي اللي فوقالان الناقص
+
+282
+00:25:55,370 --> 00:26:00,050
+الـ Q' هي الدسمية مين الـ Q وبما ان الـ Q' كانت
+
+283
+00:26:00,050 --> 00:26:04,730
+وحيدة إذا النقص هياش وحيد إذا صار عندي النتيجة
+
+284
+00:26:04,730 --> 00:26:09,710
+النهائية واضحة إذا there exists unique arrow Q
+
+285
+00:26:09,710 --> 00:26:15,920
+بحيث أن A بساوي الـ Bفي الـ Q اللي عندى زيادة الـ
+
+286
+00:26:15,920 --> 00:26:22,720
+R R أكبر يساوي صفر أخر absolute value لمن؟ لـ B أي
+
+287
+00:26:22,720 --> 00:26:29,100
+سؤال؟ أي استفسار؟ قولوا إذا كان فيه إشي يعني بدنا
+
+288
+00:26:29,100 --> 00:26:36,580
+نعيده واضح أه؟ طيب بعض الملاحظات على النظرية يعني
+
+289
+00:26:36,580 --> 00:26:40,820
+كيف بدنا نستخدم نوظف النظرية لاستخداماتنا في
+
+290
+00:26:40,820 --> 00:26:49,130
+الأسئلة أو حلول الأسئلةالان بناء على خوارزمية
+
+291
+00:26:49,130 --> 00:26:56,830
+القسم اللى حكينا عنها الان لو كان في عندى الـ AI
+
+292
+00:26:56,830 --> 00:27:01,050
+integer القسم
+
+293
+00:27:01,050 --> 00:27:05,010
+على 2 هتعملّي
+
+294
+00:27:05,010 --> 00:27:12,570
+classifications للأعداد الصحيحةإنه حاجتين يا إما
+
+295
+00:27:12,570 --> 00:27:18,910
+على صورة اللي هو المتبقي سفر يا واحد من أين جبته؟
+
+296
+00:27:18,910 --> 00:27:24,670
+خلّيني أشوف إذن الآن من قابلية القسمة على اتنين
+
+297
+00:27:24,670 --> 00:27:31,250
+اللي هي النظرية قبل شوية بس بتطبقها A انتجر والـ B
+
+298
+00:27:31,250 --> 00:27:38,370
+بتساوي اتنين إذن there exists unique ROQ such that
+
+299
+00:27:38,370 --> 00:27:47,060
+Aبتساوي B في Q اللي هي 2 Q زائد R حيث R أكبر أو
+
+300
+00:27:47,060 --> 00:27:54,710
+سوى 0 وأصغر من 100 من 2 إذا نقرنها عن الـ RHas two
+
+301
+00:27:54,710 --> 00:28:00,530
+cases only one or zero إذا .. إذا صار في عند
+
+302
+00:28:00,530 --> 00:28:05,670
+الأعداد اللي في الدنيا الصحيحة إما هتكون A على
+
+303
+00:28:05,670 --> 00:28:11,770
+صورة 2Q في حالة الأرض سفر أو A بساوة 2Q زائد 1
+
+304
+00:28:11,770 --> 00:28:18,410
+Similarly .. Similarly لو أجينا قولنا A ان انتجار
+
+305
+00:28:18,410 --> 00:28:26,060
+و اللي هو الـ B بتساوي تلاتةبرضه بخوارزمية القسمة
+
+306
+00:28:26,060 --> 00:28:33,900
+يوجد الـ Q وR واحدات حيث ايه؟ A بتسوى B في Q A
+
+307
+00:28:33,900 --> 00:28:43,540
+زائد R A في Q زائد R A بتسوى B في Q زائد R والـ R
+
+308
+00:28:43,540 --> 00:28:49,600
+أكبر بسوية سفر وأصغر من 3 اذا في عندي three cases
+
+309
+00:28:49,600 --> 00:28:56,650
+أو three forms عشان هيك بنقولالإنتجر A لديه إحدى
+
+310
+00:28:56,650 --> 00:28:58,490
+الانتجر A لديه إحدى الانتجر A لديه إحدى الانتجر A
+
+311
+00:28:58,490 --> 00:28:58,690
+لديه إحدى الانتجر A لديه إحدى الانتجر A لديه إحدى
+
+312
+00:28:58,690 --> 00:28:59,230
+الانتجر A لديه إحدى الانتجر A لديه إحدى الانتجر A
+
+313
+00:28:59,230 --> 00:29:00,750
+لديه إحدى الانتجر A لديه إحدى الانتجر A لديه إحدى
+
+314
+00:29:00,750 --> 00:29:01,130
+الانتجر A لديه إحدى الانتجر A لديه إحدى الانتجر A
+
+315
+00:29:01,130 --> 00:29:06,950
+لديه إحدى الانتجر A لديه إحدى الانتجر A لديه إحدى
+
+316
+00:29:06,950 --> 00:29:11,630
+الانتجر A لديه إحدى الانتجر A لديه إحدى الانتجر A
+
+317
+00:29:11,630 --> 00:29:12,430
+لدي
+
+318
+00:29:14,710 --> 00:29:21,770
+3 forms for the integer A is equal to 3Q A بيساوي
+
+319
+00:29:21,770 --> 00:29:30,450
+3Q plus 1 او A بيساوي 3Q plus 2 يعني
+
+320
+00:29:30,450 --> 00:29:39,070
+بمعنى آخر احنا بخوارزمية القسمة بنستطيع ان الاعداد
+
+321
+00:29:39,070 --> 00:29:44,110
+ال integers اي عدد integer في الدنياانخليه في
+
+322
+00:29:44,110 --> 00:29:49,810
+finite number of terms بحسب ما يخدمنا في السؤال
+
+323
+00:29:49,810 --> 00:29:53,850
+يعني يمكن يخدمني خمسة، يمكن يخدمني ستة، يمكن
+
+324
+00:29:53,850 --> 00:29:57,530
+يخدمني سبعة، يمكن يخدمني تمانية، إذا بالقسم على
+
+325
+00:29:57,530 --> 00:30:04,140
+اتنين، في عندي two formsبالقسم على ثلاثة بيساوي Q
+
+326
+00:30:04,140 --> 00:30:07,460
+ثلاثة Q ثلاثة Q زاد واحد ثلاثة Q ثلاثة U زاد اثنين
+
+327
+00:30:07,460 --> 00:30:10,800
+بالقسم على أربعة بيساوي 4Q ثلاثة 4Q زاد واحد ثلاثة
+
+328
+00:30:10,800 --> 00:30:14,240
+4Q زاد اثنين ثلاثة 4Q زاد ثلاثة 3 بالقسم على خمسة
+
+329
+00:30:14,240 --> 00:30:21,060
+و هكذا أي سؤال؟ اه صحيح
+
+330
+00:30:27,580 --> 00:30:31,140
+نعم تبدو كـ Odd الـ Odd بيكون على صورة اتنين Q
+
+331
+00:30:31,140 --> 00:30:38,170
+زائد واحد الـ Q انتجرلهو الـ Zero طبعا قطعا اللي
+
+332
+00:30:38,170 --> 00:30:43,430
+هو even مش الحاجة الـ Zero في بعض الكتب لكن قليلة
+
+333
+00:30:43,430 --> 00:30:47,930
+بتصنفه ك natural number وكثير من الكتب أو معظم
+
+334
+00:30:47,930 --> 00:30:52,550
+الكتب بتصنفه انه خارج ال natural number يعني هو
+
+335
+00:30:52,550 --> 00:30:56,370
+بقسم الأعداد هذي اصطلاحا يعني بقسم الأعداد إلى
+
+336
+00:30:56,370 --> 00:31:01,150
+صحيحة موجبة وصحيحة سالبةوالـ 0 اللي هو العدد اللي
+
+337
+00:31:01,150 --> 00:31:03,130
+هو الـ neutral بين الجهتي اللي هو الـ identity
+
+338
+00:31:03,130 --> 00:31:06,550
+بالعب لعبة الـ identity بالنسبة للجامع وها تمام
+
+339
+00:31:06,550 --> 00:31:10,890
+أما even لأ هو even يعني لأ الصورة 2Q يعني لا يمكن
+
+340
+00:31:10,890 --> 00:31:14,530
+كتابة الـ 0 0 لو فرضنا واحد جالب أقدر أكتب عليه 2Q
+
+341
+00:31:14,530 --> 00:31:18,750
+وزيد واحد و بعدين 2Q بس هو ناقص واحد لأ بصير الـ Q
+
+342
+00:31:18,750 --> 00:31:23,550
+is not انتجار واضح
+
+343
+00:31:23,550 --> 00:31:28,810
+أه؟ إذا أكيد اللي هو even numberبتصور انت بتقصد
+
+344
+00:31:28,810 --> 00:31:34,390
+انه zero natural او مش natural احنا
+
+345
+00:31:34,390 --> 00:31:39,650
+قولنا استلاحا استلاحا خلينا نقول المعظم الكتب
+
+346
+00:31:39,650 --> 00:31:43,530
+بتعتبر اللي هو ال zero is not a natural number
+
+347
+00:31:44,850 --> 00:31:48,270
+واللي هو بعض الكتب ما اتذكر انه في كتب عنا في
+
+348
+00:31:48,270 --> 00:31:50,510
+الاعدادية او في الكذا كانوا يعتبروه natural حاليا
+
+349
+00:31:50,510 --> 00:31:54,590
+لا اه حاليا لا يعني هذا أمر اصطلاحي يعني لكن لكن
+
+350
+00:31:54,590 --> 00:31:59,030
+الأنسب للاستعمال هو انه ما يعتبروش natural لإنها
+
+351
+00:31:59,030 --> 00:32:02,650
+تستثنى انتظرك تستثنى تحط أن الصار ليش فلس أنه فلس
+
+352
+00:32:02,650 --> 00:32:06,470
+فلع النبي عليه الصلاة والسلام الله الآن
+
+353
+00:32:08,810 --> 00:32:13,170
+قلنا الملاحظة الأولى الملاحظة الثانية the square
+
+354
+00:32:13,170 --> 00:32:19,010
+of any integer has the form 4k زائد او 4k زائد 1
+
+355
+00:32:19,010 --> 00:32:24,710
+الان بدنا نوظف معرفتنا يعني و كأنه الان بقولك show
+
+356
+00:32:24,710 --> 00:32:35,350
+that افترض ان اقول show that a تربيع has أو letbe
+
+357
+00:32:35,350 --> 00:32:45,050
+an integer show that a تربيع has one of the two
+
+358
+00:32:45,050 --> 00:32:53,730
+forms a أربع a أربع k او أربع k زائد واحد ماشي
+
+359
+00:32:53,730 --> 00:32:56,470
+الحاجة اللي أنا زي بقولها قبل و شوية بخبرزمية
+
+360
+00:32:56,470 --> 00:33:02,970
+القسمة by division algorithm by division algorithm
+
+361
+00:33:04,040 --> 00:33:12,180
+A لديه واحد من اتنين
+
+362
+00:33:12,180 --> 00:33:21,140
+كيوات او اتنين كيوات اكتر من واحد ثم ايه
+
+363
+00:33:21,140 --> 00:33:27,060
+تربيع بيساوي اتنين كيوات تربيع بيساوي اربعة كيوات
+
+364
+00:33:27,060 --> 00:33:30,480
+تربيع بيساوي اربعة كيف او some كيف يساوي كيوة
+
+365
+00:33:30,480 --> 00:33:36,770
+تربيع في هذه الحالةA تربيع يسوى 2Q plus 1 تربيع
+
+366
+00:33:36,770 --> 00:33:45,150
+يسوى 4Q تربيع زاد 4Q زاد 1 يسوى 4Q تربيع زاد Q زاد
+
+367
+00:33:45,150 --> 00:33:50,010
+1 يسوى 4K زاد 1 for some K في هذه الحالة Q تربيع
+
+368
+00:33:50,010 --> 00:33:54,750
+زاد K الـ
+
+369
+00:33:54,750 --> 00:34:00,250
+K هي عبارة عن صورة 4 في integer سميت ال integer Q
+
+370
+00:34:00,250 --> 00:34:04,480
+تربيع في هذه الحالة Kإذا قدرت أكتب ال .. ال .. ال
+
+371
+00:34:04,480 --> 00:34:08,180
+.. ال a تربيع على صورة أربعة في some integer وفي
+
+372
+00:34:08,180 --> 00:34:11,560
+الحالة الثانية أربعة في some integer زائد واحد
+
+373
+00:34:11,560 --> 00:34:16,260
+يعني in any case a تربيع has one of the two forms
+
+374
+00:34:16,260 --> 00:34:20,800
+يا يعني بمعنى أخر يا بيقبل القسم على أربعة يا إما
+
+375
+00:34:20,800 --> 00:34:25,960
+المتبقي من القسم على أربعة واحد واضح أه example
+
+376
+00:34:25,960 --> 00:34:34,880
+show that the square of n of anyodd integer is of
+
+377
+00:34:34,880 --> 00:34:43,700
+the form 8k زي 1 بدنا نثبت أنه اللي هو مربع أي odd
+
+378
+00:34:43,700 --> 00:34:51,300
+integer على صورة إيه شماله 8k زي 1 لو جينا ربعنا ل
+
+379
+00:34:51,300 --> 00:34:58,960
+2k زي 1 مش هيخدمنا الآن 8k زي 1 لو ربعنا اللي هو
+
+380
+00:34:58,960 --> 00:35:03,530
+القسم A3مش هيخدمنا لإن مبقى هو بيصير تسعة .. تسعة
+
+381
+00:35:03,530 --> 00:35:07,530
+.. تسعة .. تسعة كيو تربيع إذا .. إذا .. إت ..
+
+382
+00:35:07,530 --> 00:35:10,770
+إتنين مظبطش هيجيب التمانية لإن محدش يجيب التمانية
+
+383
+00:35:10,770 --> 00:35:15,530
+التلاتة مش هتجيب التمانية إذا مين؟ الأربعة طبعا في
+
+384
+00:35:15,530 --> 00:35:18,070
+مقارين بتجيب التمانية بتجيب التمانية لكن بديش ..
+
+385
+00:35:18,070 --> 00:35:21,050
+بديش أعلي ليش أفضل حالات كتيرة و أنا بقدر أفضل
+
+386
+00:35:21,050 --> 00:35:25,550
+حالات الأجل معايا يا شباب إذا الآن بواسطة
+
+387
+00:35:25,550 --> 00:35:30,740
+الـDivision Algorithm أيضا أي عدد في الدنياأي عدد
+
+388
+00:35:30,740 --> 00:35:37,180
+في الدنيا على صورة اربعة Q اربعة Q زائد واحد اربعة
+
+389
+00:35:37,180 --> 00:35:41,980
+Q زائد اتنين او اربعة Q زائد تلاتة لكن هو ايش بده
+
+390
+00:35:41,980 --> 00:35:51,460
+الود مزام A by differential algorithmThe odd A has
+
+391
+00:35:51,460 --> 00:35:56,860
+one of the forms ياك يو زياد واحد، ياك يو زياد
+
+392
+00:35:56,860 --> 00:36:01,780
+تلاتة، خلاص بس لإنه odd بده ياك إذا أنا بده ربحان،
+
+393
+00:36:01,780 --> 00:36:05,220
+بيصير التربيه إذا صارت الفكرة سهلة إذا أنا صار
+
+394
+00:36:05,220 --> 00:36:10,770
+عندي الـA تربيه في الحالة الأولىاربع Q زائد واحد
+
+395
+00:36:10,770 --> 00:36:15,530
+لكل تربيع ويساوي ستة عشر Q تربيع زائد تمانية Q
+
+396
+00:36:15,530 --> 00:36:20,470
+زائد واحد صح؟ ويساوي .. خد التمانية عام المشترك
+
+397
+00:36:20,470 --> 00:36:25,470
+تصبح تمانية في اتنين Q تربيع زائد Q زائد واحد
+
+398
+00:36:25,470 --> 00:36:28,990
+ويساوي تمانية K زائد واحد for some K هذا اللي هو
+
+399
+00:36:28,990 --> 00:36:32,810
+الـ K في هذا الحالة الآن الـ A تربيع في الحالة
+
+400
+00:36:32,810 --> 00:36:40,340
+التانية اربع Qزاد 3 لكل تربيع ويساوي 16 Q تربيع
+
+401
+00:36:40,340 --> 00:36:53,240
+زاد 24 Q زاد 9 ويساوي 16 Q تربيع زاد 24 Q زاد 8
+
+402
+00:36:53,240 --> 00:36:58,940
+زاد 1 صح ولا لأ؟فصلت اللي فيه تمانيات مع بعض
+
+403
+00:36:58,940 --> 00:37:06,320
+ويساوي تمانية في اتنين Q تربيع ثلاثة Q زائد واحد
+
+404
+00:37:06,320 --> 00:37:11,160
+الكل زائد واحد هذا كله سمي K بيصير تمانية K زائد
+
+405
+00:37:11,160 --> 00:37:18,020
+واحد any odd او the square of any odd integer has
+
+406
+00:37:18,020 --> 00:37:25,410
+the form تمانية K زائد واحد تمانية K زائد واحدواضح
+
+407
+00:37:25,410 --> 00:37:35,270
+أه؟ أي سؤال؟ قولوا محمد رسول الله الان prove that
+
+408
+00:37:35,270 --> 00:37:42,920
+a في a تربيع زاد اتنين على تلاتةis an integer for
+
+409
+00:37:42,920 --> 00:37:46,840
+انا ايه اكبر او ساوي ايش بساوي واحد واضح انه في
+
+410
+00:37:46,840 --> 00:37:50,020
+قسم معاه تلاتة مادام في قسم معاه تلاتة اكتر اللي
+
+411
+00:37:50,020 --> 00:37:52,820
+انا بشجعني طب انا مش هاروح للتنين اكيد اذا انا
+
+412
+00:37:52,820 --> 00:37:58,840
+هاروح لمين الواحد مش هيظبط الواحد مش هيسعفني اذا
+
+413
+00:37:58,840 --> 00:38:03,190
+انا هاروح لمين للتلاتةالقسم على واحد هو بيطلع نفس
+
+414
+00:38:03,190 --> 00:38:08,210
+العدد مش هيصيفني الان اللي هيصيفني مازال بده طالب
+
+415
+00:38:08,210 --> 00:38:11,510
+انه اثبت اشي مقسوم على تلاتة اذا انا هروح على طول
+
+416
+00:38:11,510 --> 00:38:16,110
+باتجاه مين التلاتة اذا في عندي three cases اللي هو
+
+417
+00:38:16,110 --> 00:38:22,270
+تلاتة Q by definition algorithm تلاتة Q تلاتة Q
+
+418
+00:38:22,270 --> 00:38:28,970
+زاد واحد تلاتة Q زاد اتنين وهي خط وهي خط وهي الخط
+
+419
+00:38:28,970 --> 00:38:37,110
+الثالثالآن في كل حالة بدي أحسب اللي هو الـ A الـ A
+
+420
+00:38:37,110 --> 00:38:45,610
+في الـ A تربيع زاد 2 على 3 ويساوي، هذه واضحة 3Q في
+
+421
+00:38:45,610 --> 00:38:54,950
+9Q تربيع زاد 2 على 3 3 مع 3 ويساوي Q في 9Q تربيع
+
+422
+00:38:54,950 --> 00:39:07,420
+زاد 2 is an integerمعايا هنا نفس الشيء بيصير تلاتة
+
+423
+00:39:07,420 --> 00:39:18,180
+Q زائد واحد في تلاتة Q زائد واحد تربيع زائد اتنين
+
+424
+00:39:18,180 --> 00:39:23,740
+على تلاتة ويساوي مضطر اتربي حد من هنا بيساوي تلاتة
+
+425
+00:39:23,740 --> 00:39:31,310
+Q زائد واحد اكيد هلاجيلي تلاتة اكيد فيتسعة Q تربيع
+
+426
+00:39:31,310 --> 00:39:37,810
+ستة Q زائد واحد زائد اتنين لجأت التلاتة اه هي عند
+
+427
+00:39:37,810 --> 00:39:42,370
+اتنين واحد زائد تلاتة وهذه فيها ستة Q وهذه تسعة Q
+
+428
+00:39:42,370 --> 00:39:46,910
+إذا هذه ستساوي هذه مع بعض تلاتة وهي ساوي باخد
+
+429
+00:39:46,910 --> 00:39:50,010
+التلاتة من هذول عامل مشترك بسمها محدد بطلع عنده
+
+430
+00:39:50,010 --> 00:39:55,430
+تلاتة Q زائد واحد في تلاتة Q تربيع زائد اتنين Q
+
+431
+00:39:55,430 --> 00:40:01,420
+زائد واحد الله يفتح عليكم وهذه ازعان انتجةأخيرا
+
+432
+00:40:04,080 --> 00:40:12,500
+نجي ا في تربيع زاد اتنين على تلاتة سوى تلاتة Q زاد
+
+433
+00:40:12,500 --> 00:40:19,000
+اتنين في تلاتة Q زاد اتنين لكل تربيع زاد اتنين على
+
+434
+00:40:19,000 --> 00:40:23,780
+تلاتة و قطعا هتلاقي فهذه تلاتة هي سوى تلاتة Q زاد
+
+435
+00:40:23,780 --> 00:40:29,520
+اتنين معايا يا جماعة في تسعة Q تربيع زاد اتناشر Q
+
+436
+00:40:29,520 --> 00:40:36,340
+زاد اربعة زاد اتنين على تلاتةهدولة فين ستة إذا نخد
+
+437
+00:40:36,340 --> 00:40:39,800
+التلاتة على المشترك ويصير عبارة عن تلاتة Q زاد
+
+438
+00:40:39,800 --> 00:40:49,180
+اتنين في تلاتة Q تربية زائد اربعة Q زائد اتنين ال
+
+439
+00:40:49,180 --> 00:40:55,660
+integer وهيك نكون خلصنا ال section اتنين اتنين
+
+440
+00:40:55,660 --> 00:41:02,220
+نكون معنا homework اللي هو اتنين خمسة اتنين خمسة
+
+441
+00:41:02,670 --> 00:41:05,350
+اللي هو من اتنين لعند خمسة يعني سؤال اتنين و تلتة
+
+442
+00:41:05,350 --> 00:41:12,270
+واربعة وخمسة طيب شوف عليها لان المرة الجاية بكون
+
+443
+00:41:12,270 --> 00:41:17,030
+عندى ان هنتحدث عن ال greatest common divisor ال
+
+444
+00:41:17,030 --> 00:41:20,390
+greatest common divisor ان شاء الله و الله يعطيكوا
+
+445
+00:41:20,390 --> 00:41:20,810
+العافية
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BrG6sHyCXRc.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BrG6sHyCXRc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..336c71e627f46a5477030b2ef393031a8354299b
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BrG6sHyCXRc.srt
@@ -0,0 +1,2065 @@
+1
+00:00:19,290 --> 00:00:25,590
+بسم الله الرحمن الرحيم المحاضرة رقم 15 في مساق
+
+2
+00:00:25,590 --> 00:00:32,350
+نظرية الأعداد لطلبة الجامعة الإسلامية كليتي العلوم 
+
+3
+00:00:32,350 --> 00:00:42,690
+والتربية طلاب قسم الرياضيات اليوم إن شاء الله 
+
+4
+00:00:42,690 --> 00:00:50,280
+هنناقش اللي هو الـ section الأول أو المرقم بأربعة 
+
+5
+00:00:50,280 --> 00:00:58,180
+اتنين في الكتاب لمساق نظرية الأعداد اللي بتحدث عن 
+
+6
+00:00:58,180 --> 00:01:04,560
+اللي هو الـ congruences 4.2 طلبنا عدة مسائل 
+
+7
+00:01:04,560 --> 00:01:11,180
+فيه خلينا نطلع نسمع كيف منكم أفكار ونحل مع بعض
+
+8
+00:01:11,180 --> 00:01:16,980
+اللي هو نبدأ نمر على الأسئلة اللي مطلوبة سؤال 
+
+9
+00:01:16,980 --> 00:01:26,100
+الرابع Find the remainder when 2<sup>50</sup> and 41<sup> </sup>
+
+10
+00:01:26,100 --> 00:01:34,280
+65 are divisible by 7 بدنا نشوف الرقم اللي بنحكي
+
+11
+00:01:34,280 --> 00:01:41,420
+عنه أنه 2<sup>50</sup> في الأول 2<sup>50</sup> إيش المتبقي له
+
+12
+00:01:41,420 --> 00:01:48,670
+لما نقسمه على 7 لأن احنا قلنا ده بالهيك أنه 
+
+13
+00:01:48,670 --> 00:01:57,470
+دائما الـ remainder والرقم الأصلي متطابقان مقياس
+
+14
+00:01:57,470 --> 00:02:05,570
+المقسوم عليه دائما الرقم والمتبقي له متطابقان
+
+15
+00:02:05,570 --> 00:02:10,310
+مقياس المقسوم عليه فلان هو من الدُو اللي هو الـ 52 
+
+16
+00:02:18,030 --> 00:02:23,010
+السؤال بشكل ثاني ماذا يتطابق 2<sup>50</sup>
+
+17
+00:02:26,460 --> 00:02:33,240
+modulo 7 حيث الماذا هذا ماله بين صفر وبين سبعة 
+
+18
+00:02:33,240 --> 00:02:40,300
+أكبر أو أصغر strictly من سبعة من هنا نبدأ بمشاهدة 
+
+19
+00:02:40,300 --> 00:02:49,020
+إيش بالطريقة modulo 7 سهل الأمر عند 2 أو 6 اقرأ
+
+20
+00:02:49,020 --> 00:02:54,320
+رقم 64 يتطابق 
+
+21
+00:02:55,090 --> 00:03:01,470
+الواحد مضاعف مين؟ مضاعف سبعة الأسباب 
+
+22
+00:03:01,470 --> 00:03:05,990
+معروفة ومرّينا عليها قبل هيك الآن 2<sup>6</sup> بدي 
+
+23
+00:03:05,990 --> 00:03:12,130
+أوصلها لـ 50 2<sup>6</sup> اللي هو <sup>50</sup>.. <sup></sup>
+
+24
+00:03:12,130 --> 00:03:18,830
+قديش 50 بيظبطش تطلع بـ 48 × 8 48 مقال 6 ده مش 
+
+25
+00:03:18,830 --> 00:03:25,430
+بيقول 8 بظبط اللي بعمله تطابقاللي هو 1 قصت
+
+26
+00:03:25,430 --> 00:03:31,390
+8 modulo 7 يعني بما في آخر سنة 2 قصت 
+
+27
+00:03:31,390 --> 00:03:34,730
+8 × 48 بل عندي قداش 2 قصت 2 × 4
+
+28
+00:03:34,730 --> 00:03:40,090
+فبيصير عندي 2 قصت 2 × 2  اص 8
+
+29
+00:03:40,090 --> 00:03:45,590
+× 48 يتطابق 4 modulo 7 يعني 2<sup> </sup>
+
+30
+00:03:45,590 --> 00:03:51,870
+<sup>50</sup> يتطابق 4 modulo 7 يعني بمعنى آخر the 
+
+31
+00:03:51,870 --> 00:03:56,350
+remainder when we divide 2<sup>50</sup> by 7
+
+32
+00:03:56,350 --> 00:04:05,570
+اللي هو مين هو عبارة عن الآن الـ 41 الـ 41 similarly
+
+33
+00:04:05,570 --> 00:04:17,930
+الآن عندي 41<sup>65</sup> 41<sup>65</sup> 41
+
+34
+00:04:17,930 --> 00:04:22,330
+41<sup> </sup>
+
+35
+00:04:24,480 --> 00:04:30,280
+65 يتطابق ماذا modulo 7 أو ماذا هذه اللي هو عدد بين 
+
+36
+00:04:30,280 --> 00:04:35,040
+الصفر وبين السبعة أو أكبر صفر أصغر strictly
+
+37
+00:04:35,040 --> 00:04:41,540
+من السبعة زي ما حكيته لأن 41 يتطابق -1 
+
+38
+00:04:41,540 --> 00:04:46,680
+modulo 7 على طول هذه لأنه عند 42
+
+39
+00:04:46,680 --> 00:04:52,770
+مضاعفات السبعة بصير عندنا الآن <sup>65</sup> يتطابق 
+
+40
+00:04:52,770 --> 00:04:59,910
+<sup>65</sup> وهذا عبارة عن -1 modulo 7 قبل إن آخر 
+
+41
+00:04:59,910 --> 00:05:03,710
+يتطابق 6 modulo 7 إذا الـ remainder في هذه
+
+42
+00:05:03,710 --> 00:05:09,260
+الحلقة بداش عبارة عن 6 لأن احنا عشان بدنا
+
+43
+00:05:09,260 --> 00:05:12,660
+remainder كلهم متطابقان أكيد لكن عندما 
+
+44
+00:05:12,660 --> 00:05:16,320
+نقسم الباقي القسم اللي احنا متفجين عليه أنه أكبر
+
+45
+00:05:16,320 --> 00:05:21,120
+أو يساوي صفر أصغر من مين مين مقسم عليه المقلوب
+
+46
+00:05:21,120 --> 00:05:25,120
+التالي what is the remainder when the following 
+
+47
+00:05:25,120 --> 00:05:33,160
+sum is divisible by 4 عندي اللي هو 1<sup>5</sup> زي
+
+48
+00:05:33,160 --> 00:05:42,950
+2<sup>5</sup> زي 3<sup>5</sup> زي 99<sup>5</sup> زي 100
+
+49
+00:05:42,950 --> 00:05:50,790
+<sup>5</sup> ويقول لي إيش اللي هو remainder لما نقسم
+
+50
+00:05:50,790 --> 00:05:55,550
+هذا المجموع على مين على 4 إذا اللي هي احنا
+
+51
+00:05:55,550 --> 00:06:01,530
+بنحكي عن قابلية القسمة على مين على 4 الآن لو 
+
+52
+00:06:01,530 --> 00:06:06,810
+أجينا أخدنا أي عدد في الدنيا هذا العدد يا صورته
+
+53
+00:06:06,810 --> 00:06:10,570
+4K اللي ماكتبش برهان اللي بقى اللي خلاني
+
+54
+00:06:10,570 --> 00:06:14,130
+أقول بعطيه إنت لأن البرهان كامل موجود يعني عندي أي 
+
+55
+00:06:14,130 --> 00:06:17,390
+عدد في الدنيا يا صورة 4K يا 4K + 
+
+56
+00:06:17,390 --> 00:06:21,810
+1 يا 4K + 2 يا 4K + 
+
+57
+00:06:21,810 --> 00:06:25,630
+3 إذا هدول الأرقام اللي عندي الـ 1 والـ 2 
+
+58
+00:06:25,630 --> 00:06:29,490
+والـ 3 والـ 99 والـ 100 على الصورة يا هذه 
+
+59
+00:06:29,490 --> 00:06:34,760
+يا هذه يا هذه يا هذه شوف الآن.. طبعا أنا غلطت في 
+
+60
+00:06:34,760 --> 00:06:39,780
+النهاية أشوف هذا يتطابق ماذا modulo مين modulo 4
+
+61
+00:06:39,780 --> 00:06:42,580
+و اللي بيبقى اللي هو بيكون هو ال remainder إيه
+
+62
+00:06:42,580 --> 00:06:48,500
+بيبقى الاشي معايا؟ الآن عندي العدد اللي على الصورة 
+
+63
+00:06:48,500 --> 00:06:54,880
+هذه 4K<sup>5</sup> أكيد هيطابق الصفر modulo مين 
+
+64
+00:06:54,880 --> 00:06:58,200
+modulo 4 لأن الـ 4K نفسها تتطابق الصفر لأن 
+
+65
+00:06:58,200 --> 00:07:02,610
+الـ 4K<sup>5</sup> تتطابق modulo الصفر الآن الـ 4
+
+66
+00:07:02,610 --> 00:07:09,530
+K + 1 يتطابق 1 modulo مين 4 لأن <sup>5</sup>
+
+67
+00:07:09,530 --> 00:07:15,200
+على يتطابق 1 <sup>5</sup> يعني 1 الـ 4
+
+68
+00:07:15,200 --> 00:07:21,520
+K + 2 يتطابق 2 modulo ايهاش modulo
+
+69
+00:07:21,520 --> 00:07:27,900
+4 معايا الآن <sup>5</sup> هتطابق 2 × 32
+
+70
+00:07:27,900 --> 00:07:31,500
+و 32 بالنسبة لي 4 ايهاش صفر إذا هذا
+
+71
+00:07:31,500 --> 00:07:38,260
+يتطابق الصفر modulo 4 الآن اللي بعده وخلوكم
+
+72
+00:07:38,260 --> 00:07:45,030
+معانا إنتوا اللي هو 4K + 3 الـ 3
+
+73
+00:07:45,030 --> 00:07:51,530
+أسهل لها إن أكتب مين؟ الـ -1، مظبوط ولا لأ؟
+
+74
+00:07:51,530 --> 00:07:56,070
+تطابق 3 modulo 4، و 3 نفسها بتطابق 
+
+75
+00:07:56,070 --> 00:08:00,360
+مين؟ الـ -1، لأن أكتبها -1 من العصل لأن 
+
+76
+00:08:00,360 --> 00:08:04,040
+الفأتينين لقوة 5 و هذه لقوة 5 بتبقى هي
+
+77
+00:08:04,040 --> 00:08:09,120
+أشمالها -1 إذا فإنا عندي الآن الأعداد اللي 
+
+78
+00:08:09,120 --> 00:08:12,940
+على الصورة هذه و اللي على الصورة هذه <sup>5</sup> عبارة
+
+79
+00:08:12,940 --> 00:08:16,820
+عن <sup>0</sup> بالنسبة لي الـ 4 و هذه 1 1 1
+
+80
+00:08:16,820 --> 00:08:23,810
+أشمالها -1 ماشي الحال إذا الآن عندي الأعداد
+
+81
+00:08:23,810 --> 00:08:29,710
+اللي فوق هذه اللي هما 4 أقسام القسم الأول 1 
+
+82
+00:08:29,710 --> 00:08:35,270
+<sup>5</sup> الـ 1 على صورة إش ماله 4K + 1
+
+83
+00:08:35,270 --> 00:08:41,730
+واللي بعده مين 5<sup>5</sup> واللي بعده معايا اه
+
+84
+00:08:41,730 --> 00:08:47,650
+اللي هو لما أصل لآخر واحد إش هو 4K + 1
+
+85
+00:08:50,750 --> 00:08:55,910
+97 99<sup>5</sup> 
+
+86
+00:08:58,580 --> 00:09:03,380
+لأن الـ 100 4K ننقص منها اللي هو 3 الـ 9
+
+87
+00:09:03,380 --> 00:09:06,220
+97 4K + 3 الـ 99 4K + 1 فاهمين عليها طبعا طيب الآن إذا
+
+88
+00:09:06,220 --> 00:09:10,180
+الجزء الثاني فاهمين الفكرة 2<sup>5</sup> 6<sup> </sup>
+
+89
+00:09:10,180 --> 00:09:15,440
+<sup>5</sup> إلى آخر لما أصل عند اللي هو 98<sup> </sup>
+
+90
+00:09:15,440 --> 00:09:22,340
+<sup>5</sup> هدولة كلنا إش معا الآن بتطابق الصفر الآن اللي 
+
+91
+00:09:22,340 --> 00:09:28,400
+بعده 3<sup>5</sup> أو أضيفه اللي هو بيصير 7<sup>5</sup> لما
+
+92
+00:09:28,400 --> 00:09:36,540
+أصل 99<sup>5</sup> هدولة لأن 4K + 3 هدولة 4K + 1
+
+93
+00:09:36,540 --> 00:09:45,500
+<sup>5</sup> هدولة 4K + 3<sup>5</sup> والأخير 4K، مظبوط؟ إذا
+
+94
+00:09:45,500 --> 00:09:54,120
+هذه كلها هتطابق اللي هو عبارة عن المجموعة هذه اه
+
+95
+00:09:54,120 --> 00:10:01,720
+المجموعة هذه 1 + 1 + + 1 اه 
+
+96
+00:10:01,720 --> 00:10:07,860
+المجموعة هذه صفر لأن كلهم هيكون أشمالهم
+
+97
+00:10:07,860 --> 00:10:12,450
+أصفار والمجموعة اللي بعدها زائد -1 -1
+
+98
+00:10:12,450 --> 00:10:17,750
+-1 زائد المجموعة الأخيرة أشمالها صفر هذولة
+
+99
+00:10:17,750 --> 00:10:23,590
+مع هذولة عددهم نفس الشيء بساوي داش صفر إذا صار 
+
+100
+00:10:23,590 --> 00:10:28,830
+عندي الآن الأعداد هذه لما أقسمها على 4 الـ
+
+101
+00:10:28,830 --> 00:10:33,950
+remainder إيش يعني بمعنى آخر تقبل القسمة على 4
+
+102
+00:10:33,950 --> 00:10:39,230
+اللي بعده هذا الكلب هي 25 × 4 أو أي 4 أرقام
+
+103
+00:10:39,230 --> 00:10:44,550
+متتالية بيكسب النقطة على 4 بدون البيانات، صح؟
+
+104
+00:10:44,550 --> 00:10:50,790
+بنفع.. بنفع.. بنفع.. 25 × 4.. بنفع.. بنفع
+
+105
+00:10:50,790 --> 00:10:59,890
+.. بنفع.. الـ 4 الأوليات، الـ 4 الثانيات هي
+
+106
+00:10:59,890 --> 00:11:02,930
+الفكرة قائمة عليك لو ندسنا الـ الـ الـ الـ الوية
+
+107
+00:11:09,010 --> 00:11:19,080
+خليناها 99 بيبقى له صفر لأن الـ 100 إيش صفر لكن لو 
+
+108
+00:11:19,080 --> 00:11:26,980
+شلت الـ 99 بيزيد أو بينقص عندك 1 فاهمين وهكذا
+
+109
+00:11:26,980 --> 00:11:31,270
+طيب خلينا نيجي للسؤال اللي بعده السؤال اللي بعده 
+
+110
+00:11:31,270 --> 00:11:37,990
+If A<sub>1</sub>A<sub>2</sub>...A<sub>n</sub> is a complete residue system
+
+111
+00:11:37,990 --> 00:11:42,290
+modulo N والعامل المشترك الأكبر بين الـ A والـ N
+
+112
+00:11:42,290 --> 00:11:49,650
+بيساوي 1 اثبت أن A × A<sub>1</sub> A × A<sub>2</sub> ...A × A<sub>n</sub> برضه 
+
+113
+00:11:49,650 --> 00:11:53,490
+بتعمل Complete Residue System modulo N ركزوا
+
+114
+00:11:53,490 --> 00:11:56,930
+في الـ خلينا اللي هو من خلال حل السؤال المراجع
+
+115
+00:11:57,890 --> 00:12:03,590
+اللي هو الموضوع أو نراجع اللي بنحكي عنه الـ
+
+116
+00:12:03,590 --> 00:12:09,670
+Complete Residue System Modulo N معطيك الآن مجموعة
+
+117
+00:12:09,670 --> 00:12:15,770
+من الأعداد A<sub>1</sub>, A<sub>2</sub> لـ A<sub>n</sub> هذه بتمثل Complete 
+
+118
+00:12:15,770 --> 00:12:25,410
+Residue System Modulo N الآن بقول لك لو ضربت هذه 
+
+119
+00:12:25,410 --> 00:12:33,170
+الأعداد في أي عدد A A × 1 A × 2 لـ 
+
+120
+00:12:33,170 --> 00:12:39,910
+A × A وكان العامل المشترك الأعلى هذا
+
+121
+00:12:39,910 --> 00:12:46,190
+الشرط بين الـ a والـ n يعني اللي ضربته الـ a والـ n 
+
+122
+00:12:46,190 --> 00:12:52,710
+بساهم 1 يكون هناك ضمان عندك إن المطلوب حاجة برضه
+
+123
+00:12:52,710 --> 00:12:58,430
+أشماله Complete Residue System modulo N لكن ماكانش 
+
+124
+00:12:58,430 --> 00:13:02,330
+العامل المشترك الأكبر ليس شرطا إنه يطلع عندك
+
+125
+00:13:02,330 --> 00:13:05,990
+أشماله Complete Residue System modulo N وهو الـ get 
+
+126
+00:13:05,990 --> 00:13:10,250
+ناخدها مثلًا نيجي 
+
+127
+00:13:10,250 --> 00:13:12,090
+الآن إيش المطلوب؟
+
+128
+00:13:14,150 --> 00:13:17,710
+إن A × A<sub>1</sub> و A × A<sub>2</sub> وعند A × A أقل هو
+
+129
+00:13:17,710 --> 00:13:22,310
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+130
+00:13:22,310 --> 00:13:24,550
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+131
+00:13:24,550 --> 00:13:24,730
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+132
+00:13:24,730 --> 00:13:26,850
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+133
+00:13:26,850 --> 00:13:27,610
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+134
+00:13:27,610 --> 00:13:30,250
+مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع مجتمع
+
+135
+00:13:30,250 --> 00:13:40,550
+مجتمع مجتمع 
+
+136
+00:13:41,610 --> 00:13:47,890
+الآن في معلومة ثانية قلناها إن لو في عندك set فيها
+
+137
+00:13:47,890 --> 00:13:53,030
+N من الأعداد عشان تثبت تثبت أن Complete Residue
+
+138
+00:13:53,030 --> 00:13:58,260
+System يكفي ما تثبت أنهم كلهم كلهم يحبوا بعض أو 
+
+139
+00:13:58,260 --> 00:14:02,160
+يكفي إنك تثبت إنه مش أي عدد برة congruent لها
+
+
+
+141
+00:14:02,160 --> 00:14:07,920
+لعدد موجود من بينهم يعني الآن شرط العدد العدد M
+
+142
+00:14:07,920 --> 00:14:12,520
+بيغنِي عن أحد الشرطين اللي بنحكي عنهم الآن عندي
+
+143
+00:14:12,520 --> 00:14:17,640
+هدول عددهم M إذاً يكفيني عشان أثبت إن هذا Complete
+
+144
+00:14:17,640 --> 00:14:21,840
+Residue System مُدرَك إن كوني ماشي معاهم كلهم in
+
+145
+00:14:21,840 --> 00:14:28,300
+congruent فببدأ أفترض العكس نفترض أنه في عددين هنا a
+
+146
+00:14:28,300 --> 00:14:38,940
+في ar يطابق a في ak modulo n for some r وk أكبر أو 
+
+147
+00:14:38,940 --> 00:14:45,880
+يساوي صفر أو أكبر أو يساوي واحد وأصغر من مين؟ أنه
+
+148
+00:14:45,880 --> 00:14:48,860
+لأن n ناقص واحد هنا دول أي واحد عند الـ n ما بقيش
+
+149
+00:14:48,860 --> 00:14:52,300
+الحاجة اللي هي n
+
+150
+00:14:54,720 --> 00:15:00,360
+معايا؟ هيك فرضت فرضت إنه في كنتين من هدولة
+
+151
+00:15:00,360 --> 00:15:03,240
+متطابقات وده سؤال Contradiction وأنا سألت على طول
+
+152
+00:15:03,960 --> 00:15:06,920
+بما أن العامل المشترك الأعلى بين الـ A والـ N
+
+153
+00:15:06,920 --> 00:15:12,320
+بيساوِي واحد، إذا القسمة جائزة، إذا صار عندي AR تطابق
+
+154
+00:15:12,320 --> 00:15:17,580
+الـ AK modulo n وهذا Contradiction أو Contradicts
+
+155
+00:15:17,580 --> 00:15:22,080
+the fact that A1, A2, An is a complete residue
+
+156
+00:15:22,080 --> 00:15:29,860
+system modulo n، therefore this set forms a complete
+
+157
+00:15:29,860 --> 00:15:34,320
+residue system modulo n الآن لو كان عندي مثلًا
+
+158
+00:15:34,320 --> 00:15:43,460
+نأخذ مثال بسيط عندي واحد واتنين وأربعة وخمسة عندي
+
+159
+00:15:43,460 --> 00:15:49,280
+هذا complete residue system modulo ده كده ه
+
+160
+00:15:49,280 --> 00:15:55,900
+complete residue system modulo ده كده ه هذا modulo
+
+161
+00:15:55,900 --> 00:15:56,460
+خمسة
+
+162
+00:15:59,870 --> 00:16:04,170
+الثلاثة مش موجودة اه إذًا إيش بدي أعمل؟ ده كان بدي
+
+163
+00:16:04,170 --> 00:16:11,590
+خمسة لازم أحط مين؟ الثلاثة واضح طيب الآن موجودة
+
+164
+00:16:11,590 --> 00:16:22,930
+خمسة بدي أضرب اللي هو اللي عندي فيه اثنين بيطلع
+
+165
+00:16:22,930 --> 00:16:30,750
+عندي اثنين وأربعة وستة وثمانية وعشرة هذا أشْماَلُه Complete Residue
+
+166
+00:16:30,750 --> 00:16:35,470
+System ولّا لأ؟ أكيد لأن الـ 8 و5 أشْماَلُهُمَا Relative
+
+167
+00:16:35,470 --> 00:16:38,750
+prime إذًا المضمون إن هذا Complete Residue System
+
+168
+00:16:38,750 --> 00:16:45,170
+modulo خمسة لكن لو دي اتضربت كل الأرقام هذه في
+
+169
+00:16:45,170 --> 00:16:54,850
+خمسة مثلًا كلهم في خمسة فعندي خمسة و10 و15 و20 و
+
+170
+00:16:54,850 --> 00:16:59,490
+25 هذي بتمثل Complete Residue System أصلاً هو أقيم
+
+171
+00:16:59,490 --> 00:17:04,110
+واحد بالنسبة للخمسة كلّه مقسوم واحد كلّه صفر إذا
+
+172
+00:17:04,110 --> 00:17:07,470
+لازم يكون اللي هو العامل المشترك الأعلى بين
+
+173
+00:17:07,470 --> 00:17:10,330
+المضروب في الـ Complete Residue وبين اللي هو
+
+174
+00:17:10,330 --> 00:17:14,990
+المقياس واحد عشان تضمن اللي بيطلع أشْماَلُه Complete
+
+175
+00:17:14,990 --> 00:17:18,630
+Residue System Modulo خارج اللي بعده هو Verify that
+
+176
+00:17:18,630 --> 00:17:23,710
+الـ Zero والواحد والاثنين والاثنين قصّة اثنين والاثنين
+
+177
+00:17:23,710 --> 00:17:28,350
+قصّة ثلاثة لعند الاثنين قصّة تسعة is a Complete
+
+178
+00:17:28,350 --> 00:17:37,710
+Residue System Modulo 11 But that 0 و1 تربيع و2
+
+179
+00:17:37,710 --> 00:17:43,050
+تربيع و3 تربيع و10 تربيع إيش ما قالها is not a
+
+180
+00:17:43,050 --> 00:17:51,150
+complete .. يعني أجرب للحسابات يعني
+
+181
+00:17:51,150 --> 00:17:56,430
+واضح الحل يعني ما بدوش حاجة كثير
+
+182
+00:18:04,810 --> 00:18:08,290
+إحنا قلنا قبل هيك في عندكم Complete Residue System
+
+183
+00:18:08,290 --> 00:18:10,750
+ودول قد إيش؟ هو ده 11 في Complete Residue System
+
+184
+00:18:10,750 --> 00:18:15,130
+Standard اللي هو من 0 اللي بندّيه عليه أنظمة العد
+
+185
+00:18:15,130 --> 00:18:22,090
+اللي بندّيه عليه أنظمة العد من 0 إلى 1، 2، 3، 4، 5،
+
+186
+00:18:22,090 --> 00:18:26,630
+6، 7، 8، 9، 10، 11، 11، 12، 13، 14، 15، 16، 17،
+
+187
+00:18:26,630 --> 00:18:29,030
+18، 19، 20، 21، 22، 23، 24، 25، 26، 27، 28، 29،
+
+188
+00:18:29,030 --> 00:18:29,050
+29، 30، 31، 32، 32، 33، 34، 34، 35، 34، 35، 35،
+
+189
+00:18:29,050 --> 00:18:31,730
+35، 35، 35، 35، 35، 35، 35، 35، 35، 35، 35، 35،
+
+190
+00:18:31,730 --> 00:18:31,750
+35، 35، 35، 35، 35، 35، 35، 35، 35، 35، 35، 35، 35
+
+191
+00:18:32,500 --> 00:18:38,400
+لو أثبتنا إنه كل واحد من هذولة بيخاري الواحد من
+
+192
+00:18:38,400 --> 00:18:43,200
+هذولة، بنكون خلصنا بيصير إنه كل واحد بسؤاله واحد
+
+193
+00:18:43,200 --> 00:18:46,820
+اللي في اللي جوا وهنا دولة in congruent إذا اللي
+
+194
+00:18:46,820 --> 00:18:50,120
+طلعناها in congruent وعدد هنا 11 إذا بالسؤال اللي
+
+195
+00:18:50,120 --> 00:18:53,080
+قبل شوية أشْماَلُه Complete Residual System دلوقتي
+
+196
+00:18:53,080 --> 00:18:59,540
+الصفر هو الصفر أخد الصفر يعني دي لمين؟ والواحد داخل
+
+197
+00:18:59,540 --> 00:19:06,700
+واحد يعني هذا الصفر وهذا المثل اثنين قصّة صفر وهذا
+
+198
+00:19:06,700 --> 00:19:12,540
+اثنين قصّة واحد الصفر هو الصفر والواحد هو الواحد
+
+199
+00:19:12,540 --> 00:19:17,420
+والاثنين هو الاثنين نيجي لـ 2 تربيع 2 تربيع أقل
+
+200
+00:19:17,420 --> 00:19:24,240
+عن إيش؟ عن أربعة modulo 11 2 تكعيب بيصير جد إيش؟
+
+201
+00:19:24,240 --> 00:19:31,500
+ثمانية modulo 11 2 قصّة 4 بيصير جد إيش؟ اللي هو
+
+202
+00:19:31,500 --> 00:19:38,520
+خمسة فاهمين؟ modulo 11 2 قصّة 5 بيصير عشرة
+
+203
+00:19:38,520 --> 00:19:42,960
+عشرة فاللي جاب اللي هو خلاص عشرة اللي هي modulo جد إيش؟
+
+204
+00:19:43,760 --> 00:19:50,680
+11 2 أس 26 اللي هو جد إيش؟ تسعة modulo 11
+
+205
+00:19:50,680 --> 00:19:55,500
+من طريقة الحساب السهلة بتصير 2 أس 7 تطابق
+
+206
+00:19:55,500 --> 00:20:02,020
+128 اللي هي عبارة عن 7 modulo 11 2 أس
+
+207
+00:20:02,020 --> 00:20:06,320
+8 تطابق الـ 4 مضروبة في هذه اللي هي
+
+208
+00:20:06,320 --> 00:20:12,890
+3 modulo 11 ده اللي بيجي تسعة تسعة تطابق على طول
+
+209
+00:20:12,890 --> 00:20:16,850
+في 2 أس 6 modulo 11 إذًا هذا بيعمل ليه
+
+210
+00:20:16,850 --> 00:20:21,250
+أشْماَلُه فعلاً اللي هو عندي هذول الأعداد مطابقين لأن
+
+211
+00:20:21,250 --> 00:20:26,330
+أعدادنا مطابقين الصفر والواحد والاثنين والثلاثة
+
+212
+00:20:26,330 --> 00:20:38,030
+والأربعة والخمسة والستة والسبعة والـ 8 والـ 9 والـ
+
+213
+00:20:38,030 --> 00:20:42,990
+10 خلصنا إذًا الـ 11 عاد يبقى الـ 11 من هذول
+
+214
+00:20:42,990 --> 00:20:47,490
+إذًا صار إنّه هو عند الـ 11 اللي عندي هذول اللي
+
+215
+00:20:47,490 --> 00:20:51,670
+congruent بس لواحد من هذول and only one صار إنه
+
+216
+00:20:51,670 --> 00:20:54,810
+congruent لأن الأصليات هذول congruent وعدد الـ 11
+
+217
+00:20:54,810 --> 00:20:58,590
+بتعمل إيه؟ أشْماَلُه Complete Residue System لدول 11
+
+218
+00:20:58,590 --> 00:21:02,590
+إذًا .. خليك اتجاه بصينة
+
+219
+00:21:08,360 --> 00:21:15,320
+فيه دال شغلة عندي اللي هو هذا اللي هو عندي هذول
+
+220
+00:21:15,320 --> 00:21:19,580
+أشْماَلُهم مش complete residual system مو دولو جد إيش؟
+
+221
+00:21:19,580 --> 00:21:23,600
+.. أحد عشر مظبوط اللي هو عندي ال .. ال .. ال ..
+
+222
+00:21:23,600 --> 00:21:26,440
+نأخذ مثال اللي عندنا خمسة تربيع ومين؟ وستة تربيع
+
+223
+00:21:26,440 --> 00:21:31,290
+والعشرة تربيع والواحد وهكذا المية ما هي 99
+
+224
+00:21:31,290 --> 00:21:34,990
+لما نشيلنا الواحد فاهمينها عشان هي تربيع مية و
+
+225
+00:21:34,990 --> 00:21:37,630
+الواحد واحد ناقص 2 وناقص واحد تطلع تسعة
+
+226
+00:21:37,630 --> 00:21:41,330
+وتسعين في دنيا إيش مالها؟ من مضاعفات لـ 11 دمت
+
+227
+00:21:41,330 --> 00:21:45,200
+الطبقات فاهمين عليها يا شباب؟ إحنا عشان بدنا نثبت
+
+228
+00:21:45,200 --> 00:21:49,100
+هدول بعملينش Complete Residue System Modulo 11،
+
+229
+00:21:49,100 --> 00:21:51,840
+بدنا نلاقي اثنين من هدول على الأقل أشْماَلُهُمَا
+
+230
+00:21:51,840 --> 00:21:56,220
+متطابقات، هاي عندي اللي هو ماخذين مثلًا خمسة تربيع
+
+231
+00:21:56,220 --> 00:22:00,820
+وستة تربيع، هدول متطابقات Modulo 11 ومش إيه كمان
+
+232
+00:22:00,820 --> 00:22:04,960
+وهي في غيرهم كمان اللي هو واحد تربيع يطابق العشرة
+
+233
+00:22:04,960 --> 00:22:09,900
+تربيع Modulo مين؟ Modulo 11 واحد فيهم أخل بالشرط
+
+234
+00:22:09,900 --> 00:22:13,700
+يكفي أن نقول عنه أشْماَلُهُم ليس Complete Residue
+
+235
+00:22:13,700 --> 00:22:21,880
+System Modulo 11 اطلع للي بعده سؤال
+
+236
+00:22:21,880 --> 00:22:28,080
+12 كبر بالله سؤال 12 إذا كان Greatest Common
+
+237
+00:22:28,080 --> 00:22:33,670
+Divisor بين الـ A والـ N عشان الحاجة نمر عليها من
+
+238
+00:22:33,670 --> 00:22:37,210
+كلها نسرع شوية الـ grids from divisors بين الـ A و
+
+239
+00:22:37,210 --> 00:22:43,770
+الـ N إيش بيساوي واحد prove that إنّه C وC زي
+
+240
+00:22:43,770 --> 00:22:48,540
+يعني جمع برضه هناك عملنا ضرب C زيادة إيه؟ C زيادة
+
+241
+00:22:48,540 --> 00:22:52,300
+اثنين إيه؟ C زيادة N ناقص واحد في مين؟ في إيه؟
+
+242
+00:22:52,300 --> 00:22:56,440
+forms a complete residue system modulo N for any
+
+243
+00:22:56,440 --> 00:23:02,460
+مين؟ for any C انتبهوا عندي برضه الفكرة مشابهة هو
+
+244
+00:23:02,460 --> 00:23:12,290
+يا شباب عندي في عملية الضرب لازم إنّه المقياس واللي
+
+245
+00:23:12,290 --> 00:23:15,830
+بدنا نضربه عليه المشترك الأعلى بيساوِي واحد وهنا
+
+246
+00:23:15,830 --> 00:23:24,800
+اللي بدنا نضيفه اللي هو الـ A اللي بدنا نكرره الآن
+
+247
+00:23:24,800 --> 00:23:32,360
+من المرات يكون relatively prime مع الـ N يعني C أو
+
+248
+00:23:32,360 --> 00:23:38,280
+N ناقص من واحد C وC زائد A لعند C بس أنا طبعًا اختلف
+
+249
+00:23:38,280 --> 00:23:42,500
+إنّه إحنا بنحكي على أصل مش complete residual system
+
+250
+00:23:42,500 --> 00:23:52,570
+أصل وعدد زائد C زائد A ناقص واحد هذا بيعمل Complete
+
+251
+00:23:52,570 --> 00:23:56,930
+Residue System Modulo مين؟ Modulo اللي هو الـ N
+
+252
+00:23:56,930 --> 00:24:00,710
+Complete Residue System Modulo N ماشي يا أبو يحيى
+
+253
+00:24:00,710 --> 00:24:06,560
+يعني أنا بيعطيك ال Great School Divisor بين الـ N
+
+254
+00:24:06,560 --> 00:24:13,520
+والـ A بيساوي 1 والسيادة ثابت اللي بنضيف له الـ A
+
+255
+00:24:13,520 --> 00:24:18,220
+اللي هو لما نصل لـ N ناقص واحد مضروبة في الـ A واضح
+
+256
+00:24:18,220 --> 00:24:23,120
+هاه؟ إذًا أنا أكيد بنقول هذه العدادين N يكفي عشان
+
+257
+00:24:23,120 --> 00:24:25,520
+إني أثبت إن الـ Complete Residue System يكون
+
+258
+00:24:25,520 --> 00:24:30,000
+إجمالًا Concurrent ماشي الحال؟ incongruent آسف
+
+259
+00:24:30,000 --> 00:24:34,620
+بالدفتر ده الشمال هنا إنّه في من يفي incongruent
+
+260
+00:24:34,620 --> 00:24:45,520
+so both that there exist c زائد a أم واحد وc زائد a
+
+261
+00:24:45,520 --> 00:24:57,450
+أم اثنين أم اثنين اللي هو with M1 وM2 أكبر أو 
+
+262
+00:24:57,450 --> 00:25:05,210
+يساوي 0 وأصغر أو يساوي M-1 such
+
+263
+00:25:05,210 --> 00:25:14,810
+that C زائد A M1 تطابق C زائد A M2 modulo n، 
+
+264
+00:25:14,810 --> 00:25:22,090
+مظبوط؟ سهل الأمر، سهل الأمر، هنا نشيل الـ C من هنا
+
+265
+00:25:22,090 --> 00:25:25,950
+ونشيل
+
+266
+00:25:25,950 --> 00:25:31,970
+الـ C من هنا ونشيل الـ C
+
+267
+00:25:31,970 --> 00:25:35,990
+من هنا ونشيل الـ C من هنا ونشيل الـ C من هنا ونشيل الـ C
+
+268
+00:25:35,990 --> 00:25:38,990
+من هنا ونشيل الـ C من هنا ونشيل الـ C من هنا ونشيل الـ C
+
+269
+00:25:38,990 --> 00:25:43,070
+من هنا ونشيل الـ C من هنا ونشيل الـ C من هنا أم واحد
+
+270
+00:25:43,070 --> 00:25:47,170
+وطابق أم اثنين ودول modulo n وده كنت ردّيكش ليش؟ لأن الأم
+
+271
+00:25:47,170 --> 00:25:52,170
+واحد والأم اثنين جزء من ال complete residue system
+
+272
+00:25:52,170 --> 00:25:56,670
+modulo n وإحنا طبعًا اللي هقول مفترض الأم واحد
+
+273
+00:25:56,670 --> 00:26:00,850
+والأم اثنين ما لازم هنهانة إذا ما لهنّ ما لهنّ مختلفات
+
+274
+00:26:00,850 --> 00:26:06,190
+مفترضين الأم واحد والأم اثنين إيش ما لهنّ؟ مختلفات
+
+275
+00:26:06,190 --> 00:26:13,680
+إذًا صار عند كل اللي هنّ are incongruent بس بالمناسبة
+
+276
+00:26:13,680 --> 00:26:19,480
+إحنا بالنسبة للقسم يا جماعة AX تطابق الـ B modulo
+
+277
+00:26:19,480 --> 00:26:27,940
+N إحنا لما يكون في عند قسمة يعني مثلًا انتبه لـ 6X
+
+278
+00:26:27,940 --> 00:26:37,600
+تطابق الثلاثة modulo مثلًا 12 مثلًا modulo 12 معايا
+
+279
+00:26:39,110 --> 00:26:46,130
+الآن إحنا إذا قسمنا هنا بدي أقسم هنا وأقسم هنا ولازم
+
+280
+00:26:46,130 --> 00:26:51,430
+أقسم هنا على اللي هو الجهتين في عندي اللي هو 
+
+281
+00:26:51,430 --> 00:26:56,090
+أساسا النظرية للأمر الأول أنه لو كان لـ grade
+
+282
+00:26:56,090 --> 00:27:05,490
+score and divisor بين 6 و 12 بيساوي D إذا عشان أقسم
+
+283
+00:27:05,490 --> 00:27:10,810
+على الجهتين هذا بيصير يطابق هذا مضروب 12 على الـD
+
+284
+00:27:10,810 --> 00:27:14,510
+واضح؟
+
+285
+00:27:14,510 --> 00:27:19,650
+ولو كان المشترك الأعلى بين الـ6 و12 بيساوي 1 اللي
+
+286
+00:27:19,650 --> 00:27:24,950
+هو بنسميه واحنا مرتاحين ماشي الحال يعني الآن في هذه
+
+287
+00:27:24,950 --> 00:27:30,090
+الحالة بيصير عندي الاختصار عبارة عن 2X تطابق
+
+288
+00:27:30,090 --> 00:27:37,990
+الواحد مضروب 13 مودولو 6 مودولو 4 آسف مودولو 4 الـ X
+
+289
+00:27:37,990 --> 00:27:43,470
+maximum كل عالمين على تلاتة الآن لو كان عندي مثلا
+
+290
+00:27:43,470 --> 00:27:47,170
+ثلاثين
+
+291
+00:27:47,170 --> 00:27:58,630
+X تطابق خمسة عشر مودولو اللي هو جداش اتنعش مودولو
+
+292
+00:27:58,630 --> 00:27:59,130
+اتنعش
+
+293
+00:28:05,360 --> 00:28:11,060
+الآن ركزوا معايا أنا حكيت عشان هذه النقطة لأن
+
+294
+00:28:11,060 --> 00:28:15,280
+ثلاثين X تطابق خمسة عشر ودول اتناش شغل المكينة
+
+295
+00:28:15,280 --> 00:28:19,960
+التالي الـ 30 و 15، إيش العامل المشترك اللي على
+
+296
+00:28:19,960 --> 00:28:25,840
+بيانين 15؟  أجسم هذا 15، وأجسم هذا 15، وأجسم على
+
+297
+00:28:25,840 --> 00:28:31,500
+هذه العامل المشترك اللي على بيانين 12 و 2، والـ 30
+
+298
+00:28:31,500 --> 00:28:34,600
+اللي أخدت منه، اللي أخدت .. اللي أخدته إمتى؟ أخدت
+
+299
+00:28:34,600 --> 00:28:40,550
+جزء منه زيادة كمان، إيش اللي بقصده؟ يعني الآن أنا
+
+300
+00:28:40,550 --> 00:28:43,530
+قسمت على خمسة عشر، وأنا على خمسة عشر، هنا بتقسم
+
+301
+00:28:43,530 --> 00:28:49,390
+علشان ما بيصيرش بس على تلاتة، خمسة عشر هذا، خمسة عشر،
+
+302
+00:28:49,390 --> 00:28:55,070
+خمسة عشر، خمسة عشر، بقسم هنا علشان على تلاتة من وين
+
+303
+00:28:55,070 --> 00:29:00,090
+اللي بقوله هذا؟ من وين اللي بقوله التالي، انتبه
+
+304
+00:29:00,090 --> 00:29:03,890
+عليها، ده اللي حكيت أنا قبل شوية عملتها خطوتين عشان
+
+305
+00:29:03,890 --> 00:29:06,550
+ت .. ت .. ت .. ت .. تعرف من وين جيبت أنا اللي قلته
+
+306
+00:29:06,550 --> 00:29:12,010
+الخطوة الأولى أجسم لياهم على اللي هي موجودة في
+
+307
+00:29:12,010 --> 00:29:17,150
+الكل معانا يا محمد؟ أجسمها تلاتة، بيصير عشرة X
+
+308
+00:29:17,150 --> 00:29:24,030
+تطابق الخمسة اللي هو خمسة مودولو الـ 4 أربعة
+
+309
+00:29:26,740 --> 00:29:31,640
+المشترك الأعلى الآن ال .. ال .. ال .. ال .. العشر
+
+310
+00:29:31,640 --> 00:29:37,420
+والأربعة اتنين الآن بدك تأخذ من هنا خمسة وهنا خمسة
+
+311
+00:29:37,420 --> 00:29:41,060
+الخمسة اللي بدك تأخذها أصلا ما هي علاقة في مين في
+
+312
+00:29:41,060 --> 00:29:45,260
+الأربعة فتجسم وأنت مرتاح بيصير عبارة عن اتنين X
+
+313
+00:29:45,260 --> 00:29:50,740
+وتطابق الواحد ممكن يبدأهاش مودولو مين مودولو أربعة
+
+314
+00:29:53,630 --> 00:30:00,410
+إذا ملخص الحديث لما تجسم أنت مهما كان الجسم تبنهان
+
+315
+00:30:00,410 --> 00:30:06,630
+وبنهان كبير بتجسم على اللاهانة بسبليم باللي موجود
+
+316
+00:30:06,630 --> 00:30:12,290
+على البن اللي هو إثنا عشر والثلاثين واللي موجود في
+
+317
+00:30:12,290 --> 00:30:18,770
+داخل ما قسمت عليه واضح اه أي سؤال
+
+318
+00:30:22,670 --> 00:30:28,450
+لأ أنت مش بدك تختصر هذه وهذه أنت يعني الغاية إن
+
+319
+00:30:28,450 --> 00:30:31,750
+احنا عايشين نخفف عن الـ X عشان نخلّي الـ X لحالها عشان
+
+320
+00:30:31,750 --> 00:30:36,230
+نخفف عن الـ X بدك تجسم هنا وهنا إذا في جسمها الآن
+
+321
+00:30:36,230 --> 00:30:41,330
+هذه الجسمة مع هذه فينا نحادير إذا كان هذا فيه من ال
+
+322
+00:30:41,330 --> 00:30:45,150
+.. من .. من .. من .. اللي بتقسم عليه موجود هنا
+
+323
+00:30:45,150 --> 00:30:48,330
+لازم تقسمه هنا موجود جزء منه هنا لازم تقسم على
+
+324
+00:30:48,330 --> 00:30:51,530
+الجزء اللي منه ما فيش خلاص تقسمه أنت مرتاح لو إنه
+
+325
+00:30:51,530 --> 00:30:54,390
+just common divisor بيصير إيش بيساوي واحد نطلع
+
+326
+00:30:54,390 --> 00:30:59,290
+للبرّه بيقول لك any consecutive integers form a
+
+327
+00:30:59,290 --> 00:31:03,790
+complete result of a system modulo mean modulo and
+
+328
+00:31:03,790 --> 00:31:11,780
+معايا أي .. أي .. اللي هو خمس أعداد متتالية بيعمل
+
+329
+00:31:11,780 --> 00:31:16,320
+الـ Complete Residue System Modulo خمسة أي أن من
+
+330
+00:31:16,320 --> 00:31:20,120
+الأعداد المتتالية بتعمل Complete Residue System
+
+331
+00:31:20,120 --> 00:31:26,800
+Modulo مين؟ Modulo N واضح؟ أي أن أي أم أو أي أن من
+
+332
+00:31:26,800 --> 00:31:30,080
+الأعداد المتتالية بيعمل الـ Complete Residue
+
+333
+00:31:30,080 --> 00:31:35,770
+System Modulo N شوف الآن عندي نأخذ الـ M و الـ M
+
+334
+00:31:35,770 --> 00:31:38,990
+زائد واحد و الـ M زائد M ناقص واحد هذول إيش ماله
+
+335
+00:31:38,990 --> 00:31:42,810
+مالهم؟ اللي هو إيش مالنا دوله؟ M من الأعداد
+
+336
+00:31:42,810 --> 00:31:47,130
+المتتالية هاي عندك إيش الأعداد المتتالية؟ M و M
+
+337
+00:31:47,130 --> 00:31:53,590
+زائد واحد و M زائد اتنين لما أصل عند M زائد M ناقص
+
+338
+00:31:53,590 --> 00:32:01,440
+واحد، مظبوط؟ هدول الأعداد إيش مالهم N من الأعداد
+
+339
+00:32:01,440 --> 00:32:05,000
+المتتالية أي N من الأعداد المتتالية هدول بقى من
+
+340
+00:32:05,000 --> 00:32:07,740
+الـ Complete Residue System دلوقت مش من اللي فوق
+
+341
+00:32:07,740 --> 00:32:13,260
+بس عندك الـ C هن إيش مالها اللي عبارة عن M والـ H
+
+342
+00:32:13,260 --> 00:32:20,880
+بتساوي واحد فاهمين اه؟ إذا صار ه لخافة من مين؟ من
+
+343
+00:32:20,880 --> 00:32:21,400
+اللي فوق
+
+344
+00:32:24,390 --> 00:32:30,390
+اللي فوق مش متتاليات، دير بالك اه ال .. ال .. ال
+
+345
+00:32:30,390 --> 00:32:34,790
+.. ال .. كل بقر فارق بين كل واحدة A عشر A لكن الـ A
+
+346
+00:32:34,790 --> 00:32:38,010
+.. الـ A حافظت على ال .. على Complete Residue
+
+347
+00:32:38,010 --> 00:32:42,090
+System لإنه علاقتها بالـ N ده ما إنعش مالها بيساوي
+
+348
+00:32:42,090 --> 00:32:46,290
+واحد لو ما كانتش بيساوي واحد، معناته بخاف إنه يكرر
+
+349
+00:32:46,290 --> 00:32:50,350
+إن حاله ويجيب الرقم نفس الرقم وبطل نهيش Complete
+
+350
+00:32:50,350 --> 00:32:57,210
+Residue System Modulo N طيب سي .. نقول لنا سي .. سي
+
+351
+00:32:57,210 --> 00:33:00,470
+the product of any set of n consecutive integers
+
+352
+00:33:00,470 --> 00:33:07,030
+إيش ماله؟ اللي هو is divisible by مين؟ by n .. إن
+
+353
+00:33:07,030 --> 00:33:10,750
+واحد من اللي في الطريق الحالي دي إيش ماله ب .. ب
+
+354
+00:33:10,750 --> 00:33:12,130
+.. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب
+
+355
+00:33:12,130 --> 00:33:12,150
+.. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب
+
+356
+00:33:12,150 --> 00:33:12,410
+.. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب
+
+357
+00:33:12,410 --> 00:33:13,910
+.. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب
+
+358
+00:33:13,910 --> 00:33:15,110
+.. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب
+
+359
+00:33:15,110 --> 00:33:24,340
+.. ب .. ب .. ب .. ب .. ب .. ب .. ب .. ب .. لأن هذا
+
+360
+00:33:24,340 --> 00:33:28,300
+completely residue system مدام إن بفرقه معناته إن إن
+
+361
+00:33:28,300 --> 00:33:32,240
+بتقسم هذا العجب اللي حكينا عنه وجيه ده رابطين في
+
+362
+00:33:32,240 --> 00:33:36,080
+بعض وواحد منين هو هذا ده معناه إنك تقسمها فاهمين
+
+363
+00:33:36,080 --> 00:33:46,840
+يا جماعة؟ عندي الآن حاصل ضرب هذول لازم M في M زائد
+
+364
+00:33:46,840 --> 00:33:52,620
+واحد لما أصل عند M زائد M ناقص واحد لازم الـ M
+
+365
+00:33:52,620 --> 00:34:00,720
+إيش ماله تقسم لسبب بسيط إنه بما إن M is an integer في
+
+366
+00:34:00,720 --> 00:34:05,960
+Z وهذا complete residual system modulo M إذا there
+
+367
+00:34:05,960 --> 00:34:12,260
+exist element هنا سميّه M زائد K يطابق الـ M
+
+368
+00:34:12,260 --> 00:34:22,690
+مودولو مين انر مظبوط معايا واضح يعني هيكون هذا عبارة
+
+369
+00:34:22,690 --> 00:34:29,810
+عن إيش مال العدد من مضاعفات الآن لأن هذا الآن بطابق
+
+370
+00:34:29,810 --> 00:34:35,870
+مين ندو إن الصفر فبيصير الآن تخسم مين الآن زاد كتر
+
+371
+00:34:37,910 --> 00:34:44,130
+الآن بتقسم الآن زائد K ده بتقسم حاصل الضرب كلها ده
+
+372
+00:34:44,130 --> 00:34:51,070
+اللي فيه من ضمنه M زائد K سؤال
+
+373
+00:34:51,070 --> 00:34:54,870
+13 Verify
+
+374
+00:34:54,870 --> 00:35:01,670
+that if A تطابق اللي هو الـ B modulo N واحد والـ A
+
+375
+00:35:01,670 --> 00:35:05,510
+تطابق الـ B modulo N اثنين والـ A تطابق الـ B
+
+376
+00:35:05,510 --> 00:35:10,420
+modulo N where n بيساوي least common multiple بين
+
+377
+00:35:10,420 --> 00:35:16,500
+n واحد و n اثنين إذا هيكون اللي هو الـ a تطابق الـ b
+
+378
+00:35:16,500 --> 00:35:18,800
+مودولو n واحد و n اثنين لما يكون الأعلى من المشترك
+
+379
+00:35:18,800 --> 00:35:25,040
+الأعلى اللي هو بين n واحد و n اثنين بيساوي واحد إذا
+
+380
+00:35:25,040 --> 00:35:31,980
+بدنا شغل ثاني شغل الأول هي أبدأ شوية حسابات والشغل
+
+381
+00:35:31,980 --> 00:35:34,600
+الثاني حالة خاصة من الأولى خلّينا نقول السؤال
+
+382
+00:35:34,600 --> 00:35:43,040
+ونوضحه ونبرهنه نحسب الحسابات اللي قدامكم شوفوا
+
+383
+00:35:43,040 --> 00:35:48,500
+صلى الله عليه الصلاة والسلام عندي السؤال بيقول لي
+
+384
+00:35:48,500 --> 00:35:57,280
+إيه تطابق الـ V modulo N واحد معايا
+
+385
+00:35:58,850 --> 00:36:08,610
+والـ A تطابق الـ B Modulo مين N اثنين بقول إذا الـ
+
+386
+00:36:08,610 --> 00:36:18,800
+A تطابق الـ B Modulo الـ least common multiple بين
+
+387
+00:36:18,800 --> 00:36:23,220
+N واحد ومين و N اثنين يعني الـ A تطبيق الـ B
+
+388
+00:36:23,220 --> 00:36:29,140
+modulo N حيث where الـ N بتساوي الـ least common
+
+389
+00:36:29,140 --> 00:36:35,020
+multiple بين N واحد و N إيش اثنين معايا يا جماعة؟
+
+390
+00:36:35,600 --> 00:36:40,340
+إذاً a تطابق b مقياس n واحد a تطابق b مقياس n 
+
+391
+00:36:40,340 --> 00:36:45,900
+اثنين يؤدي إلى a تطابق b مقياس العامل المضعف
+
+392
+00:36:45,900 --> 00:36:51,880
+المشترك البسيط بين مين n واحد و n اثنين معايا طيب
+
+393
+00:36:51,880 --> 00:36:56,200
+إن إن عندي نأخذ نفس الرموز اللي ماخدها عندي a
+
+394
+00:36:56,200 --> 00:37:00,800
+تطابق الـ b مودولو n اثنين مودولو n واحد معناته إن الـ n واحد
+
+395
+00:37:00,800 --> 00:37:09,120
+بيجسم الـ a minus b مظبوط ما هي معناته؟ A-B بيساوي
+
+396
+00:37:09,120 --> 00:37:19,060
+N1 كما هو مسميها K1 وهذه نستخدمها معايا ونفس الشيء
+
+397
+00:37:19,060 --> 00:37:25,460
+الـ A تطابق الـ N2 ليه تطابق B ودوله مين؟ الـ N2
+
+398
+00:37:25,460 --> 00:37:34,740
+تقسم الـ A-B يعني اللي هو A-B بيساوي N2×K2
+
+399
+00:37:37,050 --> 00:37:41,550
+لأن هالتي اللي هو إيش أعمل إن إن تقسم الـ a minus b
+
+400
+00:37:41,550 --> 00:37:46,650
+يعني في الآخر بدي إن تقسم الـ a minus b يعني بمعنى
+
+401
+00:37:46,650 --> 00:37:52,880
+آخر الـ a minus b بتساوي N في something معايا؟ بيكون
+
+402
+00:37:52,880 --> 00:37:58,760
+خلصت، اه اه طبعا، بيكون خلصت في علاقة ما بنعرفها
+
+403
+00:37:58,760 --> 00:38:02,140
+بين الـ Least common multiple والـ Greatest common
+
+404
+00:38:02,140 --> 00:38:10,380
+divisor ده أنا ناشمها اليوم في hustle دلوقتي بس
+
+405
+00:38:10,380 --> 00:38:15,500
+قبل اللي أنا بدي شغل عشان استعملها عندي الـ
+
+406
+00:38:15,500 --> 00:38:20,650
+Greatest common divisor بين N واحد و N اثنين can be
+
+407
+00:38:20,650 --> 00:38:24,230
+written as a linear combination بين N واحد و N
+
+408
+00:38:24,230 --> 00:38:27,090
+اثنين يعني بمعنى آخر there exist X not و Y not
+
+409
+00:38:27,090 --> 00:38:30,350
+element in Z such that the greatest common divisor
+
+410
+00:38:30,350 --> 00:38:35,290
+for C أوي N واحد X not زائد N اثنين في مين في Y not
+
+411
+00:38:35,290 --> 00:38:38,750
+هاي عندي اللي هو greatest common divisor بهذا
+
+412
+00:38:38,750 --> 00:38:44,430
+الصورة معايا؟ لأن زي ما أقولها هذه اللي هي عندي N
+
+413
+00:38:44,430 --> 00:38:52,420
+واحد في N اثنين إيش متساوي؟ بتساوي بتساوي الـ least
+
+414
+00:38:52,420 --> 00:38:58,220
+common multiple الـ least common multiple بين N
+
+415
+00:38:58,220 --> 00:39:02,100
+واحد و N اثنين في الـ greatest common divisor بين N
+
+416
+00:39:02,100 --> 00:39:08,660
+واحد و N اثنين Y بيساوي هذا إيش سميّنا N صح؟ و هذا
+
+417
+00:39:08,660 --> 00:39:16,620
+إيش سميّنا A N واحد X not زائد N اثنين Y not
+
+418
+00:39:16,620 --> 00:39:18,200
+معايا؟
+
+419
+00:39:20,680 --> 00:39:25,940
+الآن أنا وقعد في الآخر إن أكتب mean اللي هو a-b
+
+420
+00:39:25,940 --> 00:39:31,620
+على صورة something طيب a-b بقدر أجيبها يا من هذه
+
+421
+00:39:31,620 --> 00:39:37,540
+يا من هذه معايا a-b اللي هو عضوها على M1 في K1
+
+422
+00:39:37,540 --> 00:39:45,340
+يعني لو شيلنا هذه بيصير a-b على اللي هو K1 فإن 
+
+423
+00:39:45,340 --> 00:39:48,280
+اتنين أظبطوا اللي عملته؟
+
+424
+00:39:51,620 --> 00:39:56,940
+أه عوضت على N واحد لماذا؟ أنا في النهاية بغرب أوجد
+
+425
+00:39:56,940 --> 00:40:02,700
+A-B بيساوي N فاضي، مظبوط؟ هيعندي N جاهزة وهيمشي،
+
+426
+00:40:02,700 --> 00:40:07,080
+معايا؟ شيلت الـ N واحد منها و أدخلت الـ A-B ممكن
+
+427
+00:40:07,080 --> 00:40:10,260
+أحد ثاني يقول لأ، بفشي الـ N اثنين و أدخلت الـ A-B
+
+428
+00:40:10,260 --> 00:40:14,320
+من هنا صار عندي A-B على K واحد فإن اثنين بساوي
+
+429
+00:40:14,320 --> 00:40:18,080
+اللي هو المقدار اللي عندي صارت عندي A-B بديها
+
+430
+00:40:18,080 --> 00:40:26,130
+لحالها أنا إيش بتساوي؟ بساوي N في K واحد N واحد ×
+
+431
+00:40:26,130 --> 00:40:38,330
+not زاد K واحد K واحد فن اثنين Y not عالميا على N
+
+432
+00:40:38,330 --> 00:40:42,710
+اثنين اقسم على M اثنين حط على N اثنين وهنا على
+
+433
+00:40:42,710 --> 00:40:49,850
+اثنين راحت بظبط الآن هذا integer ولا مش integer مش 
+
+434
+00:40:49,850 --> 00:40:55,290
+عارفين لسه قد ما كسوم K1 N1 على N2 integer ولا لأ عند
+
+435
+00:40:55,290 --> 00:41:03,610
+K1 في N1 إيش مساره معايا؟ انتبهوا هذا الـ dot بتحمل 
+
+436
+00:41:03,610 --> 00:41:08,630
+level هذا الـ dot بتحمل integer ويساوي M في هذا
+
+437
+00:41:08,630 --> 00:41:16,790
+المقدار عبارة عن A minus B على M2 في X0 زائد K1 في
+
+438
+00:41:16,790 --> 00:41:21,890
+Y0 طب ما هي أصلا A minus B على M2 A minus B على M2
+
+439
+00:41:21,890 --> 00:41:30,150
+مين هي؟ K2 integer إذن ويساوي M في K2 X0 زائد K1
+
+440
+00:41:30,150 --> 00:41:38,020
+في Y0 إذا صار عند الـ N بتجسم الـ A minus B أو هذا
+
+441
+00:41:38,020 --> 00:41:44,440
+يعني أن A تطابق الـ B modulo N هاي البرهان كامل
+
+442
+00:41:44,440 --> 00:41:47,480
+هاي البرهان كامل أنا أنا ب برهنش كلام كثير بحكي و
+
+443
+00:41:47,480 --> 00:41:54,060
+بكتبوش اللي 
+
+444
+00:41:54,060 --> 00:41:54,500
+بعده
+
+445
+00:42:02,470 --> 00:42:06,090
+أه لما يكون الـ .. الـ .. الـ grade school divisor
+
+446
+00:42:06,090 --> 00:42:13,490
+بينهم بيساوي واحد أه بيصير الواحد في اثنين اللي 
+
+447
+00:42:13,490 --> 00:42:20,350
+school multiple بيصير مو دلوق مين الآن مو دلوق بدل
+
+448
+00:42:20,350 --> 00:42:25,390
+إن إيش هيصير Modulo N واحد في N اثنين لما يكون العامل
+
+449
+00:42:25,390 --> 00:42:27,810
+المشترك اللي على بين N واحد و N اثنين بيساوي واحد
+
+450
+00:42:27,810 --> 00:42:33,710
+معناه سارقة وطابق بي Modulo N واحد في N اثنين هذا
+
+451
+00:42:33,710 --> 00:42:37,970
+عندما يقول Greatest common divisor بينهم بيساوي واحد
+
+452
+00:42:37,970 --> 00:42:46,190
+كلام صحيح طيب هذا شوية الحسابات زي اللي جابناها زي
+
+453
+00:42:46,190 --> 00:42:53,210
+اللي عملناها قبل هيك طيب اطلع لفوق لنشوف اللي بعده
+
+454
+00:42:53,210 --> 00:43:01,090
+هذا 18
+
+455
+00:43:01,090 --> 00:43:05,070
+و
+
+456
+00:43:05,070 --> 00:43:09,870
+17 برضه الأسئلة سهلة يعني مش صعبة خلينا نمر عليها
+
+457
+00:43:09,870 --> 00:43:15,550
+سريعًا عند ال A تطابق ال B Modulo واحد و A تطابق الـ
+
+458
+00:43:15,550 --> 00:43:22,230
+C Modulo اثنين إذا الـ Aالـ B تطابق مين الـ C Modulo
+
+459
+00:43:22,230 --> 00:43:26,410
+مين وModulo N الـ N هو A أشماله العامل المشترك
+
+460
+00:43:26,410 --> 00:43:35,550
+الأعلى بين N واحد وN اثنين معايا أه بس بنتفجمها
+
+461
+00:43:35,550 --> 00:43:39,710
+الـ A تطابق الـ B عند A تطابق الـ B Modulo N واحد
+
+462
+00:43:39,710 --> 00:43:45,530
+بتابعين معايا أه إذا صارت اللي هي الـ N واحد بتجسم
+
+463
+00:43:45,530 --> 00:43:52,820
+الـ A minus B معايا والآن اثنين والآن اثنين بتقسم
+
+464
+00:43:52,820 --> 00:43:59,780
+a minus c وعندي الآن إيش هي الآن عبارة عن الـ
+
+465
+00:43:59,780 --> 00:44:03,180
+greatest common divisor بين N واحد ومين ون 
+
+466
+00:44:03,180 --> 00:44:07,920
+اثنين يعني N بتقسم N واحد ون بتقسم مين
+
+467
+00:44:07,920 --> 00:44:12,680
+N اثنين هذه بتعني أن N بتقسم N واحد و
+
+468
+00:44:12,680 --> 00:44:16,380
+N بتقسم N اثنين معناها تقول أن N من هذه و
+
+469
+00:44:16,380 --> 00:44:23,550
+من هذه شايفين أن بتقسم a-b وهذه أن بتقسم a-c إذا 
+
+470
+00:44:23,550 --> 00:44:26,770
+بتقسم a إيش أي linear combination بينهم من ضمن أن
+
+471
+00:44:26,770 --> 00:44:35,510
+أن بتقسم a-b زائد a ناقص a زائد c يعني أن بتقسم c
+
+472
+00:44:35,510 --> 00:44:44,190
+-b معناته c تطابق ال b Modulo n هيك المطلوبة طيب
+
+473
+00:44:44,190 --> 00:44:52,030
+ميجينا السؤال 17 السؤال 17 مش فاعل 17 بقول ثاني
+
+474
+00:44:52,030 --> 00:44:59,150
+عندك
+
+475
+00:44:59,150 --> 00:45:12,050
+A CAB تطابق CD Modulo N وعندك الـ B تطابق
+
+476
+00:45:12,050 --> 00:45:21,540
+الـ D Modulo N أو الـ Greatest Common Divisor بين
+
+477
+00:45:21,540 --> 00:45:33,340
+الـ N والـ B والـ N بيساوي واحدة إذن هذه الـ A
+
+478
+00:45:33,340 --> 00:45:39,100
+تطابق الـ C Modulo N Modulo N سلوك هذا إيش اللي هو 
+
+479
+00:45:39,100 --> 00:45:43,720
+بقول يعني بقول أنت يعني أحيانًا احنا طبعًا احنا خدنا
+
+480
+00:45:43,720 --> 00:45:50,060
+لو في عدد وعدد يعني اثنين في اثنين إيش نختصر؟ نختصر
+
+481
+00:45:50,060 --> 00:45:53,540
+اللي هنا مع اللي هنا مع اللي هو اللي هنا ده كان 
+
+482
+00:45:53,540 --> 00:45:56,480
+فيه بقت من الاثنين شيء فاهمين إيش معاناة من 
+
+483
+00:45:56,480 --> 00:45:59,300
+الاثنين شيء خلاص لجيت اللغة ده اللي ندرج عليها
+
+484
+00:45:59,300 --> 00:46:04,400
+الآن بقولك احنا بروح أبعد من هيك لو في عدد هنا
+
+485
+00:46:04,400 --> 00:46:09,380
+يعني الآن لو كانت هذه مثلًا خمسة وهنا فيه خمسة
+
+486
+00:46:09,380 --> 00:46:14,560
+وعشرين وفيه خمسة مثلًا خلوني أقول فيه ثلاثة وفيه
+
+487
+00:46:14,560 --> 00:46:19,780
+ثمانية مضربات يعني في الـA في الـC معايا وأنت
+
+488
+00:46:19,780 --> 00:46:26,170
+مرتاح وأنت مرتاح شيلها الثمانية وشيلها الثلاثة يعني
+
+489
+00:46:26,170 --> 00:46:32,730
+طريقة أخرى أكثر من طريقة العدد نفسه العدد ومطابقته
+
+490
+00:46:32,730 --> 00:46:40,030
+يختصر بحيث أن يكون هذا العدد أي مطابقة يطاقم ..
+
+491
+00:46:40,030 --> 00:46:42,110
+مضاعف الـ .. الـ .. الـ … الـ … الـ … الـ … الـ …
+
+492
+00:46:42,110 --> 00:46:42,470
+الـ … الـ … الـ … الـ … الـ … الـ … الـ … الـ …
+
+493
+00:46:42,470 --> 00:46:42,890
+الـ … الـ … الـ … الـ … الـ … الـ … الـ … الـ …
+
+494
+00:46:42,890 --> 00:46:44,070
+الـ … الـ … الـ … الـ … الـ … الـ … الـ … الـ …
+
+495
+00:46:44,070 --> 00:46:44,270
+الـ … الـ … الـ … الـ … الـ … الـ … الـ … الـ …
+
+496
+00:46:44,270 --> 00:46:47,430
+الـ … الـ … الـ … الـ … الـ … الـ … 
+
+497
+00:46:47,430 --> 00:46:48,430
+الـ …
+
+498
+00:46:53,550 --> 00:46:58,490
+لو كان بين الـ B و الـ N بيساوي واحد والـ D تطابق
+
+499
+00:46:58,490 --> 00:47:02,350
+الـ B هيكون برضه بين الـ D و الـ N أشماله بيساوي
+
+500
+00:47:02,350 --> 00:47:07,150
+واحد لأنه
+
+501
+00:47:07,150 --> 00:47:09,970
+لنفسي الغنان درو عليه امشي
+
+502
+00:47:14,860 --> 00:47:18,400
+اللي دي الآن بدنا اللي هو الـ .. الـ .. الـ .. 
+
+503
+00:47:18,400 --> 00:47:21,940
+البرهنة إيه بتطبق معي؟ حولها على طول إيش ما له؟
+
+504
+00:47:21,940 --> 00:47:29,840
+هذه N بظبط عامل هيك بي ناقص CD صح؟ والتانية N 
+
+505
+00:47:29,840 --> 00:47:38,720
+بتجسم الـ B ناقص D معايا بده يدرب الآن في إيش؟ يطير
+
+506
+00:47:38,720 --> 00:47:41,380
+اللي هو الـ D بظبط؟
+
+507
+00:47:43,080 --> 00:47:51,480
+مصير N بتقسم BC CD
+
+508
+00:47:51,480 --> 00:48:00,300
+مظبوط هيك فاهمين عليها N 
+
+509
+00:48:00,300 --> 00:48:05,620
+بتقسم هذا و N بتقسم هذا الطريقة ثانية إذا N بتقسم
+
+510
+00:48:05,620 --> 00:48:13,570
+AB ناقص CD أو زاد ما قلت قبل زاد CB ناقص CD أنا لها
+
+511
+00:48:13,570 --> 00:48:18,790
+بالنقص أنت بقدر يعني أنت رابط فيه نقص C في مشكلة
+
+512
+00:48:18,790 --> 00:48:23,510
+أي ميم ال combination واضح اللي بحكيه إذا N صار
+
+513
+00:48:23,510 --> 00:48:28,570
+عندي نقص CD مع نقص CD فبيصير ال N بتقسم ال AB نقص 
+
+514
+00:48:28,570 --> 00:48:32,710
+CB لأن العامل المشترك اللي هو هذا N يعني بتقسم الـ
+
+515
+00:48:32,710 --> 00:48:36,150
+B في A minus C العامل المشترك اللي عليه الـ B والـ 
+
+516
+00:48:36,150 --> 00:48:44,070
+N واحد إذا N بتقسم ال A minus C يعني وقالّا،
+
+517
+00:48:44,070 --> 00:48:45,330
+يعطيكم العافية
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BrG6sHyCXRc_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BrG6sHyCXRc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..add9c88036d00935f6519a0b07ab2aa89fb3f4f9
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/BrG6sHyCXRc_raw.json
@@ -0,0 +1 @@
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2423, 18173, 1034, 2202, 356, 2423, 7649, 18871, 16254, 18173, 1975, 9381, 11624, 18173, 1975, 9381, 11624, 18173, 18173, 1975, 9381], "avg_logprob": -0.3722956833931116, "compression_ratio": 1.5178571428571428, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 240.55, "end": 240.97, "word": "الان", "probability": 0.7646484375}, {"start": 240.97, "end": 242.11, "word": " ال", "probability": 0.78369140625}, {"start": 242.11, "end": 242.73, "word": " 41", "probability": 0.64111328125}, {"start": 242.73, "end": 244.17, "word": " ال", "probability": 0.362548828125}, {"start": 244.17, "end": 244.63, "word": " 41", "probability": 0.978515625}, {"start": 244.63, "end": 245.57, "word": " similarly", "probability": 0.5289713541666666}, {"start": 245.57, "end": 246.83, "word": " الان", "probability": 0.6217041015625}, {"start": 246.83, "end": 247.15, "word": " عندي", "probability": 0.686279296875}, {"start": 247.15, "end": 247.75, "word": " 41", "probability": 0.96240234375}, {"start": 247.75, "end": 247.95, "word": " اص", "probability": 0.559326171875}, {"start": 247.95, "end": 248.55, "word": " 65", "probability": 0.74267578125}, {"start": 248.55, "end": 249.77, "word": " 41", "probability": 0.7666015625}, {"start": 249.77, "end": 250.41, "word": " اص", "probability": 0.930419921875}, {"start": 250.41, "end": 251.17, "word": " 65", "probability": 0.8720703125}, {"start": 251.17, "end": 257.93, "word": " 41", "probability": 0.8740234375}, {"start": 257.93, "end": 260.09, "word": " 41", "probability": 0.85791015625}, {"start": 260.09, "end": 262.33, "word": " اص", "probability": 0.92822265625}], "temperature": 1.0}, {"id": 11, "seek": 29126, "start": 264.48, "end": 291.26, "text": "65 تطابق ماذا مدلوق 7 او ماذا هذي اللي هو عدد بين السفر وبين السبعة او اكبر سفر سفر وأصغر strictly من السبعة زي ما حكيته لأن 41 تطابق سالب واحد مدنونين مدو سبعة على طول هذه لأنه عند اتنين أربعين مضاعفات السبعة بصينا عنده الآن أس خمسة وستين", "tokens": [16824, 6055, 9566, 16758, 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لأنه", "probability": 0.6548665364583334}, {"start": 285.6, "end": 286.16, "word": " عند", "probability": 0.8505859375}, {"start": 286.16, "end": 286.42, "word": " اتنين", "probability": 0.84271240234375}, {"start": 286.42, "end": 286.68, "word": " أربعين", "probability": 0.70770263671875}, {"start": 286.68, "end": 287.2, "word": " مضاعفات", "probability": 0.91533203125}, {"start": 287.2, "end": 287.68, "word": " السبعة", "probability": 0.9666341145833334}, {"start": 287.68, "end": 288.98, "word": " بصينا", "probability": 0.5220947265625}, {"start": 288.98, "end": 289.24, "word": " عنده", "probability": 0.44439697265625}, {"start": 289.24, "end": 289.52, "word": " الآن", "probability": 0.67626953125}, {"start": 289.52, "end": 290.14, "word": " أس", "probability": 0.707275390625}, {"start": 290.14, "end": 290.7, "word": " خمسة", "probability": 0.8187255859375}, {"start": 290.7, "end": 291.26, "word": " وستين", "probability": 0.9645182291666666}], "temperature": 1.0}, {"id": 12, "seek": 30652, "start": 292.17, "end": 306.53, "text": "تطابق اص 65 وهذا عبارة عن ناقص واحد مدل سبعة قبل ان اخر تطابق الستة مدل سبعة اذا الـ remainder في هذه الحلقة بداش عبارة عن ستة", "tokens": [2655, 9566, 16758, 4587, 1975, 9381, 11624, 37037, 15730, 6225, 3555, 9640, 3660, 18871, 8717, 995, 4587, 9381, 36764, 24401, 3714, 3215, 1211, 8608, 3555, 27884, 12174, 36150, 16472, 1975, 34740, 6055, 9566, 16758, 4587, 21136, 2655, 3660, 3714, 3215, 1211, 8608, 3555, 27884, 1975, 15730, 2423, 39184, 29837, 8978, 29538, 21542, 1211, 28671, 47525, 33599, 6225, 3555, 9640, 3660, 18871, 8608, 2655, 3660], "avg_logprob": -0.265625, "compression_ratio": 1.5357142857142858, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 292.17, "end": 292.77, "word": "تطابق", "probability": 0.7850341796875}, {"start": 292.77, "end": 293.19, "word": " اص", "probability": 0.4066162109375}, {"start": 293.19, "end": 293.97, "word": " 65", "probability": 0.54052734375}, {"start": 293.97, "end": 295.59, "word": " 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"probability": 0.9816080729166666}, {"start": 302.43, "end": 302.73, "word": " سبعة", "probability": 0.96484375}, {"start": 302.73, "end": 302.95, "word": " اذا", "probability": 0.6048583984375}, {"start": 302.95, "end": 303.19, "word": " الـ", "probability": 0.523681640625}, {"start": 303.19, "end": 303.37, "word": " remainder", "probability": 0.748046875}, {"start": 303.37, "end": 303.57, "word": " في", "probability": 0.830078125}, {"start": 303.57, "end": 303.71, "word": " هذه", "probability": 0.556640625}, {"start": 303.71, "end": 303.99, "word": " الحلقة", "probability": 0.94677734375}, {"start": 303.99, "end": 304.49, "word": " بداش", "probability": 0.4205322265625}, {"start": 304.49, "end": 305.49, "word": " عبارة", "probability": 0.9326171875}, {"start": 305.49, "end": 305.83, "word": " عن", "probability": 0.9912109375}, {"start": 305.83, "end": 306.53, "word": " ستة", "probability": 0.845703125}], "temperature": 1.0}, {"id": 13, "seek": 33696, "start": 308.34, "end": 336.96, "text": "لأ احنا عشان بدنا remainder remainder كلهم متطابقات اكيد لكن عندما نقسم الباقي القسم اللي احنا متفجين عليه انه اكبر او يساوي سفره اصغر من مين مين مقسم عليه المقلوب التالي what is the remainder when the following sum is divisible by 4 عندي اللي هو واحد أس خمسة زي اتنين أس خمسة زي تلاتة أس خمسة", "tokens": [1211, 10721, 1975, 5016, 8315, 6225, 8592, 7649, 47525, 8315, 29837, 29837, 28242, 16095, 44650, 9566, 16758, 4587, 9307, 1975, 4117, 25708, 44381, 43242, 15042, 8717, 4587, 38251, 29739, 995, 38436, 25062, 38251, 13672, 1829, 1975, 5016, 8315, 44650, 5172, 7435, 9957, 47356, 16472, 3224, 1975, 4117, 26890, 1975, 2407, 7251, 3794, 995, 45865, 8608, 5172, 2288, 3224, 1975, 9381, 17082, 2288, 9154, 3714, 9957, 3714, 9957, 3714, 4587, 38251, 47356, 9673, 4587, 1211, 37746, 16712, 6027, 1829, 437, 307, 264, 29837, 562, 264, 3480, 2408, 307, 25974, 964, 538, 1017, 18871, 16254, 13672, 1829, 31439, 36764, 24401, 5551, 3794, 16490, 2304, 3794, 3660, 30767, 1829, 1975, 2655, 1863, 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2896.91, "word": " يعني", "probability": 0.52886962890625}, {"start": 2896.91, "end": 2897.05, "word": " انت", "probability": 0.758544921875}, {"start": 2897.05, "end": 2897.23, "word": " رابط", "probability": 0.8541666666666666}, {"start": 2897.23, "end": 2897.29, "word": " فيه", "probability": 0.73779296875}, {"start": 2897.29, "end": 2897.55, "word": " نقص", "probability": 0.97216796875}, {"start": 2897.55, "end": 2897.73, "word": " C", "probability": 0.55615234375}, {"start": 2897.73, "end": 2897.93, "word": " في", "probability": 0.55810546875}, {"start": 2897.93, "end": 2898.79, "word": " مشكلة", "probability": 0.8025716145833334}, {"start": 2898.79, "end": 2899.29, "word": " اي", "probability": 0.4676513671875}, {"start": 2899.29, "end": 2899.55, "word": " ميم", "probability": 0.62939453125}, {"start": 2899.55, "end": 2899.67, "word": " ال", "probability": 0.9072265625}, {"start": 2899.67, "end": 2900.23, "word": " combination", "probability": 0.92724609375}, {"start": 2900.23, "end": 2901.21, "word": " واضح", "probability": 0.9645182291666666}, {"start": 2901.21, "end": 2901.31, "word": " اللي", "probability": 0.927734375}, {"start": 2901.31, "end": 2902.19, "word": " بحكيه", "probability": 0.9640625}, {"start": 2902.19, "end": 2902.47, "word": " اذا", "probability": 0.5682373046875}, {"start": 2902.47, "end": 2903.19, "word": " الان", "probability": 0.73828125}, {"start": 2903.19, "end": 2903.51, "word": " صار", "probability": 0.957275390625}, {"start": 2903.51, "end": 2903.75, "word": " عندي", "probability": 0.7127685546875}, {"start": 2903.75, "end": 2904.09, "word": " نقص", "probability": 0.7880045572916666}, {"start": 2904.09, "end": 2904.45, "word": " CD", "probability": 0.73828125}, {"start": 2904.45, "end": 2904.89, "word": " مع", "probability": 0.98876953125}, {"start": 2904.89, "end": 2905.21, "word": " نقص", "probability": 0.9949544270833334}, {"start": 2905.21, "end": 2905.57, "word": " CD", "probability": 0.94921875}, {"start": 2905.57, "end": 2906.33, "word": " فبصير", "probability": 0.8876953125}, {"start": 2906.33, "end": 2906.51, "word": " ال", "probability": 0.84130859375}, {"start": 2906.51, "end": 2906.55, "word": " N", "probability": 0.435546875}, {"start": 2906.55, "end": 2907.05, "word": " بتقسم", "probability": 0.7427571614583334}, {"start": 2907.05, "end": 2907.21, "word": " ال", "probability": 0.720703125}, {"start": 2907.21, "end": 2907.55, "word": " AB", "probability": 0.37255859375}, {"start": 2907.55, "end": 2908.57, "word": " نقص", "probability": 0.9361979166666666}, {"start": 2908.57, "end": 2908.91, "word": " CB", "probability": 0.90478515625}, {"start": 2908.91, "end": 2910.25, "word": " لأن", "probability": 0.69580078125}, {"start": 2910.25, "end": 2910.65, "word": " العامل", "probability": 0.7330729166666666}, {"start": 2910.65, "end": 2910.97, "word": " المشترك", "probability": 0.92333984375}, {"start": 2910.97, "end": 2911.13, "word": " اللي", "probability": 0.976806640625}, {"start": 2911.13, "end": 2911.25, "word": " هو", "probability": 0.267822265625}, {"start": 2911.25, "end": 2911.45, "word": " هذا", "probability": 0.73095703125}, {"start": 2911.45, "end": 2911.73, "word": " N", "probability": 0.84716796875}, {"start": 2911.73, "end": 2911.99, "word": " يعني", "probability": 0.953125}, {"start": 2911.99, "end": 2912.47, "word": " بتقسم", "probability": 0.8990885416666666}, {"start": 2912.47, "end": 2912.71, "word": " ال", "probability": 0.904296875}, {"start": 2912.71, "end": 2913.03, "word": " B", "probability": 0.94775390625}, {"start": 2913.03, "end": 2913.79, "word": " في", "probability": 0.91650390625}, {"start": 2913.79, "end": 2914.03, "word": " A", "probability": 0.78662109375}, {"start": 2914.03, "end": 2914.27, "word": " minus", "probability": 0.468994140625}, {"start": 2914.27, "end": 2914.61, "word": " C", "probability": 0.99169921875}, {"start": 2914.61, "end": 2915.03, "word": " العامل", "probability": 0.97998046875}, {"start": 2915.03, "end": 2915.31, "word": " المشترك", "probability": 0.9886474609375}, {"start": 2915.31, "end": 2915.45, "word": " اللي", "probability": 0.843017578125}, {"start": 2915.45, "end": 2915.53, "word": " على", "probability": 0.638671875}, {"start": 2915.53, "end": 2915.73, "word": " بيه", "probability": 0.6681315104166666}, {"start": 2915.73, "end": 2915.85, "word": " ال", "probability": 0.92236328125}, {"start": 2915.85, "end": 2915.99, "word": " B", "probability": 0.95849609375}, {"start": 2915.99, "end": 2916.15, "word": " و", "probability": 0.491943359375}, {"start": 2916.15, "end": 2916.17, "word": " ال", "probability": 0.64697265625}, {"start": 2916.17, "end": 2916.37, "word": " N", "probability": 0.97802734375}, {"start": 2916.37, "end": 2917.65, "word": " واحد", "probability": 0.8955078125}, {"start": 2917.65, "end": 2918.27, "word": " اذا", "probability": 0.7734375}, {"start": 2918.27, "end": 2918.97, "word": " N", "probability": 0.66552734375}, {"start": 2918.97, "end": 2919.63, "word": " تقسم", "probability": 0.9773763020833334}, {"start": 2919.63, "end": 2919.79, "word": " ال", "probability": 0.919921875}, {"start": 2919.79, "end": 2920.05, "word": " A", "probability": 0.97705078125}, {"start": 2920.05, "end": 2920.55, "word": " minus", "probability": 0.96533203125}, {"start": 2920.55, "end": 2920.75, "word": " C", "probability": 0.97509765625}, {"start": 2920.75, "end": 2921.11, "word": " يعني", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 118, "seek": 292533, "start": 2923.47, "end": 2925.33, "text": "وقالّا، يعطيكوا الآفية", "tokens": [2407, 4587, 6027, 11703, 995, 12399, 37495, 9566, 1829, 4117, 14407, 6024, 95, 5172, 10632], "avg_logprob": -0.4704589582979679, "compression_ratio": 0.8571428571428571, "no_speech_prob": 0.0, "words": [{"start": 2923.47, "end": 2924.07, "word": "وقالّا،", "probability": 0.6060791015625}, {"start": 2924.07, "end": 2924.61, "word": " يعطيكوا", "probability": 0.6930908203125}, {"start": 2924.61, "end": 2925.33, "word": " الآفية", "probability": 0.750213623046875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2926.991375, "duration_after_vad": 2786.305624999988}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34.srt
new file mode 100644
index 0000000000000000000000000000000000000000..883b7dea2a1c5b00cd4233004e73c36d3275ee9a
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34.srt
@@ -0,0 +1,3546 @@
+1
+00:00:19,350 --> 00:00:25,850
+بسم الله الرحمن الرحيم محاضرة رقم 27 وهي عبارة عن
+
+2
+00:00:25,850 --> 00:00:34,950
+مناقشة لـ Chapter 6 سنناقش اليوم موضوعين، الموضوع 
+
+3
+00:00:34,950 --> 00:00:39,910
+الأول اللي هو number and sum of divisors، والموضوع
+
+4
+00:00:39,910 --> 00:00:43,530
+الثاني اللي هو Mobius inversion formula. نبدأ بـ 6
+
+5
+00:00:43,530 --> 00:00:50,470
+.1 اللي هو number and sum of divisors أذكركم في 
+
+6
+00:00:50,470 --> 00:00:56,450
+بعض اللي هي النتائج في هذا الفصل أو في هذا ال
+
+7
+00:00:56,450 --> 00:01:00,470
+section. لو كانت عندي N أكبر من 1، و N كتبناها على 
+
+8
+00:01:00,470 --> 00:01:05,210
+صورة الـ prime factorizations اللي هي P1 α1
+
+9
+00:01:05,210 --> 00:01:11,950
+لعند PR αR، عندي بيكون الـ sigma of N أو الـ
+
+10
+00:01:11,950 --> 00:01:18,800
+tau of N بتساوي عبارة عن α1 + 1 لما نصل
+
+11
+00:01:18,800 --> 00:01:25,460
+لعند αR + 1 مضروبة في بعض. هو Sigma of N 
+
+12
+00:01:25,460 --> 00:01:31,360
+Sigma of N في هذه الحالة عبارة عن كتبناها على صورة
+
+13
+00:01:31,360 --> 00:01:38,500
+الـ product P1 α1 P<sub>i</sub> α<sub>i</sub> + 1 
+
+14
+00:01:38,500 --> 00:01:45,910
+ناقص 1 على Pi ناقص 1، مضبوط. I من عند 1
+
+15
+00:01:45,910 --> 00:01:53,590
+لعند R، وكتبناها أيضا وكتبناها أيضا في أثناء برهان
+
+16
+00:01:53,590 --> 00:01:57,510
+سيجموغان، هذا بيساوي هذا، اللي هو إيه ده؟ بتتذكر هو
+
+17
+00:01:57,510 --> 00:02:05,450
+عبارة عن الـ product لـ 1 + Pi + Pi تربيع لما
+
+18
+00:02:05,450 --> 00:02:13,230
+نصل لآخر واحد Pi αi، I من عند 1 لعند R. هذا
+
+19
+00:02:13,230 --> 00:02:19,050
+هو النتيجتين اللي حكينا عنهم، وحكينا عن نتيجة ثالثة
+
+20
+00:02:19,050 --> 00:02:28,150
+إن لو كانت F is multiplicative، بيعطيني F of N 
+
+21
+00:02:28,150 --> 00:02:33,490
+بتساوي الـ summation للـ F of D، D بتجسم N برضه. 
+
+22
+00:02:33,490 --> 00:02:42,810
+أشمالها is multiplicative معايا؟ طيب نيجي الآن ناخد 
+
+23
+00:02:42,810 --> 00:02:48,790
+السؤال اللي هو رقم 6، السؤال رقم 6 بقول ما يلي
+
+24
+00:02:48,790 --> 00:02:58,610
+بيقول لنا لأي integer n أكبر من 1، سؤال 6: if n أكبر أو
+
+25
+00:02:58,610 --> 00:03:04,710
+يساوي 1، then الـ Sigma of N أو الـ Tau of N له أصغر
+
+26
+00:03:04,710 --> 00:03:12,410
+أو يساوي 2 في جذر الـ N. الـ Proof: أول ملاحظة طبعا
+
+27
+00:03:12,410 --> 00:03:16,310
+الـ Proof كامل مكتوب هناك. هنخلّينا نبرهن يعني مش شرط
+
+28
+00:03:16,310 --> 00:03:21,070
+نكتب كل البرهان، ولكن نتحدث عن البرهان بشكل تفصيل أساس
+
+29
+00:03:21,070 --> 00:03:26,210
+اختصارًا للوقت. بدنا نثبت أن عدد الـ Divisors للـ N 
+
+30
+00:03:26,210 --> 00:03:31,490
+أكبر أو يساوي 2 جذر الـ N، أصغر أو يساوي 2 جذر
+
+31
+00:03:31,490 --> 00:03:36,170
+الآن الآن لاحظ أول ملاحظة الحالية إن لو كان عندي
+
+32
+00:03:36,170 --> 00:03:44,870
+الـ D بقسم N، لو الـ D من قواسم الـ N، إذا أكيد أكيد الـ
+
+33
+00:03:44,870 --> 00:03:50,460
+N على D بيصير integer وبرضه بيقسم الـ N الآن لسبب بسيط
+
+34
+00:03:50,460 --> 00:03:55,960
+لأن الآن في هذه الحالة هتساوي N على D في مين؟ في 
+
+35
+00:03:55,960 --> 00:03:59,700
+D، بما أن هذا فرضنا أن D بتجسم N يعني هذا N على
+
+36
+00:03:59,700 --> 00:04:03,180
+D integer، إذا N صار عندي الآن بيساوي هذا في هذا، إذا 
+
+37
+00:04:03,180 --> 00:04:07,460
+هذه بتوحي أن D بتجسم N، وإن N على D بتجسم مين؟ N.
+
+38
+00:04:07,460 --> 00:04:11,140
+يعني وكأنه بقول لك أنا إنه 
+
+39
+00:04:13,420 --> 00:04:17,920
+القواسم تحدث أزواجًا، يعني واحد بيكون D، والثاني اللي
+
+40
+00:04:17,920 --> 00:04:22,580
+عاجباله على طول إيش بيكون؟ N على D ماشي الحال ما فيش 
+
+41
+00:04:22,580 --> 00:04:28,140
+غير هدول اللي هو القواسم بيحدثون اللي هي لـ N يعني 
+
+42
+00:04:28,140 --> 00:04:30,920
+لو كان D بيكسب N على طول الـ N على D بيكسب مين؟ الـ 
+
+43
+00:04:30,920 --> 00:04:34,500
+N، وقد يكون إن N على D يساوي في حالات إيش بيساوي؟ 
+
+44
+00:04:34,500 --> 00:04:38,040
+بيساوي D ماشي الحال، خلّي هذا الملاحظة أولًا
+
+45
+00:04:38,040 --> 00:04:47,970
+الملاحظة الثانية لو جينا بدنا نشوف اللي هو الـ D 
+
+46
+00:04:47,970 --> 00:04:52,430
+والـ N على D، واحد من الاتنين هذول، سواء الـ D أو
+
+47
+00:04:52,430 --> 00:04:57,430
+الـ N على D، واحد منهم .. واحد منهم هيكون أصغر أو 
+
+48
+00:04:57,430 --> 00:05:03,170
+يساوي جذر الـ N، واحد
+
+49
+00:05:03,170 --> 00:05:08,160
+هيكون أصغر أو يساوي مين؟ جذر الـ N، واحد على الأقل 
+
+50
+00:05:08,160 --> 00:05:12,640
+حيكون أصغر أو يساوي جذر الـ N. الإدعاء عشان تسمعوا
+
+51
+00:05:12,640 --> 00:05:16,840
+الإدعاء وبعدين هأقول لكم ليش. الإدعاء إن واحد من هذول
+
+52
+00:05:16,840 --> 00:05:21,940
+على الأقل حيكون أصغر أو يساوي جذر الـ N، ليش؟ لسبب
+
+53
+00:05:21,940 --> 00:05:26,620
+بسيط إن لو كان الاتنين أكبر strictly من جذر الـ N
+
+54
+00:05:26,620 --> 00:05:31,260
+معناته بيصير حاصل ضربه أكبر من الـ N، بينما حاصل 
+
+55
+00:05:31,260 --> 00:05:37,150
+ضربه مش مساوي كمان مرة الـ N، الـ D والـ N على D 
+
+56
+00:05:37,150 --> 00:05:45,410
+واحد منهم على الأقل أصغر أو يساوي جذر الـ N، لأنه 
+
+57
+00:05:45,410 --> 00:05:50,630
+لو كان الاتنين هذا وهذا، يعني الـ D أكبر strictly 
+
+58
+00:05:50,630 --> 00:05:53,770
+من جذر الـ N، والـ N على D أكبر strictly من جذر 
+
+59
+00:05:53,770 --> 00:05:58,430
+الـ N، هذا بيؤدي إلى أن الـ N في الـ D على N اللي
+
+60
+00:05:58,430 --> 00:06:02,330
+هو بيساوي N، أكبر strictly من مين؟ من الـ N، وهذا 
+
+61
+00:06:02,330 --> 00:06:07,070
+مستحيل، Contradiction إذن المعلومة الثانية عندك الآن 
+
+62
+00:06:07,070 --> 00:06:15,030
+واحد من هذول على أقل هيكون أكبر أو يساوي مين؟ أصغر
+
+63
+00:06:15,030 --> 00:06:20,750
+أو يساوي جذر الـ N، إذن .. إذن الآن لو بدي عدد
+
+64
+00:06:20,750 --> 00:06:30,050
+divisors اللي من 1 لعند جذر الـ N للـ N، يعني بتعد
+
+65
+00:06:30,050 --> 00:06:36,190
+قواسم الـ N اللي أصغر أو يساوي جذر الـ N، يعني اللي
+
+66
+00:06:36,190 --> 00:06:40,450
+من 1 لـ جذر الـ N هيكون عددهم على الأكثر، على الأكثر 
+
+67
+00:06:40,450 --> 00:06:43,310
+على الأكثر جديش؟ جذر الـ N، جذر الـ N، جذر الـ N
+
+68
+00:06:43,310 --> 00:06:52,070
+جذر الـ N، جذر الـ N، جذر الـ N، جذر الـ N، جذر الـ N، جذر
+
+69
+00:06:52,070 --> 00:06:56,090
+الـ N، جذر الـ N، جذر الـ N، جذر الـ N، جذر الـ N، جذر الـ N
+
+70
+00:06:56,090 --> 00:06:57,170
+جذر الـ N، جذر الـ N، جذر الـ N، جذر الـ N، جذر الـ N، جذر
+
+71
+00:06:57,170 --> 00:06:57,230
+الـ N، جذر الـ N، جذر الـ N، جذر الـ N، جذر الـ N، جذر الـ N
+
+72
+00:06:57,230 --> 00:06:58,510
+جذر الـ N، جذر الـ N، جذر الـ N، جذر الـ N، جذر الـ N، ماشي
+
+73
+00:06:58,510 --> 00:07:03,250
+الحال. ما هو كل divisor فيه لعقبّاله divisor يحدث 
+
+74
+00:07:03,250 --> 00:07:08,570
+أزواجًا، إذا صار عندي مجموع ال divisors كلهم على 
+
+75
+00:07:08,570 --> 00:07:18,510
+الأكثر 2 جذر N وهو المطلوب. كمان مرة النقطة هذه
+
+76
+00:07:18,510 --> 00:07:24,550
+نلخّص السؤال على السريع لأنكم الآن النقطة الأولى أن 
+
+77
+00:07:24,550 --> 00:07:30,640
+ال divisors تحدث أزواجًا. النقطة الثانية إنه الآن في
+
+78
+00:07:30,640 --> 00:07:34,360
+واحد من هذول على الأقل أصغر أو يساوي 100 جذر الـ N
+
+79
+00:07:34,360 --> 00:07:37,680
+في كل زوج في على الأقل واحد منهم أصغر أو يساوي 100
+
+80
+00:07:37,680 --> 00:07:42,400
+جذر الـ N. عدد الـ divisors للـ N اللي أصغر أو يساوي 
+
+81
+00:07:42,400 --> 00:07:46,240
+100 جذر الـ N على الأكثر يساوي 100 جذر الـ N وفي
+
+82
+00:07:46,240 --> 00:07:51,750
+عقبّالهم اللي هو أشمالهم اللي هو جذر الـ N فبيصير
+
+83
+00:07:51,750 --> 00:07:54,530
+على الأكثر على الأكثر اللي هو جدّاش؟ عدد الـ 
+
+84
+00:07:54,530 --> 00:07:58,490
+divisors 2 جذر الـ N، مع أنه ممكن ينقص لأنه ممكن
+
+85
+00:07:58,490 --> 00:08:01,590
+يكون اللي هو الـ D والـ N على D في حالة إيش بيساوي .. 
+
+86
+00:08:01,590 --> 00:08:07,230
+بيساوي واحدة في النهاية اللي هو دائما Tau of N بتظلّ 
+
+87
+00:08:07,230 --> 00:08:12,290
+أصغر أو يساوي 2 جذر الـ N. اللي بعده السؤال اللي بعده
+
+88
+00:08:18,440 --> 00:08:24,740
+و prove the following: Tau of N is an odd number or 
+
+89
+00:08:24,740 --> 00:08:29,580
+odd integer if and only if N is a perfect square.
+
+90
+00:08:29,580 --> 00:08:33,820
+كمان
+
+91
+00:08:33,820 --> 00:08:45,240
+مرة. السؤال عندي سؤال سبعة A: Tau of N is odd if and
+
+92
+00:08:45,240 --> 00:08:50,760
+only if N is a perfect square. perfect square معناته
+
+93
+00:08:50,760 --> 00:08:55,760
+إيش ماله؟ مربع كامل يعني هيكون على صورة N تربيع for
+
+94
+00:08:55,760 --> 00:09:05,220
+some M، ماشي الحال. الـ N دائما
+
+95
+00:09:05,220 --> 00:09:10,160
+في حالة الـ Sigma أو حتى حالة الـ number theoretic
+
+96
+00:09:10,160 --> 00:09:17,960
+functions بصورة عامة أسهل لي أن أحسب للي برايم وبعد
+
+97
+00:09:17,960 --> 00:09:21,300
+ما أحسب للـ prime، بحسب لمين؟ للـ function نفسها
+
+98
+00:09:21,300 --> 00:09:23,740
+خصوصًا إذا كانت الـ function is multiplicative 
+
+99
+00:09:23,740 --> 00:09:32,350
+بتصير الأمور سهلة، نشوف إيش المقصود الآن، بس خلّوني 
+
+100
+00:09:32,350 --> 00:09:35,710
+مادام بتحكي عن الـ prime factorization للـ N إذا
+
+101
+00:09:35,710 --> 00:09:40,870
+لازم الـ N تبقى تكون أكبر من مين؟ من 1، معايا؟
+
+102
+00:09:40,870 --> 00:09:43,270
+إذا نخليني أنا أخد حالة الواحد. حالة الواحد is a 
+
+103
+00:09:43,270 --> 00:09:48,590
+trivial case، ليش؟ لإن Tau of 1 بيساوي 1، 1
+
+104
+00:09:48,590 --> 00:09:52,510
+مربع كامل. إذا أنت تتحقق اللي هي الطرفين هذه إن Tau 
+
+105
+00:09:52,510 --> 00:09:56,150
+of N is odd، و إن N إيش مالها؟ is a perfect 
+
+106
+00:09:56,150 --> 00:10:01,740
+square نأتي الآن ناخد حالة مين؟ الـ N أكبر من 1
+
+107
+00:10:01,740 --> 00:10:08,980
+بتاخد Proof حالة الـ N أكبر من 1 إيش بدا أقول؟ بدا
+
+108
+00:10:08,980 --> 00:10:13,100
+أقول Suppose that
+
+109
+00:10:13,100 --> 00:10:22,360
+N is a perfect square، ماشي؟
+
+110
+00:10:22,360 --> 00:10:29,040
+يعني N إيش مالها؟ مربع كامل يعني N بتساوي M تربيع
+
+111
+00:10:29,040 --> 00:10:33,480
+الـ M نفسها أكيد هتكون أكبر من 1، مدام الـ M
+
+112
+00:10:33,480 --> 00:10:37,060
+أكبر من 1، مدام الـ M أكبر من 1 إذا اللي هو
+
+113
+00:10:37,060 --> 00:10:40,040
+بقدر اكتبه على صورة اللي هو product of the primes 
+
+114
+00:10:40,040 --> 00:10:44,200
+فبتكون على صورة P1 α1، canonical form
+
+115
+00:10:44,200 --> 00:10:51,870
+لعند PR αR، لكل أشماله تربيع. واضح؟  هيك مفترضين
+
+116
+00:10:51,870 --> 00:10:54,910
+إنه هنا perfect square يعني بمعنى آخر إلا إنه على
+
+117
+00:10:54,910 --> 00:11:00,270
+صورة P1 2α1 لعند PR 2αR،
+
+118
+00:11:00,270 --> 00:11:08,230
+واضحة الصورة. إذا الآن إذا صار عندي الـ sigma آسف 
+
+119
+00:11:08,230 --> 00:11:13,070
+الـ Tau of N هيساوي حسب اللي الـ Tau of N إيش هتكون؟
+
+120
+00:11:13,070 --> 00:11:20,600
+اللي هو 2α1 + 1 لما أصل عند 2αR 
+
+121
+00:11:20,600 --> 00:11:25,580
++ 1، هذه زوجي، هذه كلها على بعض إيش مالها؟ فردي
+
+122
+00:11:25,580 --> 00:11:28,500
+إذا فردي مضروب في فردي مضروب في فردي مضروب في فردي
+
+123
+00:11:28,500 --> 00:11:33,020
+إذا إيش كدا كلها على بعض؟ إذا صارت Tau of N إيش مالها؟ 
+
+124
+00:11:33,020 --> 00:11:38,440
+فردي، متى؟ لما كانت الـ N is a perfect square، إذا المهم في 
+
+125
+00:11:38,440 --> 00:11:42,340
+الموضوع أن أنا أعرف أعمل representation as a 
+
+126
+00:11:42,340 --> 00:11:46,640
+product of primes للـ N، واضح؟ Conversely
+
+127
+00:11:53,590 --> 00:12:02,010
+Conversely: Suppose that sigma of n is a odd، بدا 
+
+128
+00:12:02,010 --> 00:12:06,270
+يثبت لك أن n إيش مالها؟ perfect square، Tau of n is
+
+129
+00:12:06,270 --> 00:12:11,730
+odd، بدا يثبت لك أن n إيش مالها؟ perfect square. 
+
+130
+00:12:13,960 --> 00:12:16,900
+الآن احنا مفترضينها من رأس الدور إن هي أكبر من 100
+
+131
+00:12:16,900 --> 00:12:22,060
+من 1، إذا الآن تابعتنا بقدر أكتبه على صورة by
+
+132
+00:12:22,060 --> 00:12:24,900
+unique، by unique factorization theorem على صورة
+
+133
+00:12:24,900 --> 00:12:28,460
+اللي هو product of power of primes P1 β1
+
+134
+00:12:28,460 --> 00:12:36,940
+لعند PR βR، واضح؟ طيب احسب للـ tau لهذه
+
+135
+00:12:36,940 --> 00:12:46,610
+إذا Tau of N بيساوي β1 + 1 في β2 + 1 
+
+136
+00:12:46,610 --> 00:12:53,100
+لما أصل لآخر واحدة في βR + 1. الآن ما عطيلي
+
+137
+00:12:53,100 --> 00:12:58,220
+هذا أشماله tau of n is odd، مدام tau of n is odd
+
+138
+00:12:58,220 --> 00:13:03,600
+وعندي product of numbers لازم كل واحد فيه يكون odd.
+
+139
+00:13:03,600 --> 00:13:06,160
+ما ينفعش واحد يكون زوجي، لو واحد زوجي معناه تصير
+
+140
+00:13:06,160 --> 00:13:13,240
+ضربها زوجي، إذا حيكون عندي P1 + 1 أو P
+
+141
+00:13:13,240 --> 00:13:20,700
+i زائد 1 is odd for every i ما دام بي اي
+
+142
+00:13:20,700 --> 00:13:23,240
+زائد 1 الزدد ده أكيد ال بي اي اللي حالها اي
+
+143
+00:13:23,240 --> 00:13:27,280
+شمالها is even بي اي even معناته ال بي اي اي
+
+144
+00:13:27,280 --> 00:13:32,120
+شمالها هتكون على صورة 2 Alpha I for some Alpha
+
+145
+00:13:32,120 --> 00:13:39,060
+I معايا ما دام بي Beta I is even إذا على صورة 2
+
+146
+00:13:39,060 --> 00:13:45,940
+Alpha I إذا صار عند ال N تبعتنا ال N تبعتنا بتساوي
+
+147
+00:13:47,370 --> 00:13:52,430
+ب1 2 الفا 1 فاهمين لعند ب ار 2 الفا ار
+
+148
+00:13:52,430 --> 00:13:57,170
+اللي هي بتساوي ب1 الفا 1 لعند ب ار الفا ار
+
+149
+00:13:57,170 --> 00:14:02,390
+الكل تربيع إذا صارت اللي هو n is a perfect square
+
+150
+00:14:02,390 --> 00:14:08,770
+إذا لما كانت ال ال tau of n is odd طلعت ال n عند a
+
+151
+00:14:08,770 --> 00:14:15,730
+شمالها is a perfect square نيجي الآن لسؤال b
+
+152
+00:14:26,720 --> 00:14:33,480
+شوف عندي صلى الله عليه وسلم جزء بيه ايش بقول ليه
+
+153
+00:14:33,480 --> 00:14:39,500
+اللي هو لو كان عندي بقولي sigma of n is odd if and
+
+154
+00:14:39,500 --> 00:14:46,340
+only if n is a perfect square or twice perfect
+
+155
+00:14:46,340 --> 00:14:51,450
+square يعني بيقول لي أن الـ N يا هتكون على صورة N
+
+156
+00:14:51,450 --> 00:14:56,670
+تربيع اللي هي perfect square أو 2 N تربيع for
+
+157
+00:14:56,670 --> 00:15:03,810
+some M ثمان مرة السؤال السؤال اللي بيقول لي prove
+
+158
+00:15:03,810 --> 00:15:09,810
+that sigma of N is odd if and only if N is a
+
+159
+00:15:09,810 --> 00:15:17,170
+perfect square or twice perfect square واضح؟ نيجي
+
+160
+00:15:17,170 --> 00:15:24,110
+البرهنA proof Suppose that
+
+161
+00:15:24,110 --> 00:15:31,670
+N is a perfect square or twice perfect square
+
+162
+00:15:31,670 --> 00:15:43,090
+بيثبتلك
+
+163
+00:15:43,090 --> 00:15:49,040
+إن sigma of N في الحالتين أزدادطيب شو N بتساوي N
+
+164
+00:15:49,040 --> 00:15:54,500
+تربيع نعملها قبل بشوية يعني N بتساوي B1 اللي هو
+
+165
+00:15:54,500 --> 00:16:04,520
+20001 لعين PR 2000R مظبوط و ال R في الحالة اللي N
+
+166
+00:16:04,520 --> 00:16:10,300
+بتساوي 2N تربيع اللي هو ركزوا معاه فN بتساوي اللي
+
+167
+00:16:10,300 --> 00:16:16,580
+هو 2B1 بدي أغير الآن الـ B1 بدي أغير الان الـ B1
+
+168
+00:16:16,580 --> 00:16:17,180
+بدي أغير الان الـ B1 بدي أغير الان الـ B1 بدي أغير
+
+169
+00:16:17,180 --> 00:16:19,380
+الان الـ B1 بدي أغير الان الـ B1 بدي أغير الان الـ
+
+170
+00:16:19,380 --> 00:16:25,200
+B1 بدي أغير الان الـ
+
+171
+00:16:25,200 --> 00:16:27,320
+B1 بدي أغير الان الـ B1 بدي أغير الان الـ B1 بدي
+
+172
+00:16:27,320 --> 00:16:27,340
+أغير الان الـ B1 بدي أغير الان الـ B1 بدي أغير
+
+173
+00:16:27,340 --> 00:16:27,860
+الان الـ B1 بدي أغير الان الـ B1 بدي أغير الان الـ
+
+174
+00:16:27,860 --> 00:16:30,800
+أغير الان الـ B1 بدي أغير الان الـ B1 بدي أغيرأه
+
+175
+00:16:30,800 --> 00:16:35,360
+ممكن تكون 2 وممكن تكون odd أصلا ماشي الحل عشان
+
+176
+00:16:35,360 --> 00:16:39,440
+أكتب الحالتين في كتابة واحدة بدي أكتبها على صورة
+
+177
+00:16:39,440 --> 00:16:46,320
+هذه بيساوي 2 أس 2 ألف واحد زائد 1 في B2 أس 2
+
+178
+00:16:46,320 --> 00:16:55,720
+ألف 2 لعين B R 2 ألف Rأيش اللي كتبته هذه و
+
+179
+00:16:55,720 --> 00:17:02,160
+Alpha 1 عندي أكبر أو ساوي 0 و Alpha 2 عند Alpha R
+
+180
+00:17:02,160 --> 00:17:06,120
+أكبر أو ساوي 1 شوف
+
+181
+00:17:09,650 --> 00:17:14,850
+الان انا عندى twice perfect square هى مربع كامل
+
+182
+00:17:14,850 --> 00:17:19,090
+هذا المربع الكامل قد يكون ان هو اول prime له في ال
+
+183
+00:17:19,090 --> 00:17:23,230
+prime factorization 2 وممكن يكون ايه اش مفيش
+
+184
+00:17:23,230 --> 00:17:28,210
+2 ممكن يكون ايه اش ادت الان انا كتبته على
+
+185
+00:17:28,210 --> 00:17:35,130
+الصورة هذه على صورة 2001 زي 1 في الباقي الان لو
+
+186
+00:17:35,130 --> 00:17:40,760
+الان ال 1100أنا كتبت ألف واحد أكبر سوى إيش؟ لو
+
+187
+00:17:40,760 --> 00:17:44,760
+الألف واحد سفر معناه صار 2 بس واحد وخلاص اه
+
+188
+00:17:44,760 --> 00:17:49,840
+يعني هي ال2 لو الآن ألف واحد صارت 1 بيصير
+
+189
+00:17:49,840 --> 00:17:54,440
+2 زائد 1 وبتبقى لها twice perfect square
+
+190
+00:17:54,440 --> 00:18:01,440
+واضح؟ طيب نيجي الآن نحسب مين؟ sigma of n إذا sigma
+
+191
+00:18:01,440 --> 00:18:09,760
+of n في الحالتينما هتساوي ال product 1
+
+192
+00:18:09,760 --> 00:18:13,220
+زائد بي اي زائد بي اي تربيع لما يقصى الاخر واحدة
+
+193
+00:18:13,220 --> 00:18:21,180
+اللي هو ال product لأ واحد زائد بي اي زائد بي اي
+
+194
+00:18:21,180 --> 00:18:27,200
+أُس 2 الف اي اي من عند 1 لعند ار هذا في
+
+195
+00:18:27,200 --> 00:18:35,140
+الحالة الأولىلاحظ .. لاحظ ان هذولا عددهن زوجي صح
+
+196
+00:18:35,140 --> 00:18:39,560
+ولا لأ معايا؟
+
+197
+00:18:39,560 --> 00:18:44,380
+اه هاي 2 الفاية اه من عند 1 عند 2
+
+198
+00:18:44,380 --> 00:18:47,780
+الفاية إذا العدد هنا إشمال، هنا زوجي إذا كانت
+
+199
+00:18:47,780 --> 00:18:56,320
+2ات، هاي زوجي إذا كانت فرديات عددها زوجي
+
+200
+00:18:56,320 --> 00:19:02,300
+ومجموعات لبعض، برضه زوجيإذا صار هذا كله مجموع زوجي
+
+201
+00:19:02,300 --> 00:19:08,540
+مع 1 صار فردي إذا صار هذا فردي product of فردي
+
+202
+00:19:08,540 --> 00:19:15,000
+إيش حيطلع إذا حيطلع product حالة
+
+203
+00:19:15,000 --> 00:19:23,980
+تالية اللي هي اللي بعد هذه or خليني
+
+204
+00:19:23,980 --> 00:19:32,430
+بس أكمل or areSigma of n بتساوي في الحالة التانية
+
+205
+00:19:32,430 --> 00:19:39,870
+Twice perfect square هيصير بتفصلها product هذه في
+
+206
+00:19:39,870 --> 00:19:40,710
+product هذه
+
+207
+00:19:44,470 --> 00:19:49,310
+للأساس 2 بيصير 1 زائد 2 زائد 2
+
+208
+00:19:49,310 --> 00:19:54,630
+تربيع لم أصل آخر أُس 2 ألف واحد زائد مضروب في
+
+209
+00:19:54,630 --> 00:20:00,670
+الباقي الباقي مين هو هذا الاند عبارة عن 1 زائد
+
+210
+00:20:00,670 --> 00:20:08,690
+بي اي زائد بي اي أس 2 ألف اي الآن اي من وين مش
+
+211
+00:20:08,690 --> 00:20:15,220
+من 1 من 2 لعند الاربنفس اللي فوق بالظبط
+
+212
+00:20:15,220 --> 00:20:21,240
+هدول عددهم زوجي وهنا اللي هي فرديات فمجموحا هيكون
+
+213
+00:20:21,240 --> 00:20:26,840
+زوجي زائد 1 مش هيطلع فردي معايا ال product
+
+214
+00:20:26,840 --> 00:20:32,780
+الفردي بيطلع اي اسم اذا هذا هيطلع عند اطيب
+
+215
+00:20:32,780 --> 00:20:38,780
+ماخلصناش نيجي لهذا هدول مهمة مجموحين زوجي وفي 1
+
+216
+00:20:38,780 --> 00:20:42,780
+إذا صار فردي فردي مضلوب في فردي إذا هذا صار odd
+
+217
+00:20:42,780 --> 00:20:50,080
+برضه في odd إيش هيساوي odd إذا في كل الحالتين ال
+
+218
+00:20:50,080 --> 00:20:54,700
+sigma of n سواء في حالة ال perfect square أو twice
+
+219
+00:20:54,700 --> 00:20:59,580
+perfect square ال sigma of n إيش طلعت is odd اسألي
+
+220
+00:20:59,580 --> 00:20:59,980
+محمد
+
+221
+00:21:06,450 --> 00:21:10,430
+الان عندى high perfect square وهنا twice perfect
+
+222
+00:21:10,430 --> 00:21:14,510
+square twice perfect square يعني 2 في high
+
+223
+00:21:14,510 --> 00:21:21,460
+perfect squareالان هذا ال factorization ال P1 يمكن
+
+224
+00:21:21,460 --> 00:21:26,800
+تكون 2 ويمكن تكون odd ماشي الحال الان انا عساس
+
+225
+00:21:26,800 --> 00:21:31,140
+ان احمد ظهري واخد الحالتين كتبت اول واحد اللي هو
+
+226
+00:21:31,140 --> 00:21:35,240
+هذا هو عبارة عن 2 اقصد 2 اد الف واحد زائد
+
+227
+00:21:35,240 --> 00:21:40,580
+واحد والباجي اللي هي ال odd prime اللي وجدت الان
+
+228
+00:21:40,580 --> 00:21:46,750
+هذا هل بحتمي للحالتين ان يكون اللي هو twice سواء
+
+229
+00:21:46,750 --> 00:21:51,470
+كانت الـ 2 لحالها أو بـ 2 أُص غير الـ 2، أه
+
+230
+00:21:51,470 --> 00:21:54,990
+بيختمل، ليش؟ لإن أخدت الـ Alpha 1 أشمالها أكبر
+
+231
+00:21:54,990 --> 00:22:00,150
+بساوية 0 لما Alpha 1 بـ 0، بيصير 2 في هذا لما تصير
+
+232
+00:22:00,150 --> 00:22:05,770
+Alpha 1 بتساوي 1 مثلا أو 2 أو 3، بيصير 2 زائد 1
+
+233
+00:22:05,770 --> 00:22:12,190
+ثلاثة، بيصير برضه 2 في Perfect Square، واضح؟ نيجي
+
+234
+00:22:12,190 --> 00:22:12,450
+الآن
+
+235
+00:22:18,810 --> 00:22:25,170
+ماذا جعلنا نكتبها 1 zpi؟ قالي أين؟ أول لحظة sigma
+
+236
+00:22:25,170 --> 00:22:31,890
+هذا؟ هذا شرحناه في المحاضرة ماعرفش أشرح المحاضرة
+
+237
+00:22:31,890 --> 00:22:35,370
+من جديد أنا كتبت لك من رأس الدورة عشان الان sigma
+
+238
+00:22:35,370 --> 00:22:39,870
+of n أيش بيساوي؟ بيساوي ال product هذا هذا للنظرية
+
+239
+00:22:39,870 --> 00:22:46,500
+في شرح النظرية بدأنا وقلنا ليش سبب هيك؟المجموع الـ
+
+240
+00:22:46,500 --> 00:22:49,240
+divisors دي مش هنتيجي على الموضوع لإنه فيه تفاصيل
+
+241
+00:22:49,240 --> 00:22:52,220
+مجموع الـ divisors بساوي اللي هو عبارة عن ال
+
+242
+00:22:52,220 --> 00:22:54,860
+product 1 زائد بي آي زائد بي آي تربيع زائد بي
+
+243
+00:22:54,860 --> 00:22:58,520
+آي ألف آي سببه البسيط لإنه أصلا ال divisors للبي
+
+244
+00:22:58,520 --> 00:23:03,840
+آي ألف آي هيها فلما الآن أضربهم في بعض بيصير عندي
+
+245
+00:23:03,840 --> 00:23:07,780
+بيجيب كل ال divisors و بيجمحل لبعض فبتطلع إياه
+
+246
+00:23:07,780 --> 00:23:11,600
+شماله sum of divisors وهذا شرحناه سابقاً طيب
+
+247
+00:23:14,750 --> 00:23:19,990
+نأخد الان الـ conversely نفترض
+
+248
+00:23:19,990 --> 00:23:23,610
+ان
+
+249
+00:23:23,610 --> 00:23:33,210
+sigma of n is odd برضه
+
+250
+00:23:33,210 --> 00:23:38,130
+هتلاقوا اللي هو تقاطعات البرهان الكتيرة هنكرر كلام
+
+251
+00:23:38,130 --> 00:23:40,930
+حكي لان suppose that
+
+252
+00:23:43,830 --> 00:23:51,950
+that sigma of N is odd ماشي الحل N أكبر من 1
+
+253
+00:23:51,950 --> 00:23:59,030
+إذا الـ N عندي هتصير عبارة عن بي 1 بيتا 1
+
+254
+00:23:59,030 --> 00:24:04,390
+لعند بي ار بيتا ايش ار حيث بي 1 و بي 2 و بي
+
+255
+00:24:04,390 --> 00:24:12,570
+ار ار distinct primes معاياالآن بتاخد حالتين عندي
+
+256
+00:24:12,570 --> 00:24:18,830
+الـ B1 إما هتكون odd أو هتكون even مظبوط ولا لا؟
+
+257
+00:24:18,830 --> 00:24:27,910
+الآن الحالة الأولى case 1 B1 is odd الحالة التانية
+
+258
+00:24:27,910 --> 00:24:38,960
+B1 is even في حالة الـ B1 is oddهيصير ان كله odd
+
+259
+00:24:38,960 --> 00:24:42,980
+لان هدول ايش كاتبلن في ال canonical four بي 1
+
+260
+00:24:42,980 --> 00:24:45,540
+اصغر من بي 2 اصغر من بي 3 لو انت اصغر من
+
+261
+00:24:45,540 --> 00:24:51,740
+بي ار اذا ال sigma of n تبعتي لما بدى احسبها في
+
+262
+00:24:51,740 --> 00:24:54,860
+الحساب العادي اللي عندي هذه او هذه التانية اللي
+
+263
+00:24:54,860 --> 00:25:00,520
+هتوصلنا هو عبارة عن ال product للواحد زائد بي اي
+
+264
+00:25:00,810 --> 00:25:09,790
+لما أصل لعند بي أس آي أس بي أس بي ل .. اللي هو ايه
+
+265
+00:25:09,790 --> 00:25:18,150
+او Beta I I من عند 1 لعندها، بصجوط؟ طيب الآن
+
+266
+00:25:18,150 --> 00:25:23,990
+احنا مفترضين Sigma of N ايش مالها؟ is odd إذا
+
+267
+00:25:23,990 --> 00:25:27,730
+هذا ال product يعني اللي طلع عندي مفترض ليه أنه
+
+268
+00:25:27,730 --> 00:25:34,790
+ايه إيش؟ oddما دام ال product is odd عندي أعداد
+
+269
+00:25:34,790 --> 00:25:41,150
+مضروبة في بعض odd لازم يطلع كل واحد ايهاش لأنه و
+
+270
+00:25:41,150 --> 00:25:44,410
+لو واحد فيه even زي ما قولنا بده يطلع even إذا صار
+
+271
+00:25:44,410 --> 00:25:50,350
+عندي هذا 1 زائد بي اي زائد بي اي بيتا اي is odd
+
+272
+00:25:50,350 --> 00:25:55,670
+for every i عندي الان هذا 1 الانصار المتبقي
+
+273
+00:25:55,670 --> 00:26:04,790
+اشماله زوجي ماشي هذا المتبقي مجموع زوجي معايا الان
+
+274
+00:26:04,790 --> 00:26:11,370
+كل واحد منهم odd إذا لازم يكون عددهم even حشان
+
+275
+00:26:11,370 --> 00:26:16,990
+يطلع زوجي لإن لو كان عددهم odd ومجموعات لبعض هيطلع
+
+276
+00:26:16,990 --> 00:26:25,730
+odd لإن كلهم odd تات كمان مرة عندي الآنالعدد الكل
+
+277
+00:26:25,730 --> 00:26:29,930
+odd معطينيا وهي
+
+278
+00:26:29,930 --> 00:26:36,630
+العدد كله هذا عبارة عن product of numbers إذا each
+
+279
+00:26:36,630 --> 00:26:42,470
+number must be odd عشان نحصل على النتيجة odd إذا
+
+280
+00:26:42,470 --> 00:26:50,670
+صار عندي 1 زائد bi زائد bi أس beta i كل term من 
+
+281
+00:26:50,670 --> 00:26:56,570
+هذول odd ما شي الحال إذا بدون الواحد صار الـ even
+
+282
+00:26:56,570 --> 00:27:03,130
+طيب الآن هذول مجموعات إلى بعض و هم even المجموع
+
+283
+00:27:03,130 --> 00:27:09,370
+even ما شي الحال و كل واحد فيه نقض عشان يكون مجموع
+
+284
+00:27:09,370 --> 00:27:16,560
+نقض لازم يكون عددهم عددهم زوجي لأن لو كنا عند أعداد
+
+285
+00:27:16,560 --> 00:27:20,060
+فردي تلاتة و خمسة و سبعة بيطلع odd لكن تلاتة و خمسة
+
+286
+00:27:20,060 --> 00:27:24,300
+even تلاتة و خمسة و سبعة و تسعة even وهكذا إذن
+
+287
+00:27:24,300 --> 00:27:30,240
+حيكون عددهن even عددهن bi إذن ال bi إيش هتكون 
+
+288
+00:27:30,240 --> 00:27:37,230
+على صورة اتنين Alpha I even طبعا 2000I إذا صارت 
+
+289
+00:27:37,230 --> 00:27:43,010
+عندي بي اي بيساوي 2000I for every I بمعنى صار عندي
+
+290
+00:27:43,010 --> 00:27:47,470
+الآن اللي فوق إذا اللي عندي فوق هتسوي
+
+291
+00:27:47,470 --> 00:27:51,970
+على صورة بي واحد 2000 واحد لعين بي ار 2000
+
+292
+00:27:51,970 --> 00:27:58,560
+آر وهذه إيش بتساوي B1 2000 واحد لعين بي آر 2000
+
+293
+00:27:58,560 --> 00:28:03,920
+آر لكل تربيع يعني لما كانت الـ Sigma of أنيا محمد 
+
+294
+00:28:03,920 --> 00:28:08,880
+is odd أعطتني في هذه الحالة إنه إيش الآن is a 
+
+295
+00:28:08,880 --> 00:28:13,940
+perfect square هذه الحالة الأولى هذا كله في حالة بي
+
+296
+00:28:13,940 --> 00:28:18,600
+واحد إيش مالها بدنا الآن نشوف بي واحد إيش مالها 
+
+297
+00:28:18,600 --> 00:28:26,160
+is even هذي هتطلعلي إما اللي هو perfect square أو 
+
+298
+00:28:26,160 --> 00:28:33,940
+twice perfect square ما شي الحالة بتنشوف كيف بي
+
+299
+00:28:33,940 --> 00:28:39,960
+واحد is even معناته صارت عندي وين أكتب صارت عندي 
+
+300
+00:28:39,960 --> 00:28:40,360
+خليني
+
+301
+00:28:44,150 --> 00:28:48,530
+معلش خليني أكثر هنا، أه؟ نحفظناها دي، والـOnly
+
+302
+00:28:48,530 --> 00:28:55,980
+بتستخدمها بعد شوية عند الآن يا جماعة نيجي نشتغل بي
+
+303
+00:28:55,980 --> 00:29:01,200
+واحد is إيش is even علم النفس مهم طيب بي واحد is
+
+304
+00:29:01,200 --> 00:29:05,380
+إيش is even طيب صلوا على النبي عليه الصلاة 
+
+305
+00:29:05,380 --> 00:29:10,820
+والسلام كمان مرة عند الآن صارت اللي هي عبارة عن
+
+306
+00:29:10,820 --> 00:29:14,200
+بي واحد بيتا واحد وهاد ال بي واحد بيتا واحد 
+
+307
+00:29:14,200 --> 00:29:19,220
+اتنينات أه يعني صارت اللي هي عند عبارة عن اتنين أس
+
+308
+00:29:19,220 --> 00:29:26,760
+بيتا واحد معايا في B2 أُس Beta 2 لعند B R أُس Beta
+
+309
+00:29:26,760 --> 00:29:33,760
+R اتفجنا؟ هذه الحالة التانية إذا صارت عندي الـ B1
+
+310
+00:29:33,760 --> 00:29:40,580
+even صار عندي الآن Sigma of N بتحسبها، بتساوي طبعا 
+
+311
+00:29:40,580 --> 00:29:45,180
+هو ما عطينا الـ Sigma of N is odd وبدنا نستنتج إنه 
+
+312
+00:29:45,180 --> 00:29:48,900
+N يا perfect square يا twice perfect square عشان
+
+313
+00:29:48,900 --> 00:29:52,250
+ما تنسوش أشي اللي بدنا يقع الآن حسب الحسبة هذا
+
+314
+00:29:52,250 --> 00:29:57,090
+بيصير عبارة عن واحد زاد اتنين زاد اتنين تربيع لما 
+
+315
+00:29:57,090 --> 00:30:02,510
+أصل لتنين أس بيط واحد مضروبة في البجيات فاهمين
+
+316
+00:30:02,510 --> 00:30:08,530
+البجيات مين هم اللي هو بي واحد زاد بي اي زاد بي اي 
+
+317
+00:30:08,530 --> 00:30:14,630
+تربيع لما أصل لعند بي اي أس بيط اي اي من عند اتنين
+
+318
+00:30:14,630 --> 00:30:19,430
+لعند مين لعند ار معايا شباب
+
+319
+00:30:22,540 --> 00:30:26,840
+الآن متفجرين إن الـSigma of N is Odd إذا الهادي
+
+320
+00:30:26,840 --> 00:30:31,160
+على بعض أكيد إيه شمالها؟ Odd وعملناها قبل بشوية 
+
+321
+00:30:31,160 --> 00:30:36,740
+عملناها وطلعتلنا إن هادي هتكون على صورة B2 2
+
+322
+00:30:36,740 --> 00:30:41,220
+Alpha 2 لعين بي R 2 Alpha R طلعناها من اللي قبل صح
+
+323
+00:30:41,220 --> 00:30:45,960
+ولا لأ؟ طيب الآن هادي وبرضه هادي غصب عنها هتطلع 
+
+324
+00:30:45,960 --> 00:30:53,150
+إيش؟ Odd مزام odd طب ما هن هدوء لكل ينقش مال هن
+
+325
+00:30:53,150 --> 00:31:00,650
+اللي هو even أه وهذه واحد إذا هذا odd من ذاتها 
+
+326
+00:31:00,650 --> 00:31:07,870
+odd من إيش من ذاتها سواء beta واحد even ولا odd
+
+327
+00:31:07,870 --> 00:31:17,380
+إذا بتصير هذه لحالتين B1 is even وB1 is odd إذا B
+
+328
+00:31:17,380 --> 00:31:22,000
+يعني بتساوي هذه عبارة عن هيصير عبارة عن هذه يعني 
+
+329
+00:31:22,000 --> 00:31:27,160
+الأم تبعتنا هذه هتصير عبارة عن اللي هو أوجد نص هنا
+
+330
+00:31:27,160 --> 00:31:34,590
+ماشي بيصير اتنين أس بيتا واحد بيتنين أس 2000
+
+331
+00:31:34,590 --> 00:31:39,870
+اتنين لعند بي ار 2000 ار هدولة جذبنا إن هي
+
+332
+00:31:39,870 --> 00:31:44,330
+اكسرتهم الأهالي ما جذبناش بي واحد ممكن تكون even
+
+333
+00:31:44,330 --> 00:31:48,990
+ممكن تكون إيش قد دا نفيه لحالتين حالة إن تكون
+
+334
+00:31:48,990 --> 00:31:56,090
+even يعني حصورة إيش مع الها 2000 واحد أو حالة
+
+335
+00:31:56,090 --> 00:32:00,680
+إنها تكون odd اللي هي 2000 واحد زاد في بي 
+
+336
+00:32:00,680 --> 00:32:05,960
+2000 2000 2 لعند بي ار 2000 ار
+
+337
+00:32:05,960 --> 00:32:13,580
+الأولى هتطلعلي perfect square الأولى هتطلعلي 
+
+338
+00:32:13,580 --> 00:32:17,460
+perfect square اللي هو 2 بي 2 لعند بي ار
+
+339
+00:32:17,460 --> 00:32:23,540
+الكل تربيع 2000 2000 ار الثانية إيش هتطلعليه
+
+340
+00:32:24,590 --> 00:32:29,930
+2 perfect square twice perfect square هتطلع
+
+341
+00:32:29,930 --> 00:32:37,110
+للثانية اللي هو 2 في 2 أس 
+
+342
+00:32:37,110 --> 00:32:43,290
+2000 واحد بي 2000 2 لعين بي ار 2000 ار لكل 
+
+343
+00:32:43,290 --> 00:32:53,000
+تاريخ لما كانت sigma n is odd Sigma n is odd طلعتني
+
+344
+00:32:53,000 --> 00:32:58,100
+الآن يا بتطلع perfect square يا twice إيش
+
+345
+00:32:58,100 --> 00:33:09,740
+perfect square أي سؤال اللي بعده يلا لا 
+
+346
+00:33:09,740 --> 00:33:13,200
+اللي بعده اللي بعده اطلع سؤال تمانية أيوة أكبر أي
+
+347
+00:33:13,200 --> 00:33:16,500
+سؤال تمانية أيوة اطلع لفوق اطلع السؤال إيش بدك فيه 
+
+348
+00:33:16,500 --> 00:33:23,030
+سؤال تمانية ما شي الحال الأسئلة عموما كلها محلولة بس 
+
+349
+00:33:23,030 --> 00:33:26,590
+خلينا ناخد الأسئلة اللي إحنا طلبناها منكم لأن مش
+
+350
+00:33:26,590 --> 00:33:33,330
+هنلاحق الآن بدنا نثبت ال summation واحد على دي دي 
+
+351
+00:33:33,330 --> 00:33:37,990
+بتكسب ان بسوا sigma of n على مين على ان نطلع عليها 
+
+352
+00:33:37,990 --> 00:33:39,950
+ونشوف كيف نتعامل مع حياتك أسئلة 
+
+353
+00:33:57,320 --> 00:34:02,620
+هقولنا يا شباب السؤال اللي هو تمانية show that 
+
+354
+00:34:02,620 --> 00:34:09,400
+اللي هو summation واحد على دي دي بتكسب n هذه ال 
+
+355
+00:34:09,400 --> 00:34:12,580
+summation واحد على دي دي بتكسب n دي هو ال replic
+
+356
+00:34:12,580 --> 00:34:16,320
+اللي هو إنات زي ما بدك في الدار هتلاقيها دائما
+
+357
+00:34:16,320 --> 00:34:25,760
+بتساوي sigma of n على n ال proof إحنا حكينا المرة
+
+358
+00:34:25,760 --> 00:34:29,720
+الماضية وقبل شوية حكيتها عشان أستخدمها إنه لو
+
+359
+00:34:29,720 --> 00:34:41,120
+كانت F is multiplicative then F of N على صورة F of 
+
+360
+00:34:41,120 --> 00:34:46,000
+D دي بتجسم N برضه شمالها multiple
+
+361
+00:34:48,130 --> 00:34:54,510
+إذا لما نكون في عندي summation على دي بتقسم ان لا
+
+362
+00:34:54,510 --> 00:35:00,290
+إيش جوا أول ما يخطر ببالي أروح باتجاه إن ال
+
+363
+00:35:00,290 --> 00:35:04,030
+summation كله مع ال function اللي جوا إني أقول
+
+364
+00:35:04,030 --> 00:35:09,410
+عنها رايحة باتجاه ال multiplicative ومن ثم إيجادها
+
+365
+00:35:09,410 --> 00:35:13,990
+بيصير سهل باستخدام ال multiplicative إيش اللي
+
+366
+00:35:13,990 --> 00:35:17,900
+بقوله؟ خليني أشوف بس على الحالة سؤال قبل الـ 1 على 
+
+367
+00:35:17,900 --> 00:35:19,840
+D لما أخد فانشين F of D بيسوي 1 على D 
+
+368
+00:35:19,840 --> 00:35:23,780
+multiplicative برضه اللي هو شعوري إنه هو
+
+369
+00:35:23,780 --> 00:35:27,100
+multiplicative وهتلاقي إنه فعلا multiplicative
+
+370
+00:35:27,100 --> 00:35:30,420
+وسادف بقى إنها multiplicative إذا أول شيء بدي 
+
+371
+00:35:30,420 --> 00:35:37,360
+أحاول أجايف هذه للصورة هذه بدي أقول له let F of D
+
+372
+00:35:37,360 --> 00:35:43,440
+بيسوي 1 على D ما شي الحال الآن F بتدعي إنها
+
+373
+00:35:43,440 --> 00:35:49,070
+multiplicative ليش Multiplicative؟ تستسهل Let D1
+
+374
+00:35:49,070 --> 00:35:51,930
+و D2 element in Z بحيث الـ Greatest common divisor 
+
+375
+00:35:51,930 --> 00:36:00,230
+بينهما يكون 1 وحسبني F of D1 في D2 بساوة اللي هو
+
+376
+00:36:00,230 --> 00:36:05,470
+حسب القانون هو 1 على D1 في D2 صح ولا لأ اللي هي
+
+377
+00:36:05,470 --> 00:36:11,330
+بيساوي 1 على D1 في 1 على D2 ويساوي F of D1 في F of
+
+378
+00:36:11,330 --> 00:36:16,790
+D إذا واضح أن F is a multiplicative function ما شي
+
+379
+00:36:16,790 --> 00:36:22,850
+الحال طيب مدام F multiplicative بتشجعني إن أقول
+
+380
+00:36:22,850 --> 00:36:31,820
+let F of N بساوية الـ summation للـ F of D دي
+
+381
+00:36:31,820 --> 00:36:36,720
+بتجسمها اللي يمين اللي عبارة عن summation واحد على
+
+382
+00:36:36,720 --> 00:36:43,120
+D دي بتجسم اللي أنا بدور عليها بما أن F is
+
+383
+00:36:43,120 --> 00:36:47,200
+multiplicative إذا ال summation هذا شماله is 
+
+384
+00:36:47,200 --> 00:36:50,380
+multiplicative حسب النظرية اللي عندنا إذا صارت ال
+
+385
+00:36:50,380 --> 00:36:56,170
+F كابتنة شماله is multiplicative الآن أنا بستخدم
+
+386
+00:36:56,170 --> 00:36:59,470
+الـ Multiplicative عشان تسهّل عليّ عملية الحسابات
+
+387
+00:36:59,470 --> 00:37:02,370
+طب عملية الحسابات كيف تسهّل في حالة الـ
+
+388
+00:37:02,370 --> 00:37:05,690
+Multiplicative إنه أنا بكتبها على صورة Product of 
+
+389
+00:37:05,690 --> 00:37:10,130
+Primes فبيصير إيجاد اللي هي الـ Function للـ Primes
+
+390
+00:37:10,130 --> 00:37:14,370
+في الغالب الأسئلة اللي بالشكل هذا أسهل من نوجد للـ
+
+391
+00:37:14,370 --> 00:37:17,410
+N in general طب مدة بدي أروح باتجاه الـ Product 
+
+392
+00:37:17,410 --> 00:37:21,030
+of Primes لأن الـ N التابعةتي بتكون أكبر من مين؟ من 
+
+393
+00:37:21,030 --> 00:37:24,930
+واحد إذا بدي أعالج حالتي الواحد لحالة مثل ما عالجنا 
+
+394
+00:37:24,930 --> 00:37:29,270
+قبل قليل حالتي الواحد معالجة وخالصة يعني من رأس
+
+395
+00:37:29,270 --> 00:37:54,600
+الدهر لو كتبنا إذا N أكبر من 1 إذا N
+
+396
+00:37:54,600 --> 00:38:03,520
+أكبر من 1 إذا N أكبر من 1 إذاً by unique 
+
+397
+00:38:03,520 --> 00:38:07,700
+factorization theorem N can be written as N بساوية
+
+398
+00:38:07,700 --> 00:38:15,740
+P1 Alpha 1 لعين PR Alpha HR معايا يا شباب؟ إذا صار
+
+399
+00:38:15,740 --> 00:38:22,520
+عندي F of N حسب تسهلة بساوية F of P1 Alpha 1 لعين 
+
+400
+00:38:22,520 --> 00:38:27,040
+PR Alpha R بساوية F is multiplicative إذاً by
+
+401
+00:38:27,040 --> 00:38:30,180
+induction one can easily show that اللي هو بساوية 
+
+402
+00:38:30,180 --> 00:38:39,610
+Fof b1 α1 عن bA F of bR αR ليش؟ لأن كل واحد منهم 
+
+403
+00:38:39,610 --> 00:38:43,290
+بي واحد ومع الـ B التاني بي اتنين مع بي تلاتة R 
+
+404
+00:38:43,290 --> 00:38:47,770
+Relatively Primes in Pairs فأكيد اللي هو بتتوزع 
+
+405
+00:38:47,770 --> 00:38:52,110
+الـ F إذن الآن صارت التحول للسؤال إن بس أودد مين؟
+
+406
+00:38:52,110 --> 00:38:56,990
+F of bI αI بدي أوددهم، بضربهم في بعض، بيطلع اللي هو 
+
+407
+00:38:56,990 --> 00:39:01,580
+المطلوب تمشيوف كيف، إذن استراتيجية الحل سهلة بتظهر
+
+408
+00:39:01,580 --> 00:39:07,680
+عملية عملية اللي هو مهارات حسابات لأن أحسب f of bi
+
+409
+00:39:07,680 --> 00:39:14,540
+αi بساوي إيش اللي القانون عنده اللي هو f of n 
+
+410
+00:39:14,540 --> 00:39:17,500
+بساوي ال summation واحد على دي يعني بيساوي ال
+
+411
+00:39:17,500 --> 00:39:24,500
+summation واحد على دي دي بتجسمين الآن bi αi وهنا
+
+412
+00:39:24,500 --> 00:39:31,710
+سهولة ال prime اللي هو قواسم ال bi αi كلها واحد، 
+
+413
+00:39:31,710 --> 00:39:35,750
+يا بي آي، يا بي آي تربيع، يا بي آي تكعيب، لعند ما
+
+414
+00:39:35,750 --> 00:39:40,510
+أصل لعند مين؟ بي آي ألف آي، كل إن هدولة قواصم للبي
+
+415
+00:39:40,510 --> 00:39:45,710
+آي ألف آي، يعني القواصم مش او، و، و، و، يعني
+
+416
+00:39:45,710 --> 00:39:49,330
+القواسم هي واحد، وبي آي، وبي آي تربيع، وبي آي 
+
+417
+00:39:49,330 --> 00:39:54,170
+تكعيب لعند ما أصل بي آي ألف آي، إذا صار عندي
+
+418
+00:39:54,170 --> 00:39:59,880
+ويساوي، هذا صار summation، واحد على واحد، زائد واحد 
+
+419
+00:39:59,880 --> 00:40:07,880
+على بي آي زائد واحد
+
+420
+00:40:07,880 --> 00:40:13,520
+على بي آي تربيع لما أصل عند واحد على بي آي ألف آي 
+
+421
+00:40:15,110 --> 00:40:20,810
+هذه المتتالية أساسها 1 على بي آي ألفا آي 
+
+422
+00:40:20,810 --> 00:40:24,810
+قانونها زي ما كنا نقول زمان ريح أس ألفا آي ونقص واحد عليها
+
+423
+00:40:24,810 --> 00:40:29,210
+ريح نقص واحد نون اللي هو عدد مين عدد الحدود لأن
+
+424
+00:40:29,210 --> 00:40:34,470
+عدد الحدود هنا أشماله Alpha I زائد واحد لأن هنا
+
+425
+00:40:34,470 --> 00:40:38,270
+عندنا Alpha I وهي عندي كمان term بيصير Alpha I
+
+426
+00:40:38,270 --> 00:40:44,860
+زائد واحد بيصير اللي هو مجموعها ولا بساوي اللي هو
+
+427
+00:40:44,860 --> 00:40:54,620
+واحد على بي آي الأساس أس ألفا آي زائد واحد ناقص
+
+428
+00:40:54,620 --> 00:41:00,300
+فاهمين عليها واحد على واحد على بي آي ناقص واحد
+
+429
+00:41:00,300 --> 00:41:08,140
+ماشي الحال الآن اضرب فوق و تحت اضرب فوق و تحت عشان
+
+430
+00:41:08,140 --> 00:41:14,040
+ابسطها بي آي ألفا آي زائد واحد على بي آي ألفا آي 
+
+431
+00:41:14,040 --> 00:41:21,760
+زائد واحد بيصير عندي هذا المقدار بعد إذا كنت بدأ
+
+432
+00:41:21,760 --> 00:41:22,460
+امسحه
+
+433
+00:41:41,940 --> 00:41:47,860
+شوفوا يا شباب بدّي صارت عندي F of F of P I Alpha I
+
+434
+00:41:47,860 --> 00:41:57,060
+F of P I Alpha I بتساوي اللي هو هذا المقدار ضربته
+
+435
+00:41:57,060 --> 00:42:01,420
+فوق P I Alpha I زائد واحد وتحت نفس الشيء هذا بيصير
+
+436
+00:42:01,420 --> 00:42:09,980
+عبارة عن واحد ناقص P I Alpha I زائد واحد على بي أس
+
+437
+00:42:09,980 --> 00:42:17,380
+ألفا آي ناقص بي أس ألفا آي زائد واحد، مظبوط؟ طلع لي
+
+438
+00:42:17,380 --> 00:42:28,860
+اللي هو واحد على بي آي ألفا آي كعامل مشترك زائد
+
+439
+00:42:28,860 --> 00:42:33,640
+واحد، لأ لأ بدون زائد واحد، خلي واحد ده، بيضل
+
+440
+00:42:33,640 --> 00:42:37,910
+اللي جوا مين هو؟ وبدي أضرب بالمرة فوق بناقص وتحت 
+
+441
+00:42:37,910 --> 00:42:44,930
+بناقص بعد إذنكم بيصير بي آي ألفا آي زائد واحد
+
+442
+00:42:44,930 --> 00:42:49,190
+ناقص واحد على لما أخد عامل مشترك بي آي ألفا واحد
+
+443
+00:42:49,190 --> 00:42:53,270
+بيصير واحد ناقص بي آي لما أضربه في ناقص في السيرة
+
+444
+00:42:53,270 --> 00:43:00,370
+الشماله بي آي ناقص واحد واضح ها واضح اللي سويته
+
+445
+00:43:00,370 --> 00:43:06,920
+لأن هذه ال F of واحدة منهم الآن F of N إيش مالها؟
+
+446
+00:43:06,920 --> 00:43:11,520
+حاصل ضربهم كلهم، مظبوط؟ إذا الـ F of N هي ال
+
+447
+00:43:11,520 --> 00:43:15,120
+product للـ F of P واحد Alpha واحد لعند F of P R
+
+448
+00:43:15,120 --> 00:43:21,780
+Alpha R إذا صار عندي F of N بساوي له product لهذه
+
+449
+00:43:21,780 --> 00:43:26,780
+اللي هو عبارة عن ال product لواحد على P I Alpha I
+
+450
+00:43:27,860 --> 00:43:33,680
+معايا يا شباب في بي آي ألفا آي زائد واحد ناقص واحد
+
+451
+00:43:33,680 --> 00:43:39,840
+على بي آي ناقص واحد I من عند واحد لعند مين R الآن
+
+452
+00:43:39,840 --> 00:43:44,300
+ال product لهذه بي واحد ألف واحد بي اتنين ألف
+
+453
+00:43:44,300 --> 00:43:48,140
+اتنين بي تلت ألف تلت لعند بي R ألف R من هي الان
+
+454
+00:43:48,140 --> 00:43:53,120
+إذا صار هذا ال product عبارة عن واحد على N مضروب
+
+455
+00:43:53,120 --> 00:43:59,020
+فيه ال product هذا هو عبارة عن sigma of N إذا صار
+
+456
+00:43:59,020 --> 00:44:03,380
+عبارة عن 1 على N في sigma of N of N آخر sigma of N
+
+457
+00:44:03,380 --> 00:44:10,120
+على N وهو المقبول إذا صار عندي اللي هو sigma of N
+
+458
+00:44:10,120 --> 00:44:14,900
+على N بساوي اللي هو F of N F of N مين هي أصلا اللي
+
+459
+00:44:14,900 --> 00:44:19,240
+عبارة عن فرضناها اللي هو summation 1 على D D بتكسب 
+460
+00:44:19,240 --> 00:44:19,420
+N
+
+461
+00:44:27,090 --> 00:44:32,150
+هدولة مين هنا؟ هدولة مين هنا؟ هدول ال product اللي
+
+462
+00:44:32,150 --> 00:44:38,310
+هنا 1 على B1 Alpha 1 في 1 على B2 Alpha 2 لما 1 على
+
+463
+00:44:38,310 --> 00:44:44,990
+B R Alpha R عصر ضرب إن هدولة مين هنا؟ لأ مش ال
+
+464
+00:44:44,990 --> 00:44:50,770
+factorization لأن مش هي الآن اه و يساوي 1 على N
+
+465
+00:44:50,770 --> 00:44:53,630
+أي سؤال؟
+
+466
+00:44:55,560 --> 00:45:04,400
+بعد تبانية نيجي لسؤال 12 12 .. 12 .. 12 الأسئلة ..
+
+467
+00:45:04,400 --> 00:45:10,340
+الأسئلة .. الأسئلة جزء مهم من المادة خصوصا في الـ
+
+468
+00:45:10,340 --> 00:45:15,340
+Chapter هذا لأن الأسئلة بتحمل فكرة عديدة إن ما
+
+469
+00:45:15,340 --> 00:45:19,660
+حلتهاش هتحس حالك اللي هو في عندك نقص كبير في الفهم
+
+470
+00:45:19,660 --> 00:45:28,380
+للمادة نيجي ل .. بدنا نحل اللي هو المعادلة أو الـ
+
+471
+00:45:28,380 --> 00:45:35,900
+possible solutions for tau of n بتساوي عشرة طبعا
+
+472
+00:45:35,900 --> 00:45:38,480
+الـ الـ الـ الـ الـ الـ الـ الـ الـ 
+
+473
+00:45:38,480 --> 00:45:39,140
+الـ الـ الـ الـ الـ الـ الـ الـ 
+
+474
+00:45:39,140 --> 00:45:39,780
+الـ الـ الـ الـ الـ الـ الـ الـ 
+
+475
+00:45:39,780 --> 00:45:39,800
+الـ الـ الـ الـ الـ الـ الـ الـ 
+
+476
+00:45:39,800 --> 00:45:39,880
+الـ الـ الـ الـ الـ الـ الـ الـ 
+
+477
+00:45:39,880 --> 00:45:39,980
+الـ الـ الـ الـ الـ الـ الـ الـ 
+
+478
+00:45:39,980 --> 00:45:40,080
+الـ الـ الـ الـ الـ الـ الـ الـ 
+
+479
+00:45:40,080 --> 00:45:40,500
+الـ الـ الـ الـ الـ الـ الـ الـ 
+
+480
+00:45:40,500 --> 00:45:40,560
+الـ الـ الـ الـ الـ الـ الـ الـ 
+
+481
+00:45:40,560 --> 00:45:51,360
+الـ الـ الـ 
+
+482
+00:45:51,360 --> 00:45:53,300
+الـ الـ 
+
+483
+00:45:54,890 --> 00:45:59,150
+البرمجة naive اللي بيكون تميها طيب لنتشوف سؤال
+
+484
+00:45:59,150 --> 00:46:04,570
+12 find the form of the positive of all positive
+
+485
+00:46:04,570 --> 00:46:08,650
+integers n satisfying tau of n بساوة عشرة
+
+486
+00:46:08,650 --> 00:46:13,230
+بقول لي أوجد كل ال positive integers اللي بيحقق إن
+
+487
+00:46:13,230 --> 00:46:19,130
+tau of n إيش بساوي بساوي عشرة وبقول لي بعدين
+
+488
+00:46:19,130 --> 00:46:25,510
+أوجد أصغر واحد من هنا What is the smallest integer
+
+489
+00:46:25,510 --> 00:46:33,970
+لهو for such ends ناشي؟ بده نوجد أصغر واحد فيهم هو
+
+490
+00:46:33,970 --> 00:46:38,670
+الجزء الأول هو خلّيني أقول هو اللي فيه الفكرة
+
+491
+00:46:38,670 --> 00:46:41,490
+الجزء الثاني على طول بطلع لإنه بيصير أصغر واحد
+
+492
+00:46:41,490 --> 00:46:44,890
+تعرف أصغر واحد سهل يجيده صلى على النبي عليه الصلاة
+
+493
+00:46:44,890 --> 00:46:48,530
+والسلام solution إحنا
+
+494
+00:46:49,500 --> 00:46:53,820
+جابل بشوية لما جينا كتبنا Tau of N لـ N بتساوي P1
+
+495
+00:46:53,820 --> 00:46:58,380
+α1 لعند PR αR من وجه الفكرة Tau of N إيش بتساوي
+
+496
+00:46:58,380 --> 00:47:03,060
+عبارة عن ألفا واحد زائد واحد لعند Alpha R زائد إيش
+
+497
+00:47:03,060 --> 00:47:07,640
+واحد إذا Tau of N هي عبارة عن اللي هي جاية من مين
+
+498
+00:47:07,640 --> 00:47:13,500
+من أسس الـ Primes تبعات اللي هي ال factors لمين لـ
+
+499
+00:47:13,500 --> 00:47:19,350
+N مظبوط ولا لأ طيب الآن الفكرة في الحل إن هذه
+
+500
+00:47:19,350 --> 00:47:23,710
+العشرة بتشوف .. طبعا ال product توفر إن عبارة عن
+
+501
+00:47:23,710 --> 00:47:29,070
+product of أسس بتشوف كل productات الممكنة للعشرة
+
+502
+00:47:29,070 --> 00:47:34,710
+ماشي الحال ال Product الممكن للأول عشر إيش هي؟
+
+503
+00:47:34,710 --> 00:47:38,110
+اتنين وثلاثة وخمسة سيبك من الواحد لأن الواحد مش
+
+504
+00:47:38,110 --> 00:47:40,830
+هيكون له قيمة لأنه بيصير Alpha واحد زائد واحد
+
+505
+00:47:40,830 --> 00:47:43,910
+بيساوي واحد بيطلع Alpha واحد بيساوي صفر بيصير و
+
+506
+00:47:43,910 --> 00:47:46,470
+كأنه الواحد إحنا نقول الـ unique factorization
+
+507
+00:47:46,470 --> 00:47:52,950
+theorem خلاص ما هو إحنا الواحد الواحد neglected اه
+
+508
+00:47:52,950 --> 00:48:00,700
+طيب بناء عليه إنه انسى جثة الواحد ك factor إلى أن
+
+509
+00:48:00,700 --> 00:48:03,660
+نقول عشرة في واحد واحد كله ما هو عشرة في واحد في
+
+510
+00:48:03,660 --> 00:48:06,660
+واحد في واحد في واحد وكله مش عامل غلب حالك كل اللي
+
+511
+00:48:06,660 --> 00:48:10,240
+هييطلع إن إيش حاجة واحدة لإن الألفات تبعتك هيطلع إن
+
+512
+00:48:10,240 --> 00:48:13,020
+إيش وما هي اللي تبعت الواحد صفر هل جيت تفهم شو
+
+513
+00:48:13,020 --> 00:48:17,540
+معناته؟ حتفهم؟ طيب، إذا الآن الفكرة العشرة ميل
+
+514
+00:48:17,540 --> 00:48:20,960
+الـ divisors لها لإن بتكتبها على صورة ال product
+
+515
+00:48:20,960 --> 00:48:25,440
+عشرة، بقدر أكتبها على صورة عشرة هو عشرة بقى قدر
+
+516
+00:48:25,440 --> 00:48:30,940
+اكتبها على سورة 2؟ في غير هيك؟ لأ طبعا أكيد لأ
+
+517
+00:48:30,940 --> 00:48:37,960
+طبعا نيجي الآن بنقول العشرة الـ tau of N العشرة
+
+518
+00:48:37,960 --> 00:48:43,100
+هذه عبارة عن .. هتعملني عبارة عن tau of N بساوي
+
+519
+00:48:43,100 --> 00:48:50,380
+Alpha 1 زي 1 يعني الحالة الأولى F اللي هو أو case
+
+520
+00:48:50,380 --> 00:48:59,190
+1 ألفا واحد زائد واحد بيساوي عشرة case two ألفا
+
+521
+00:48:59,190 --> 00:49:04,810
+واحد زائد واحد في ألفا اثنين زائد واحد بيساوي
+
+522
+00:49:04,810 --> 00:49:09,830
+اثنين في مين؟ مظبوط ولا لا؟ في غير هيك؟ لأ اللي
+
+523
+00:49:09,830 --> 00:49:12,290
+فيجيبني العشرة بس إن اثنين في الخمسة هو العشرة
+
+524
+00:49:12,290 --> 00:49:17,070
+وقول لي ليش هذه بتعطيني إذا ألفا واحد ده إيش
+
+525
+00:49:17,070 --> 00:49:26,780
+بيساوي إذا انتبعتنا هتصير عبارة عن بي أس تسعة ماشي
+
+526
+00:49:26,780 --> 00:49:30,240
+الحال من وين هذه اللي قد جاية ما إحنا قلنا أصل
+
+527
+00:49:30,240 --> 00:49:33,320
+الموضوع إن بأس بي واحد ألفا واحد إن بي أر ألفا أر
+
+528
+00:49:33,320 --> 00:49:38,080
+التوقف عن هو عدد ال devices اللي هي حاسن product
+
+529
+00:49:38,080 --> 00:49:44,040
+of الأسس لأن بما إنه product of numbers عندي بدي
+
+530
+00:49:44,040 --> 00:49:47,920
+أوجد هذول الاحتماليات اللي بيولدون العشرة التوقف إن
+
+531
+00:49:47,920 --> 00:49:51,970
+تولد العشرة هي أما بعشرة لحالها يا أما بـ 2×5 في حال
+
+532
+00:49:51,970 --> 00:49:55,870
+تولد بـ 10 لحالها وهذا قيمة التوف إن إذا قيمتها على
+
+533
+00:49:55,870 --> 00:49:58,870
+صورة ألفا واحد زائد واحد أخدتها كمية واحدة أول شيء
+
+534
+00:49:58,870 --> 00:50:02,390
+إذا الألفا واحد إيش صارت بساوي تسعة إذا الآن
+
+535
+00:50:02,390 --> 00:50:08,430
+تبعتها عبارة عن بي واحد أس تسعة يعني تبعتها بي أس
+
+536
+00:50:08,430 --> 00:50:14,430
+تسعة نيجي الآن التانية عبارة عن ألفا واحد بساوي
+
+537
+00:50:14,430 --> 00:50:20,870
+اثنين أسف واحد فاهمين اه؟ ألفا اثنين بيساوي إيش
+
+538
+00:50:20,870 --> 00:50:32,270
+أربعة معايا يعني عندي اللي هو ال M عندي هتصير بي
+
+539
+00:50:32,270 --> 00:50:41,830
+واحد في Q أو بي واحد بي اثنين اص إيش اص أربعة
+
+540
+00:50:45,110 --> 00:50:49,470
+و بي واحد و بي اثنين أنا بـ Primes أنا Distinct
+
+541
+00:50:49,470 --> 00:50:57,310
+Primes اه و بيه هذي وهذي يعني الآن .. يعني كلهم
+
+542
+00:50:57,310 --> 00:51:00,970
+هذولة وكلهم هذولة هذولة Infinite وهذولة Infinite
+
+543
+00:51:00,970 --> 00:51:05,760
+دي البالة هؤلاء أي برايم في الدنيا ترفع إلى تسعة
+
+544
+00:51:05,760 --> 00:51:09,600
+تطلع الـ tau van الواش بتساوي عشرة وأي برايم في
+
+545
+00:51:09,600 --> 00:51:14,420
+الدنيا بي واحد في بي اثنين أس أربعة تطلع برضه
+
+546
+00:51:14,420 --> 00:51:21,750
+جداش عشرة إذا the set of all such ands are the set
+
+547
+00:51:21,750 --> 00:51:28,230
+of all such numbers in the form b9 where b is any
+
+548
+00:51:28,230 --> 00:51:36,730
+prime and بتساوي b1, b2 to the 4 where b1 and b2
+
+549
+00:51:36,730 --> 00:51:42,090
+are any distinct primes الآن طلب اللي بعده هي إيش
+
+550
+00:51:42,090 --> 00:51:48,310
+هو find the smallest Find the smallest من الـ
+
+551
+00:51:48,310 --> 00:51:52,210
+smallest الآن أصغر واحد في الـ Formة هذه أصغر واحد
+
+552
+00:51:52,210 --> 00:51:58,210
+في الـ Formة هذه اللي هو 2 أس 9 أصغر واحد في الـ
+
+553
+00:51:58,210 --> 00:52:06,750
+Formة هذه على طول بيجي عبالك أنت 2 في 3 أس 4 أو 3
+
+554
+00:52:06,750 --> 00:52:13,750
+في 2 أس 4 واضح مين الأصغر هذا أصغر من اللي فوق صح
+
+555
+00:52:13,750 --> 00:52:18,430
+ولا لأ الآن الآن هذا برضه أصغر من اللي فوق لإن هذا
+
+556
+00:52:18,430 --> 00:52:21,390
+في لسه ذاك هذا مضروب في تلاتة و ذاك مضروب في اثنين
+
+557
+00:52:21,390 --> 00:52:26,810
+أس خمسة إذا مين the smallest one اللي هو تلاتة في
+
+558
+00:52:26,810 --> 00:52:36,850
+اثنين أس أربعة واضح ها حل السؤال اتناش طيب الآن
+
+559
+00:52:36,850 --> 00:52:45,280
+التاني بقول لك ممكن أقول لك find the solution if
+
+560
+00:52:45,280 --> 00:52:52,320
+exists for sigma of n بتساوي عشرة اه sigma of n 
+
+561
+00:52:52,320 --> 00:52:57,660
+بتساوي عشان آه
+
+562
+00:52:57,660 --> 00:53:03,360
+فكرة فكرة السيجما إن الـ sigma هي عبارة عن إيش
+
+563
+00:53:03,360 --> 00:53:08,410
+مجموع الـ divisors مثلما تموّع الـ divisors إذا الـ
+
+564
+00:53:08,410 --> 00:53:11,530
+N اللي نفسها اللي بدّينا لها الـ Sigma واحدة منهن
+
+565
+00:53:11,530 --> 00:53:18,130
+آه فالآن لما أقول sigma of N بتساوي اللي هو مية إذا 
+
+566
+00:53:18,130 --> 00:53:24,530
+أنا قطعاً قطعاً قطعاً ببحثش عن الحلول من مية وطالع
+
+567
+00:53:24,530 --> 00:53:33,780
+ليش؟ لأن sigma of اللي هي المية هتصير أكبر من مية
+
+568
+00:53:33,780 --> 00:53:38,140
+يعني أكيد وهذا الكلام صحيح لكل ومية وواحد ومية
+
+569
+00:53:38,140 --> 00:53:39,860
+واتنين ومية وتلاتة ومية واتنين وتلاتة ومية
+
+570
+00:53:39,860 --> 00:53:39,880
+اتنين وتلاتة ومية اتنين وتلاتة ومية اتنين و
+
+571
+00:53:39,880 --> 00:53:40,040
+تلاتة ومية اتنين وتلاتة ومية اتنين وتلاتة و
+
+572
+00:53:40,040 --> 00:53:40,380
+مية اتنين وتلاتة ومية اتنين وتلاتة ومية اتنين
+
+573
+00:53:40,380 --> 00:53:41,420
+وتلاتة ومية اتنين وتلاتة ومية اتنين وتلاتة و
+
+574
+00:53:41,420 --> 00:53:44,720
+مية اتنين وتلاتة ومية اتنين وتلاتة ومية اتنين
+
+575
+00:53:44,720 --> 00:53:48,790
+وتلاتة ومية واتنين وماشي احنا بنشتغل على شيء ع
+
+576
+00:53:48,790 --> 00:53:52,490
+جدنا اللي هو ع جد المعلومات اللي حتى الآن بنيت هنا
+
+577
+00:53:52,490 --> 00:53:57,390
+جهلنا إن sigma of n بتساوي عشرة find all solutions
+
+578
+00:53:57,390 --> 00:54:06,380
+if exist إذا بدي أقول له we investigate only on n
+
+579
+00:54:06,380 --> 00:54:13,400
+less than عشرة أو less than or equal تسعة why?
+
+580
+00:54:13,660 --> 00:54:20,060
+because sigma of n is always greater strictly than
+
+581
+00:54:20,060 --> 00:54:25,700
+ten أو sigma of n is strictly greater than n
+
+582
+00:54:25,700 --> 00:54:31,860
+فاهمين علينا بقولها احنا بنبحث في الأجل من الـ n
+
+583
+00:54:32,940 --> 00:54:37,580
+اللي ما عطيناها، اللي هي العشرة لأجل من عشرة لأن الـ
+
+584
+00:54:37,580 --> 00:54:42,060
+Sigma of عشرة واللي بعيدها دائماً أكبر من عشرة
+
+585
+00:54:42,060 --> 00:54:48,900
+للحقيقة اللي بتقولك Sigma of N أكبر من N for every
+
+586
+00:54:48,900 --> 00:54:52,620
+N بنأخذ
+
+587
+00:54:52,620 --> 00:55:02,090
+عليه لما بيقول Find a solution of sigma of n بتساوي
+
+588
+00:55:02,090 --> 00:55:11,990
+عشرة if exist بدي أقول له sigma of واحد solution
+
+589
+00:55:11,990 --> 00:55:16,690
+sigma of واحد بنجده بتساوي واحد sigma of اتنين
+
+590
+00:55:16,690 --> 00:55:26,110
+تلاتة sigma of أربعة اللي هو لأ شو خمسة اتنين قصة
+
+591
+00:55:26,110 --> 00:55:31,890
+اللي هو بيطلع سبعة لأ 2 أس 2 سيجما of 4 2 أس 2
+
+592
+00:55:31,890 --> 00:55:37,790
+ناقص 1 على 2 أس ناقص 1 ماشي الحالة مظبوط 2 أس 2
+
+593
+00:55:37,790 --> 00:55:43,410
+ناقص فاهمين إيش بقولها عقل ناقص 1 على 2 أس 1 و
+
+594
+00:55:43,410 --> 00:55:50,910
+بيساوي 2 أس 1 زائد 1 وبيساوي 8 ناقص 1 ناقص 7 ناقص 7
+
+595
+00:55:50,910 --> 00:55:59,960
+مظبوط سيجما of 5 6 خمسة درجة واحد ستة البرامج سهلة
+
+596
+00:55:59,960 --> 00:56:04,680
+Sigma of ستة اللي هي اتنين في تلاتة اتنين جداش
+
+597
+00:56:04,680 --> 00:56:10,220
+تلاتة و Sigma of تلاتة ما جبناهاش Sigma of تلاتة
+
+598
+00:56:10,220 --> 00:56:17,200
+أربعة هذا أربعة في تلاتة اتناشر Sigma of مين؟ of ستة
+
+599
+00:56:17,200 --> 00:56:22,220
+فاهمين عليش بقولها Sigma of سبعة تمانية Sigma of
+
+600
+00:56:22,220 --> 00:56:27,830
+ثمانية اللي هي 2 أس 4 ناقص هو بيساوي 15 سيجما of 9
+
+601
+00:56:27,830 --> 00:56:34,110
+تلاتة تربيع تلاتة تكعيب ليه؟ آه ليه 26 ع 2 13
+
+602
+00:56:34,110 --> 00:56:41,510
+مظبوط طيب سيجما of 10 قولنا بلاش سيجما of 10 أو
+
+603
+00:56:41,510 --> 00:56:45,530
+سيجما of N أكبر من 10 for every N أكبر يساوي 10
+
+604
+00:56:45,530 --> 00:56:56,860
+therefore no such N exists بالظبط؟ ما فيش ولا واحدة
+
+605
+00:56:56,860 --> 00:57:03,280
+طلعت عشانها اللي بعده؟ إيش السؤال اللي بعده اللي
+
+606
+00:57:03,280 --> 00:57:09,120
+احنا طالبينه؟ حسابات السؤال
+
+607
+00:57:09,120 --> 00:57:15,280
+اللي بعده نحسب .. خليني بس أكمل هذا show that أو
+
+608
+00:57:15,280 --> 00:57:19,640
+show each of the following عندي N .. طبعاً الـ K
+
+609
+00:57:19,640 --> 00:57:22,800
+أشمخد أكبر يساوي 2 عشان .. اللي هو اختصار الوقت
+
+610
+00:57:22,800 --> 00:57:26,100
+لأنه خلص المحاضرة N بيساوي 2 أس k Minus 1
+
+611
+00:57:26,100 --> 00:57:30,120
+satisfying the equation Sigma of N بيساوي 2N ناقص
+
+612
+00:57:30,120 --> 00:57:36,760
+إيهاش 1 بدنا نثبت إن Sigma of هذه الـ N بيساوي 2N
+
+613
+00:57:36,760 --> 00:57:41,950
+ناقص مين؟ ناقص 1 حسابات وبس حسابات ماشي ال sigma
+
+614
+00:57:41,950 --> 00:57:46,990
+of n بيساوي sigma of 2 أس k-1 أس 2 2 أس k-1
+
+615
+00:57:46,990 --> 00:57:51,630
+اللي هو معروفة اللي هي قيمتها بتضيف 1 وناقص 1 على
+
+616
+00:57:51,630 --> 00:57:56,810
+2 ناقص 1 حيث الأساس إيش 2 معايا الآن هذي بيصير
+
+617
+00:57:56,810 --> 00:58:02,370
+عبارة عن 2 أس k ناقص 1 خذ الـ 2 برة هذي بيصير 2 في
+
+618
+00:58:02,370 --> 00:58:10,460
+2 k-1 ناقص 1 اللي هي عبارة عن 2 n ناقص 1 واضح؟ الآن
+
+619
+00:58:10,460 --> 00:58:14,920
+اللي بعضه بيه برضه similarly اتنين أس k ماينس
+
+620
+00:58:14,920 --> 00:58:17,760
+واحد is a prime ما أعطيك إن اتنين أس k ماينس واحد
+
+621
+00:58:17,760 --> 00:58:20,200
+كله عكت على بعض إيه إيه إيه إيه إيه إيه إيه إيه
+
+622
+00:58:20,200 --> 00:58:22,540
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+623
+00:58:22,540 --> 00:58:22,960
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+624
+00:58:22,960 --> 00:58:23,320
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+625
+00:58:23,320 --> 00:58:23,360
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+626
+00:58:37,630 --> 00:58:41,550
+يعني sigma of n طلعت لك هنا 2n نقص واحد هنا
+
+627
+00:58:41,550 --> 00:58:45,970
+وطلعت لك إيهاش 2n وأحياناً تطلع sigma of n إيش
+
+628
+00:58:45,970 --> 00:58:51,730
+بالساوية n زائد واحد إذا ما فيش rule معينة معايا لأ
+
+629
+00:58:51,730 --> 00:58:55,790
+يعني إن بدلالة n مباشرة أما الـ rule موجودة لياك
+
+630
+00:58:55,790 --> 00:59:02,970
+طيب عندي sigma of n اللي هي n هيهابساوي sigma of
+
+631
+00:59:02,970 --> 00:59:05,610
+الأول في sigma of الثاني لأن الاثنين أشماليا
+
+632
+00:59:05,610 --> 00:59:09,650
+relative الـ prime و sigma is multiplicative sigma
+
+633
+00:59:09,650 --> 00:59:14,110
+للثاني اللي هو أشماله الثاني عبارة عن الـ prime هذا
+
+634
+00:59:14,110 --> 00:59:19,930
+إذا إيش قيمته هو زائد واحد في sigma لهذا بيصير
+
+635
+00:59:19,930 --> 00:59:26,370
+عندي الآن sigma of n بتساوي اللي هي 2 sigma of
+
+636
+00:59:26,370 --> 00:59:28,950
+n بتساوي 2 أس k minus واحد
+
+637
+00:59:31,860 --> 00:59:39,720
+ناقص واحد ناقص واحد زائد واحد المفروض آه اتنين
+
+638
+00:59:39,720 --> 00:59:47,410
+سيجموفران سيجموفران بتساوي 2 أس k 2-k-1 prime
+
+639
+00:59:47,410 --> 00:59:53,930
+آه زائد واحد المفروض وهذه إيش القيمة إلها بنحسبها
+
+640
+00:59:53,930 --> 00:59:58,890
+آه اللي هي عبارة عن 2k-1 على 2-1 اللي هي نفسها
+
+641
+00:59:58,890 --> 01:00:06,060
+فمين آه هذه هذه هي هذه كيف هذه موجودة لا اصبر عليها
+
+642
+01:00:06,060 --> 01:00:11,600
+هذه إيش قيمتها اتنين اتنين أس الأس زائد واحد
+
+643
+01:00:11,600 --> 01:00:15,800
+الأس هنا K ناقص واحد زائد واحد بيطلع K بيصير
+
+644
+01:00:15,800 --> 01:00:19,140
+2 أس K ناقص واحد على الأساس ناقص واحد اتنين
+
+645
+01:00:19,140 --> 01:00:24,160
+ناقص واحد اللي هو إيش إذا صارت sigma of هذه هيها
+
+646
+01:00:27,900 --> 01:00:32,200
+آه الآن بدي أجيبها على الـ form اللي عندي صارت عندي
+
+647
+01:00:32,200 --> 01:00:36,880
+لأن sigma of n بتساوي هذا المقدار في هذا المقدار
+
+648
+01:00:36,880 --> 01:00:40,820
+أخذ الآن زي ما بتقول خذ التنين عامل مشترك بيصير
+
+649
+01:00:40,820 --> 01:00:44,180
+2 K minus واحد أو خلّيني أقول سحب التنين مش
+
+650
+01:00:44,180 --> 01:00:46,140
+عامل مشترك سحب التنين يا عزيزي بيصير 2 في
+
+651
+01:00:46,140 --> 01:00:50,380
+2 K minus واحد هذا كله مين هو؟ الآن صارت 2
+
+652
+01:00:50,380 --> 01:00:56,340
+اثنان فعلاً اطلع لفوق اطلع
+
+653
+01:00:56,340 --> 01:01:01,680
+لبعد لأ ضايل .. ضايل .. إيه ضايلة هذه أيوة ضايل
+
+654
+01:01:01,680 --> 01:01:09,660
+سؤالين لسه يلا خليني أكمل .. خليني أكمل عندي الآن
+
+655
+01:01:09,660 --> 01:01:16,740
+اللي جاب له .. السؤال اللي جاب له عندي C نفترض أن
+
+656
+01:01:16,740 --> 01:01:22,020
+2 أس k ناقص ثلاثة أشمالها prime وماخذ n
+
+657
+01:01:22,020 --> 01:01:28,060
+بتساوي هذا في الـ prime مشابه للي قبل بنفس السلوب
+
+658
+01:01:28,060 --> 01:01:32,360
+sigma of n sigma لهذه لها sigma لهذه في sigma لهذه
+
+659
+01:01:32,360 --> 01:01:36,860
+اللتي في الـ prime sigma للأولى اللي هي عبارة عن
+
+660
+01:01:36,860 --> 01:01:40,640
+هذا الـ prime إذا صار 2k ناقص ثلاثة زائد
+
+661
+01:01:40,640 --> 01:01:44,460
+واحد بس أنتم كيف عملوا هذه في 2 أس k ناقص
+
+662
+01:01:44,460 --> 01:01:52,180
+واحد الآن وزّع 2 أس k على هذه مكة كتلة واحدة
+
+663
+01:01:52,180 --> 01:01:58,010
+طلعت هذه بعدين 2 أس k ضربها في هذه هيها بعدين
+
+664
+01:01:58,010 --> 01:02:01,850
+الآن ناقص واحد ضربها في هذه كلها هذه عبارة عن
+
+665
+01:02:01,850 --> 01:02:05,230
+2 أس k ناقص 2 صارت فناقص الها بيصير ناقص
+
+666
+01:02:05,230 --> 01:02:08,150
+2 أس k زاد 2 ليش عمل هيك؟ بدي يحافظ على
+
+667
+01:02:08,150 --> 01:02:12,150
+هذه عشان يحصل على 2n زاد 2 الآن هذه مع
+
+668
+01:02:12,150 --> 01:02:16,270
+هذه بتروح بيصير هذا المقدار زاد 2 هذا المقدار
+
+669
+01:02:16,270 --> 01:02:23,330
+هو هذا أخذت 2 من الأولى صارت عبارة عن 2N زائد إيش 2
+
+670
+01:02:23,330 --> 01:02:30,670
+اطلع لفوقه الآن السؤال اللي بعده على السريعة اللي
+
+671
+01:02:30,670 --> 01:02:35,140
+هو F و G multiplicative functions F و G
+
+672
+01:02:35,140 --> 01:02:37,520
+Multiplicative Functions وقال لك إن الـ Two
+
+673
+01:02:37,520 --> 01:02:41,280
+Multiplicative Functions بتتساوى بس عند مين؟ عند
+
+674
+01:02:41,280 --> 01:02:44,700
+الـ Power of the Primes يعني قال لك F of Bk بتساوي
+
+675
+01:02:44,700 --> 01:02:50,580
+D of Bk معناته إن الـ F و G أشمالهم متساويات وقال
+
+676
+01:02:50,580 --> 01:02:59,420
+لك إذا كان الـ F of Gk بتساوي D of Bk عند الـ
+
+677
+01:02:59,420 --> 01:03:12,560
+Prime هتكون F هي نفس من الـ G في عندي يا شباب أنتم
+
+678
+01:03:12,560 --> 01:03:20,880
+مساجلين؟ خلاص بدأ أمشي بشواش من زمان شوف سؤال 18
+
+679
+01:03:20,880 --> 01:03:27,840
+معطيني f و g multiplicative ماشي الحاجة
+
+680
+01:03:27,840 --> 01:03:35,150
+multiplicative functions ومعطيني إن fof bk بتساوي
+
+681
+01:03:35,150 --> 01:03:39,690
+g of bk for every prime بتساوي g of bk for every
+
+682
+01:03:39,690 --> 01:03:39,910
+prime بتساوي g of bk for every prime بتساوي g of
+
+683
+01:03:39,910 --> 01:03:40,450
+bk for every prime بتساوي g of bk for every prime
+
+684
+01:03:40,450 --> 01:03:46,850
+بتساوي g of bk for every prime بتساوي g of bk for
+
+685
+01:03:46,850 --> 01:03:48,090
+every prime بتساوي g of bk for every prime بتساوي
+
+686
+01:03:48,090 --> 01:03:49,070
+prime بتساوي g of bk for every prime بتساوي g of
+
+687
+01:03:49,070 --> 01:03:50,690
+بتساوي g of bk for every prime بتساوي g of bk for
+
+688
+01:03:50,690 --> 01:03:53,470
+every prime بتساوي g of bk for every prime بتساوي
+
+689
+01:03:53,470 --> 01:03:59,450
+g of bk for every prime بتساوي g of bk for
+
+690
+01:04:02,940 --> 01:04:10,240
+الـ F بتساوي صفر أو الـ G بتساوي صفر على طول إذا F
+
+691
+01:04:10,240 --> 01:04:16,460
+بتساوي صفر صار G of B كي بتساوي صفر لكل Prime إذا
+
+692
+01:04:16,460 --> 01:04:21,000
+الـ G هتساوي إيش؟ صفر عارفين ليش؟ لأن الـ G of N
+
+693
+01:04:21,000 --> 01:04:23,620
+multiplicative أو الـ G multiplicative بتبصير G of
+
+694
+01:04:23,620 --> 01:04:27,160
+N بتساوي G of B واحد ألف واحد G of B اتنين ألف
+
+695
+01:04:27,160 --> 01:04:29,400
+اتنين و G of B أر الف أر كل واحدة من هنا صفر لأن
+
+696
+01:04:29,400 --> 01:04:36,330
+إيش بيبقى هنا صفر فاهمين؟ الآن لو كانت الـ F مش صفر
+
+697
+01:04:36,330 --> 01:04:46,550
+أكيد الـ G إيش معها؟ مش صفر لأنه صفر لو F مش صفر
+
+698
+01:04:46,550 --> 01:04:50,650
+و G بتساوي صفر معناته الـ F إيش معناه صفر ومن ثم
+
+699
+01:04:50,650 --> 01:04:53,830
+هتطلع عندي الـ F في واحد بتساوي G في واحد إيش
+
+700
+01:04:53,830 --> 01:05:01,880
+بتساوي؟ بتساوي واحد ماشي الحال الذي يصل إلى أنه في 
+
+701
+01:05:01,880 --> 01:05:04,080
+حالة الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ 
+
+702
+01:05:04,080 --> 01:05:04,260
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+703
+01:05:04,260 --> 01:05:05,400
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+704
+01:05:05,400 --> 01:05:07,120
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+705
+01:05:07,120 --> 01:05:08,560
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+706
+01:05:08,560 --> 01:05:17,200
+الـ الـ
+
+707
+01:05:17,200 --> 01:05:17,740
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+708
+01:05:17,740 --> 01:05:17,760
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+709
+01:05:17,760 --> 01:05:27,780
+الـ الـ الـ الـ الـ الـ الـ الـ الـ 
+
+710
+01:05:28,090 --> 01:05:33,520
+بتثبتها لكل N من ضمنها N  بتساوي واحد لو كانت الـ
+
+711
+01:05:33,520 --> 01:05:36,880
+F هي الـ Zero function Automatically الـ G هتصبح 
+
+712
+01:05:36,880 --> 01:05:40,940
+Zero function وخلصنا منها بيصير F عند الواحد وغير 
+
+713
+01:05:40,940 --> 01:05:43,300
+الواحد و الـ G عند الواحد وغير الواحد، كلها نصفار
+
+714
+01:05:43,300 --> 01:05:47,700
+لكن لو كانت الـ F مش الـ صفر و الـ G مش الـ صفر، طبيعًا
+
+715
+01:05:47,700 --> 01:05:54,220
+هتتبعها، بدي أحسب لكم الـ F of واحد إنها لازم 
+
+716
+01:05:54,220 --> 01:05:59,520
+تساوي الـ G of واحد، ماشي الحال، عندي الآن
+
+717
+01:06:03,600 --> 01:06:11,920
+F of واحد F is multiplicative إذا هتساوي F of واحد
+
+718
+01:06:11,920 --> 01:06:18,860
+عملناها قبل ايه؟ هتساوي F of واحد تربيع مظبوط؟ جيبها
+
+719
+01:06:18,860 --> 01:06:22,880
+على الجهة الثانية بيصير F تربيع of واحد ناقص F of 
+
+720
+01:06:22,880 --> 01:06:27,880
+واحد بيساوي صفر عملناها قبل ايه؟ F of واحد في F of
+
+721
+01:06:27,880 --> 01:06:35,130
+واحد ناقص واحد بيساوي صفر و F أصلا مش الـ صفر أه إذا 
+
+722
+01:06:35,130 --> 01:06:40,130
+عندي ال F في واحد إيش بتساوي؟ بتساوي واحد معايا؟
+
+723
+01:06:40,130 --> 01:06:46,150
+خلصنا و زيها ال G ما هي Multiplicated و مش صفر إذا
+
+724
+01:06:46,150 --> 01:06:49,190
+ال G بتساوي واحد طيب خلصنا من هذه ناخد إذا ال N
+
+725
+01:06:49,190 --> 01:06:54,270
+إياش N أكبر من واحد إذا ال N بتساوي بي واحد ألف
+
+726
+01:06:54,270 --> 01:07:01,270
+واحد لأن بي R ألف إياش ألف ار معايا إذا صارت
+
+727
+01:07:01,270 --> 01:07:06,190
+multiplicative إذا صارت f of n بساوي f بسؤال سهل
+
+728
+01:07:06,190 --> 01:07:11,470
+بي واحد الف واحد لعند بي ار الف ار ويساوي f of بي
+
+729
+01:07:11,470 --> 01:07:17,470
+واحد الف واحد لعند f of بي ار الف ار ويساوي من
+
+730
+01:07:17,470 --> 01:07:24,030
+المعطى g لو مultiplicative الثانية ترجع زي ما كانت
+
+731
+01:07:24,030 --> 01:07:33,360
+بساوي gof P1 ألفة واحد لعين PR ألفة R ويساوي GE of
+
+732
+01:07:33,360 --> 01:07:39,740
+R واضح؟ طيب إيه اللي بعده؟
+
+733
+01:07:39,740 --> 01:07:47,800
+خلاص اطلع اللي على الـ .. ال section اللي بعده لأ
+
+734
+01:07:47,800 --> 01:07:48,400
+جابل ال section 
+
+735
+01:07:55,560 --> 01:07:59,900
+أيوة خلّيني .. الأسئلة الستة اللي هو .. بس هنا تلت
+
+736
+01:07:59,900 --> 01:08:03,860
+أسئلة اللي أعطيكم إياها .. واحد و تلت و أربع ظنني
+
+737
+01:08:03,860 --> 01:08:09,540
+شوف .. الآن
+
+738
+01:08:09,540 --> 01:08:13,160
+بدنا نحكي عن Mobius inversion formula ال Mobius
+
+739
+01:08:13,160 --> 01:08:17,540
+inversion formula أو الأول إيش هي الـ .. M U of N
+
+740
+01:08:17,540 --> 01:08:23,680
+عارفينها، مذكرينها، بدنا نراجع
+
+741
+01:08:26,530 --> 01:08:36,770
+MU of N بساوي واحد أو صفر أو ناقص واحد أُس R مش
+
+742
+01:08:36,770 --> 01:08:43,050
+ذاكرين؟ MU of N بتساوي واحد لما N بتساوي واحد و
+
+743
+01:08:43,050 --> 01:08:48,990
+بساوي صفر إذا كان في B تربيع بقسم مين الـ N و
+
+744
+01:08:48,990 --> 01:08:52,970
+بساوي ناقص واحد أُس R إذا كانت M على صورة B واحد
+
+745
+01:08:52,970 --> 01:08:57,230
+لعند PR و بي واحد و بي اتنين و بي اتنين و بي اتنين
+
+746
+01:08:57,230 --> 01:08:57,510
+و بي اتنين و بي اتنين و بي اتنين
+
+747
+01:08:57,510 --> 01:08:59,010
+و بي اتنين و بي اتنين و بي اتنين 
+
+748
+01:08:59,010 --> 01:09:02,230
+و بي اتنين و بي اتنين و بي اتنين
+
+749
+01:09:02,230 --> 01:09:06,830
+و بي اتنين و بي اتنين و بي اتنين
+
+750
+01:09:06,830 --> 01:09:10,630
+و بي اتنين و بي اتنين و بي اتنين
+
+751
+01:09:10,630 --> 01:09:18,970
+و بي اتنين و بي اتنين و بي اتنين 
+
+752
+01:09:18,970 --> 01:09:22,870
+و بي اتنين و
+
+753
+01:09:22,870 --> 01:09:32,970
+بالإن السبب بسيط أن أي أربع أرقام متتالية لازم 
+
+754
+01:09:32,970 --> 01:09:40,150
+واحد فيها يكون على صورة 4K مظبوط؟
+
+755
+01:09:40,150 --> 01:09:47,470
+لأن لو كان هذا 4K خلصنا لو هذا 4K زائد واحد بيطلع 
+
+756
+01:09:47,470 --> 01:09:52,780
+هذا 4K زائد 4 اللي هو 4M لو كان أربعة كيه زائد
+
+757
+01:09:52,780 --> 01:09:55,780
+اثنين بيطلع هذا الأعلى أربعة كيه أربعة كيه زائد
+
+758
+01:09:55,780 --> 01:10:01,700
+ثلاثة بيطلع هذا واضح إذا any number any اللي هو 
+
+759
+01:10:01,700 --> 01:10:07,160
+four consecutive numbers must have one of the four
+
+760
+01:10:07,160 --> 01:10:13,770
+أربعة كيه ماشي الحال إذا واحد من هذول بقسم مين؟ 
+
+761
+01:10:13,770 --> 01:10:19,090
+الأربعة يعني فيه اثنين تربيع يعني ميوه تبعته إيش
+
+762
+01:10:19,090 --> 01:10:24,570
+بتساوي؟ يعني إذا حصل الربيع إيش هيساوي؟ يلا اللي
+
+763
+01:10:24,570 --> 01:10:33,090
+بعده اللي بعده بقولك لأي عدد لأي عدد M أكبر 
+
+764
+01:10:33,090 --> 01:10:39,590
+أو يساوي واحد اثبت إن المجموع للـMew of K factorial
+
+765
+01:10:40,670 --> 01:10:45,830
+كي من عند واحد إلى مالانهاية ولا عند ان حتى لو
+
+766
+01:10:45,830 --> 01:10:51,650
+مالانهاية بيساوي إيش بيساوي واحد ال summation هذا 
+
+767
+01:10:51,650 --> 01:10:56,690
+بيساوي ميو اف واحد فكتوريال زائد ميو اف اثنين
+
+768
+01:10:56,690 --> 01:11:01,750
+فكتوريال زائد ميو اف ثلاثة فكتوريال زائد ميو اف أربعة 
+
+769
+01:11:01,750 --> 01:11:09,610
+فكتوريال زائد زائد ميو اف ان فكتوريال اه 
+
+770
+01:11:11,420 --> 01:11:15,620
+الآن أكبر
+
+771
+01:11:15,620 --> 01:11:24,820
+أو يساوي ثلاثة اه لأن فعلنا اثنين لأ بتصير اثنين 
+
+772
+01:11:24,820 --> 01:11:31,800
+ثلاثة مظبوط طيب هنا واحد صح هنا اللي هي اثنين ناقص
+
+773
+01:11:31,800 --> 01:11:38,540
+واحد مظبوط اثنين سالب واحد الثلاثة 
+
+774
+01:11:40,090 --> 01:11:46,050
+ثلاثة في اثنين اللي هو واحد عارفين مش بساومك ولا 
+
+775
+01:11:46,050 --> 01:11:49,550
+كذا؟ اه لاتكونوا مش فاهمين اش بساومك زائد واحد
+
+776
+01:11:49,550 --> 01:11:56,250
+واللي بعده كله فيه أربعات يعني فيه اثنين تربيعات
+
+777
+01:11:56,250 --> 01:12:02,450
+يعني كلها زائد صفر ويساوي هذا مع حد أو مع اللي 
+
+778
+01:12:02,450 --> 01:12:09,390
+جابله ويساوي واحد واضح اه الفكرة واضحة الـAسؤال 
+
+779
+01:12:09,390 --> 01:12:18,930
+ثلاثة let let let n بتساوي بي واحد كي واحد بي ار
+
+780
+01:12:18,930 --> 01:12:23,950
+كي ار بي برايم factorization of n أكبر من واحد إذا
+
+781
+01:12:23,950 --> 01:12:28,250
+كانت f is multiplicative prove that اللي موجود
+
+782
+01:12:28,250 --> 01:12:37,160
+انتبهوا على دي خليني برضه أذكركم بعض النظريات أو 
+
+783
+01:12:37,160 --> 01:12:42,860
+المادة النظرية اللي موجودة في ال section هذا بدي
+
+784
+01:12:42,860 --> 01:12:48,140
+الآن F multiplicative السؤال
+
+785
+01:12:48,140 --> 01:12:58,900
+الثلاثة implies أنه summation mu of D F of D D
+
+786
+01:12:58,900 --> 01:13:07,800
+بتجسم N بساوي ال product لواحد ناقص F of BiI من
+
+787
+01:13:07,800 --> 01:13:20,680
+واحد لعند مين مع عند أنا واضح اه؟ طيب عندي F
+
+788
+01:13:20,680 --> 01:13:23,760
+is multiplicative مع أن في نظرية بتحكي على طول 
+
+789
+01:13:23,760 --> 01:13:29,540
+بالجيبة F multiplicative و Mu multiplicative هتطلع
+
+790
+01:13:29,540 --> 01:13:33,400
+عندي Mu في F أشمالها is multiplicative بتعرفوا
+
+791
+01:13:33,400 --> 01:13:42,030
+تعملوها اه؟ لو سمينا هذه G of D بسوء Mu of D في F
+
+792
+01:13:42,030 --> 01:13:54,000
+of D G of D1 D2 بسوء Mu of D1D2 FD1 FD2 FD2 FD1
+
+793
+01:13:54,000 --> 01:13:56,820
+FD2 FD2 FD2 FD2 FD2 FD2 FD2 FD2 FD2 FD2 FD2 FD2
+
+794
+01:13:56,820 --> 01:14:07,900
+FD2 FD2 FD2 FD2 FD2 FD2 FD2
+
+795
+01:14:08,670 --> 01:14:12,730
+معايا نظرية قبل شوية أخذنا قول لمجموع اللي هو جوا 
+
+796
+01:14:12,730 --> 01:14:15,870
+ال summation هذا is multiplication و ال summation
+
+797
+01:14:15,870 --> 01:14:18,410
+على D بتقسم N إذا ال summation نفسه إيش ماله
+
+798
+01:14:18,410 --> 01:14:25,430
+Multiplicative إذا صار عندي F of N بساوي summation
+
+799
+01:14:25,430 --> 01:14:34,750
+Mu of D F of D D بتقسم N is multiplicative أن إيش
+
+800
+01:14:34,750 --> 01:14:44,430
+ما تينيها بتساوي بتساوي اللي فوق صح؟ الآن بيصير عندي
+
+801
+01:14:44,430 --> 01:14:53,850
+F of N F of N بيساوي ال product لمين؟ إيش الآن 
+
+802
+01:14:53,850 --> 01:14:57,770
+ماخدها أنا؟ P1 ألف واحد عند PR ألف ألف
+
+803
+01:14:57,770 --> 01:15:03,930
+Multiplicative إذا بيصير ال product لل F of PI KI 
+
+804
+01:15:03,930 --> 01:15:06,430
+ولا الف I؟ KI مظبوط؟
+
+805
+01:15:08,390 --> 01:15:16,110
+I من عند واحد لعند إيش R فاهمين أشي اللي بعمله لأن
+
+806
+01:15:16,110 --> 01:15:25,010
+F مالها Multiplicative ويساوي نوجد من F of BIKI F
+
+807
+01:15:25,010 --> 01:15:30,830
+of BIKI من هنا هيها ال summation يعني بيساوي ال
+
+808
+01:15:30,830 --> 01:15:35,000
+productI من عند 1 لعند R لـSummation مين
+
+809
+01:15:35,000 --> 01:15:41,960
+الـSummation؟ الـSummation ميو أف دي F of D D
+
+810
+01:15:41,960 --> 01:15:51,800
+بتقسم بي آي كي آي معايا؟ الآن القواسم بي آي كي آي
+
+811
+01:15:51,800 --> 01:16:03,810
+واحد بي تربيع و البدايات لعند بي أصف كي آي أه الآن 
+
+812
+01:16:03,810 --> 01:16:10,370
+عند الواحد و ال بي واحد الهنقية و الباد أسفار مافي 
+
+813
+01:16:10,370 --> 01:16:15,870
+ليش بيساوي ال product I من عند واحد لعند R لأ
+
+814
+01:16:15,870 --> 01:16:23,830
+summation اللي هو ميو of واحد F of واحد زائد ميو of 
+
+815
+01:16:23,830 --> 01:16:34,160
+بي I F of بي I زائد ميو of بي I تربيع f of bi تربيع
+
+816
+01:16:34,160 --> 01:16:43,900
+زائد لما أصلاً عند آخر واحد ميو of bi ki f of bi أس 
+
+817
+01:16:43,900 --> 01:16:50,180
+ki صح ولا لأ هذه من عند هنا وطالع لميو تبعتنا ايه
+
+818
+01:16:50,180 --> 01:16:57,890
+إيش صفر اه بيظل مين عندي هذا وهذا ويساوي الـ
+
+819
+01:16:57,890 --> 01:17:02,690
+Product I من عند واحد لعند R لأ الـ Mu of واحد ده 
+
+820
+01:17:02,690 --> 01:17:10,230
+إيش بيساوي واحد الآن عندي F of واحد نفسها بيصير F
+
+821
+01:17:10,230 --> 01:17:19,830
+of واحد الآن Mu of BY سالب واحد أيها الـ Mu of الـ 
+
+822
+01:17:19,830 --> 01:17:25,990
+Prime اللي هو ناقص واحد قصة R مش غير Prime واحد أي 
+
+823
+01:17:25,990 --> 01:17:30,810
+سؤال؟ إذا في إيش مش واضح بعيده ميوف في اثنين إيش
+
+824
+01:17:30,810 --> 01:17:35,910
+متساوي ميوف
+
+825
+01:17:35,910 --> 01:17:40,010
+ثلاثة ميوف 
+
+826
+01:17:40,010 --> 01:17:46,650
+خمسة إذا ميوف أي برايم إيش متساوي ميوف بي واحد في 
+
+827
+01:17:46,650 --> 01:17:52,390
+بي اثنين سالب واحد وسط اثنين يعني إيش معناه واحد
+
+828
+01:17:54,410 --> 01:18:02,390
+واضح؟ طيب إذا u of bi عبارة عن كدا سالب واحد
+
+829
+01:18:02,390 --> 01:18:11,810
+بيصير ناقص f of bi فهو المطلوب صارت عندي f of n
+
+830
+01:18:11,810 --> 01:18:19,170
+بساوي هذه f of n مين هي ال summation تمام مرة يا
+
+831
+01:18:19,170 --> 01:18:24,860
+شباب f of n مين هي ال Summation و F of N مين هي
+
+832
+01:18:24,860 --> 01:18:30,340
+طلعت؟ إذا صار عند ال Summation لـ Mu of D في F of 
+
+833
+01:18:30,340 --> 01:18:35,400
+D D بتقسم N بساوي هذا ال product مين ال product
+
+834
+01:18:35,400 --> 01:18:43,180
+هذا؟ F of 1 ناقص F of B 1 لما أصل عند F of 1 ناقص 
+
+835
+01:18:43,180 --> 01:18:53,390
+F of B R و ال F of 1 و ال F of 1 ده إيش بتساوي؟ لأن
+
+836
+01:18:53,390 --> 01:19:01,510
+F أشمالها multiplicative واضح وهو المقلد يعني 
+
+837
+01:19:01,510 --> 01:19:05,790
+كل F في واحد بيقعش في واحد اللي بعده نيجي لسؤال
+
+838
+01:19:05,790 --> 01:19:11,600
+أربعة السؤال الرابع السؤال الرابع if n أكبر من واحد
+
+839
+01:19:11,600 --> 01:19:14,680
+has a prime factorization n بسوء بي واحد كواحد عند 
+
+840
+01:19:14,680 --> 01:19:19,160
+بي ار كي ار used problem 4 to establish the 
+
+841
+01:19:19,160 --> 01:19:22,220
+following the summation μ f of d τ f of d d
+
+842
+01:19:22,220 --> 01:19:27,680
+بتكسب إن بيساوي ناقص واحد أيش أسر اللي عندي الـ τ 
+
+843
+01:19:27,680 --> 01:19:31,680
+is multiplicative، مظبوط؟ احنا قبل شوية أثبتنا 
+
+844
+01:19:31,680 --> 01:19:39,120
+summation μ f of d  F of D دي بتجسم الـ N إيش
+
+845
+01:19:39,120 --> 01:19:44,840
+بيساوي اللي هو عبارة عن 1 أو F اللي هو الـ ..
+
+846
+01:19:44,840 --> 01:19:47,320
+ذاكروني الـ product
+
+847
+01:19:50,540 --> 01:19:57,000
+1- F of B I I من عند 1 لعند R صح ولا لأ هذا اللي
+
+848
+01:19:57,000 --> 01:20:02,620
+أثبتناه قبل شوية الآن بدي أستخدم مين لهذا السؤال
+
+849
+01:20:02,620 --> 01:20:06,880
+في تطبيقه على الحالات اللي معطيني إياها بده لأن الـ
+
+850
+01:20:06,880 --> 01:20:12,800
+summation لـ μ of D هذا أيه 4A بده الـ summation
+
+851
+01:20:12,800 --> 01:20:20,110
+لـ μ of D τ of D دي بتجسم الـ N بيساوي اللي هو
+
+852
+01:20:20,110 --> 01:20:28,370
+عبارة عن الـ product لـ 1 ناقص
+
+853
+01:20:28,370 --> 01:20:35,230
+τ of Bi من عند 1 لعند مين R عدد الـ
+
+854
+01:20:35,230 --> 01:20:41,230
+divisors للـ Bi قداش 1 1 2 لأن الـ
+
+855
+01:20:41,230 --> 01:20:47,440
+divisors اللي هي الواحد و الـ Bi فاهمين Y بيساوي هو
+
+856
+01:20:47,440 --> 01:20:52,440
+الـ product لـ 1 ناقص 2 قاعدين عند 1 لعند
+
+857
+01:20:52,440 --> 01:20:55,820
+R Y بيساوي كم مرة معدودات هذول R من المرات اللي
+
+858
+01:20:55,820 --> 01:21:03,100
+بيساوي ناقص 1 قُس R نيجي لـ B الـ summation من مين
+
+859
+01:21:03,100 --> 01:21:12,200
+بده μ of D σ of D دي بتكسب 100 لأن بيساوي
+
+860
+01:21:12,200 --> 01:21:17,520
+اللي هو الـ product لـ 1 ناقص الـ σ of Bi I من
+
+861
+01:21:17,520 --> 01:21:23,360
+عند 1 لعند R واضح ها صار سهل لو بدك تيجي
+
+862
+01:21:23,360 --> 01:21:26,020
+توجه تقول حاجة لك دي عمال مشكلة بس احنا بنين على
+
+863
+01:21:26,020 --> 01:21:32,680
+السؤال قبله وبيساوي اللي هو الـ product I من عند 1
+
+864
+01:21:32,680 --> 01:21:36,960
+لعند R لـ 1 ناقص مجموع الـ divisors ده الـ Bi
+
+865
+01:21:36,960 --> 01:21:43,380
+اللي هي 1 زائد Bi مظبوط ناقص 1 ناقص Bi
+
+866
+01:21:43,380 --> 01:21:50,360
+صح اللي عملته وبيساوي اللي هو الـ product لـ ناقص Bi
+
+867
+01:21:50,360 --> 01:22:01,370
+I من عند 1 لعند R وبيساوي N صح ناقص 1-R B1
+
+868
+01:22:01,370 --> 01:22:08,670
+BR وهو المطلوب والبعد
+
+869
+01:22:08,670 --> 01:22:15,310
+هو بنفس الأسلوب μ of D على D خلّيني أعملها بالمرة
+
+870
+01:22:15,310 --> 01:22:21,570
+Summation of μ of C الآن C
+
+871
+01:22:21,570 --> 01:22:27,370
+μ of D على D بيصير الـ function اللي عندنا مين هي
+
+872
+01:22:27,370 --> 01:22:37,690
+1 على D معايا اللي هي بتساوي summation μ of D في F
+
+873
+01:22:37,690 --> 01:22:44,150
+of D D بتجسم N where F of D إيش هتساوي يا شباب
+
+874
+01:22:44,150 --> 01:22:49,930
+1 على D صح ولا لا الـ 1 على D is
+
+875
+01:22:49,930 --> 01:22:54,030
+multiplicative عملناها إذا صار عندي عبارة عن π
+
+876
+01:22:54,030 --> 01:23:03,570
+في 1 ناقص F من مين؟ من Bi من Bi من Bi 
+
+877
+01:23:03,570 --> 01:23:07,370
+من Bi من Bi من Bi من Bi من Bi من Bi
+
+878
+01:23:07,370 --> 01:23:07,990
+من Bi من Bi من Bi من Bi من Bi
+
+879
+01:23:07,990 --> 01:23:08,210
+من Bi من Bi من Bi من Bi من Bi
+
+880
+01:23:08,210 --> 01:23:15,810
+من Bi من Bi من Bi من Bi من Bi
+
+881
+01:23:15,810 --> 01:23:26,930
+من Bi من Bi من Bi من Bi
+
+882
+01:23:29,360 --> 01:23:36,240
+انزل الـ .. الآن D بيقف D بنفس الأسلوب F of D
+
+883
+01:23:36,240 --> 01:23:39,500
+بتساوي D في هذه الحالة و الـ D is multiplicative
+
+884
+01:23:39,500 --> 01:23:45,460
+إذا بيصير 1 ناقص F of P1 اللي هي P1 لما
+
+885
+01:23:45,460 --> 01:23:50,080
+أصل عنده 1 ناقص F of PR اللي هي PR فبتصير اللي
+
+886
+01:23:50,080 --> 01:23:55,940
+هو على طول مباشرة وإلى لقاء آخر إن شاء الله الله
+
+887
+01:23:55,940 --> 01:23:56,400
+عفواكم 
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..2c46579a7af9d3db026698d5801478b0799bdf01
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4795, "start": 19.35, "end": 47.95, "text": "بسم الله الرحمن الرحيم محاضرة رقم 27 وهي عبارة عن مناقشة لـ Chapter 6 سنناقش اليوم موضوعين الموضوع الأول اللي هو number and sum of divisors والموضوع التاني اللي هو Mobius inversion formula نبدأ ب 6 واحد اللي هو number and sum of divisors", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 3714, 5016, 46958, 25720, 12602, 4587, 2304, 7634, 37037, 1829, 6225, 3555, 9640, 3660, 18871, 3714, 8315, 4587, 8592, 3660, 5296, 39184, 18874, 1386, 8608, 1863, 8315, 4587, 8592, 45595, 20498, 3714, 2407, 11242, 45367, 9957, 9673, 2407, 11242, 45367, 16247, 12610, 13672, 1829, 31439, 1230, 293, 2408, 295, 25974, 830, 4032, 45340, 2407, 11242, 45367, 16712, 7649, 1829, 13672, 1829, 31439, 37920, 4872, 43576, 8513, 8717, 44510, 10721, 4724, 1386, 36764, 24401, 13672, 1829, 31439, 1230, 293, 2408, 295, 25974, 830], "avg_logprob": -0.14121942691828893, "compression_ratio": 1.7019230769230769, 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37.99, "word": " of", "probability": 0.9833984375}, {"start": 37.99, "end": 38.75, "word": " divisors", "probability": 0.987060546875}, {"start": 38.75, "end": 39.91, "word": " والموضوع", "probability": 0.881396484375}, {"start": 39.91, "end": 40.31, "word": " التاني", "probability": 0.94140625}, {"start": 40.31, "end": 40.47, "word": " اللي", "probability": 0.939453125}, {"start": 40.47, "end": 40.67, "word": " هو", "probability": 0.98681640625}, {"start": 40.67, "end": 41.27, "word": " Mobius", "probability": 0.7000732421875}, {"start": 41.27, "end": 41.81, "word": " inversion", "probability": 0.6025390625}, {"start": 41.81, "end": 42.61, "word": " formula", "probability": 0.96630859375}, {"start": 42.61, "end": 43.27, "word": " نبدأ", "probability": 0.9348958333333334}, {"start": 43.27, "end": 43.35, "word": " ب", "probability": 0.83349609375}, {"start": 43.35, "end": 43.53, "word": " 6", "probability": 0.415771484375}, {"start": 43.53, "end": 44.01, "word": " واحد", "probability": 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" برايم", "probability": 0.8375651041666666}], "temperature": 1.0}, {"id": 21, "seek": 56900, "start": 557.24, "end": 569.0, "text": "وبعد ما أحسب للـ prime بحسب لمين للـ function نفسها خصوصاً إذا كانت الـ function is multiplicative بتصير الأمور سهلة نشوف أشي المقصود", "tokens": [37746, 22488, 19446, 5551, 5016, 35457, 24976, 39184, 5835, 4724, 5016, 35457, 32767, 9957, 24976, 39184, 2445, 8717, 36178, 11296, 16490, 9381, 2407, 9381, 995, 14111, 11933, 15730, 25961, 2655, 2423, 39184, 2445, 307, 17596, 1166, 39894, 9381, 13546, 16247, 2304, 13063, 8608, 3224, 37977, 8717, 8592, 38688, 5551, 8592, 1829, 9673, 4587, 9381, 23328], "avg_logprob": -0.2783203178218433, "compression_ratio": 1.3529411764705883, "no_speech_prob": 0.0, "words": [{"start": 557.24, "end": 557.96, "word": "وبعد", "probability": 0.716796875}, {"start": 557.96, "end": 558.08, "word": " ما", "probability": 0.28125}, {"start": 558.08, "end": 558.34, "word": " أحسب", "probability": 0.7572428385416666}, {"start": 558.34, 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odd", "probability": 0.466064453125}, {"start": 721.33, "end": 722.01, "word": " بدا", "probability": 0.211669921875}, {"start": 722.01, "end": 722.31, "word": " تثبت", "probability": 0.87841796875}, {"start": 722.31, "end": 722.49, "word": " لك", "probability": 0.6488037109375}, {"start": 722.49, "end": 722.59, "word": " أن", "probability": 0.53857421875}, {"start": 722.59, "end": 722.89, "word": " n", "probability": 0.27197265625}, {"start": 722.89, "end": 723.15, "word": " إيش", "probability": 0.6312255859375}, {"start": 723.15, "end": 723.27, "word": " ما", "probability": 0.80615234375}, {"start": 723.27, "end": 723.41, "word": " لها", "probability": 0.842529296875}, {"start": 723.41, "end": 723.93, "word": " perfect", "probability": 0.81494140625}, {"start": 723.93, "end": 725.19, "word": " square", "probability": 0.705078125}, {"start": 725.19, "end": 725.61, "word": " تاو", "probability": 0.6787923177083334}, {"start": 725.61, "end": 725.75, "word": " of", "probability": 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731.73, "word": " square", "probability": 0.90185546875}], "temperature": 1.0}, {"id": 28, "seek": 75794, "start": 733.96, "end": 757.94, "text": "الان احنا مفترضينها من رأس الدور انها اكبر من 100 من 1 اذا الان تابعتنا بقدر اكتبها على صورة by unique by unique factorization theorem على صورة اللي هو product of power of primes بي واحد بيتا واحد لعند بي ار بيتا ار واضح؟ طيب احسب للتاولة هذه اذا", "tokens": [6027, 7649, 1975, 5016, 8315, 3714, 5172, 2655, 43042, 9957, 11296, 9154, 12602, 10721, 3794, 32748, 13063, 16472, 11296, 1975, 4117, 26890, 9154, 2319, 9154, 502, 1975, 15730, 2423, 7649, 6055, 16758, 34268, 8315, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 11296, 15844, 20328, 13063, 3660, 538, 3845, 538, 3845, 5952, 2144, 20904, 15844, 20328, 13063, 3660, 13672, 1829, 31439, 1674, 295, 1347, 295, 582, 1532, 4724, 1829, 36764, 24401, 4724, 36081, 995, 36764, 24401, 5296, 3615, 41260, 4724, 1829, 1975, 2288, 4724, 36081, 995, 1975, 2288, 4032, 46958, 5016, 22807, 23032, 1829, 3555, 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صار", "probability": 0.98046875}, {"start": 1544.41, "end": 1544.81, "word": " عندي", "probability": 0.9541015625}, {"start": 1544.81, "end": 1545.93, "word": " هذا", "probability": 0.95263671875}, {"start": 1545.93, "end": 1546.77, "word": " واحد", "probability": 0.933837890625}, {"start": 1546.77, "end": 1547.15, "word": " زائد", "probability": 0.7908528645833334}, {"start": 1547.15, "end": 1547.43, "word": " بي", "probability": 0.477294921875}, {"start": 1547.43, "end": 1547.57, "word": " اي", "probability": 0.736328125}, {"start": 1547.57, "end": 1547.87, "word": " زائد", "probability": 0.8865559895833334}, {"start": 1547.87, "end": 1548.15, "word": " بي", "probability": 0.983154296875}, {"start": 1548.15, "end": 1548.37, "word": " اي", "probability": 0.888671875}, {"start": 1548.37, "end": 1548.83, "word": " بيتا", "probability": 0.6796061197916666}, {"start": 1548.83, "end": 1549.27, "word": " اي", "probability": 0.862060546875}, {"start": 1549.27, "end": 1549.89, "word": " is", 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"word": " على", "probability": 0.283447265625}, {"start": 2116.6, "end": 2116.88, "word": " الحالة", "probability": 0.7408040364583334}, {"start": 2116.88, "end": 2117.06, "word": " سؤال", "probability": 0.91796875}, {"start": 2117.06, "end": 2117.28, "word": " قبل", "probability": 0.5921630859375}, {"start": 2117.28, "end": 2117.48, "word": " الـ", "probability": 0.6044921875}, {"start": 2117.48, "end": 2117.66, "word": " 1", "probability": 0.53173828125}, {"start": 2117.66, "end": 2117.9, "word": " على", "probability": 0.4443359375}, {"start": 2117.9, "end": 2118.02, "word": " D", "probability": 0.7060546875}, {"start": 2118.02, "end": 2118.22, "word": " لما", "probability": 0.865234375}, {"start": 2118.22, "end": 2118.46, "word": " أخد", "probability": 0.8294270833333334}, {"start": 2118.46, "end": 2118.84, "word": " فانشين", "probability": 0.59521484375}, {"start": 2118.84, "end": 2118.94, "word": " F", "probability": 0.58642578125}, {"start": 2118.94, "end": 2119.06, "word": " of", "probability": 0.38134765625}, {"start": 2119.06, "end": 2119.16, "word": " D", "probability": 0.9853515625}, {"start": 2119.16, "end": 2119.4, "word": " بيسوي", "probability": 0.6575927734375}, {"start": 2119.4, "end": 2119.54, "word": " 1", "probability": 0.91650390625}, {"start": 2119.54, "end": 2119.7, "word": " على", "probability": 0.8603515625}, {"start": 2119.7, "end": 2119.84, "word": " D", "probability": 0.9912109375}, {"start": 2119.84, "end": 2120.66, "word": " multiplicative", "probability": 0.5758056640625}, {"start": 2120.66, "end": 2122.02, "word": " برضه", "probability": 0.9239908854166666}, {"start": 2122.02, "end": 2122.36, "word": " اللي", "probability": 0.85205078125}, {"start": 2122.36, "end": 2122.72, "word": " هو", "probability": 0.9697265625}, {"start": 2122.72, "end": 2123.46, "word": " شعوري", "probability": 0.9169921875}, {"start": 2123.46, "end": 2123.58, "word": " ان", "probability": 0.2467041015625}, {"start": 2123.58, "end": 2123.78, "word": " هو", "probability": 0.3203125}, {"start": 2123.78, "end": 2124.76, "word": " multiplicative", "probability": 0.857421875}, {"start": 2124.76, "end": 2124.88, "word": " و", "probability": 0.42236328125}, {"start": 2124.88, "end": 2125.32, "word": " هتلاقي", "probability": 0.8409423828125}, {"start": 2125.32, "end": 2125.94, "word": " انه", "probability": 0.801025390625}, {"start": 2125.94, "end": 2126.36, "word": " فعلا", "probability": 0.9480794270833334}, {"start": 2126.36, "end": 2127.1, "word": " multiplicative", "probability": 0.730712890625}, {"start": 2127.1, "end": 2127.62, "word": " وسادف", "probability": 0.6102701822916666}, {"start": 2127.62, "end": 2127.8, "word": " بقى", "probability": 0.87841796875}, {"start": 2127.8, "end": 2128.0, "word": " انها", "probability": 0.840576171875}, {"start": 2128.0, "end": 2128.68, "word": " multiplicative", "probability": 0.8896484375}, {"start": 2128.68, "end": 2129.6, "word": " اذا", "probability": 0.6971435546875}, {"start": 2129.6, "end": 2129.96, "word": " اول", "probability": 0.78369140625}, {"start": 2129.96, "end": 2130.18, "word": " اشي", "probability": 0.8406575520833334}, {"start": 2130.18, "end": 2130.42, "word": " بدي", "probability": 0.58251953125}, {"start": 2130.42, "end": 2130.84, "word": " احاول", "probability": 0.76226806640625}, {"start": 2130.84, "end": 2131.76, "word": " اجايف", "probability": 0.758544921875}, {"start": 2131.76, "end": 2132.16, "word": " هذه", "probability": 0.65380859375}, {"start": 2132.16, "end": 2133.26, "word": " للصورة", "probability": 0.95458984375}, {"start": 2133.26, "end": 2133.56, "word": " هذه", "probability": 0.7578125}, {"start": 2133.56, "end": 2134.5, "word": " بدي", "probability": 0.827880859375}, {"start": 2134.5, "end": 2134.74, "word": " اقول", "probability": 0.911865234375}, {"start": 2134.74, "end": 2134.84, "word": " له", "probability": 0.4765625}, {"start": 2134.84, "end": 2135.26, "word": " let", "probability": 0.6083984375}, {"start": 2135.26, "end": 2136.8, "word": " F", "probability": 0.85546875}, {"start": 2136.8, "end": 2137.04, "word": " of", "probability": 0.92529296875}, {"start": 2137.04, "end": 2137.36, "word": " D", "probability": 0.99462890625}, {"start": 2137.36, "end": 2138.84, "word": " بيسوي", "probability": 0.7939453125}, {"start": 2138.84, "end": 2139.14, "word": " 1", "probability": 0.9677734375}, {"start": 2139.14, "end": 2139.5, "word": " على", "probability": 0.90576171875}, {"start": 2139.5, "end": 2139.8, "word": " D", "probability": 0.9931640625}, {"start": 2139.8, "end": 2140.56, "word": " ماشي", "probability": 0.8219401041666666}, {"start": 2140.56, "end": 2141.64, "word": " الحالة", "probability": 0.762451171875}, {"start": 2141.64, "end": 2142.02, "word": " الان", "probability": 0.7200927734375}, {"start": 2142.02, "end": 2142.58, "word": " F", "probability": 0.875}, {"start": 2142.58, "end": 2143.22, "word": " بتدعي", "probability": 0.8494873046875}, {"start": 2143.22, "end": 2143.44, "word": " انها", "probability": 0.944091796875}, {"start": 2143.44, "end": 2144.24, "word": " multiplicative", "probability": 0.925048828125}], "temperature": 1.0}, {"id": 83, "seek": 215871, "start": 2144.95, "end": 2158.71, "text": "ليش Multiplicative؟ تستسهل Let D1 وD2 element in Z بحيث الـ Greatest common divisor بينهما يكون 1 وحسبني F of D1 في D2 بساوة", "tokens": [20292, 8592, 29238, 4770, 1166, 22807, 6055, 14851, 3794, 3224, 1211, 961, 413, 16, 4032, 35, 17, 4478, 294, 1176, 4724, 5016, 1829, 12984, 2423, 39184, 3769, 377, 2689, 25974, 284, 49374, 3224, 15042, 7251, 30544, 502, 4032, 5016, 35457, 22653, 479, 295, 413, 16, 8978, 413, 17, 4724, 3794, 995, 2407, 3660], "avg_logprob": -0.4401041556287695, "compression_ratio": 1.1073825503355705, "no_speech_prob": 0.0, "words": [{"start": 2144.95, "end": 2145.25, "word": "ليش", "probability": 0.5889892578125}, {"start": 2145.25, "end": 2145.97, "word": " Multiplicative؟", "probability": 0.626861572265625}, {"start": 2145.97, "end": 2146.91, "word": " تستسهل", "probability": 0.87744140625}, {"start": 2146.91, "end": 2148.17, "word": " Let", "probability": 0.2393798828125}, {"start": 2148.17, "end": 2149.07, "word": " D1", "probability": 0.833251953125}, {"start": 2149.07, "end": 2149.63, "word": " وD2", "probability": 0.86767578125}, {"start": 2149.63, "end": 2150.09, "word": " element", "probability": 0.58642578125}, {"start": 2150.09, "end": 2150.33, "word": " in", "probability": 0.86669921875}, {"start": 2150.33, "end": 2150.55, "word": " Z", "probability": 0.79248046875}, {"start": 2150.55, "end": 2150.85, "word": " بحيث", "probability": 0.8345947265625}, {"start": 2150.85, "end": 2151.03, "word": " الـ", "probability": 0.62060546875}, {"start": 2151.03, "end": 2151.35, "word": " Greatest", "probability": 0.27691650390625}, {"start": 2151.35, "end": 2151.49, "word": " common", "probability": 0.393310546875}, {"start": 2151.49, "end": 2151.93, "word": " divisor", "probability": 0.7255859375}, {"start": 2151.93, "end": 2152.25, "word": " بينهما", "probability": 0.7233072916666666}, {"start": 2152.25, "end": 2152.37, "word": " يكون", "probability": 0.434814453125}, {"start": 2152.37, "end": 2153.55, "word": " 1", "probability": 0.40673828125}, {"start": 2153.55, "end": 2154.97, "word": " وحسبني", "probability": 0.60711669921875}, {"start": 2154.97, "end": 2155.33, "word": " F", "probability": 0.69140625}, {"start": 2155.33, "end": 2156.17, "word": " of", "probability": 0.306640625}, {"start": 2156.17, "end": 2156.93, "word": " D1", "probability": 0.949462890625}, {"start": 2156.93, "end": 2157.17, "word": " في", "probability": 0.5537109375}, {"start": 2157.17, "end": 2157.81, "word": " D2", "probability": 0.99072265625}, {"start": 2157.81, "end": 2158.71, "word": " بساوة", "probability": 0.6634765625}], "temperature": 1.0}, {"id": 84, "seek": 218683, "start": 2159.69, "end": 2186.83, "text": "اللي هو حسب القانون هو 1 على D1 في D2 صح ولا لأ اللي هي بيساوي 1 على D1 في 1 على D2 ويساوي F of D1 في F of D إذا واضح أن F is a multiplicative function ماشي الحال طيب مدام F multiplicative بتشجعني أن أقول let F of N", "tokens": [6027, 20292, 31439, 11331, 35457, 25062, 7649, 11536, 31439, 502, 15844, 413, 16, 8978, 413, 17, 20328, 5016, 49429, 5296, 10721, 13672, 1829, 39896, 4724, 1829, 3794, 995, 45865, 502, 15844, 413, 16, 8978, 502, 15844, 413, 17, 4032, 1829, 3794, 995, 45865, 479, 295, 413, 16, 8978, 479, 295, 413, 11933, 15730, 4032, 46958, 5016, 14739, 479, 307, 257, 17596, 1166, 2445, 3714, 33599, 1829, 21542, 6027, 23032, 1829, 3555, 3714, 3215, 10943, 479, 17596, 1166, 39894, 8592, 7435, 3615, 22653, 14739, 5551, 39648, 718, 479, 295, 426], "avg_logprob": -0.18107638623979355, "compression_ratio": 1.6197916666666667, "no_speech_prob": 1.0728836059570312e-06, "words": [{"start": 2159.69, "end": 2160.01, "word": "اللي", "probability": 0.744873046875}, {"start": 2160.01, "end": 2160.23, "word": " هو", "probability": 0.94384765625}, {"start": 2160.23, "end": 2160.55, "word": " حسب", 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0.28173828125}, {"start": 2165.47, "end": 2165.87, "word": " بيساوي", "probability": 0.81865234375}, {"start": 2165.87, "end": 2166.17, "word": " 1", "probability": 0.8857421875}, {"start": 2166.17, "end": 2166.39, "word": " على", "probability": 0.84814453125}, {"start": 2166.39, "end": 2167.09, "word": " D1", "probability": 0.974365234375}, {"start": 2167.09, "end": 2167.33, "word": " في", "probability": 0.9140625}, {"start": 2167.33, "end": 2167.61, "word": " 1", "probability": 0.94140625}, {"start": 2167.61, "end": 2167.91, "word": " على", "probability": 0.908203125}, {"start": 2167.91, "end": 2168.57, "word": " D2", "probability": 0.995361328125}, {"start": 2168.57, "end": 2169.29, "word": " ويساوي", "probability": 0.89189453125}, {"start": 2169.29, "end": 2169.49, "word": " F", "probability": 0.76416015625}, {"start": 2169.49, "end": 2169.67, "word": " of", "probability": 0.52294921875}, {"start": 2169.67, "end": 2170.33, "word": " D1", "probability": 0.8291015625}, {"start": 2170.33, "end": 2170.89, "word": " في", "probability": 0.849609375}, {"start": 2170.89, "end": 2171.11, "word": " F", "probability": 0.9580078125}, {"start": 2171.11, "end": 2171.33, "word": " of", "probability": 0.94873046875}, {"start": 2171.33, "end": 2171.63, "word": " D", "probability": 0.9951171875}, {"start": 2171.63, "end": 2172.65, "word": " إذا", "probability": 0.640625}, {"start": 2172.65, "end": 2173.19, "word": " واضح", "probability": 0.9573567708333334}, {"start": 2173.19, "end": 2173.39, "word": " أن", "probability": 0.52197265625}, {"start": 2173.39, "end": 2173.69, "word": " F", "probability": 0.78271484375}, {"start": 2173.69, "end": 2173.93, "word": " is", "probability": 0.84375}, {"start": 2173.93, "end": 2174.09, "word": " a", "probability": 0.93896484375}, {"start": 2174.09, "end": 2174.87, "word": " multiplicative", "probability": 0.9306640625}, {"start": 2174.87, "end": 2175.51, "word": " function", "probability": 0.962890625}, {"start": 2175.51, "end": 2176.79, "word": " ماشي", "probability": 0.8907877604166666}, {"start": 2176.79, "end": 2177.13, "word": " الحال", "probability": 0.979736328125}, {"start": 2177.13, "end": 2178.39, "word": " طيب", "probability": 0.8190104166666666}, {"start": 2178.39, "end": 2179.57, "word": " مدام", "probability": 0.7158203125}, {"start": 2179.57, "end": 2179.75, "word": " F", "probability": 0.93701171875}, {"start": 2179.75, "end": 2180.83, "word": " multiplicative", "probability": 0.73828125}, {"start": 2180.83, "end": 2182.03, "word": " بتشجعني", "probability": 0.97919921875}, {"start": 2182.03, "end": 2182.19, "word": " أن", "probability": 0.625}, {"start": 2182.19, "end": 2182.85, "word": " أقول", "probability": 0.774658203125}, {"start": 2182.85, "end": 2184.49, "word": " let", "probability": 0.67919921875}, {"start": 2184.49, "end": 2186.25, "word": " F", "probability": 0.79931640625}, {"start": 2186.25, "end": 2186.53, "word": " of", "probability": 0.90234375}, {"start": 2186.53, "end": 2186.83, "word": " N", "probability": 0.8017578125}], "temperature": 1.0}, {"id": 85, "seek": 221390, "start": 2187.56, "end": 2213.9, "text": "بساوية الـ summation للـ F of D دي بتجسمها اللي يمين اللي عبارة عن summation واحد على D دي بتجسم اللي أنا بدور عليها بما أن F is multiplicative إذا ال summation هذا إشماله is multiplicative حسب النظرية اللي عندنا إذا صارت ال F كابتنة إشمالها is multiplicative", "tokens": [3555, 3794, 995, 2407, 10632, 2423, 39184, 28811, 24976, 39184, 479, 295, 413, 11778, 1829, 39894, 7435, 38251, 11296, 13672, 1829, 7251, 2304, 9957, 13672, 1829, 6225, 3555, 9640, 3660, 18871, 28811, 36764, 24401, 15844, 413, 11778, 1829, 39894, 7435, 38251, 13672, 1829, 41850, 47525, 13063, 25894, 11296, 4724, 15042, 14739, 479, 307, 17596, 1166, 11933, 15730, 2423, 28811, 23758, 11933, 8592, 2304, 6027, 3224, 307, 17596, 1166, 11331, 35457, 28239, 19913, 2288, 10632, 13672, 1829, 43242, 8315, 11933, 15730, 20328, 9640, 2655, 2423, 479, 9122, 16758, 2655, 1863, 3660, 11933, 8592, 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"end": 4282.58, "word": " لأ", "probability": 0.391357421875}, {"start": 4282.58, "end": 4283.22, "word": " بتسير", "probability": 0.5555013020833334}, {"start": 4283.22, "end": 4284.82, "word": " اتنين", "probability": 0.9698486328125}, {"start": 4284.82, "end": 4285.4, "word": " تلاتة", "probability": 0.9189453125}, {"start": 4285.4, "end": 4285.92, "word": " مظبوط", "probability": 0.7427734375}, {"start": 4285.92, "end": 4286.98, "word": " طيب", "probability": 0.9046223958333334}, {"start": 4286.98, "end": 4287.66, "word": " هنا", "probability": 0.7744140625}, {"start": 4287.66, "end": 4288.18, "word": " واحد", "probability": 0.992919921875}, {"start": 4288.18, "end": 4289.32, "word": " صح", "probability": 0.977294921875}, {"start": 4289.32, "end": 4290.6, "word": " هنا", "probability": 0.80078125}, {"start": 4290.6, "end": 4290.84, "word": " اللي", "probability": 0.77294921875}, {"start": 4290.84, "end": 4290.98, "word": " هي", "probability": 0.6943359375}, {"start": 4290.98, 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واحد كي واحد بي ار كي ار بي برايم factorization of n أكبر من واحد إذا كانت f is multiplicative prove that اللي موجود انتبهوا عن دي خليني برضه أذكركم بعض النظريات", "tokens": [3794, 33604, 6027, 6055, 1211, 9307, 3660, 718, 718, 718, 297, 39894, 3794, 995, 45865, 4724, 1829, 36764, 24401, 9122, 1829, 36764, 24401, 4724, 1829, 1975, 2288, 9122, 1829, 1975, 2288, 4724, 1829, 4724, 23557, 32640, 5952, 2144, 295, 297, 5551, 4117, 26890, 9154, 36764, 24401, 11933, 15730, 25961, 2655, 283, 307, 17596, 1166, 7081, 300, 13672, 1829, 3714, 29245, 23328, 16472, 2655, 3555, 3224, 14407, 18871, 11778, 1829, 16490, 1211, 9957, 1829, 4724, 43042, 3224, 5551, 8848, 37983, 24793, 45030, 11242, 28239, 19913, 16572, 9307], "avg_logprob": -0.2500000013702217, "compression_ratio": 1.5435897435897437, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4328.91, "end": 4329.39, "word": "سؤال", "probability": 0.912109375}, {"start": 4329.39, "end": 4330.15, "word": " تلاتة", "probability": 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{"start": 5018.12, "end": 5018.2, "word": " ال", "probability": 0.4130859375}, {"start": 5018.2, "end": 5018.32, "word": " D", "probability": 0.69677734375}, {"start": 5018.32, "end": 5018.48, "word": " is", "probability": 0.697265625}, {"start": 5018.48, "end": 5019.5, "word": " multiplicative", "probability": 0.85791015625}, {"start": 5019.5, "end": 5020.18, "word": " اذا", "probability": 0.5823974609375}, {"start": 5020.18, "end": 5020.78, "word": " بيصير", "probability": 0.8306884765625}, {"start": 5020.78, "end": 5021.6, "word": " واحد", "probability": 0.8955078125}, {"start": 5021.6, "end": 5022.12, "word": " ناقص", "probability": 0.86187744140625}, {"start": 5022.12, "end": 5022.62, "word": " F", "probability": 0.9267578125}, {"start": 5022.62, "end": 5023.26, "word": " of", "probability": 0.88916015625}, {"start": 5023.26, "end": 5023.42, "word": " P", "probability": 0.52294921875}, {"start": 5023.42, "end": 5023.96, "word": " واحد", "probability": 0.94482421875}, {"start": 5023.96, "end": 5024.1, "word": " اللي", "probability": 0.821044921875}, {"start": 5024.1, "end": 5024.24, "word": " هي", "probability": 0.6416015625}, {"start": 5024.24, "end": 5024.4, "word": " P", "probability": 0.91845703125}, {"start": 5024.4, "end": 5024.92, "word": " واحد", "probability": 0.97509765625}, {"start": 5024.92, "end": 5025.46, "word": " لما", "probability": 0.890625}, {"start": 5025.46, "end": 5025.78, "word": " أصل", "probability": 0.71923828125}, {"start": 5025.78, "end": 5026.22, "word": " عنده", "probability": 0.59619140625}, {"start": 5026.22, "end": 5026.56, "word": " واحد", "probability": 0.84912109375}, {"start": 5026.56, "end": 5026.92, "word": " ناقص", "probability": 0.9798583984375}, {"start": 5026.92, "end": 5027.1, "word": " F", "probability": 0.88623046875}, {"start": 5027.1, "end": 5027.28, "word": " of", "probability": 0.90869140625}, {"start": 5027.28, "end": 5027.6, "word": " PR", "probability": 0.75732421875}, {"start": 5027.6, "end": 5027.78, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..707fa2786b4064bb24acfd9daabff373a189e5cf
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34_raw.srt
@@ -0,0 +1,3580 @@
+1
+00:00:19,350 --> 00:00:25,850
+بسم الله الرحمن الرحيم محاضرة رقم 27 وهي عبارة عن
+
+2
+00:00:25,850 --> 00:00:34,950
+مناقشة لـ Chapter 6 سنناقش اليوم موضوعين الموضوع
+
+3
+00:00:34,950 --> 00:00:39,910
+الأول اللي هو number and sum of divisors والموضوع
+
+4
+00:00:39,910 --> 00:00:43,530
+التاني اللي هو Mobius inversion formula نبدأ ب 6
+
+5
+00:00:43,530 --> 00:00:50,470
+واحد اللي هو number and sum of divisorsأذكركم في
+
+6
+00:00:50,470 --> 00:00:56,450
+بعض اللي هي النتائج في هذا الفصل أو في هذا ال
+
+7
+00:00:56,450 --> 00:01:00,470
+section لو كانت عندي N أكبر من 1 و N كتبناها على
+
+8
+00:01:00,470 --> 00:01:05,210
+صورة الـ prime factorizations اللي بي واحد ألف
+
+9
+00:01:05,210 --> 00:01:11,950
+واحد لعند PR ألف R عندي بيكون ال sigma of N أو ال
+
+10
+00:01:11,950 --> 00:01:18,800
+tau of N جبل بتساويبارة عن Alpha 1 زي 1 لما نصل
+
+11
+00:01:18,800 --> 00:01:25,460
+لعند Alpha R زي 1 مضربات في بعض هو Sigma of N
+
+12
+00:01:25,460 --> 00:01:31,360
+Sigma of N في هذه الحالة عبارة عن كتبناها على صورة
+
+13
+00:01:31,360 --> 00:01:38,500
+ل product بي واحد Alpha واحد بي آي Alpha I زي واحد
+
+14
+00:01:38,500 --> 00:01:45,910
+ناقص واحد على بي آي ناقص واحدمظبوط I من عند واحد
+
+15
+00:01:45,910 --> 00:01:53,590
+لعند R وكتبناها أيضا وكتبناها أيضا في أثناء برهان
+
+16
+00:01:53,590 --> 00:01:57,510
+سيجموغان هذا بساوي هذا اللي هو إيه ده بتتذكر هو
+
+17
+00:01:57,510 --> 00:02:05,450
+عبارة عن ال product ل 1 زائد bi زائد bi تربيع لما
+
+18
+00:02:05,450 --> 00:02:13,230
+أصل لآخر واحد bi Alpha I I من عند واحد لعند Rهذا
+
+19
+00:02:13,230 --> 00:02:19,050
+هو النتيجتين اللي حكينا عنهم وحكينا عن نتيجة ثالثة
+
+20
+00:02:19,050 --> 00:02:28,150
+انه لو كانت F is multiplicative بيعطيني F of N
+
+21
+00:02:28,150 --> 00:02:33,490
+بتساوي ال summation لل F of D D بتجسم N برضه
+
+22
+00:02:33,490 --> 00:02:42,810
+اشمالها is multiplicativeمعايا؟ طيب نيجي الآن ناخد
+
+23
+00:02:42,810 --> 00:02:48,790
+السؤال اللي هو رقم 6 السؤال رقم 6 بقول ما يلي
+
+24
+00:02:48,790 --> 00:02:58,610
+بقولنا لأي integer n أكبر من 1 سؤال 6 if n أكبر أو
+
+25
+00:02:58,610 --> 00:03:04,710
+سوى 1 thenالـ Sigma of N أو الـ Tau of N له أصغر
+
+26
+00:03:04,710 --> 00:03:12,410
+أو يساوي 2 في جدر الـ N الـ Proof أول ملاحظة طبعا
+
+27
+00:03:12,410 --> 00:03:16,310
+الـ Proof كامل مكتوب هناك هنخلنا نبرهن يعني مش شرط
+
+28
+00:03:16,310 --> 00:03:21,070
+نكتب كل البرهان ولكن نتحدث البرهان بشكل تفصيل أساس
+
+29
+00:03:21,070 --> 00:03:26,210
+اختصارا للوقت بدنا نثبت أن عدد الـ Divisors للـ N
+
+30
+00:03:26,210 --> 00:03:31,490
+أكبر يساوي 200 جدر الـ Nأصغر أو ساوى اتنين جذر
+
+31
+00:03:31,490 --> 00:03:36,170
+الان الان لاحظ اول ملاحظة الحالية ان لو كان عندي
+
+32
+00:03:36,170 --> 00:03:44,870
+ال D بقسم N لو ال D من قواسم ال N اذا اكيد اكيد ال
+
+33
+00:03:44,870 --> 00:03:50,460
+N على D بيصير integer و برضه بيقسمينالان لسبب بسيط
+
+34
+00:03:50,460 --> 00:03:55,960
+لأن الان في هذه الحالة هتساوي ان على دي في مين في
+
+35
+00:03:55,960 --> 00:03:59,700
+دي بما ان هذا فرضنا ان دي بتجسم ان يعني هذا ان على
+
+36
+00:03:59,700 --> 00:04:03,180
+دي انتجر اذا انصار عند الان بساوي هذا في هذا اذا
+
+37
+00:04:03,180 --> 00:04:07,460
+هذه بتوحي ان دي بتجسم ان وان على دي بتجسم مين ان
+
+38
+00:04:07,460 --> 00:04:11,140
+يعني وكأنه بقولك انا انه
+
+39
+00:04:13,420 --> 00:04:17,920
+القواسم تحدث أزواجا يعني واحد بيكون D والتان اللي
+
+40
+00:04:17,920 --> 00:04:22,580
+عاجباله على طول ايش بيكون N على D ماشي الحال مافيش
+
+41
+00:04:22,580 --> 00:04:28,140
+غير هدول اللي هو القواسم بيحدثون اللي هي لـ N يعني
+
+42
+00:04:28,140 --> 00:04:30,920
+لو كان D بيكسب N على طول الـ N على D بيكسب مين الـ
+
+43
+00:04:30,920 --> 00:04:34,500
+N وقد يكون ان N على D يساوي في حالات ايش بيساوي
+
+44
+00:04:34,500 --> 00:04:38,040
+بيساوي D ماشي الحال خلّي هذا الملاحظة أولا
+
+45
+00:04:38,040 --> 00:04:47,970
+الملاحظة التانيةلو جينا بدنا نشوف اللي هو الـ D
+
+46
+00:04:47,970 --> 00:04:52,430
+والـ N على D واحد من الاتنين هذوله سواء الـ D أو
+
+47
+00:04:52,430 --> 00:04:57,430
+الـ N على D واحد منهم .. واحد منهم هيكون أصغر أو
+
+48
+00:04:57,430 --> 00:05:03,170
+يساوي جذر الـ N واحد
+
+49
+00:05:03,170 --> 00:05:08,160
+هيكون أصغر أو يساوي مين؟جذر الأن واحد على الأقل
+
+50
+00:05:08,160 --> 00:05:12,640
+حيكون أصغر أو يساوي جذر الأن الإدعاء عشان تسمعوا
+
+51
+00:05:12,640 --> 00:05:16,840
+الإدعاء وبعدين هقولكم ليش الإدعاء إن واحد من هذولة
+
+52
+00:05:16,840 --> 00:05:21,940
+على الأقل حيكون أصغر أو يساوي جذر الأن ليش لسبب
+
+53
+00:05:21,940 --> 00:05:26,620
+بسيط إنه لو كان الاتنين أكبر strictly من جذر الأن
+
+54
+00:05:26,620 --> 00:05:31,260
+معناته بيصير حاصل ضربه أكبر من الأن بينما حاصل
+
+55
+00:05:31,260 --> 00:05:37,150
+ضربه مش مساوى كمان مرةالأن الـ D و الـ N على D
+
+56
+00:05:37,150 --> 00:05:45,410
+واحد منهم على الأقل أصغر أو يساوي جذر الـ N لأنه
+
+57
+00:05:45,410 --> 00:05:50,630
+لو كان الاتنين هذا و هذا يعني الـ D أكبر strictly
+
+58
+00:05:50,630 --> 00:05:53,770
+من جذر الـ N و الـ N على D أكبر strictly من جذر
+
+59
+00:05:53,770 --> 00:05:58,430
+الـ N هذا بيؤدي إلى أن الـ N في الـ D على N اللي
+
+60
+00:05:58,430 --> 00:06:02,330
+هو بساوي N أكبر strictly من مين؟ من الـ N وهذا
+
+61
+00:06:02,330 --> 00:06:07,070
+مستحيل Contradictionإذن المعلومة التانية عندك الآن
+
+62
+00:06:07,070 --> 00:06:15,030
+واحد من هذول على أقل هيكون أكبر أو يساوي مين أصغر
+
+63
+00:06:15,030 --> 00:06:20,750
+أو يساوي جذر الآن إذن .. إذن الآن لو بدي عدة
+
+64
+00:06:20,750 --> 00:06:30,050
+divisors اللي من واحد لعين جذر الآنللان يعني بتعد
+
+65
+00:06:30,050 --> 00:06:36,190
+قواسم الان اللي أصغر أو يساوي جذر الان يعني اللي
+
+66
+00:06:36,190 --> 00:06:40,450
+من واحد لان جذر الان هيكون عددهم عال أكتر عال أكتر
+
+67
+00:06:40,450 --> 00:06:43,310
+عال أكتر جديش جذر الان جذر الان جذر الان جذر الان
+
+68
+00:06:43,310 --> 00:06:52,070
+جذر الان جذر الان جذر الان جذر الان جذر الان جذر
+
+69
+00:06:52,070 --> 00:06:56,090
+الان جذر الان جذر الان جذر الان جذر الان جذر الان
+
+70
+00:06:56,090 --> 00:06:57,170
+جذر الان جذر الان جذر الان جذر الان جذر الان جذر
+
+71
+00:06:57,170 --> 00:06:57,230
+الان جذر الان جذر الان جذر الان جذر الان جذر الان
+
+72
+00:06:57,230 --> 00:06:58,510
+جذر الان جذر الان جذر الان جذر الان جذر الانماشي
+
+73
+00:06:58,510 --> 00:07:03,250
+الحال ما هو كل divisor فيه لعقباله divisor تحدث
+
+74
+00:07:03,250 --> 00:07:08,570
+أزواجا إذا صار عندي مجموع ال divisors كلهم على
+
+75
+00:07:08,570 --> 00:07:18,510
+الأكثر اتنين جذر و هو المطلوب كمان مرة النقطة هذه
+
+76
+00:07:18,510 --> 00:07:24,550
+نلخص السؤال على السريع لأنكم الان النقطة الأولى أن
+
+77
+00:07:24,550 --> 00:07:30,640
+ال divisors تحدث أزواجاالنقطة الثانية أنه الآن في
+
+78
+00:07:30,640 --> 00:07:34,360
+واحد من هذول على الأقل أصغر أو يساوي 100 جدر الأن
+
+79
+00:07:34,360 --> 00:07:37,680
+في كل زوج في على الأقل واحد منهم أصغر أو يساوي 100
+
+80
+00:07:37,680 --> 00:07:42,400
+جدر الأن عدد الـ divisors للأن اللي أصغر أو يساوي
+
+81
+00:07:42,400 --> 00:07:46,240
+100 جدر الأن على الأكتر يساوي 100 جدر الأن وفي
+
+82
+00:07:46,240 --> 00:07:51,750
+عجبالهم اللي هو أشمالهماللي هو الجدر الأن فبصير
+
+83
+00:07:51,750 --> 00:07:54,530
+على الأكتر على الأكتر اللي هو جداش عدد الـ
+
+84
+00:07:54,530 --> 00:07:58,490
+divisors اتنين جدر الأن مع أنه ممكن ينقص لأنه ممكن
+
+85
+00:07:58,490 --> 00:08:01,590
+يكون اللي هو الـD والأن ع دي في حالة إيش بيساوي ..
+
+86
+00:08:01,590 --> 00:08:07,230
+بيساوي واحدة في النهاية اللي هو دائما توف أن أظل
+
+87
+00:08:07,230 --> 00:08:12,290
+سوى اتنين جدر الأن اللي بعده السؤال اللي بعده
+
+88
+00:08:18,440 --> 00:08:24,740
+و prove the following Tau of N is an odd number or
+
+89
+00:08:24,740 --> 00:08:29,580
+odd integer if and only if N is a perfect square
+
+90
+00:08:29,580 --> 00:08:33,820
+كمان
+
+91
+00:08:33,820 --> 00:08:45,240
+مرة السؤال عندي سؤال سبعة A Tau of N is odd if and
+
+92
+00:08:45,240 --> 00:08:50,760
+only ifN is a perfect square perfect square معناته
+
+93
+00:08:50,760 --> 00:08:55,760
+إيش ماله مربع كامل يعني هيكون على صورة N تربيع for
+
+94
+00:08:55,760 --> 00:09:05,220
+some M باشي الحال ال N دائما
+
+95
+00:09:05,220 --> 00:09:10,160
+في حالة ال Sigma أو حتى حالة ال number theoretic
+
+96
+00:09:10,160 --> 00:09:17,960
+functions بصورة عامة أسهلني أن أحسب للي برايموبعد
+
+97
+00:09:17,960 --> 00:09:21,300
+ما أحسب للـ prime بحسب لمين للـ function نفسها
+
+98
+00:09:21,300 --> 00:09:23,740
+خصوصاً إذا كانت الـ function is multiplicative
+
+99
+00:09:23,740 --> 00:09:32,350
+بتصير الأمور سهلة نشوف أشي المقصودالان بس خلوني
+
+100
+00:09:32,350 --> 00:09:35,710
+مادام بتحكي عن ال prime factorization للان إذا
+
+101
+00:09:35,710 --> 00:09:40,870
+لازم الان تبقى تكون أكبر من مين؟ من واحد معايا؟
+
+102
+00:09:40,870 --> 00:09:43,270
+إذا نخليني أنا أخد حالة الواحد حالة الواحد is a
+
+103
+00:09:43,270 --> 00:09:48,590
+trivial case ليش؟ لإن تاو of واحد بسوء واحد واحد
+
+104
+00:09:48,590 --> 00:09:52,510
+مربع كامل إذا انت تتحقق اللي هي الطرفين هذه ان تاو
+
+105
+00:09:52,510 --> 00:09:56,150
+of ان is odd فاندول اف اش مالها ان is a perfect
+
+106
+00:09:56,150 --> 00:10:01,740
+squareنأتي الآن ناخد حالة مين الـ N أكبر من 1
+
+107
+00:10:01,740 --> 00:10:08,980
+بتاخد proof حالة الـ N أكبر من 1 إيش بدأ أقول؟ بدأ
+
+108
+00:10:08,980 --> 00:10:13,100
+أقول suppose that
+
+109
+00:10:13,100 --> 00:10:22,360
+N is a perfect square ماشي؟
+
+110
+00:10:22,360 --> 00:10:29,040
+يعني N إيش مالها؟ مربع كامل يعني Nبتساوي M تربية
+
+111
+00:10:29,040 --> 00:10:33,480
+الـ M نفسها أكيد هتكون أكبر من واحد مدام الـ M
+
+112
+00:10:33,480 --> 00:10:37,060
+أكبر من واحد مدام الـ M أكبر من واحد اذا اللي هو
+
+113
+00:10:37,060 --> 00:10:40,040
+بقدر اكتبه على صورة اللي هو product of the primes
+
+114
+00:10:40,040 --> 00:10:44,200
+فبتكون على صورة بي واحد Alpha واحد canonical form
+
+115
+00:10:44,200 --> 00:10:51,870
+لعند بي R Alpha R لكل أشماله تربية واضح؟هك مفترضين
+
+116
+00:10:51,870 --> 00:10:54,910
+إنه هنا perfect square يعني بمعنى آخر إلا إنه على
+
+117
+00:10:54,910 --> 00:11:00,270
+صورة بي واحد اتنين ألف واحد لعند بي ار اتنين ألف
+
+118
+00:11:00,270 --> 00:11:08,230
+ار واضحة الصورة إذا الأن إذا صار عندي ال sigma آسف
+
+119
+00:11:08,230 --> 00:11:13,070
+ال Tao of N هيساوي حسب اللي ال Tao of N إيش هتكون
+
+120
+00:11:13,070 --> 00:11:20,600
+اللي هو اتنين ألف واحد زائد واحدلما أصل عند 2 α R
+
+121
+00:11:20,600 --> 00:11:25,580
+زائد 1 هذه زوجي هذه كلها على بعض إيش مالها فردي
+
+122
+00:11:25,580 --> 00:11:28,500
+إذا فردي مضروب فى فردي مضروب فى فردي مضروب فى فردي
+
+123
+00:11:28,500 --> 00:11:33,020
+إذا إيش كدا كلها على بعض إذا صارت T of N إيش مالها
+
+124
+00:11:33,020 --> 00:11:38,440
+متى لما كانت ال N is a perfect square إذا المهم في
+
+125
+00:11:38,440 --> 00:11:42,340
+الموضوع أن أنا أعرف أعمل representation as a
+
+126
+00:11:42,340 --> 00:11:46,640
+product of primes لل N واضح؟ conversely
+
+127
+00:11:53,590 --> 00:12:02,010
+Conversely Suppose that sigma of n is a odd بدا
+
+128
+00:12:02,010 --> 00:12:06,270
+تثبت لك أن n إيش ما لها perfect square تاو of n is
+
+129
+00:12:06,270 --> 00:12:11,730
+odd بدا تثبت لك أن n إيش ما لها perfect square
+
+130
+00:12:13,960 --> 00:12:16,900
+الان احنا مفترضينها من رأس الدور انها اكبر من 100
+
+131
+00:12:16,900 --> 00:12:22,060
+من 1 اذا الان تابعتنا بقدر اكتبها على صورة by
+
+132
+00:12:22,060 --> 00:12:24,900
+unique by unique factorization theorem على صورة
+
+133
+00:12:24,900 --> 00:12:28,460
+اللي هو product of power of primes بي واحد بيتا
+
+134
+00:12:28,460 --> 00:12:36,940
+واحد لعند بي ار بيتا ار واضح؟ طيب احسب للتاولة هذه
+
+135
+00:12:36,940 --> 00:12:46,610
+اذاTau of N بساوي Beta 1 زائد 1 في Beta 2 زائد 1
+
+136
+00:12:46,610 --> 00:12:53,100
+لما أصل لآخر واحدة في Beta R زائد 1الان ماعطيلي
+
+137
+00:12:53,100 --> 00:12:58,220
+هذا يشماله التوفان is odd مدام التوفان is odd
+
+138
+00:12:58,220 --> 00:13:03,600
+وعندي product of numbers لازم كل واحد فيه يكون odd
+
+139
+00:13:03,600 --> 00:13:06,160
+مانفعش واحد يكون زوجي لو واحد زوجي معناه تصار
+
+140
+00:13:06,160 --> 00:13:13,240
+ضرباش زوجي إذا حيكون عندي بي واحد زائد واحد أو بي
+
+141
+00:13:13,240 --> 00:13:20,700
+اي زائد واحد is odd for every mean iما دم بي اي
+
+142
+00:13:20,700 --> 00:13:23,240
+زائد واحد الزدد ده اكيد ال بي اي اللي حالها اي
+
+143
+00:13:23,240 --> 00:13:27,280
+شمالها is even بي اي even معناته ال بي اي اي
+
+144
+00:13:27,280 --> 00:13:32,120
+شمالها هتكون على صورة اتنين Alpha I for some Alpha
+
+145
+00:13:32,120 --> 00:13:39,060
+I معايا ما دم بي Beta I is even اذا على صورة اتنين
+
+146
+00:13:39,060 --> 00:13:45,940
+Alpha I اذا صار عند ال N تبعتنا ال N تبعتنا بتساوي
+
+147
+00:13:47,370 --> 00:13:52,430
+ب1 اتنين الفا واحد فاهمين لعند ب ار اتنين الفا ار
+
+148
+00:13:52,430 --> 00:13:57,170
+اللي هي بتساوي ب واحد الفا واحد لعند ب ار الفا ار
+
+149
+00:13:57,170 --> 00:14:02,390
+الكل تربيع اذا صارت اللي هو n is a perfect square
+
+150
+00:14:02,390 --> 00:14:08,770
+اذا لما كانت ال ال tau of n is odd طلعت ال n عند a
+
+151
+00:14:08,770 --> 00:14:15,730
+شمالها is a perfect square نيجي الآن لسؤال b
+
+152
+00:14:26,720 --> 00:14:33,480
+شوف عندي صلى الله عليه وسلم جزء بيه ايش بقول ليه
+
+153
+00:14:33,480 --> 00:14:39,500
+اللي هو لو كان عندي بقولي sigma of n is odd if and
+
+154
+00:14:39,500 --> 00:14:46,340
+only if n is a perfect square رقص or twice perfect
+
+155
+00:14:46,340 --> 00:14:51,450
+squareيعني بيقول لي أن الـ N يا هتكون على صورة N
+
+156
+00:14:51,450 --> 00:14:56,670
+تربيع اللي هي perfect square أو اتنين N تربيع for
+
+157
+00:14:56,670 --> 00:15:03,810
+some M ثمان مرة السؤال السؤال اللي بيقول لي prove
+
+158
+00:15:03,810 --> 00:15:09,810
+that sigma of N is odd if and only if N is a
+
+159
+00:15:09,810 --> 00:15:17,170
+perfect square or twice perfect square واضح؟ نيجي
+
+160
+00:15:17,170 --> 00:15:24,110
+البرهنA proof Suppose that
+
+161
+00:15:24,110 --> 00:15:31,670
+N is a perfect square or twice perfect square
+
+162
+00:15:31,670 --> 00:15:43,090
+بيثبتلك
+
+163
+00:15:43,090 --> 00:15:49,040
+إن sigma of N في الحالتين أزدادطيب شو N بتساوي N
+
+164
+00:15:49,040 --> 00:15:54,500
+تربيع نعملها قبل بشوية يعني N بتساوي B1 اللي هو
+
+165
+00:15:54,500 --> 00:16:04,520
+20001 لعين PR 2000R مظبوط و ال R في الحالة اللي N
+
+166
+00:16:04,520 --> 00:16:10,300
+بتساوي 2N تربيع اللي هو ركزوا معاه فN بتساوي اللي
+
+167
+00:16:10,300 --> 00:16:16,580
+هو 2B1 بدي أغير الآن الـ B1 بدي أغير الان الـ B1
+
+168
+00:16:16,580 --> 00:16:17,180
+بدي أغير الان الـ B1 بدي أغير الان الـ B1 بدي أغير
+
+169
+00:16:17,180 --> 00:16:19,380
+الان الـ B1 بدي أغير الان الـ B1 بدي أغير الان الـ
+
+170
+00:16:19,380 --> 00:16:25,200
+B1 بدي أغير الان الـ
+
+171
+00:16:25,200 --> 00:16:27,320
+B1 بدي أغير الان الـ B1 بدي أغير الان الـ B1 بدي
+
+172
+00:16:27,320 --> 00:16:27,340
+أغير الان الـ B1 بدي أغير الان الـ B1 بدي أغير
+
+173
+00:16:27,340 --> 00:16:27,860
+الان الـ B1 بدي أغير الان الـ B1 بدي أغير الان الـ
+
+174
+00:16:27,860 --> 00:16:27,860
+B1 بدي أغير الان الـ B1 بدي أغير الان الـ B1 بدي
+
+175
+00:16:27,860 --> 00:16:30,800
+أغير الان الـ B1 بدي أغير الان الـ B1 بدي أغيرأه
+
+176
+00:16:30,800 --> 00:16:35,360
+ممكن تكون اتنين وممكن تكون odd أصلا ماشي الحل عشان
+
+177
+00:16:35,360 --> 00:16:39,440
+أكتب الحالتين في كتابة واحدة بدي أكتبها على صورة
+
+178
+00:16:39,440 --> 00:16:46,320
+هذه بيساوي 2 أس 2 ألف واحد زائد واحد في B2 أس 2
+
+179
+00:16:46,320 --> 00:16:55,720
+ألف اتنين لعين B R 2 ألف Rأيش اللي كتبته هذه و
+
+180
+00:16:55,720 --> 00:17:02,160
+Alpha 1 عندي أكبر أو ساوي 0 و Alpha 2 عند Alpha R
+
+181
+00:17:02,160 --> 00:17:06,120
+أكبر أو ساوي 1 شوف
+
+182
+00:17:09,650 --> 00:17:14,850
+الان انا عندى twice perfect square هى مربع كامل
+
+183
+00:17:14,850 --> 00:17:19,090
+هذا المربع الكامل قد يكون ان هو اول prime له في ال
+
+184
+00:17:19,090 --> 00:17:23,230
+prime factorization اتنين وممكن يكون ايه اش مفيش
+
+185
+00:17:23,230 --> 00:17:28,210
+اتنين ممكن يكون ايه اش ادت الان انا كتبته على
+
+186
+00:17:28,210 --> 00:17:35,130
+الصورة هذه على صورة 2001 زي 1 في الباقي الان لو
+
+187
+00:17:35,130 --> 00:17:40,760
+الان ال 1100أنا كتبت ألف واحد أكبر سوى إيش؟ لو
+
+188
+00:17:40,760 --> 00:17:44,760
+الألف واحد سفر معناه صار اتنين بس واحد وخلاص اه
+
+189
+00:17:44,760 --> 00:17:49,840
+يعني هي الأتنين لو الآن ألف واحد صارت واحد بيصير
+
+190
+00:17:49,840 --> 00:17:54,440
+اتنين زائد واحد وبتبقى لها twice perfect square
+
+191
+00:17:54,440 --> 00:18:01,440
+واضح؟ طيب نيجي الآن نحسب مين؟ sigma of n إذا sigma
+
+192
+00:18:01,440 --> 00:18:09,760
+of n في الحالتينما هتساوي ال product واحد
+
+193
+00:18:09,760 --> 00:18:13,220
+زائد بي اي زائد بي اي تربيع لما يقصى الاخر واحدة
+
+194
+00:18:13,220 --> 00:18:21,180
+اللي هو ال product لأ واحد زائد بي اي زائد بي اي
+
+195
+00:18:21,180 --> 00:18:27,200
+أُس اتنين الف اي اي من عند واحد لعند ار هذا في
+
+196
+00:18:27,200 --> 00:18:35,140
+الحالة الأولىلاحظ .. لاحظ ان هذولا عددهن زوجي صح
+
+197
+00:18:35,140 --> 00:18:39,560
+ولا لأ معايا؟
+
+198
+00:18:39,560 --> 00:18:44,380
+اه هاي اتنين الفاية اه من عند واحد عند اتنين
+
+199
+00:18:44,380 --> 00:18:47,780
+الفاية إذا العدد هنا إشمال، هنا زوجي إذا كانت
+
+200
+00:18:47,780 --> 00:18:56,320
+اتنينات، هاي زوجي إذا كانت فرديات عددها زوجي
+
+201
+00:18:56,320 --> 00:19:02,300
+ومجموعات لبعض، برضه زوجيإذا صار هذا كله مجموع زوجي
+
+202
+00:19:02,300 --> 00:19:08,540
+مع واحد صار فردي إذا صار هذا فردي product of فردي
+
+203
+00:19:08,540 --> 00:19:15,000
+إيش حيطلع إذا حيطلع product حالة
+
+204
+00:19:15,000 --> 00:19:23,980
+تالية اللي هي اللي بعد هذه or خليني
+
+205
+00:19:23,980 --> 00:19:32,430
+بس أكمل or areSigma of n بتساوي في الحالة التانية
+
+206
+00:19:32,430 --> 00:19:39,870
+Twice perfect square هيصير بتفصلها product هذه في
+
+207
+00:19:39,870 --> 00:19:40,710
+product هذه
+
+208
+00:19:44,470 --> 00:19:49,310
+للأساس اتنين بيصير واحد زائد اتنين زائد اتنين
+
+209
+00:19:49,310 --> 00:19:54,630
+تربيع لم أصل آخر أُس اتنين ألف واحد زائد مضروب في
+
+210
+00:19:54,630 --> 00:20:00,670
+الباقي الباقي مين هو هذا الاند عبارة عن واحد زائد
+
+211
+00:20:00,670 --> 00:20:08,690
+بي اي زائد بي اي أس اتنين ألف اي الآن اي من وين مش
+
+212
+00:20:08,690 --> 00:20:15,220
+من واحد من اتنين لعند الاربنفس اللي فوق بالظبط
+
+213
+00:20:15,220 --> 00:20:21,240
+هدول عددهم زوجي وهنا اللي هي فرديات فمجموحا هيكون
+
+214
+00:20:21,240 --> 00:20:26,840
+زوجي زائد واحد مش هيطلع فردي معايا ال product
+
+215
+00:20:26,840 --> 00:20:32,780
+الفردي بيطلع اي اسم اذا هذا هيطلع عند اطيب
+
+216
+00:20:32,780 --> 00:20:38,780
+ماخلصناش نيجي لهذا هدول مهمة مجموحين زوجي وفي واحد
+
+217
+00:20:38,780 --> 00:20:42,780
+إذا صار فردي فردي مضلوب في فردي إذا هذا صار odd
+
+218
+00:20:42,780 --> 00:20:50,080
+برضه في odd إيش هيساوي odd إذا في كل الحالتين ال
+
+219
+00:20:50,080 --> 00:20:54,700
+sigma of n سواء في حالة ال perfect square أو twice
+
+220
+00:20:54,700 --> 00:20:59,580
+perfect square ال sigma of n إيش طلعت is odd اسألي
+
+221
+00:20:59,580 --> 00:20:59,980
+محمد
+
+222
+00:21:06,450 --> 00:21:10,430
+الان عندى high perfect square وهنا twice perfect
+
+223
+00:21:10,430 --> 00:21:14,510
+square twice perfect square يعني اتنين في high
+
+224
+00:21:14,510 --> 00:21:21,460
+perfect squareالان هذا ال factorization ال P1 يمكن
+
+225
+00:21:21,460 --> 00:21:26,800
+تكون اتنين ويمكن تكون odd ماشي الحال الان انا عساس
+
+226
+00:21:26,800 --> 00:21:31,140
+ان احمد ظهري واخد الحالتين كتبت اول واحد اللي هو
+
+227
+00:21:31,140 --> 00:21:35,240
+هذا هو عبارة عن اتنين اقصد اتنين اد الف واحد زائد
+
+228
+00:21:35,240 --> 00:21:40,580
+واحد والباجي اللي هي ال odd prime اللي وجدت الان
+
+229
+00:21:40,580 --> 00:21:46,750
+هذا هل بحتمي للحالتين ان يكون اللي هو twiceسواء
+
+230
+00:21:46,750 --> 00:21:51,470
+كانت الـ 2 لحالها أو بـ 2 أُص غير الـ 2، أه
+
+231
+00:21:51,470 --> 00:21:54,990
+بيختمل، ليش؟ لإن أخدت الـ Alpha 1 أشمالها أكبر
+
+232
+00:21:54,990 --> 00:22:00,150
+بساوية 0 لما Alpha 1 بـ 0، بيصير 2 في هذا لما تصير
+
+233
+00:22:00,150 --> 00:22:05,770
+Alpha 1 بتساوي 1 مثلا أو 2 أو 3، بيصير 2 زائد 1
+
+234
+00:22:05,770 --> 00:22:12,190
+ثلاثة، بيصير برضه 2 في Perfect Square، واضح؟ نيجي
+
+235
+00:22:12,190 --> 00:22:12,450
+الآن
+
+236
+00:22:18,810 --> 00:22:25,170
+ماذا جعلنا نكتبها 1 zpi؟ قالي أين؟ أول لحظة sigma
+
+237
+00:22:25,170 --> 00:22:31,890
+هذا؟ هذا شرحناه في المحاضرة ماعرفش أشرح المحاضرة
+
+238
+00:22:31,890 --> 00:22:35,370
+من جديد أنا كتبت لك من رأس الدورة عشان الان sigma
+
+239
+00:22:35,370 --> 00:22:39,870
+of n أيش بيساوي؟ بيساوي ال product هذا هذا للنظرية
+
+240
+00:22:39,870 --> 00:22:46,500
+في شرح النظرية بدأنا وقلنا ليش سبب هيك؟المجموع الـ
+
+241
+00:22:46,500 --> 00:22:49,240
+divisors دي مش هنتيجي على الموضوع لإنه فيه تفاصيل
+
+242
+00:22:49,240 --> 00:22:52,220
+مجموع الـ divisors بساوي اللي هو عبارة عن ال
+
+243
+00:22:52,220 --> 00:22:54,860
+product واحد زائد بي آي زائد بي آي تربيع زائد بي
+
+244
+00:22:54,860 --> 00:22:58,520
+آي ألف آي سببه البسيط لإنه أصلا ال divisors للبي
+
+245
+00:22:58,520 --> 00:23:03,840
+آي ألف آي هيها فلما الآن أضربهم في بعض بيصير عندي
+
+246
+00:23:03,840 --> 00:23:07,780
+بيجيب كل ال divisors و بيجمحل لبعض فبتطلع إياه
+
+247
+00:23:07,780 --> 00:23:11,600
+شماله sum of divisors وهذا شرحناه سابقاً طيب
+
+248
+00:23:14,750 --> 00:23:19,990
+نأخد الان الـ conversely نفترض
+
+249
+00:23:19,990 --> 00:23:23,610
+ان
+
+250
+00:23:23,610 --> 00:23:33,210
+sigma of n is odd برضه
+
+251
+00:23:33,210 --> 00:23:38,130
+هتلاقوا اللي هو تقاطعات البرهان الكتيرة هنكرر كلام
+
+252
+00:23:38,130 --> 00:23:40,930
+حكي لان suppose that
+
+253
+00:23:43,830 --> 00:23:51,950
+that sigma of N is odd ماشي الحل N أكبر من واحد
+
+254
+00:23:51,950 --> 00:23:59,030
+إذا الـ N عندي هتصير عبارة عن بي واحد بيتا واحد
+
+255
+00:23:59,030 --> 00:24:04,390
+لعند بي ار بيتا ايش ار حيث بي واحد و بي اتنين و بي
+
+256
+00:24:04,390 --> 00:24:12,570
+ار ار distinct primes معاياالآن بتاخد حالتين عندي
+
+257
+00:24:12,570 --> 00:24:18,830
+الـ B1 إما هتكون odd أو هتكون even مظبوط ولا لا؟
+
+258
+00:24:18,830 --> 00:24:27,910
+الآن الحالة الأولى case 1 B1 is odd الحالة التانية
+
+259
+00:24:27,910 --> 00:24:38,960
+B1 is even في حالة الـ B1 is oddهيصير ان كله نود
+
+260
+00:24:38,960 --> 00:24:42,980
+لان هدول ايش كاتبلن في ال canonical four بي واحد
+
+261
+00:24:42,980 --> 00:24:45,540
+اصغر من بي اتنين اصغر من بي تلاتة لو انت اصغر من
+
+262
+00:24:45,540 --> 00:24:51,740
+بي ار اذا ال sigma of n تبعتي لما بدى احسبها في
+
+263
+00:24:51,740 --> 00:24:54,860
+الحساب العادى اللى عندى هذه او هذه التانية اللى
+
+264
+00:24:54,860 --> 00:25:00,520
+هتوصلنا هو عبارة عن ال product للواحد زائد بي اي
+
+265
+00:25:00,810 --> 00:25:09,790
+لما أصل لعند بي أس آي أس بي أس بي ل .. اللي هو ايه
+
+266
+00:25:09,790 --> 00:25:18,150
+او Beta I I من عند واحد لعندها، بصجوط؟ طيب الآن
+
+267
+00:25:18,150 --> 00:25:23,990
+احنا مفترضين Sigma of N إيه اش مالها؟ is odd إذا
+
+268
+00:25:23,990 --> 00:25:27,730
+هذا ال product يعني اللي طلع عندي مفترض ليه أنه
+
+269
+00:25:27,730 --> 00:25:34,790
+إيه إيش؟ oddما دام ال product is odd عندي أعداد
+
+270
+00:25:34,790 --> 00:25:41,150
+مضروبة في بعض odd لازم يطلع كل واحد إيهاش لأنه و
+
+271
+00:25:41,150 --> 00:25:44,410
+لو واحد فيه even زي ما قولنا بده يطلع even إذا صار
+
+272
+00:25:44,410 --> 00:25:50,350
+عندي هذا واحد زائد بي اي زائد بي اي بيتا اي is odd
+
+273
+00:25:50,350 --> 00:25:55,670
+for every iعندي الان هذا واحد الانصار المتبقي
+
+274
+00:25:55,670 --> 00:26:04,790
+اشماله زوجي ماشي هذا المتبقي مجموع زوجي معايا الان
+
+275
+00:26:04,790 --> 00:26:11,370
+كل واحد منهم odd إذا لازم يكون عددهم even حشان
+
+276
+00:26:11,370 --> 00:26:16,990
+يطلع زوجي لإن لو كان عددهم odd ومجموعات لبعض هيطلع
+
+277
+00:26:16,990 --> 00:26:25,730
+odd لإن كلهم odd تات كمان مرة عندي الآنالعدد الكل
+
+278
+00:26:25,730 --> 00:26:29,930
+odd معطينيا وهي
+
+279
+00:26:29,930 --> 00:26:36,630
+العدد كله هذا عبارة عن product of numbers إذا each
+
+280
+00:26:36,630 --> 00:26:42,470
+number must be odd عشان نحصل على النتيجة odd إذا
+
+281
+00:26:42,470 --> 00:26:50,670
+صار عندي واحد زائد bi زائد bi أس beta i كل term من
+
+282
+00:26:50,670 --> 00:26:56,570
+هذول is oddماشي الحال إذا بدون الواحد صار الـ even
+
+283
+00:26:56,570 --> 00:27:03,130
+طيب الآن هذول مجموعات إلى بعض و هم even المجموع
+
+284
+00:27:03,130 --> 00:27:09,370
+even ماشي الحال و كل واحد فيه نقض عشان يكون مجموح
+
+285
+00:27:09,370 --> 00:27:16,560
+نقض لازم يكون عددهم عددهم زوجيلأن لو كنا عند ادهين
+
+286
+00:27:16,560 --> 00:27:20,060
+فردي تلاتة و خمسة و سبعة بطلع odd لكن تلاتة و خمسة
+
+287
+00:27:20,060 --> 00:27:24,300
+even تلاتة و خمسة و سبعة و تسعة even و هكذا إذن
+
+288
+00:27:24,300 --> 00:27:30,240
+حيكون عددهين even عددهين bi إذن ال bi إيش هتكون
+
+289
+00:27:30,240 --> 00:27:37,230
+على صورة اتنين Alpha Ieven طبعا 2000I إذا صارت
+
+290
+00:27:37,230 --> 00:27:43,010
+عندي بي اي بيساوي 2000I for every I بمعنى صار عندي
+
+291
+00:27:43,010 --> 00:27:47,470
+الآن الان اللي فوق إذا الان اللي عندي فوق هتسوي
+
+292
+00:27:47,470 --> 00:27:51,970
+على صورة بي واحد اتنين الف واحد لعين بي ار اتنين
+
+293
+00:27:51,970 --> 00:27:58,560
+الف ار وهذه ايش بتساويB1 ألف واحد لعين بي آر ألف
+
+294
+00:27:58,560 --> 00:28:03,920
+آر لكل تربية يعني لما كانت الـ Sigma of أنيا محمد
+
+295
+00:28:03,920 --> 00:28:08,880
+is odd أعطتني في هذه الحالة انه ايش الآن is a
+
+296
+00:28:08,880 --> 00:28:13,940
+perfect square هذه الحالة الأولىهذا كله في حالة بي
+
+297
+00:28:13,940 --> 00:28:18,600
+واحد إيش ما لها بدنا الآن نشوف بي واحد إيش ما لها
+
+298
+00:28:18,600 --> 00:28:26,160
+is even هذي هتطلعلي إما اللي هو perfect square أو
+
+299
+00:28:26,160 --> 00:28:33,940
+twice perfect square ماشي الحالة بتنشوف كيف بي
+
+300
+00:28:33,940 --> 00:28:39,960
+واحد is even معناته صارت عندي وين أكتب صارت عندي
+
+301
+00:28:39,960 --> 00:28:40,360
+خليني
+
+302
+00:28:44,150 --> 00:28:48,530
+معلش خلّيني أكتر هنا، أه؟ نحفظناها دي، و الـOnly
+
+303
+00:28:48,530 --> 00:28:55,980
+بتستخدمها بعد شويةعند الآن يا جماعة نيجي نشتغل بي
+
+304
+00:28:55,980 --> 00:29:01,200
+واحد is إياش is even علم النفس مهم طيب بي واحد is
+
+305
+00:29:01,200 --> 00:29:05,380
+إياش is even طيب صلوا على النبي عليه الصلاة
+
+306
+00:29:05,380 --> 00:29:10,820
+والسلام كمان مرة عند الآن صارت الان الان عبارة عن
+
+307
+00:29:10,820 --> 00:29:14,200
+بي واحد بيتا واحد و هاد ال بي واحد بيتا واحد
+
+308
+00:29:14,200 --> 00:29:19,220
+اتنينات اه يعني صارت الان عند عبارة عن اتنين أس
+
+309
+00:29:19,220 --> 00:29:26,760
+بيتا واحدمعايا في B2 أُس Beta 2 لعند B R أُس Beta
+
+310
+00:29:26,760 --> 00:29:33,760
+R اتفجنا؟ هذه الحالة التانية إذا صارت عندي الـ B1
+
+311
+00:29:33,760 --> 00:29:40,580
+even صار عندي الآن Sigma of N بتحسبها، بتساوي طبعا
+
+312
+00:29:40,580 --> 00:29:45,180
+هو ماعطينا الـ Sigma of N is odd وبدنا نستنتج إنه
+
+313
+00:29:45,180 --> 00:29:48,900
+N يا perfect square يا twice perfect square عشان
+
+314
+00:29:48,900 --> 00:29:52,250
+ما تنسوش أشي اللي بدنا يقعالآن حسب الحسبة هذا
+
+315
+00:29:52,250 --> 00:29:57,090
+بيصير عبارة عن واحد زاد اتنين زاد اتنين تربيع لما
+
+316
+00:29:57,090 --> 00:30:02,510
+أصل لتنين أس بيط واحد مضروبة في البجيات فاهمين
+
+317
+00:30:02,510 --> 00:30:08,530
+البجيات مين هم اللي هو بي واحد زاد بي اي زاد بي اي
+
+318
+00:30:08,530 --> 00:30:14,630
+تربيع لما أصل لعند بي اي أس بيط اي اي من عند اتنين
+
+319
+00:30:14,630 --> 00:30:19,430
+لعند مين لعند ار معايا شباب
+
+320
+00:30:22,540 --> 00:30:26,840
+الان متفجرين ان الـSigma of N is Odd إذا الهادي
+
+321
+00:30:26,840 --> 00:30:31,160
+على بعض أكيد إيه شمالها؟ Odd وعملناها قبل بشوية
+
+322
+00:30:31,160 --> 00:30:36,740
+عملناها و طلعتلنا إن هادي هتكون على صورة B2 2
+
+323
+00:30:36,740 --> 00:30:41,220
+Alpha 2 لعين بي R 2 Alpha R طلعناها من اللي قبل صح
+
+324
+00:30:41,220 --> 00:30:45,960
+ولا لأ؟ طيب الآن هادي وبرضه هادي غصب عنها هتطلع
+
+325
+00:30:45,960 --> 00:30:53,150
+إيش؟ Oddمزام odd طب ما هن هدوء لكل ينقش مال هن
+
+326
+00:30:53,150 --> 00:31:00,650
+اللي هو even اه و هذه واحد اذا هذا odd من ذاتها
+
+327
+00:31:00,650 --> 00:31:07,870
+odd من ايش من ذاتها سواء beta واحد even ولا odd
+
+328
+00:31:07,870 --> 00:31:17,380
+اذا بتصير هذه لحالتينB1 is even وB1 is odd إذا B
+
+329
+00:31:17,380 --> 00:31:22,000
+يعني بتساوي هذه عبارة عن هيصير عبارة عن هذه يعني
+
+330
+00:31:22,000 --> 00:31:27,160
+الأم تبعتنا هذه هتصير عبارة عن اللي هو أوجد نص هنا
+
+331
+00:31:27,160 --> 00:31:34,590
+ماشي بيصير اتنين أس بيتا واحدبيتنين أس اتنين ألف
+
+332
+00:31:34,590 --> 00:31:39,870
+اتنين لعند بي ار اتنين ألف ار هدولة جذبنا ان هي
+
+333
+00:31:39,870 --> 00:31:44,330
+اكسرتهم الاهالي ماجذبناش بيت واحد ممكن تكون even
+
+334
+00:31:44,330 --> 00:31:48,990
+ممكن تكون ايش قد دا نفيه لحالتين حالة انها تكون
+
+335
+00:31:48,990 --> 00:31:56,090
+even يعني حصورة ايش مع الها اتنين ألف واحد او حالة
+
+336
+00:31:56,090 --> 00:32:00,680
+انها تكون odd اللي هي اتنين ألف واحد زادفى بي
+
+337
+00:32:00,680 --> 00:32:05,960
+اتنين الف اتنين الف اتنين لعند بي ار اتنين الف ار
+
+338
+00:32:05,960 --> 00:32:13,580
+الاولى هتطلعلي perfect square الاولى هتطلعلي
+
+339
+00:32:13,580 --> 00:32:17,460
+perfect square اللى هو اتنين بي اتنين لعند بي ار
+
+340
+00:32:17,460 --> 00:32:23,540
+الكل تربيع الف اتنين الف ار التانى ايش هتطلعليه
+
+341
+00:32:24,590 --> 00:32:29,930
+تنين perfect square twice perfect square هتطلع
+
+342
+00:32:29,930 --> 00:32:37,110
+للتاني اللي هو تنين في تنين أس
+
+343
+00:32:37,110 --> 00:32:43,290
+الف واحد بي اتنين الف اتنين لعين بي ار الف ار لكل
+
+344
+00:32:43,290 --> 00:32:53,000
+تاريخ لما كانت sigma n is oddSigma n is odd طلعتني
+
+345
+00:32:53,000 --> 00:32:58,100
+الان يا بتطلع perfect square يا twice ايهاش
+
+346
+00:32:58,100 --> 00:33:09,740
+perfect square اي سؤال اللي بعده يلا لا
+
+347
+00:33:09,740 --> 00:33:13,200
+اللي بعده اللي بعده اطلع سؤال تمانية ايوة اكبر اي
+
+348
+00:33:13,200 --> 00:33:16,500
+سؤال تمانية ايوة اطلع لفوق اطلع السؤال ايش بدك فيه
+
+349
+00:33:16,500 --> 00:33:23,030
+سؤال تمانية ماشي الحالالأسئلة عموما كلها محلولة بس
+
+350
+00:33:23,030 --> 00:33:26,590
+خلينا ناخد الأسئلة اللي احنا طلبناها منكم لان مش
+
+351
+00:33:26,590 --> 00:33:33,330
+هنلاحق الان بدنا نثبت ال summation واحد على دي دي
+
+352
+00:33:33,330 --> 00:33:37,990
+بتكسب ان بسوا sigma of n على مين على ان نطلع عليها
+
+353
+00:33:37,990 --> 00:33:39,950
+و نشوف كيف نتعامل مع حياتك أسئلة
+
+354
+00:33:57,320 --> 00:34:02,620
+هقولنا يا شباب السؤال اللي هو تمانية show that
+
+355
+00:34:02,620 --> 00:34:09,400
+اللي هو summation واحد على دي دي بتكسب n هذه ال
+
+356
+00:34:09,400 --> 00:34:12,580
+summation واحد على دي دي بتكسب n دي هو ال replic
+
+357
+00:34:12,580 --> 00:34:16,320
+اللي هو أنات زي ما بدك في الدار هتلاقيها دايما
+
+358
+00:34:16,320 --> 00:34:25,760
+بتساوي sigma of n على n ال proofأحنا حكينا المرة
+
+359
+00:34:25,760 --> 00:34:29,720
+الماضية و قبل شوية حكيتها عشان أستخدمها أنه لو
+
+360
+00:34:29,720 --> 00:34:41,120
+كانت F is multiplicative then F of N على صورة F of
+
+361
+00:34:41,120 --> 00:34:46,000
+D دي بتجسم N برضه أشمالها multiple
+
+362
+00:34:48,130 --> 00:34:54,510
+إذا لما نكون في عندي summation على دي بتقسم ان لا
+
+363
+00:34:54,510 --> 00:35:00,290
+إش جوا أول ما أخطر بالي أروح باتجاه ان ال
+
+364
+00:35:00,290 --> 00:35:04,030
+summation كله مع ال function اللي جوا اني أقول
+
+365
+00:35:04,030 --> 00:35:09,410
+عنها رايحة باتجاه ال multiplicative ومن ثم إيجادها
+
+366
+00:35:09,410 --> 00:35:13,990
+بيصير سهل باستخدام ال multiplicative إيش اللي
+
+367
+00:35:13,990 --> 00:35:17,900
+بقوله؟ خليني أشوفبس على الحالة سؤال قبل الـ 1 على
+
+368
+00:35:17,900 --> 00:35:19,840
+D لما أخد فانشين F of D بيسوي 1 على D
+
+369
+00:35:19,840 --> 00:35:23,780
+multiplicative برضه اللي هو شعوري ان هو
+
+370
+00:35:23,780 --> 00:35:27,100
+multiplicative و هتلاقي انه فعلا multiplicative
+
+371
+00:35:27,100 --> 00:35:30,420
+وسادف بقى انها multiplicative اذا اول اشي بدي
+
+372
+00:35:30,420 --> 00:35:37,360
+احاول اجايف هذه للصورة هذه بدي اقول له let F of D
+
+373
+00:35:37,360 --> 00:35:43,440
+بيسوي 1 على D ماشي الحالة الان F بتدعي انها
+
+374
+00:35:43,440 --> 00:35:49,070
+multiplicativeليش Multiplicative؟ تستسهل Let D1
+
+375
+00:35:49,070 --> 00:35:51,930
+وD2 element in Z بحيث الـ Greatest common divisor
+
+376
+00:35:51,930 --> 00:36:00,230
+بينهما يكون 1 وحسبني F of D1 في D2 بساوةاللي هو
+
+377
+00:36:00,230 --> 00:36:05,470
+حسب القانون هو 1 على D1 في D2 صح ولا لأ اللي هي
+
+378
+00:36:05,470 --> 00:36:11,330
+بيساوي 1 على D1 في 1 على D2 ويساوي F of D1 في F of
+
+379
+00:36:11,330 --> 00:36:16,790
+D إذا واضح أن F is a multiplicative function ماشي
+
+380
+00:36:16,790 --> 00:36:22,850
+الحال طيب مدام F multiplicative بتشجعني أن أقول
+
+381
+00:36:22,850 --> 00:36:31,820
+let F of Nبساوية الـ summation للـ F of D دي
+
+382
+00:36:31,820 --> 00:36:36,720
+بتجسمها اللي يمين اللي عبارة عن summation واحد على
+
+383
+00:36:36,720 --> 00:36:43,120
+D دي بتجسم اللي أنا بدور عليها بما أن F is
+
+384
+00:36:43,120 --> 00:36:47,200
+multiplicative إذا ال summation هذا إشماله is
+
+385
+00:36:47,200 --> 00:36:50,380
+multiplicative حسب النظرية اللي عندنا إذا صارت ال
+
+386
+00:36:50,380 --> 00:36:56,170
+F كابتنة إشمالها is multiplicativeالآن أنا بستخدم
+
+387
+00:36:56,170 --> 00:36:59,470
+الـ Multiplicative عشان تسهّل عليّ عملية الحسابات
+
+388
+00:36:59,470 --> 00:37:02,370
+طب عملية الحسابات كيف تسهّل في حالة الـ
+
+389
+00:37:02,370 --> 00:37:05,690
+Multiplicative أنه أنا بكتبها على صورة Product of
+
+390
+00:37:05,690 --> 00:37:10,130
+Primes فبصير إيجاد اللي هي الـ Function للـ Primes
+
+391
+00:37:10,130 --> 00:37:14,370
+في الغالب الأسئلة اللي بالشكل هذا أسهل من نوجد للـ
+
+392
+00:37:14,370 --> 00:37:17,410
+N in general طب مدهن بدي أروح باتجاه الـ Product
+
+393
+00:37:17,410 --> 00:37:21,030
+of Primes لأن الـ N التابعتي بتكون أكبر من مين؟ من
+
+394
+00:37:21,030 --> 00:37:24,930
+واحدأذا بدي أعالج حالتي الواحد لحالة مثل ما علجنا
+
+395
+00:37:24,930 --> 00:37:29,270
+قبل قليل حالتي الواحد معالجة و خالصة يعني من رأس
+
+396
+00:37:29,270 --> 00:37:54,600
+الدهر لو كتبناإذا N أكبر من 1 إذا N
+
+397
+00:37:54,600 --> 00:38:03,520
+أكبر من 1 إذا N أكبر من 1إذاً by unique
+
+398
+00:38:03,520 --> 00:38:07,700
+factorization theorem N can be written as N بساوية
+
+399
+00:38:07,700 --> 00:38:15,740
+P1 Alpha 1 لعين PR Alpha HR معايا يا شباب؟ إذا صار
+
+400
+00:38:15,740 --> 00:38:22,520
+عندي F of N حسب تسهلة بساوية F of P1 Alpha 1 لعين
+
+401
+00:38:22,520 --> 00:38:27,040
+PR Alpha R بساوية F is multiplicative إذاً by
+
+402
+00:38:27,040 --> 00:38:30,180
+induction one can easily show that اللي هو بساوية
+
+403
+00:38:30,180 --> 00:38:39,610
+Fof b1 α1 عن bA F of bR αR ليش؟ لأن كل واحد منهم
+
+404
+00:38:39,610 --> 00:38:43,290
+بي واحد ومع الـ B التاني بي اتنين مع بي تلاتة R
+
+405
+00:38:43,290 --> 00:38:47,770
+Relatively Primes in Pairs فأكيد اللي هو بتتوزع
+
+406
+00:38:47,770 --> 00:38:52,110
+الـ F إذن الآن صارت التحول للسؤال إن بس أودد مين؟
+
+407
+00:38:52,110 --> 00:38:56,990
+F of bI αI بدي أوددهم، بضربهم في بعض، بطلع اللي هو
+
+408
+00:38:56,990 --> 00:39:01,580
+المطلوب تمشيوف كيف، إذن استراتيجية الحل سهلةبتظهر
+
+409
+00:39:01,580 --> 00:39:07,680
+عملية عملية اللي هو مهارات حسابات لان احسب f of bi
+
+410
+00:39:07,680 --> 00:39:14,540
+αi بساوي ايش اللي القانون عنده اللي هو f of n
+
+411
+00:39:14,540 --> 00:39:17,500
+بساوي ال summation واحد على دي يعني بيساوي ال
+
+412
+00:39:17,500 --> 00:39:24,500
+summation واحد على دي دي بتجسمين الان bi αi وهنا
+
+413
+00:39:24,500 --> 00:39:31,710
+سهولة ال prime اللي هو قواسم ال bi αi كتليا واحد،
+
+414
+00:39:31,710 --> 00:39:35,750
+يا بي آي، يا بي آي تربيع، يا بي آي تكعيب، لعند ما
+
+415
+00:39:35,750 --> 00:39:40,510
+أصل لعند مين؟ بي آي ألف آي، كل إن هدولة قواصم للبي
+
+416
+00:39:40,510 --> 00:39:45,710
+آي ألف آي، يعني القواصم مش او، و، و، و، يعني
+
+417
+00:39:45,710 --> 00:39:49,330
+القواصمة هي واحد، وبي آي، وبي آي تربيع، وبي آي
+
+418
+00:39:49,330 --> 00:39:54,170
+تكعيب لعند ما أصل بي آي ألف آي، إذا صار عندي
+
+419
+00:39:54,170 --> 00:39:59,880
+ويساوي، هذا صار summation، واحد على واحد،زائد واحد
+
+420
+00:39:59,880 --> 00:40:07,880
+على بي آي زائد واحد
+
+421
+00:40:07,880 --> 00:40:13,520
+على بي آي تربيع لما أصل عند واحد على بي آي ألف آي
+
+422
+00:40:15,110 --> 00:40:20,810
+هذه المتتالية أساسها مين واحد على بي آي ايش
+
+423
+00:40:20,810 --> 00:40:24,810
+قانونها زي ما كنا نقول زمان ريح أسن ونقص واحد علي
+
+424
+00:40:24,810 --> 00:40:29,210
+ريح نقص واحد نون اللي هو عدد مين عدد الحدود لأن
+
+425
+00:40:29,210 --> 00:40:34,470
+عدد الحدود هنا أشماله Alpha I زائد واحد لأن هنا
+
+426
+00:40:34,470 --> 00:40:38,270
+عندنا Alpha I وهي عندي كمان term بيصير Alpha I
+
+427
+00:40:38,270 --> 00:40:44,860
+زائد واحد بيصير اللي هو مجموحة ولا بساوياللي هو
+
+428
+00:40:44,860 --> 00:40:54,620
+واحد على بي آي الأساس أس الف آي زائد واحد ناقص
+
+429
+00:40:54,620 --> 00:41:00,300
+فاهمين عليها واحد على واحد على بي آي ناقص واحد
+
+430
+00:41:00,300 --> 00:41:08,140
+ماشي الحالالان اضرب فوق و تحت اضرب فوق و تحت عشان
+
+431
+00:41:08,140 --> 00:41:14,040
+ابسطها بي آي الف آي زائد واحد على بي آي الف آي
+
+432
+00:41:14,040 --> 00:41:21,760
+زائد واحد بصير عندي هذا المقدار بعد اذا كنت بدأ
+
+433
+00:41:21,760 --> 00:41:22,460
+امسحه
+
+434
+00:41:41,940 --> 00:41:47,860
+شوفوا يا شباب بدّي صارت عندي F of F of P I Alpha I
+
+435
+00:41:47,860 --> 00:41:57,060
+F of P I Alpha I بتساوي اللي هو هذا المقدار ضربته
+
+436
+00:41:57,060 --> 00:42:01,420
+فوق P I Alpha I زائد واحد وتحت نفس الاشي هذا بيصير
+
+437
+00:42:01,420 --> 00:42:09,980
+عبارة عن واحد ناقص P I Alpha I زائد واحد علىبي أس
+
+438
+00:42:09,980 --> 00:42:17,380
+ألف آي ناقص بي أس ألف آي زائد واحد، مظبوط؟ طلّع لي
+
+439
+00:42:17,380 --> 00:42:28,860
+اللي هو واحد على بي آي ألف آي كعامل مشترك زائد
+
+440
+00:42:28,860 --> 00:42:33,640
+واحد، لأ لأ بدون زائد واحد، خلّي واحد ده، بيضل
+
+441
+00:42:33,640 --> 00:42:37,910
+اللي جوا مين هو؟وبدي أضرب بالمرة فوق بناقص و تحت
+
+442
+00:42:37,910 --> 00:42:44,930
+باش بناقص بعد أذنكم بيصير بي آي ألف آي زائد واحد
+
+443
+00:42:44,930 --> 00:42:49,190
+ناقص واحد على لما أخد عامل مشترك بي آي ألف واحد
+
+444
+00:42:49,190 --> 00:42:53,270
+بيصير واحد ناقص بي آي لما أضربه في ناقص في السيرة
+
+445
+00:42:53,270 --> 00:43:00,370
+الشمالها بي آي ناقص واحد واضح ها واضح اللي سويته
+
+446
+00:43:00,370 --> 00:43:06,920
+لأن هذه ال F of واحدة منهمالأن F of N إيش مالها؟
+
+447
+00:43:06,920 --> 00:43:11,520
+حاصل ضربهم كلهم، مظبوط؟ إذا الـ F of N هي ال
+
+448
+00:43:11,520 --> 00:43:15,120
+product للـ F of P واحد Alpha واحد لعند F of P R
+
+449
+00:43:15,120 --> 00:43:21,780
+Alpha R إذا صار عندي F of N بساوي له product لهذه
+
+450
+00:43:21,780 --> 00:43:26,780
+اللي هو عبارة عن ال product لواحد على P I Alpha I
+
+451
+00:43:27,860 --> 00:43:33,680
+معايا يا شباب في بي آي ألف آي زائد واحد ناقص واحد
+
+452
+00:43:33,680 --> 00:43:39,840
+على بي آي ناقص واحد I من عند واحد لعند مين R الآن
+
+453
+00:43:39,840 --> 00:43:44,300
+ال product لهذه بي واحد ألف واحد بي اتنين ألف
+
+454
+00:43:44,300 --> 00:43:48,140
+اتنين بي تلت ألف تلت لعند بي R ألف R من هي الان
+
+455
+00:43:48,140 --> 00:43:53,120
+إذا صار هذا ال product عبارة عن واحد علان مضروب
+
+456
+00:43:53,120 --> 00:43:59,020
+فيهالـ product هذا هو عبارة عن sigma of N إذا صار
+
+457
+00:43:59,020 --> 00:44:03,380
+عبارة عن 1 على N في sigma of N of N أخر sigma of N
+
+458
+00:44:03,380 --> 00:44:10,120
+على N وهو المقبول إذا صار عندي اللي هو sigma of N
+
+459
+00:44:10,120 --> 00:44:14,900
+على N بساوي اللي هو F of N F of N مين هي أصلا اللي
+
+460
+00:44:14,900 --> 00:44:19,240
+عبارة عن فرضناها اللي هو summation 1 على D D بتكسب
+
+461
+00:44:19,240 --> 00:44:19,420
+N
+
+462
+00:44:27,090 --> 00:44:32,150
+هدولة مين هنا؟ هدولة مين هنا؟ هدول ال product اللي
+
+463
+00:44:32,150 --> 00:44:38,310
+هنا 1 على B1 Alpha 1 في 1 على B2 Alpha 2 لما 1 على
+
+464
+00:44:38,310 --> 00:44:44,990
+B R Alpha R عصر ضرب ان هدولة مين هنا؟ لأ مش ال
+
+465
+00:44:44,990 --> 00:44:50,770
+factorization للأن مش هي الأن اه و يساوي 1 على N
+
+466
+00:44:50,770 --> 00:44:53,630
+أي سؤال؟
+
+467
+00:44:55,560 --> 00:45:04,400
+بعد تبانية نيجي لسؤال 12 12 .. 12 .. 12 الأسئلة ..
+
+468
+00:45:04,400 --> 00:45:10,340
+الأسئلة .. الأسئلة جزء مهم من المادة خصوصا في الـ
+
+469
+00:45:10,340 --> 00:45:15,340
+Chapter هذا لأن الأسئلة بتحمل فكرة عديدة إن ما
+
+470
+00:45:15,340 --> 00:45:19,660
+حلتهاش هتحس حالك اللي هو في عندك نقص كبير في الفهم
+
+471
+00:45:19,660 --> 00:45:28,380
+للمادة نيجي ل .. بدنا نحلاللي هو المعادلة أو الـ
+
+472
+00:45:28,380 --> 00:45:35,900
+possible solutions for tau of n بتساوية عشرة طبعا
+
+473
+00:45:35,900 --> 00:45:38,480
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+474
+00:45:38,480 --> 00:45:39,140
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+475
+00:45:39,140 --> 00:45:39,780
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+476
+00:45:39,780 --> 00:45:39,780
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+477
+00:45:39,780 --> 00:45:39,800
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+478
+00:45:39,800 --> 00:45:39,880
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+479
+00:45:39,880 --> 00:45:39,980
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+480
+00:45:39,980 --> 00:45:40,080
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+481
+00:45:40,080 --> 00:45:40,500
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+482
+00:45:40,500 --> 00:45:40,560
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+483
+00:45:40,560 --> 00:45:40,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+484
+00:45:40,560 --> 00:45:51,360
+.. ال .. ال ..
+
+485
+00:45:51,360 --> 00:45:53,300
+ال .. ال ..
+
+486
+00:45:54,890 --> 00:45:59,150
+البرمجة النايه اللي بيكون تمنيها طيب لنتشوف سؤال
+
+487
+00:45:59,150 --> 00:46:04,570
+12 find the form of the positive of all positive
+
+488
+00:46:04,570 --> 00:46:08,650
+integers and satisfying tau of n بساوة عشانها
+
+489
+00:46:08,650 --> 00:46:13,230
+بقوللي أوجد كل ال positive integers اللي بيحقق إن
+
+490
+00:46:13,230 --> 00:46:19,130
+tau of n إيش بساوة بساوة عشانها و بقوللي بعدين
+
+491
+00:46:19,130 --> 00:46:25,510
+أوجد أصغر واحدمن هنا What is the smallest integer
+
+492
+00:46:25,510 --> 00:46:33,970
+لهو for such ends ناشي؟ بده نوجد أصغر واحد فيهم هو
+
+493
+00:46:33,970 --> 00:46:38,670
+الجزء الأول هو خلّيني أقول هو اللي فيه الفكرة
+
+494
+00:46:38,670 --> 00:46:41,490
+الجزء الثاني على طول بطلع لإنه بيصير أصغر واحد
+
+495
+00:46:41,490 --> 00:46:44,890
+تعرف أصغر واحد سهل يجده صلى على النبي عليه الصلاة
+
+496
+00:46:44,890 --> 00:46:48,530
+والسلام solution إحنا
+
+497
+00:46:49,500 --> 00:46:53,820
+جابل بشوية لما جينا كتبنا Tau of N لـ N بتساوي P1
+
+498
+00:46:53,820 --> 00:46:58,380
+α1 لعند PR αR من وجه الفكرة Tau of N إيش بتساوي
+
+499
+00:46:58,380 --> 00:47:03,060
+عبارة عن الف واحد زائد واحد لعند Alpha R زائد إيش
+
+500
+00:47:03,060 --> 00:47:07,640
+واحد إذا Tau of N هي عبارة عن اللي هي جاية من مين
+
+501
+00:47:07,640 --> 00:47:13,500
+من أسس الـ Primes تبعات اللي هي ال factors لمين لـ
+
+502
+00:47:13,500 --> 00:47:19,350
+N مظبوط ولا لأ طيبالان الفكرة في الحل ان هذه
+
+503
+00:47:19,350 --> 00:47:23,710
+العشرة بتشوف .. طبعا ال product توفر ان عبارة عن
+
+504
+00:47:23,710 --> 00:47:29,070
+product of أسس بتشوف كل productات الممكنة للعشرة
+
+505
+00:47:29,070 --> 00:47:34,710
+ماشي الحالالـ Product الممكن للأول عشر أيش هي؟
+
+506
+00:47:34,710 --> 00:47:38,110
+اتنين و تلاتة و خمسة سيبك من الواحد لأن الواحد مش
+
+507
+00:47:38,110 --> 00:47:40,830
+هيكون له قيمة لأنه بيصير Alpha واحد زاد واحد
+
+508
+00:47:40,830 --> 00:47:43,910
+بيساوي واحد بيطلع Alpha واحد بيساوي سفر بيصير و
+
+509
+00:47:43,910 --> 00:47:46,470
+كأنه الواحد احنا نقول الـ unique factorization
+
+510
+00:47:46,470 --> 00:47:52,950
+theorem خلاص ما هو احنا الواحد الواحد neglected اه
+
+511
+00:47:52,950 --> 00:48:00,700
+طيببناء عليه إنه انسى جثة الواحد ك factor إلى أن
+
+512
+00:48:00,700 --> 00:48:03,660
+نقول عشر في واحد واحد كله ما هو عشر في واحد في
+
+513
+00:48:03,660 --> 00:48:06,660
+واحد في واحد في واحد وكله مش عامل غلب حالك كل اللي
+
+514
+00:48:06,660 --> 00:48:10,240
+هيطلع إن إيش حاجة واحدة لإن الألفات تبعتك هيطلع إن
+
+515
+00:48:10,240 --> 00:48:13,020
+إيش وما هي اللي تبعت الواحد سفر هل جيت تفهم شو
+
+516
+00:48:13,020 --> 00:48:17,540
+معناته؟ حتفهم؟ طيب، إذا الآن الفكرة العشر ميل
+
+517
+00:48:17,540 --> 00:48:20,960
+الـdivisors لها لإن بتكتبها على صورة ال product
+
+518
+00:48:20,960 --> 00:48:25,440
+عشرة، بقدر أكتبها على صورة عشرةهو عشرة بقى قدر
+
+519
+00:48:25,440 --> 00:48:30,940
+اكتبها على سورة 2؟ في غير هيك؟ لأ طبعا أكيد لأ
+
+520
+00:48:30,940 --> 00:48:37,960
+طبعا نيجي الآن بنقول العشرة الـ tau of N العشرة
+
+521
+00:48:37,960 --> 00:48:43,100
+هذه عبارة عن .. هتعملني عبارة عن tau of N بساوي
+
+522
+00:48:43,100 --> 00:48:50,380
+Alpha 1 زي 1 يعني الحالة الأولى F اللي هو او case
+
+523
+00:48:50,380 --> 00:48:59,190
+1الفا واحد زائد واحد بيساوي عشرة case two الفا
+
+524
+00:48:59,190 --> 00:49:04,810
+واحد زائد واحد في الفا اتنين زائد واحد بيساوي
+
+525
+00:49:04,810 --> 00:49:09,830
+اتنين في مين؟ مظبوط ولا لا؟ في غير هيك؟ لأ اللي
+
+526
+00:49:09,830 --> 00:49:12,290
+فيجيبني العشرة بس ان اتنين في الخمسة هو العشرة
+
+527
+00:49:12,290 --> 00:49:17,070
+وقول لي ليش هذه بتعطيني إذا الفا واحد ده إيش
+
+528
+00:49:17,070 --> 00:49:26,780
+بيساوي إذا انتبعتنا هتصير عبارة عن بيأُس تسعة ماشي
+
+529
+00:49:26,780 --> 00:49:30,240
+الحال من وين هذه اللي قد جاية ما احنا قلنا أصل
+
+530
+00:49:30,240 --> 00:49:33,320
+الموضوع أن بسوء بي واحد ألف واحد أن بي أر ألف أر
+
+531
+00:49:33,320 --> 00:49:38,080
+التوقف عن هو عدد ال devices اللي هي حاسن product
+
+532
+00:49:38,080 --> 00:49:44,040
+of الأسس لأن بما أنه product of numbers عندي بدي
+
+533
+00:49:44,040 --> 00:49:47,920
+أوجد هذول الاحتماليات اللي بيولدن العشرة التوقف أن
+
+534
+00:49:47,920 --> 00:49:51,970
+تولد العشرة هي اما بعشرة لحالهايا أما بـ2×5 في حال
+
+535
+00:49:51,970 --> 00:49:55,870
+تولد بـ10 لحالها وهذا قيمة التوف أن إذا قيمتها على
+
+536
+00:49:55,870 --> 00:49:58,870
+صورة ألف واحد زائد واحد أخدتها كمية واحدة أول شيء
+
+537
+00:49:58,870 --> 00:50:02,390
+إذا الألف واحد ايش صارت بالساوية تسعة إذا الأن
+
+538
+00:50:02,390 --> 00:50:08,430
+تبعتها عبارة عن بي واحد أس تسعة يعني تبعتها بي أس
+
+539
+00:50:08,430 --> 00:50:14,430
+تسعة نجي الآن التانية عبارة عن ألف واحد بالساوية
+
+540
+00:50:14,430 --> 00:50:20,870
+اتنين أسف واحد فاهمين أه؟ألف اتنين بيساوي اياش
+
+541
+00:50:20,870 --> 00:50:32,270
+اربع معايا يعني عندي اللي هو ال M عندي هتصير بي
+
+542
+00:50:32,270 --> 00:50:41,830
+وحد في Q او بي واحد بي اتنين اص اياش اص اربع
+
+543
+00:50:45,110 --> 00:50:49,470
+و بيه واحد و بيه اتنين انا بـ Primes انا Distinct
+
+544
+00:50:49,470 --> 00:50:57,310
+Primes اه و بيه هذي و هذي يعني الآن .. يعني كلهم
+
+545
+00:50:57,310 --> 00:51:00,970
+هذولة و كلهم هذولة هذولة Infinite و هذولة Infinite
+
+546
+00:51:00,970 --> 00:51:05,760
+دي البالةهؤلاء أي برايم في الدنيا ترفع إلى تسعة
+
+547
+00:51:05,760 --> 00:51:09,600
+تطلع الـ tau van الواش بتساوي عشرة وأي برايم في
+
+548
+00:51:09,600 --> 00:51:14,420
+الدنيا بي واحد في بي اثنين واسة أربعة تطلع برضه
+
+549
+00:51:14,420 --> 00:51:21,750
+جداش عشرةإذا the set of all such ands are the set
+
+550
+00:51:21,750 --> 00:51:28,230
+of all such numbers in the form b9 where b is any
+
+551
+00:51:28,230 --> 00:51:36,730
+prime and بتسوى b1, b2 to the 4 where b1 and b2
+
+552
+00:51:36,730 --> 00:51:42,090
+are any distinct primes الآن طلب اللي بعيد هي إيش
+
+553
+00:51:42,090 --> 00:51:48,310
+هو find the smallestFind the smallest من الـ
+
+554
+00:51:48,310 --> 00:51:52,210
+smallest الآن أصغر واحد في الـ Formة هذه أصغر واحد
+
+555
+00:51:52,210 --> 00:51:58,210
+في الـ Formة هذه اللي هو 2 أُس 9 أصغر واحد في الـ
+
+556
+00:51:58,210 --> 00:52:06,750
+Formة هذه على طول بيجي عبالك أنت 2 في 3 أُس 4 أو 3
+
+557
+00:52:06,750 --> 00:52:13,750
+في 2 أُس 4واضح مين الأصغر هذا أصغر من اللي فوق صح
+
+558
+00:52:13,750 --> 00:52:18,430
+ولا لأ الان الان هذا برضه أصغر من اللي فوق لإن هذا
+
+559
+00:52:18,430 --> 00:52:21,390
+في لسه ذاك هذا مضروب في تلاتة وذاك مضروب في اتنين
+
+560
+00:52:21,390 --> 00:52:26,810
+أس خمسة اذا مين the smallest one اللي هو تلاتة في
+
+561
+00:52:26,810 --> 00:52:36,850
+اتنين أس أربع واضح ها حل السؤال اتناش طيب الان
+
+562
+00:52:36,850 --> 00:52:45,280
+التانيبقول لك ممكن اقول لك find the solution if
+
+563
+00:52:45,280 --> 00:52:52,320
+exists for sigma of n بتساوى عشان اه sigma of n
+
+564
+00:52:52,320 --> 00:52:57,660
+بتساوى عشان اه
+
+565
+00:52:57,660 --> 00:53:03,360
+فكرة فكرة السيجمات انه ال sigma هي عبارة عن ايش
+
+566
+00:53:03,360 --> 00:53:08,410
+مجموع ال divisorsمثلما تموّع الـ divisors إذا الـ
+
+567
+00:53:08,410 --> 00:53:11,530
+N اللي نفسها اللي بوديت لها الـ Sigma واحدة منهن
+
+568
+00:53:11,530 --> 00:53:18,130
+آه فالآن لما أقول sigma of N بساوي اللي هو مية إذا
+
+569
+00:53:18,130 --> 00:53:24,530
+أنا قطعاً قطعاً قطعاً ببحثش عن الحلول من مية وطالع
+
+570
+00:53:24,530 --> 00:53:33,780
+ليش؟ لأن sigma of اللي هي ميةهتصير أكبر من مية
+
+571
+00:53:33,780 --> 00:53:38,140
+يعني أكيد و هذا الكلام صحيح لكل و مية و واحد و مية
+
+572
+00:53:38,140 --> 00:53:39,860
+و اتنين و مية و تلاتة و مية اتنين و تلاتة و مية
+
+573
+00:53:39,860 --> 00:53:39,880
+اتنين و تلاتة و مية اتنين و تلاتة و مية اتنين و
+
+574
+00:53:39,880 --> 00:53:40,040
+تلاتة و مية اتنين و تلاتة و مية اتنين و تلاتة و
+
+575
+00:53:40,040 --> 00:53:40,380
+مية اتنين و تلاتة و مية اتنين و تلاتة و مية اتنين
+
+576
+00:53:40,380 --> 00:53:41,420
+و تلاتة و مية اتنين و تلاتة و مية اتنين و تلاتة و
+
+577
+00:53:41,420 --> 00:53:44,720
+مية اتنين و تلاتة و مية اتنين و تلاتة و مية اتنين
+
+578
+00:53:44,720 --> 00:53:48,790
+و تلاتة و مية اتنين وماشي احنا بنشتغل على اشي ع
+
+579
+00:53:48,790 --> 00:53:52,490
+جدنا اللي هو ع جد المعلومات اللي حتى الان بنيت هنا
+
+580
+00:53:52,490 --> 00:53:57,390
+جهلنا انه sigma of n بسوء عشرة find all solutions
+
+581
+00:53:57,390 --> 00:54:06,380
+if exist اذا بدي اقوله we investigate onlyon n
+
+582
+00:54:06,380 --> 00:54:13,400
+less than عشرة او less than or equal تسعة why?
+
+583
+00:54:13,660 --> 00:54:20,060
+because sigma of n is always greater strictly than
+
+584
+00:54:20,060 --> 00:54:25,700
+ten او sigma of n is strictly greater than n
+
+585
+00:54:25,700 --> 00:54:31,860
+فاهمين علينا بقولها احنا بنبحث في الأجل من الـ n
+
+586
+00:54:32,940 --> 00:54:37,580
+اللي ماعطيها، اللي هي العشرة لأجل من عشرة لأن الـ
+
+587
+00:54:37,580 --> 00:54:42,060
+Sigma of عشرة واللي بعيدها دايماً أكبر من عشرة
+
+588
+00:54:42,060 --> 00:54:48,900
+للحقيقة اللي بتقولك Sigma of N أكبر من N for every
+
+589
+00:54:48,900 --> 00:54:52,620
+N بناقل
+
+590
+00:54:52,620 --> 00:55:02,090
+عليه لما بيقول Find a solutionof sigma of n بساوية
+
+591
+00:55:02,090 --> 00:55:11,990
+عشرة if exist بدي بقوله sigma of واحد solution
+
+592
+00:55:11,990 --> 00:55:16,690
+sigma of واحد بوجده بساوية واحد sigma of اتنين
+
+593
+00:55:16,690 --> 00:55:26,110
+تلاتة sigma of اربعة اللي هو لأ شو خمسة اتنين قصة
+
+594
+00:55:26,110 --> 00:55:31,890
+اللي هو بطلع سبعة لأ2 أُس 2 سيجما of 4 2 أُس 2
+
+595
+00:55:31,890 --> 00:55:37,790
+ناقص 1 على 2 أُس ناقص 1 ماشي الحالة مظبط 2 أُس 2
+
+596
+00:55:37,790 --> 00:55:43,410
+ناقص فاهمين ايش بقولها عقل ناقص 1 على 2 أس 1 و
+
+597
+00:55:43,410 --> 00:55:50,910
+يساوي 2 أس 1 زائد 1 و يساوي 8 ناقص 1 ناقص 7 ناقص 7
+
+598
+00:55:50,910 --> 00:55:59,960
+مظبط سيجما of 5 6خمسة درجة واحد ستة البرامج سهلة
+
+599
+00:55:59,960 --> 00:56:04,680
+Sigma of ستة اللي هي اتنين في تلاتة اتنين جداش
+
+600
+00:56:04,680 --> 00:56:10,220
+تلاتة و Sigma of تلاتة ماجيبنهاش Sigma of تلاتة
+
+601
+00:56:10,220 --> 00:56:17,200
+اربع هذا اربع في تلاتة اتناش Sigma of مين؟ of ستة
+
+602
+00:56:17,200 --> 00:56:22,220
+فاهمين عليش بقولها Sigma of سبعة تمانية Sigma of
+
+603
+00:56:22,220 --> 00:56:27,830
+تمانيةاللي هي 2 أس 4 ناقص هو يساوي 15 سيجما of 9
+
+604
+00:56:27,830 --> 00:56:34,110
+تلاتة تربيع تلاتة تكعيب ليه؟ اه ليه 26 ع 2 13
+
+605
+00:56:34,110 --> 00:56:41,510
+مظبوط طيب سيجما of 10 قولنا بلاش سيجما of 10 او
+
+606
+00:56:41,510 --> 00:56:45,530
+سيجما of N أكبر من 10 for every N أكبر يساوي 10
+
+607
+00:56:45,530 --> 00:56:56,860
+therefore no such N existsبالظبط؟ مافيش ولا واحدة
+
+608
+00:56:56,860 --> 00:57:03,280
+طلعت عشانها اللي بعده؟ إيش السؤال اللي بعده اللي
+
+609
+00:57:03,280 --> 00:57:09,120
+إحنا طالبينه؟ إحسابات السؤال
+
+610
+00:57:09,120 --> 00:57:15,280
+اللي بعده نحسب .. خليني بس أكمل هذا show that أو
+
+611
+00:57:15,280 --> 00:57:19,640
+show each of the followingعندي N .. طبعا الـ K
+
+612
+00:57:19,640 --> 00:57:22,800
+أشمخد أكبر يساوي 2 عشان .. اللي هو اختصار الوقت
+
+613
+00:57:22,800 --> 00:57:26,100
+لإنه خلص المحاضرة N بيساوي 2 أسكت Minus 1
+
+614
+00:57:26,100 --> 00:57:30,120
+satisfying the equation Sigma of N بيساوي 2 N ناقص
+
+615
+00:57:30,120 --> 00:57:36,760
+إيهاش 1 بدنا نثبت إنه Sigma of هذه الـ N بيساوي 2N
+
+616
+00:57:36,760 --> 00:57:41,950
+ناقص مين؟ ناقص 1 إحسابات و بس إحساباتماشي ال sigma
+
+617
+00:57:41,950 --> 00:57:46,990
+of n بيساوي sigma of 2 أُس k-1 أُس 2 2 أُس k-1
+
+618
+00:57:46,990 --> 00:57:51,630
+اللي هو معروفة اللي هي قيمتها بتضيف 1 وناقص 1 على
+
+619
+00:57:51,630 --> 00:57:56,810
+2 ناقص 1 حيث الأساس إيش 2 معايا الان هذي بيصير
+
+620
+00:57:56,810 --> 00:58:02,370
+عبارة عن 2 أُس k ناقص 1 خد ال 2 برا هذي بيصير 2 في
+
+621
+00:58:02,370 --> 00:58:10,460
+2 k-1 ناقص 1 اللي هي عبارة عن 2 n ناقص 1 واضح؟الان
+
+622
+00:58:10,460 --> 00:58:14,920
+اللي بعضه بيه برضه similarly اتنين أسكيه ماينس
+
+623
+00:58:14,920 --> 00:58:17,760
+واحد is a prime ماعطيك انه اتنين أسكيه ماينس واحد
+
+624
+00:58:17,760 --> 00:58:20,200
+كله عكت على بعض ايه ايه ايه ايه ايه ايه ايه ايه
+
+625
+00:58:20,200 --> 00:58:22,540
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+626
+00:58:22,540 --> 00:58:22,960
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+627
+00:58:22,960 --> 00:58:23,320
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+628
+00:58:23,320 --> 00:58:23,360
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+629
+00:58:37,630 --> 00:58:41,550
+يعني sigma of n طلعت لك هنا اتنين n نقص واحد هنا
+
+630
+00:58:41,550 --> 00:58:45,970
+وطلعت لك اياش اتنين n و أحيانا تطلع sigma of n ايش
+
+631
+00:58:45,970 --> 00:58:51,730
+بالساوية n زائد واحد إذا مافيش role معينة معايا لأ
+
+632
+00:58:51,730 --> 00:58:55,790
+يعني انه بدلالة n مباشرة أما ال role موجودة لياك
+
+633
+00:58:55,790 --> 00:59:02,970
+طيب عندي sigma of n اللي هي n هيهابساوي sigma of
+
+634
+00:59:02,970 --> 00:59:05,610
+الأول في sigma of التاني لإن الاتنين أشماليا
+
+635
+00:59:05,610 --> 00:59:09,650
+relative ال prime و sigma is multiplicative sigma
+
+636
+00:59:09,650 --> 00:59:14,110
+للتاني اللي هو أشماله التاني عبارة عن ال prime هذا
+
+637
+00:59:14,110 --> 00:59:19,930
+إذا إيش قيمته هو زائد واحد في sigma لهذا بيصير
+
+638
+00:59:19,930 --> 00:59:26,370
+عندي الآن sigma of n بساوي اللي هي اتنين sigma of
+
+639
+00:59:26,370 --> 00:59:28,950
+n بساوي اتنين أسكت minus واحد
+
+640
+00:59:31,860 --> 00:59:39,720
+نقص واحد نقص واحد زائد واحد المفروض اه اتنين
+
+641
+00:59:39,720 --> 00:59:47,410
+سيجموفران سيجموفران بيسوي اتنين اوس كي2-k-1 prime
+
+642
+00:59:47,410 --> 00:59:53,930
+أه زائد واحد المفروض و هذه أيش القيمة إلها بحسبها
+
+643
+00:59:53,930 --> 00:59:58,890
+أه اللي هي عبارة عن 2k-1 على 2-1 اللي هي نفسها
+
+644
+00:59:58,890 --> 01:00:06,060
+فمين أه هذه هذه هي هذه كيف هذه موجودةلا اصبر عليها
+
+645
+01:00:06,060 --> 01:00:11,600
+هذه ايش قيمتها اتنين اتنين أُس الأُس زائد واحد
+
+646
+01:00:11,600 --> 01:00:15,800
+الأُس هنا K ناقص واحد زائد واحد بيطلع K بيصير
+
+647
+01:00:15,800 --> 01:00:19,140
+اتنين أس K ناقص واحد على الأساس ناقص واحد اتنين
+
+648
+01:00:19,140 --> 01:00:24,160
+ناقص واحد اللي هو ايش إذا صارت sigma of هذه هيها
+
+649
+01:00:27,900 --> 01:00:32,200
+أه الآن بدي أجيبها على ال form اللي عندي صارت عندي
+
+650
+01:00:32,200 --> 01:00:36,880
+لأن sigma of n بساوي هذا المقدار في هذا المقدار
+
+651
+01:00:36,880 --> 01:00:40,820
+أخد الآن زي ما بتقول أخد التنين عامل مشترك بيصير
+
+652
+01:00:40,820 --> 01:00:44,180
+اتنين K minus واحد أو خلّيني أقول سحب التنين مش
+
+653
+01:00:44,180 --> 01:00:46,140
+عامل مشترك سحب التنين يا عزيزي بيصير اتنين في
+
+654
+01:00:46,140 --> 01:00:50,380
+اتنين K minus واحد هذا كله مين هو؟ الآن صارت اتنين
+
+655
+01:00:50,380 --> 01:00:56,340
+اثنان فعلا اطلع لفوق اطلع
+
+656
+01:00:56,340 --> 01:01:01,680
+لبعدلأ ضايل .. ضايل .. ايه ضايلة هذه ايوة ضايل
+
+657
+01:01:01,680 --> 01:01:09,660
+سؤالين لسه يلا خليني اكمل .. خليني اكمل عندي الآن
+
+658
+01:01:09,660 --> 01:01:16,740
+اللي جابله .. السؤال اللي جابله عندي Cنفترض أن
+
+659
+01:01:16,740 --> 01:01:22,020
+اتنين أس كيه ناقص ثلاثة أشمالها prime وماخد n
+
+660
+01:01:22,020 --> 01:01:28,060
+بتساوي هذا في ال prime مشابه للي قبل بنفس السلوب
+
+661
+01:01:28,060 --> 01:01:32,360
+sigma of n sigma لهذه لها sigma لهذه في sigma لهذه
+
+662
+01:01:32,360 --> 01:01:36,860
+اللتي في ال prime sigma للأولى اللي هي عبارة عن
+
+663
+01:01:36,860 --> 01:01:40,640
+هذا ال prime إذا صار اتنين كيه ناقص ثلاثة زائد
+
+664
+01:01:40,640 --> 01:01:44,460
+واحد بس انتم كيف عملوا هذه في اتنين أس كيه ناقص
+
+665
+01:01:44,460 --> 01:01:52,180
+واحدالآن وزّع اثنين أسكيه على هذه مكة كتلة واحدة
+
+666
+01:01:52,180 --> 01:01:58,010
+طلعت هذهبعدين اتنين أسكيه ضربها في هذه هيها بعدين
+
+667
+01:01:58,010 --> 01:02:01,850
+الان ناقص واحد ضربها في هذه كلها هذه عبارة عن
+
+668
+01:02:01,850 --> 01:02:05,230
+اتنين أسكيه ناقص اتنين صارت فناقص الها بيصير ناقص
+
+669
+01:02:05,230 --> 01:02:08,150
+اتنين أسكيه زاد اتنين ليش عمل هيك؟ بدي يحافظ على
+
+670
+01:02:08,150 --> 01:02:12,150
+هذه عشان يحصل على اتنين ان زاد اتنين الان هذه مع
+
+671
+01:02:12,150 --> 01:02:16,270
+هذه بتروح بيصير هذا المقدار زاد اتنين هذا المقدار
+
+672
+01:02:16,270 --> 01:02:23,330
+هو هذاأخدت 2 من الأولى صارت عبارة عن 2N زائداش 2
+
+673
+01:02:23,330 --> 01:02:30,670
+اطلع لفوقه الآن السؤال اللي بعده على السريعه اللي
+
+674
+01:02:30,670 --> 01:02:35,140
+هو F و G multiplicative functionsF و G
+
+675
+01:02:35,140 --> 01:02:37,520
+Multiplicative Functions وقال لك أن الـ Two
+
+676
+01:02:37,520 --> 01:02:41,280
+Multiplicative Functions بتتساوى بس عند مين؟ عند
+
+677
+01:02:41,280 --> 01:02:44,700
+الـ Power of the Primes يعني قال لك F of BK بيساوي
+
+678
+01:02:44,700 --> 01:02:50,580
+D of BK معناته أن الـ F و G أشمالهم متساويات وقال
+
+679
+01:02:50,580 --> 01:02:59,420
+لك إذا كان الـ F of GK بيساوي D of BK عند الـ
+
+680
+01:02:59,420 --> 01:03:12,560
+Prime هتكون F هي نفس من الـ Gفي عنديا شباب أنتم
+
+681
+01:03:12,560 --> 01:03:20,880
+مساجلين؟ خلاص بدأ أمشي بشواش من زمان شوف سؤال 18
+
+682
+01:03:20,880 --> 01:03:27,840
+معطيني f و g multiplicative ماشي الحاجة
+
+683
+01:03:27,840 --> 01:03:35,150
+multiplicative functions ومعطيني أن fof bk بيساوي
+
+684
+01:03:35,150 --> 01:03:39,690
+g of bk for every prime بيساوي g of bk for every
+
+685
+01:03:39,690 --> 01:03:39,910
+prime بيساوي g of bk for every prime بيساوي g of
+
+686
+01:03:39,910 --> 01:03:40,450
+bk for every prime بيساوي g of bk for every prime
+
+687
+01:03:40,450 --> 01:03:46,850
+بيساوي g of bk for every prime بيساوي g of bk for
+
+688
+01:03:46,850 --> 01:03:48,090
+every prime بيساوي g of bk for every prime بيساوي
+
+689
+01:03:48,090 --> 01:03:48,090
+g of bk for every prime بيساوي g of bk for every
+
+690
+01:03:48,090 --> 01:03:49,070
+prime بيساوي g of bk for every prime بيساوي g of
+
+691
+01:03:49,070 --> 01:03:49,070
+bk for every prime بيساوي g of bk for every prime
+
+692
+01:03:49,070 --> 01:03:50,690
+بيساوي g of bk for every prime بيساوي g of bk for
+
+693
+01:03:50,690 --> 01:03:53,470
+every prime بيساوي g of bk for every prime بيساوي
+
+694
+01:03:53,470 --> 01:03:59,450
+g of bk for every prime بيساوي g of bk for
+
+695
+01:04:02,940 --> 01:04:10,240
+الـ F بتساوي سفر أو الـ G بتساوي سفر على طول إذا F
+
+696
+01:04:10,240 --> 01:04:16,460
+بتساوي سفر صار G of B كي بيساوي سفر لكل Prime إذا
+
+697
+01:04:16,460 --> 01:04:21,000
+الـ G هتساوي إيش؟ سفر عارفين ليش؟ لإن الـ G of N
+
+698
+01:04:21,000 --> 01:04:23,620
+multiplicative أو الـ G multiplicative بتبصير G of
+
+699
+01:04:23,620 --> 01:04:27,160
+N بيساوي G of B واحد ألف واحد G of B اتنين ألف
+
+700
+01:04:27,160 --> 01:04:29,400
+اتنين وG of B أر الف أر كل واحدة من هنا سفر لإن
+
+701
+01:04:29,400 --> 01:04:36,330
+إيش بيبقى هنا سفر فاهمين؟الآن لو كانت الـ F مش صفر
+
+702
+01:04:36,330 --> 01:04:46,550
+أكيد الـ G أيش معلها؟ مش صفر لأنه صفر لو F مش صفر
+
+703
+01:04:46,550 --> 01:04:50,650
+و G بيساوي صفر معناته الـ F أيش معناه صفر ومن ثم
+
+704
+01:04:50,650 --> 01:04:53,830
+هتطلع عندي الـ F في واحد بيساوي G في واحد أيش
+
+705
+01:04:53,830 --> 01:05:01,880
+بتساوي؟ بتساوي واحد ماشي الحالالذي يصل إلى أنه في
+
+706
+01:05:01,880 --> 01:05:04,080
+حالة الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+707
+01:05:04,080 --> 01:05:04,080
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+708
+01:05:04,080 --> 01:05:04,260
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+709
+01:05:04,260 --> 01:05:05,400
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+710
+01:05:05,400 --> 01:05:07,120
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+711
+01:05:07,120 --> 01:05:08,560
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+712
+01:05:08,560 --> 01:05:17,200
+الـ الـ
+
+713
+01:05:17,200 --> 01:05:17,740
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+714
+01:05:17,740 --> 01:05:17,760
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+715
+01:05:17,760 --> 01:05:27,780
+الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+716
+01:05:28,090 --> 01:05:33,520
+بتثبتها لكل N من ضمنها Nاش بتساوي واحدلو كانت الـ
+
+717
+01:05:33,520 --> 01:05:36,880
+F هي الـ Zero function Automatically الـ G هتصبح
+
+718
+01:05:36,880 --> 01:05:40,940
+Zero function وخلصنا منها بيصير F عند الواحد وغير
+
+719
+01:05:40,940 --> 01:05:43,300
+الواحد و الـ G عند الواحد وغير الواحد، كلها نصفار
+
+720
+01:05:43,300 --> 01:05:47,700
+لكن لو كانت الـ F مش السفر و الـ G مش السفر، طبيعا
+
+721
+01:05:47,700 --> 01:05:54,220
+هتتبعها، بدي أحسب لكم الـ F of واحد إنها لازم
+
+722
+01:05:54,220 --> 01:05:59,520
+تساومين الـ G of واحد، ماشي الحال، عندي الآن
+
+723
+01:06:03,600 --> 01:06:11,920
+F of واحد F is multiplicative اذا هتساوي F of واحد
+
+724
+01:06:11,920 --> 01:06:18,860
+عملها قبل ايه؟ هتساوي F of واحد تربيع مظبوط؟ جيبها
+
+725
+01:06:18,860 --> 01:06:22,880
+على الجهة الثانية بيصير F تربيع of واحد ناقص F of
+
+726
+01:06:22,880 --> 01:06:27,880
+واحد بيساوي سفر عملتها قبل ايه؟ F of واحد في F of
+
+727
+01:06:27,880 --> 01:06:35,130
+واحدنقص واحد بيساوي سفر و F أصلا مش السفر أه إذا
+
+728
+01:06:35,130 --> 01:06:40,130
+عندي ال F في واحد إيش بتساوي؟ بتساوي واحد معايا؟
+
+729
+01:06:40,130 --> 01:06:46,150
+خلصنا و زيها ال G ما هي Multiplicated و مش سفر إذا
+
+730
+01:06:46,150 --> 01:06:49,190
+ال G بتساوي واحد طيب خلصنا من هذه ناخد إذا ال N
+
+731
+01:06:49,190 --> 01:06:54,270
+إياش N أكبر من واحد إذا ال N بتساوي بي واحد ألف
+
+732
+01:06:54,270 --> 01:07:01,270
+واحد لأن بي R ألف إياشالف ار معايا إذا صارت
+
+733
+01:07:01,270 --> 01:07:06,190
+multiplicative إذا صارت f of n بساوي f بسؤال سهل
+
+734
+01:07:06,190 --> 01:07:11,470
+بي واحد الف واحد لعند بي ار الف ار ويساوي f of بي
+
+735
+01:07:11,470 --> 01:07:17,470
+واحد الف واحد لعند f of بي ار الف ار ويساوي من
+
+736
+01:07:17,470 --> 01:07:24,030
+المعطى g لو مultiplicative التانية ترجع زي ما كانت
+
+737
+01:07:24,030 --> 01:07:33,360
+بساوي gof P1 ألفة واحد لعين PR ألفة R ويساوي GE of
+
+738
+01:07:33,360 --> 01:07:39,740
+R واضح؟ طيب إيه اللي بعده؟
+
+739
+01:07:39,740 --> 01:07:47,800
+خلاص اطلع اللي على ال .. ال section اللي بعده لأ
+
+740
+01:07:47,800 --> 01:07:48,400
+جابل ال section
+
+741
+01:07:55,560 --> 01:07:59,900
+أيوة خلّيني .. الأسئلة الستة اللي هو .. بس هنا تلت
+
+742
+01:07:59,900 --> 01:08:03,860
+أسئلة اللي أعطيكم إياها .. واحد و تلت و أربع ظنني
+
+743
+01:08:03,860 --> 01:08:09,540
+شوف .. الآن
+
+744
+01:08:09,540 --> 01:08:13,160
+بدنا نحكي عن Mobius inversion formula ال Mobius
+
+745
+01:08:13,160 --> 01:08:17,540
+inversion formula أو الأول إيش هي ال .. M U of N
+
+746
+01:08:17,540 --> 01:08:23,680
+عارفينها، مذكرينها، بدنا نراجع
+
+747
+01:08:26,530 --> 01:08:36,770
+MU of N بساوي واحد أو سفر أو ناقص واحد أُس R مش
+
+748
+01:08:36,770 --> 01:08:43,050
+ذاكرين؟ MU of N بتساوي واحد لما N بتساوي واحد و
+
+749
+01:08:43,050 --> 01:08:48,990
+بساوي سفر إذا كان في B تربيع بكسم مين الـ N و
+
+750
+01:08:48,990 --> 01:08:52,970
+بساوي ناقص واحد أُس R إذا كانت M على صورة B واحد
+
+751
+01:08:52,970 --> 01:08:57,230
+لعند PRو بي واحد و بي اتنين و بي اتنين و بي اتنين
+
+752
+01:08:57,230 --> 01:08:57,510
+و بي اتنين و بي اتنين و بي اتنين و بي اتنين و بي
+
+753
+01:08:57,510 --> 01:08:59,010
+اتنين و بي اتنين و بي اتنين و بي اتنين و بي اتنين
+
+754
+01:08:59,010 --> 01:09:02,230
+و بي اتنين و بي اتنين و بي اتنين و بي اتنين و بي
+
+755
+01:09:02,230 --> 01:09:06,830
+اتنين و بي اتنين و بي اتنين و بي اتنين و بي اتنين
+
+756
+01:09:06,830 --> 01:09:10,630
+و بي اتنين و بي اتنين و بي اتنين و بي اتنين و بي
+
+757
+01:09:10,630 --> 01:09:18,970
+اتنين و بي اتنين و بي اتنين و بي اتنين و بي اتنين
+
+758
+01:09:18,970 --> 01:09:22,870
+و بي اتنين و
+
+759
+01:09:22,870 --> 01:09:32,970
+بالان السبب بسيط ان اي اربع ارقام متتالية لازم
+
+760
+01:09:32,970 --> 01:09:40,150
+واحد فيه نكون على صورة 4K مظبوط؟
+
+761
+01:09:40,150 --> 01:09:47,470
+لأن لو كان هذا 4K خلصنا لو هذا 4K زائد واحد بطلع
+
+762
+01:09:47,470 --> 01:09:52,780
+هذا 4K زائد 4 اللي هو 4Mلو كان اربعة كيه زائد
+
+763
+01:09:52,780 --> 01:09:55,780
+اتنين بيطلع هذا الاعلى اربعة كيه اربعة كيه زائد
+
+764
+01:09:55,780 --> 01:10:01,700
+تلتة بيطلع هذا واضح اذا any number any اللي هو
+
+765
+01:10:01,700 --> 01:10:07,160
+four consecutive numbers must have one of the four
+
+766
+01:10:07,160 --> 01:10:13,770
+اربعة كيه ماشي الحالة اذا واحد من هذولةبِكسِن مين؟
+
+767
+01:10:13,770 --> 01:10:19,090
+الأربعة يعني فيه اتنين تربية يعني ميوه تبعته إيش
+
+768
+01:10:19,090 --> 01:10:24,570
+بتساوي؟ يعني إذا حصل الدرب إيش هيساوي؟ يلّا اللي
+
+769
+01:10:24,570 --> 01:10:33,090
+بعده اللي بعده بقولك لأي انتجار لأي انتجار M أكبر
+
+770
+01:10:33,090 --> 01:10:39,590
+أو يساوي واحد أثبت إن الصماش للـMew of K factorial
+
+771
+01:10:40,670 --> 01:10:45,830
+كي من عند واحد الى مالة نهاية ولا عند ان حتى لو
+
+772
+01:10:45,830 --> 01:10:51,650
+مالة نهاية بيساوي ايش بيساوي واحد ال summation هذا
+
+773
+01:10:51,650 --> 01:10:56,690
+بيساوي ميو اف واحد فكتوريال زاد ميو اف اتنين
+
+774
+01:10:56,690 --> 01:11:01,750
+فكتوريال زاد ميو اف تلاتة فكتوريال زاد ميو اف اربع
+
+775
+01:11:01,750 --> 01:11:09,610
+فكتوريال زاد زاد ميو اف ان فكتوريال اه
+
+776
+01:11:11,420 --> 01:11:15,620
+الان اكبر
+
+777
+01:11:15,620 --> 01:11:24,820
+او يساوي تلاتة اه لان فعلت اتنين لأ بتسير اتنين
+
+778
+01:11:24,820 --> 01:11:31,800
+تلاتة مظبوط طيب هنا واحد صح هنا اللي هي اتنين ماقص
+
+779
+01:11:31,800 --> 01:11:38,540
+واحد مظبوط اتنين سالب واحد التلاتة
+
+780
+01:11:40,090 --> 01:11:46,050
+تلاتة في اتنين اللي هو واحد عارفين مش بساومك ولا
+
+781
+01:11:46,050 --> 01:11:49,550
+كده؟ اه لاتكونوا مش فاهمين اش بساومك زائد واحد
+
+782
+01:11:49,550 --> 01:11:56,250
+واللي بعده كله فيه أربعات يعني فيه اتنين تربعات
+
+783
+01:11:56,250 --> 01:12:02,450
+يعني كلها زائد صفر ويساوي هذا مع حد او مع اللي
+
+784
+01:12:02,450 --> 01:12:09,390
+جابله ويساوي واحد واضح اه الفكرة واضحة الـAسؤال
+
+785
+01:12:09,390 --> 01:12:18,930
+تلاتة let let let n بتساوي بي واحد كي واحد بي ار
+
+786
+01:12:18,930 --> 01:12:23,950
+كي ار بي برايم factorization of n أكبر من واحد إذا
+
+787
+01:12:23,950 --> 01:12:28,250
+كانت f is multiplicative prove that اللي موجود
+
+788
+01:12:28,250 --> 01:12:37,160
+انتبهوا عن دي خليني برضه أذكركم بعض النظرياتأو
+
+789
+01:12:37,160 --> 01:12:42,860
+المادة النظرية اللي موجودة في ال section هذا بدي
+
+790
+01:12:42,860 --> 01:12:48,140
+الآن F multiplicative السؤال
+
+791
+01:12:48,140 --> 01:12:58,900
+التلاتة implies أنه summation mu of D F of D D
+
+792
+01:12:58,900 --> 01:13:07,800
+بتجسم N بساوي ال product لواحد ناقص F of BiI من
+
+793
+01:13:07,800 --> 01:13:20,680
+واحد لعند مين مع عند انا واضح اه؟ طيب عندي F
+
+794
+01:13:20,680 --> 01:13:23,760
+is multiplicative مع ان في نظرية بتحكي على طول
+
+795
+01:13:23,760 --> 01:13:29,540
+بالجيبة F multiplicative و Mu multiplicative هتطلع
+
+796
+01:13:29,540 --> 01:13:33,400
+عندي Mu في F أشمالها is multiplicative بتعرفوا
+
+797
+01:13:33,400 --> 01:13:42,030
+تعملوها اه؟لو صميتها هذي G of D بسوء Mu of D في F
+
+798
+01:13:42,030 --> 01:13:54,000
+of D G of D1 D2 بسوء Mu of D1D2 FD1 FD2 FD2 FD1
+
+799
+01:13:54,000 --> 01:13:56,820
+FD2 FD2 FD2 FD2 FD2 FD2 FD2 FD2 FD2 FD2 FD2 FD2
+
+800
+01:13:56,820 --> 01:14:07,900
+FD2 FD2 FD2 FD2 FD2 FD2 FD2
+
+801
+01:14:08,670 --> 01:14:12,730
+معايا نظرية قبل شوية أخدنا قول لمزام اللي هو جوا
+
+802
+01:14:12,730 --> 01:14:15,870
+ال summation هذا is multiplication و ال summation
+
+803
+01:14:15,870 --> 01:14:18,410
+على D بتقسم N إذا ال summation نفسه إيش ماله
+
+804
+01:14:18,410 --> 01:14:25,430
+Multiplicative إذا صار عندي F of N بساوي summation
+
+805
+01:14:25,430 --> 01:14:34,750
+Mu of D F of D D بتقسم N is multiplicative أن إيش
+
+806
+01:14:34,750 --> 01:14:44,430
+ماتينيها بتساويبتساوي اللي فوق صح؟ الان بيصير عندى
+
+807
+01:14:44,430 --> 01:14:53,850
+F of N F of N بيساوي ال product لمين؟ ايش الآن
+
+808
+01:14:53,850 --> 01:14:57,770
+ماخدها انا؟ P1 ألف واحد عند PR ألف ألف
+
+809
+01:14:57,770 --> 01:15:03,930
+Multiplicative اذا بيصير ال product لل F of PI KI
+
+810
+01:15:03,930 --> 01:15:06,430
+ولا الف I؟ KI مظبوط؟
+
+811
+01:15:08,390 --> 01:15:16,110
+I من عند واحد لعندياش R فاهمين أشي اللي بعمله لأن
+
+812
+01:15:16,110 --> 01:15:25,010
+F مالها Multiplicative ويساوي نوجد من F of BIKI F
+
+813
+01:15:25,010 --> 01:15:30,830
+of BIKI من هنا هيها ال summation يعني بيساوي ال
+
+814
+01:15:30,830 --> 01:15:35,000
+productI من عند 1 لعند R لـSummation مين
+
+815
+01:15:35,000 --> 01:15:41,960
+الـSummation؟ الـSummation ميو أف دي F of D D
+
+816
+01:15:41,960 --> 01:15:51,800
+بتكسب بي آي كي آي معايا؟ الآن القواسم بي آي كي آي
+
+817
+01:15:51,800 --> 01:16:03,810
+واحد بي تربيع و البديات لعند بي أصف كي آيأه الان
+
+818
+01:16:03,810 --> 01:16:10,370
+عند الواحد و ال بي واحد الهنقية و الباد اسفار مافي
+
+819
+01:16:10,370 --> 01:16:15,870
+ليش بيساوي ال product I من عند واحد لعند R لأ
+
+820
+01:16:15,870 --> 01:16:23,830
+summation اللي هو ميو of واحد F of واحد زاد ميو of
+
+821
+01:16:23,830 --> 01:16:34,160
+بي I F of بي I زاد ميو of بي I تربيعf of bi تربيه
+
+822
+01:16:34,160 --> 01:16:43,900
+زاد لما اصلا عند اخر واحد ميو of bi ki f of bi اس
+
+823
+01:16:43,900 --> 01:16:50,180
+ki صح ولا لأ هذه من عند هنا و طالع لميو تبعتنا ايه
+
+824
+01:16:50,180 --> 01:16:57,890
+ايش سفر اه بيظل مين عنده هذا و هذا و يساويالـ
+
+825
+01:16:57,890 --> 01:17:02,690
+Product I من عند واحد لعند R لأ الـ Mu of واحد ده
+
+826
+01:17:02,690 --> 01:17:10,230
+ايش بيساوي واحد الان عندي F of واحد نفسها بيصير F
+
+827
+01:17:10,230 --> 01:17:19,830
+of واحد الان Mu of BY سالب واحد ايها الـ Mu of الـ
+
+828
+01:17:19,830 --> 01:17:25,990
+Prime اللي هو ناقص واحد قصة R مش غير Prime واحد اي
+
+829
+01:17:25,990 --> 01:17:30,810
+سؤال؟إذا فى إيش مش واضح بعيده ميوف فى اتنين إيش
+
+830
+01:17:30,810 --> 01:17:35,910
+متساوي ميوف
+
+831
+01:17:35,910 --> 01:17:40,010
+تلاتة ميوف
+
+832
+01:17:40,010 --> 01:17:46,650
+خمسة إذا ميوف أي برايم إيش متساوي ميوف بي واحد فى
+
+833
+01:17:46,650 --> 01:17:52,390
+بي اتنين سانب واحد وسط اتنين يعني إيش معله واحد
+
+834
+01:17:54,410 --> 01:18:02,390
+واضح؟ طيب إذا u of bi عبارة عن كداش سالب واحد
+
+835
+01:18:02,390 --> 01:18:11,810
+بيصير ناقص f of bi فهو المطلوب صارت عندي f of n
+
+836
+01:18:11,810 --> 01:18:19,170
+بساوي هذه f of n مين هي ال summation تمام مرة يا
+
+837
+01:18:19,170 --> 01:18:24,860
+شباب f of n مين هيالـ Summation و F of N مين هي
+
+838
+01:18:24,860 --> 01:18:30,340
+طلعت؟ إذا صار عند الـ Summation لـ Mu of D في F of
+
+839
+01:18:30,340 --> 01:18:35,400
+D D بتقسم N بساوي هذا ال product مين ال product
+
+840
+01:18:35,400 --> 01:18:43,180
+هذا؟ F of 1 ناقص F of B 1 لما أصل عند F of 1 ناقص
+
+841
+01:18:43,180 --> 01:18:53,390
+F of B R و ال F of 1 و ال F of 1 ده إيش بتساوي؟لأن
+
+842
+01:18:53,390 --> 01:19:01,510
+F أشمالها multiplicative واضح وهو المقلد يعني
+
+843
+01:19:01,510 --> 01:19:05,790
+كل F في واحد بيقعش في واحد اللي بعده نيجي لسؤال
+
+844
+01:19:05,790 --> 01:19:11,600
+أربعةالسؤال الرابع السؤال الرابع if n أكبر من واحد
+
+845
+01:19:11,600 --> 01:19:14,680
+has a prime factorization n بسوء بي واحد كواحد عند
+
+846
+01:19:14,680 --> 01:19:19,160
+بي ار كي ار used problem 4 to establish the
+
+847
+01:19:19,160 --> 01:19:22,220
+following ال summation ميو اف دي تاو اف دي دي
+
+848
+01:19:22,220 --> 01:19:27,680
+بتكسب ان بيسوء ناقص واحد اياش أسر اللي عندي التاو
+
+849
+01:19:27,680 --> 01:19:31,680
+is multiplicative، مظبوط؟ احنا قبل شوية أثبتنا
+
+850
+01:19:31,680 --> 01:19:39,120
+summation ميو اف ديF of D دي بتجسم الـ N إيش
+
+851
+01:19:39,120 --> 01:19:44,840
+بيساوي اللي هو عبارة عن واحد او F اللي هو ال ..
+
+852
+01:19:44,840 --> 01:19:47,320
+ذاكروني ال product
+
+853
+01:19:50,540 --> 01:19:57,000
+1- F of B I I من عند 1 لعند R صح ولا لأ هذا اللي
+
+854
+01:19:57,000 --> 01:20:02,620
+أثبتناه قبل شوية الآن بدى أستخدم مين لهذا السؤال
+
+855
+01:20:02,620 --> 01:20:06,880
+في تطبيقه على الحالات اللي معطينيها بده لأن ال
+
+856
+01:20:06,880 --> 01:20:12,800
+summation لـ Mu of D هذا ايه 4A بده ال summation
+
+857
+01:20:12,800 --> 01:20:20,110
+لـ Mu of D Tau of D دي بتجسب الـ N بساويةاللي هو
+
+858
+01:20:20,110 --> 01:20:28,370
+عبارة عن ال product لا واحد
+
+859
+01:20:28,370 --> 01:20:35,230
+ناقص توقف بي اي من عند واحد عند مين ار عدد ال
+
+860
+01:20:35,230 --> 01:20:41,230
+divisors لل بي اي قداش واحد واحد اتنين لان ال
+
+861
+01:20:41,230 --> 01:20:47,440
+divisors اللي هي الواحد و ال بي اي فاهمينY ساوي هو
+
+862
+01:20:47,440 --> 01:20:52,440
+الـ product لواحد ماقص اتنين قايمين عند واحد لعند
+
+863
+01:20:52,440 --> 01:20:55,820
+R Y ساوي اكم مرة معدودات هذول R من المرات اللي
+
+864
+01:20:55,820 --> 01:21:03,100
+يسالب واحد قُس R نيجي لـ B الـ summation من مين
+
+865
+01:21:03,100 --> 01:21:12,200
+بده ميو of D سيجما of Dدى بتكسب 100 لان بساوية
+
+866
+01:21:12,200 --> 01:21:17,520
+اللى هو ال product لواحد ماقع ال sigma of bi I من
+
+867
+01:21:17,520 --> 01:21:23,360
+عند واحد لعين دهار واضح ها صار سهل لو بدك تيجي
+
+868
+01:21:23,360 --> 01:21:26,020
+توجه تقول حاجة لك دى عمال مشكلة بس احنا بنين على
+
+869
+01:21:26,020 --> 01:21:32,680
+السؤال قبله ويساوياللي هو ال product I من عند واحد
+
+870
+01:21:32,680 --> 01:21:36,960
+لعند R لواحد ناقص مجموع ال divisors ده ال بي آي
+
+871
+01:21:36,960 --> 01:21:43,380
+اللي هي واحد زاد بي آي نظبوت ناقص واحد ناقص بي آي
+
+872
+01:21:43,380 --> 01:21:50,360
+صح اللي عملته ويساوي اللي هو ال product لناقص بي
+
+873
+01:21:50,360 --> 01:22:01,370
+آي I من عند واحد لعند R ويساوي N صح ناقص واحد-R B1
+
+874
+01:22:01,370 --> 01:22:08,670
+BR وهو المطلوب والبعد
+
+875
+01:22:08,670 --> 01:22:15,310
+هو بنفس الأسلوب Mu of D على D خلّيني أعملها بالمرة
+
+876
+01:22:15,310 --> 01:22:21,570
+Summation of Mu of C الان C
+
+877
+01:22:21,570 --> 01:22:27,370
+Mu of D على D بيصير ال function اللي عندنا مين هي
+
+878
+01:22:27,370 --> 01:22:37,690
+1 على Dمعايا اللي هي بتساوي summation mu of D في F
+
+879
+01:22:37,690 --> 01:22:44,150
+of D D بتجسم N where F of D ايش هتساوي يا شباب
+
+880
+01:22:44,150 --> 01:22:49,930
+واحد على D صح ولا لا الواحد على D is
+
+881
+01:22:49,930 --> 01:22:54,030
+multiplicative عملناها اذا صار عندي عبارة عن باي
+
+882
+01:22:54,030 --> 01:23:03,570
+في واحد ناقص Fف من مين؟ من بي آي فمن بي آي فمن بي
+
+883
+01:23:03,570 --> 01:23:07,370
+آي فمن بي آي فمن بي آي فمن بي آي فمن بي آي فمن بي
+
+884
+01:23:07,370 --> 01:23:07,990
+آي فمن بي آي فمن بي آي فمن بي آي فمن بي آي فمن بي
+
+885
+01:23:07,990 --> 01:23:08,210
+آي فمن بي آي فمن بي آي فمن بي آي فمن بي آي فمن بي
+
+886
+01:23:08,210 --> 01:23:08,210
+آي فمن بي آي فمن بي آي فمن بي آي فمن بي آي فمن بي
+
+887
+01:23:08,210 --> 01:23:08,210
+آي فمن بي آي فمن بي آي فمن بي آي فمن بي آي فمن بي
+
+888
+01:23:08,210 --> 01:23:15,810
+آي فمن بي آي فمن بي آي فمن بي آي فمن بي آي فمن بي
+
+889
+01:23:15,810 --> 01:23:26,930
+آي فمن بي آي فمن بي آي فمن بي آي فمن بي
+
+890
+01:23:29,360 --> 01:23:36,240
+انزل ال .. الان D بيقف D بنفس الأسلوب F of D
+
+891
+01:23:36,240 --> 01:23:39,500
+بتساوي D في هذه الحالة و ال D is multiplicative
+
+892
+01:23:39,500 --> 01:23:45,460
+اذا بيصير واحد ناقص F of P واحد اللي هي P واحد لما
+
+893
+01:23:45,460 --> 01:23:50,080
+أصل عنده واحد ناقص F of PR اللي هي PR فبتصير اللي
+
+894
+01:23:50,080 --> 01:23:55,940
+هو على طول مباشرة و إلى لقاء آخر ان شاء الله الله
+
+895
+01:23:55,940 --> 01:23:56,400
+عفوكم
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/Kh9giSSYjLg.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/Kh9giSSYjLg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..16856a31f58d075d8b3b8e3206a4c29e3c5ef695
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/Kh9giSSYjLg.srt
@@ -0,0 +1,2098 @@
+1
+00:00:20,050 --> 00:00:25,030
+بسم الله الرحمن الرحيم محاضرة
+
+2
+00:00:25,030 --> 00:00:28,610
+اليوم هي المحاضرة العاشرة في مساق نظرية الأعداد
+
+3
+00:00:28,610 --> 00:00:39,330
+الجامعة الإسلامية، قسم الرياضيات في كليتي العلوم 
+
+4
+00:00:39,330 --> 00:00:50,880
+والتربية، حديث اليوم هو عبارة عن مناقشة للأعداد 
+
+5
+00:00:50,880 --> 00:00:54,720
+الأولية لـ chapter ثلاثة، الـ section الأول 3.1 و
+
+6
+00:00:54,720 --> 00:00:56,440
+الـ section الثاني 3.2، وإن شاء الله الـ
+
+7
+00:00:56,440 --> 00:01:02,540
+section الثالث 3.3، الـ homework اللي كانت 
+
+8
+00:01:02,540 --> 00:01:09,940
+معنا في أسئلة محددة منها 3.1 من 1 لـ 4
+
+9
+00:01:09,940 --> 00:01:13,100
+عشر، الأسئلة اللي بعثت لكم إياها، خلينا نمر على الأسئلة
+
+10
+00:01:13,100 --> 00:01:17,460
+مدام بتخلّيني أمر على الأسئلة كلها، أعطيني السؤال 
+
+11
+00:01:17,460 --> 00:01:21,880
+الأول، السؤال اللي بيحكي التالي: It has been
+
+12
+00:01:21,880 --> 00:01:25,600
+conjectured that there are infinitely many primes
+
+13
+00:01:25,600 --> 00:01:30,620
+of the form n تربيع ناقص 2. الآن، للإدعاء هذا
+
+14
+00:01:30,620 --> 00:01:34,720
+بقول إن في عندي عدد لانهائي من الـ primes على صورة
+
+15
+00:01:34,720 --> 00:01:38,900
+n تربيع ناقص 2، المطلوب في سؤالنا بس اللي هو
+
+16
+00:01:38,900 --> 00:01:42,840
+أوجد لي خمسة من هذه الـ primes، بتبقى خمسة من 
+
+17
+00:01:42,840 --> 00:01:50,460
+الـ primes اللي على صورة n تربيع ناقص 2، الآن
+
+18
+00:01:50,460 --> 00:01:54,600
+السؤال بسيط، الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+19
+00:01:54,600 --> 00:01:55,080
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+20
+00:01:55,080 --> 00:01:55,540
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+21
+00:01:55,540 --> 00:01:57,000
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+22
+00:01:57,000 --> 00:02:05,780
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+23
+00:02:05,780 --> 00:02:06,400
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+24
+00:02:06,400 --> 00:02:08,060
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+25
+00:02:08,060 --> 00:02:09,020
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+26
+00:02:09,020 --> 00:02:16,460
+الـ الـ الـ
+
+27
+00:02:16,460 --> 00:02:19,100
+الـ الـ الـ
+
+28
+00:02:19,670 --> 00:02:27,050
+أيضا، تحصل على خمسة آخرين، وهكذا. لبعد السؤال اثنين
+
+29
+00:02:27,050 --> 00:02:30,270
+اثنين
+
+30
+00:02:30,270 --> 00:02:36,370
+اثنين Give an example to show that the following
+
+31
+00:02:36,370 --> 00:02:41,140
+conjecture is not true. الإدعاء التالي مش صحيح، اللي
+
+32
+00:02:41,140 --> 00:02:44,620
+هو every positive integer can be written in the
+
+33
+00:02:44,620 --> 00:02:48,820
+form b زائد a تربيع، where b is either prime or one
+
+34
+00:02:48,820 --> 00:02:55,640
+and a أكبر أو يساوي صفر. بقولنا اللي هو في conjecture
+
+35
+00:02:55,640 --> 00:03:02,460
+الإدعاء أنه أي positive integer can be written على
+
+36
+00:03:02,460 --> 00:03:10,740
+صورة b زائد a تربيع حيث a أكبر أو يساوي 0 و b يساوي 
+
+37
+00:03:10,740 --> 00:03:17,840
+1 أو prime. الآن، بدنا نجيب مثال يبين لنا أن هذا
+
+38
+00:03:17,840 --> 00:03:23,400
+المثال اللي هو الـ 25 لا يمكن كتابته على صورة b 
+
+39
+00:03:23,400 --> 00:03:28,380
+زائد a تربيع. وانتم في البيت بتبحثوا على
+
+40
+00:03:28,380 --> 00:03:34,270
+أرقام غير الـ 25، ناخد الـ 25 كمثال، بتثبت لك إن الـ
+
+41
+00:03:34,270 --> 00:03:39,530
+n، الـ 25 لا يمكن كتابته على صورة a تربيعي، يعني مربع 
+
+42
+00:03:39,530 --> 00:03:46,050
+كامل، زائد مين؟ زائد اللي هو b حيث b يا prime يا 
+
+43
+00:03:46,050 --> 00:03:54,250
+إيش؟ يا واحد. طيب، عند الـ a العدد عندي 25، الـ a تبعتي
+
+44
+00:03:54,250 --> 00:03:59,750
+هذه بتبدأ منها، الـ a أكبر أو يساوي 0 عشان تصل لـ 25، يا
+
+45
+00:03:59,750 --> 00:04:07,450
+عبارة عن صفر، يا واحد، 2، 3، 4، 5، وغيرها. 3 لا يمكن
+
+46
+00:04:07,450 --> 00:04:11,770
+أنها تكون 25، ماشي الحال؟ فقد أقول لك في الخمس حلوات
+
+47
+00:04:11,770 --> 00:04:16,750
+أو الست حلوات اللي بذكرها مش هيتحقق أنه يمكن كتابة
+
+48
+00:04:16,750 --> 00:04:20,930
+25 على صورة b زائد a تربيع. في هذه الحالة، بيكون 25
+
+49
+00:04:20,930 --> 00:04:23,870
+is a counter example of a number أو positive
+
+50
+00:04:23,870 --> 00:04:27,750
+number that can't be written of the form b زائد a 
+
+51
+00:04:27,750 --> 00:04:31,730
+تربيع، حيث الـ b prime or one والـ a أكبر أو يساوي 
+
+52
+00:04:31,730 --> 00:04:37,270
+صفر. طيب، في حالة الـ a تساوي 0، الـ 25 بيصير الـ ..
+
+53
+00:04:37,270 --> 00:04:45,290
+اللي هي 25 زائد 0، وهذه أشمالها not prime nor one
+
+54
+00:04:45,290 --> 00:04:51,050
+nor one, it's neither prime nor one. الآن، في حالة 
+
+55
+00:04:51,050 --> 00:05:00,600
+الـ a بتساوي 1، اللي هي بيصير 1 أو 24 زائد 1. الـ 24
+
+56
+00:05:00,600 --> 00:05:05,640
+برضه أشمالها لا هي prime ولا هي واحد. Similarly، حالة
+
+57
+00:05:05,640 --> 00:05:12,740
+الـ a بيساوي 2، اللي هي عبارة عن 4 زائد 21، وهذا
+
+58
+00:05:12,740 --> 00:05:17,260
+أيضًا لا هي prime ولا هي واحد. حالة الـ a بيساوي 3 
+
+59
+00:05:17,260 --> 00:05:23,500
+وضحت الصورة، 9 زائد 16. في حالة الـ a بيساوي 4، 9 زائد
+
+60
+00:05:23,500 --> 00:05:32,740
+16. في حالة الـ a بيساوي 5، 25 أو 0 زائد 25. وفي كل
+
+61
+00:05:32,740 --> 00:05:40,780
+الحالات ولا واحد من هدول prime أو one. طيب، نجي
+
+62
+00:05:40,780 --> 00:05:45,660
+للسؤال ثلاثة ثلاثة
+
+63
+00:05:45,660 --> 00:05:54,420
+بيها، 3.3. الآن prove each of the 
+
+64
+00:05:54,420 --> 00:05:55,280
+statements below.
+
+65
+00:05:58,670 --> 00:06:02,770
+بنثبت ما يلي: الفرع الأول أن أي prime of the form 
+
+66
+00:06:02,770 --> 00:06:09,990
+3n زائد 1 is also of the form 6n زائد 1. الآن، عندي
+
+67
+00:06:09,990 --> 00:06:13,810
+أنا
+
+68
+00:06:13,810 --> 00:06:18,550
+بحكي الفكرة، طبعًا، لأن البرهان موجود
+
+69
+00:06:18,550 --> 00:06:27,400
+عندي، بدي أثبت أن أي prime بيكون على صورة 3n زائد 
+
+70
+00:06:27,400 --> 00:06:34,680
+واحد لازم يعطيني إن الـ b على صورة 3k أو 6k زائد 
+
+71
+00:06:34,680 --> 00:06:40,360
+إيش؟ زائد واحد أو 6n زائد واحد، معي؟
+
+72
+00:06:42,300 --> 00:06:47,580
+مدام ب prime على صورة 3n زائد 1، إذا واضح إن هو
+
+73
+00:06:47,580 --> 00:06:52,520
+عبارة عن إيش؟ ما له أكبر من 2، يعني قد prime، ماشي
+
+74
+00:06:52,520 --> 00:06:59,980
+الحال. مدام قد prime، إذا الـ b لا يمكن تكون على 
+
+75
+00:06:59,980 --> 00:07:06,260
+صورة اللي هو عدد زوجي أكيد، ماشي الحال؟ طيب، الآن 
+
+76
+00:07:06,260 --> 00:07:12,650
+الـ n اللي عندي هذه، لها احتمالين، لها 2k يا 2k
+
+77
+00:07:12,650 --> 00:07:17,170
+زائد واحد. بتثبت لك إنه لا يمكن تكون على صورة 2k
+
+78
+00:07:17,170 --> 00:07:21,830
+زائد واحد. ليش؟ لأنه لو كانت الآن على صورة
+
+79
+00:07:21,830 --> 00:07:25,870
+2k زائد واحد، بيصير الـ b، الـ prime تبعتنا على
+
+80
+00:07:25,870 --> 00:07:31,430
+صورة 6k زائد 3 زائد 1، هيساوي 6k زائد 
+
+81
+00:07:31,430 --> 00:07:39,730
+4، which is not prime، واضح. إذا الـ n، الـ b، الـ n 
+
+82
+00:07:39,730 --> 00:07:44,390
+تبعتنا هتكون أشمالها على صورة 2k، يعني بمعنى آخر الـ
+
+83
+00:07:44,390 --> 00:08:00,070
+b تبعتنا هتكون على صورة 6k زائد 1، وهو المطلوب. نمشي 
+
+84
+00:08:00,070 --> 00:08:06,040
+prime. عشان هيك اللي هو هذه الحالة لا يمكن أن تحدث
+
+85
+00:08:06,040 --> 00:08:10,220
+لأن ب احنا مش حاطين عليها أشمالها عبارة عن الـ
+
+86
+00:08:10,220 --> 00:08:15,600
+prime. أي سؤال؟ اللي بعده، سؤال ب على الصفحة الثانية
+
+87
+00:08:15,600 --> 00:08:20,820
+each integer of the form ثلاثة n زائد 2 has a 
+
+88
+00:08:20,820 --> 00:08:28,440
+prime factor of this form. معي 
+
+89
+00:08:28,440 --> 00:08:37,520
+يا شباب، الآن بنقول إن أي عدد على صورة .. أي عدد على 
+
+90
+00:08:37,520 --> 00:08:43,440
+صورة الـ prime number، أي 
+
+91
+00:08:43,440 --> 00:08:55,060
+prime number بـ .. ب على صورة ثلاثة n زائد اثنين
+
+92
+00:08:55,060 --> 00:09:05,360
+لازم يحتوي في داخله على الـ prime factor، أي عدد
+
+93
+00:09:05,360 --> 00:09:10,600
+طبعًا، عدد ما عطينا آه، any number على صورة ثلاثة n 
+
+94
+00:09:10,600 --> 00:09:15,900
+زائد اثنين لازم يكون في داخله اللي هو الـ prime
+
+95
+00:09:15,900 --> 00:09:22,340
+factor على هذه الصورة، يعني لازم نلاقي b prime 
+
+96
+00:09:22,340 --> 00:09:26,180
+بيقسم الـ n، وهذا الـ b اللي بحكي عنه على صورة 
+97
+00:09:26,180 --> 00:09:33,450
+ثلاثة n زائد اثنين. الآن، إيش؟ إذا كان الـ n نفسه
+
+98
+00:09:33,450 --> 00:09:37,670
+prime، بيكون خلصنا، لأنه هو نفسه على صورة ثلاثة n زائد
+
+99
+00:09:37,670 --> 00:09:42,770
+اثنين. إذا كان الـ n composite، يعني أكبر من واحد، و
+
+100
+00:09:42,770 --> 00:09:46,190
+composite، إذا by unique factorization theorem، n
+
+101
+00:09:46,190 --> 00:09:50,330
+can be written على صورة b1، b2، لعند الـ 
+
+102
+00:09:50,330 --> 00:09:57,200
+br  for some r. طيب، الآن البرهان الكامل موجود، و
+
+103
+00:09:57,200 --> 00:10:01,420
+تفاصيله الآن. خليني أعطيك اللي هو فكرة البرهان
+
+104
+00:10:01,420 --> 00:10:05,860
+الآن، الـ .. الـ .. الـ n هتكون على صورة b1، b2، 
+
+105
+00:10:05,860 --> 00:10:10,280
+b r، حيث الـ b اللي عندي إيش؟ أشمالها عبارة
+
+106
+00:10:10,280 --> 00:10:15,840
+عن prime numbers. الآن، أي عدد في الدنيا، ملطبنه الـ
+
+107
+00:10:15,840 --> 00:10:21,280
+primes هدول يا على صورة ثلاثة k، يا ثلاثة k زائد
+
+108
+00:10:21,280 --> 00:10:27,120
+واحد، يا ثلاثة k زائد مين؟ اثنين، مظبوط؟ ثلاثة k زائد 
+
+109
+00:10:27,120 --> 00:10:32,380
+اثنين. هو معطيني إن الـ n هذا على صورة ثلاثة n زائد 
+
+110
+00:10:32,380 --> 00:10:38,620
+اثنين، فمش وارد إطلاقًا أن يكون واحد منهم على صورة
+
+111
+00:10:38,620 --> 00:10:42,420
+مين؟ ثلاثة k. لأن لو كان في واحد منهم على صورة ثلاثة
+
+112
+00:10:42,420 --> 00:10:48,230
+k، بيطلع كله على صورة ثلاثة m for some m. ليش؟ لأنه
+
+113
+00:10:48,230 --> 00:10:52,290
+لو افترضنا هذا p1 هو على صورة 3k، صار اللي هو حصل 
+
+114
+00:10:52,290 --> 00:10:56,570
+الضرب هذا على صورة 3k في هذا، يعني ثلاثة n. ولكن
+
+115
+00:10:56,570 --> 00:11:00,530
+عددنا على صورة ثلاثة n زائد 2. إذا مش وارد أن
+
+116
+00:11:00,530 --> 00:11:04,990
+يكون أي عدد منهم على صورة 3k. إذا هذا مش وارد
+
+117
+00:11:04,990 --> 00:11:10,750
+دلوقت، الآن بدنا نفهم شغلة ثانية كمان. أنا بقول
+
+118
+00:11:10,750 --> 00:11:16,610
+مستحيل يكون كله على صورة ثلاثة k زائد واحد. ليش؟ 
+
+119
+00:11:16,610 --> 00:11:19,950
+لأن لو كان كله على صورة ثلاثة k زائد واحد، وخدمة
+
+120
+00:11:19,950 --> 00:11:24,030
+نظرية، جايب هيك إن the product of two integers of
+
+121
+00:11:24,030 --> 00:11:26,770
+the form ثلاثة k زائد واحد لازم يكون على صورة
+
+122
+00:11:26,770 --> 00:11:32,840
+ثلاثة k زائد واحد. إذا لو كان كل العصور ثلاثة k
+
+123
+00:11:32,840 --> 00:11:36,480
+زائد واحد، ما هتحصل ضرب إنه هيطلع ع صورة ثلاثة k 
+
+124
+00:11:36,480 --> 00:11:40,540
+زائد واحد. إذا في واحد منهم على الأقل هنا ع صورة
+
+125
+00:11:40,540 --> 00:11:45,220
+ثلاثة k زائد اثنين. إذا أكيد فيه prime factor 
+
+126
+00:11:45,220 --> 00:11:48,860
+على صورة ثلاثة k زائد اثنين. لبعده 
+
+127
+00:11:58,500 --> 00:12:03,760
+ايه؟ خلصناها وبيخلصناها؟ ضال مين؟ ضال ج. شوف الآن 
+
+128
+00:12:03,760 --> 00:12:09,360
+برضه ناخذ الفكرة: The only prime of the form n
+
+129
+00:12:09,360 --> 00:12:15,160
+تكعيب ناقص واحد is مين؟ is seven. لأن السؤال أو
+
+130
+00:12:15,160 --> 00:12:21,160
+الفرض من هذا السؤال بيقول لي إن هو الـ prime الوحيد
+
+131
+00:12:21,160 --> 00:12:26,920
+الـ prime الوحيد اللي على صورة n تكعيب ناقص واحد لازم 
+
+132
+00:12:26,920 --> 00:12:31,920
+يطلع مين؟ هو السبعة. يعني، عشان هيك بنقول، خلينا نفترض
+
+133
+00:12:31,920 --> 00:12:37,480
+أن b بتساوي n تكعيب ناقص واحد، حيث b is a prime
+
+134
+00:12:37,480 --> 00:12:42,400
+let b a prime such that b بتساوي n تكعيب ناقص
+
+135
+00:12:42,400 --> 00:12:46,520
+واحد، بدي أثبت لك إن هذا الـ b لازم يطلع معنا مين؟ هو
+
+136
+00:12:46,520 --> 00:12:53,590
+بيساوي السبعة. الآن، n تكعيب ناقص واحد، فرق بين مكعبين
+
+137
+00:12:53,590 --> 00:12:59,770
+بنحللها: n ناقص واحد في n تربيع زائد n زائد واحد
+
+138
+00:12:59,770 --> 00:13:05,990
+معي؟ لأن هذا تحليل فرق بين مكعبين. الآن،صار عندي 
+
+139
+00:13:05,990 --> 00:13:12,320
+prime مكتوب على صورة حاصل ضرب عددين. إذا واحنا ما 
+
+140
+00:13:12,320 --> 00:13:16,680
+نعرف إن الـ b فيش قواسم إلا إلا غير هو والواحد. 
+
+141
+00:13:16,680 --> 00:13:21,680
+إذا عندي يا هذا هو الـ prime و هذا الواحد أو هذا 
+
+142
+00:13:21,680 --> 00:13:26,500
+الواحد و هذا إيش ال prime الآن بدي أثبت لك إنه
+
+143
+00:13:26,500 --> 00:13:32,540
+مستحيل يكون هذا واحد و هذا prime هيبقى عندك إن هذا
+
+144
+00:13:32,540 --> 00:13:37,480
+هو الواحد و هذا إيش ال prime إذا في عندي حالتين يا
+
+145
+00:13:37,480 --> 00:13:45,260
+أما an ناقص واحد بيساوي Band an تربيع زائد an زائد واحد
+
+146
+00:13:45,260 --> 00:13:52,220
+أشماله يساوي واحد الحالة الثانية an ناقص واحد
+
+147
+00:13:52,220 --> 00:13:56,740
+بيساوي واحد and an تربيع زائد an زائد واحد بيساوي 
+
+148
+00:13:56,740 --> 00:14:01,160
+مين؟ لبران الحالة اللي فوق هتثبت لك إنه غير حادثة
+
+149
+00:14:01,160 --> 00:14:06,710
+والحالة اللي تحت هتلزمني إنه تكون طلع ال B هنا
+
+150
+00:14:06,710 --> 00:14:12,050
+تنينه لأن لما تحل هذه بصير an تربيع زائد an بيساوي
+
+151
+00:14:12,050 --> 00:14:17,530
+صفر معناته an بتساوي صفر أو an إيش بتساوي سالب 
+
+152
+00:14:17,530 --> 00:14:21,470
+واحد في حالة ال an بصفر بطلع ال b ناقص واحد
+
+153
+00:14:21,470 --> 00:14:25,130
+contradiction لأن ال b is prime أكبر من واحد في
+
+154
+00:14:25,130 --> 00:14:28,530
+حالة ال an بتساوي سالب واحد بطلع إنك سالب واحد
+
+155
+00:14:28,530 --> 00:14:30,990
+سالب واحد يعني إيش؟ سالب اثنين و ال b بتساوي سالب
+
+156
+00:14:30,990 --> 00:14:35,290
+اثنين لأ ال b عندنا إيش مالها؟ أكبر من اللي هو واحد
+
+157
+00:14:36,320 --> 00:14:42,060
+واضحة إذا هذه الحادثة لا يمكن إنه يكون عندي ال an 
+
+158
+00:14:42,060 --> 00:14:45,940
+بتساوي ال .. ال .. ال an تربيع زائد an زائد واحد
+
+159
+00:14:45,940 --> 00:14:49,340
+هي الواحد إذا نأخذ الحالة الثانية اللي هو an ناقص 
+
+160
+00:14:49,340 --> 00:14:51,280
+واحد بيساوي واحد و an تربيع زائد an زائد واحد
+
+161
+00:14:51,280 --> 00:14:54,920
+بيساوي ايه؟ هذه الحالة مش هتعطيني an بتساوي اثنين 
+
+162
+00:14:54,920 --> 00:15:03,230
+ومن ثم فبيعطيني 4 زائد 2 زائد 1 اللي هو بيساوي الـ B
+
+163
+00:15:03,230 --> 00:15:10,650
+اللي هو بيساوي 7 إذا أي رقم على صورة n تكعيب ناقص 1
+
+164
+00:15:10,650 --> 00:15:17,510
+و prime لازم يكون إيش؟ أشماله بيساوي 7 أي سؤال؟ نيجي
+
+165
+00:15:17,510 --> 00:15:24,960
+إلى الفرع اللي هو الثالث اللي بيقول التالي the only
+
+166
+00:15:24,960 --> 00:15:29,640
+prime for which 3P زائد واحد is a perfect
+
+167
+00:15:29,640 --> 00:15:37,680
+square is five الفكرة شبيهة
+
+168
+00:15:37,680 --> 00:15:41,880
+مربع
+
+169
+00:15:41,880 --> 00:15:45,120
+كامل مربع كامل
+
+170
+00:15:48,610 --> 00:15:57,750
+بنقول p p p
+
+171
+00:15:57,750 --> 00:16:09,330
+p
+
+172
+00:16:09,330 --> 00:16:13,530
+p p p p p p p p p p p p p p p p
+
+173
+00:16:13,530 --> 00:16:13,870
+p p p p p p p p p p p p p p p p
+
+174
+00:16:13,870 --> 00:16:20,030
+p p p p بتلاتة p زائد واحد بيساوي a تربيع
+
+175
+00:16:20,030 --> 00:16:25,530
+for some a element in Z يعني نفترض إنه p برايم
+
+176
+00:16:25,530 --> 00:16:31,450
+وفي نفس الوقت اللي هو تلاتة p زائد واحد أشماله
+
+177
+00:16:31,450 --> 00:16:37,090
+مربع كامل اللي هو عبارة عن a تربيع نفس الفكرة
+
+178
+00:16:37,090 --> 00:16:41,530
+اللي قبل بشوية منها انطلاق البرهان عند مدام اللي 
+
+179
+00:16:41,530 --> 00:16:47,790
+هو بيصير عند الـ 3B بيساوي a تربيع ناقص واحد و بيساوي 
+
+180
+00:16:47,790 --> 00:16:51,970
+ناقص واحد فارق بين المربعين في a زائد واحد التلاتة
+
+181
+00:16:51,970 --> 00:16:58,850
+prime و الـ B prime إذن عندك مدام اللي في حالتين a 
+
+182
+00:16:58,850 --> 00:17:03,030
+ناقص واحد بيساوي تلاتة و في نفس الوقت B بيساوي a
+
+183
+00:17:03,030 --> 00:17:08,170
+زائد واحد في الحالة الثانية a زائد واحد بيساوي 
+
+184
+00:17:08,170 --> 00:17:15,070
+تلاتة و and اللي هو a ناقص واحد بيساوي الـ B معايا 
+
+185
+00:17:15,070 --> 00:17:24,310
+يا جماعة بيثبت لك إن الحالة الثانية غير حادثة يعني
+
+186
+00:17:24,310 --> 00:17:26,970
+الـ a زائد واحد بيساوي تلاتة معناته و ال a بيساوي 
+
+187
+00:17:26,970 --> 00:17:33,250
+إيش؟ اثنين ومنه الـ B بيساوي واحد which is 
+
+188
+00:17:33,250 --> 00:17:39,450
+impossible because B is a prime ماشي إذا الحالة
+
+189
+00:17:39,450 --> 00:17:43,950
+الأولى هي الحادثة يعني a بيساوي أربعة ومنه b 
+
+190
+00:17:43,950 --> 00:17:50,710
+بتساوي خمسة إذا the only prime for which three b 
+
+191
+00:17:50,710 --> 00:17:59,510
+plus one is a perfect square is b بتساوي five اللي
+
+192
+00:17:59,510 --> 00:17:59,950
+بعده
+
+193
+00:18:02,720 --> 00:18:06,500
+The only prime of the form n تربيع ناقص أربعة is
+
+194
+00:18:06,500 --> 00:18:10,840
+إيش؟ is خمسة و هذا similarly نشهر العيد اللي لدك 
+
+195
+00:18:10,840 --> 00:18:14,860
+بنقول اللي هو n تربيع ناقص أربعة بيساوي اللي هو
+
+196
+00:18:14,860 --> 00:18:19,620
+بيسميه prime و بيصير p بيساوي n ناقص اثنين و n زائد
+
+197
+00:18:19,620 --> 00:18:22,900
+اثنين تأخذ ال two cases زي ما أخذنا قبل بشوية و
+
+198
+00:18:22,900 --> 00:18:26,960
+بيطلع عندك لازم اللي هو ال p إيش بتساوي؟ بتساوي خمسة
+
+199
+00:18:27,770 --> 00:18:29,830
+طبعاً على اللي بعدنا طيب صلونا على النبي عليه
+
+200
+00:18:29,830 --> 00:18:32,710
+الصلاة والسلام السؤال نزل على الأربعة نشوف الأربعة 
+
+201
+00:18:32,710 --> 00:18:38,110
+معايا الشغلات اللي بدي أحسب بس هنقول لكم كيف اللي ده 
+
+202
+00:18:38,110 --> 00:18:42,970
+كنتوا تحسبوا لحالكم الآن if b أكبر سواء خمسة is a
+
+203
+00:18:42,970 --> 00:18:48,170
+prime number show that b تربيع زائد اثنين is a
+
+204
+00:18:48,170 --> 00:18:55,050
+composite number الآن عندي ال .. ال b أكبر سواء 
+
+205
+00:18:55,050 --> 00:18:56,330
+خمسة من خمسة وطالع
+
+206
+00:18:59,060 --> 00:19:06,840
+عندي اللي هي أي b أو أي عدد كان b written على
+
+207
+00:19:06,840 --> 00:19:13,620
+صورة 6k 6k زائد 1 6k زائد 2 6k زائد 3 6k زائد 4 6k
+
+208
+00:19:13,620 --> 00:19:19,980
+زائد 5 الآن b عندي prime b عندي prime الـ Prime 
+
+209
+00:19:19,980 --> 00:19:24,320
+بالذنب يقول لي مدام الـ Prime إذا أنا يا إما على
+
+210
+00:19:24,320 --> 00:19:29,700
+صورة 6K زائد واحد أو 6K زائد مين؟ زائد خمسة طبعا
+
+211
+00:19:29,700 --> 00:19:32,900
+حالتين واحد يقول لي طب ليش ما قسمنا على خمسة؟
+
+212
+00:19:32,900 --> 00:19:36,920
+أخذنا القسمة على خمسة الحالة الخامسة مش هتسعفني
+
+213
+00:19:36,920 --> 00:19:44,560
+لأنه هضطر اخذ اللي هي حالة الخمسة K لأن الـ Prime
+
+214
+00:19:44,560 --> 00:19:49,260
+خمسة ممكن تبع صورة خمسة K أو خمسة K زائد واحد لأنه 
+
+215
+00:19:49,260 --> 00:19:53,100
+مش عارف إبراهيم ولا لأ خمسة K زائد اثنين مش عارف 
+
+216
+00:19:53,100 --> 00:19:56,040
+إبراهيم ولا لأ خمسة K زائد تلاتة مش عارف إبراهيم و
+
+217
+00:19:56,040 --> 00:19:58,820
+لا لأ خمسة K زائد .. ما عندي تاخد كل الحالات لأ أسهل
+
+218
+00:19:58,820 --> 00:20:03,220
+لي اخذ مين اللي هو ستة K زائد واحد و ستة K زائد 
+
+219
+00:20:03,220 --> 00:20:09,200
+خمسة وهذه طبعا واضح إنه الحالات الثانية ماكونيش
+
+220
+00:20:09,200 --> 00:20:12,740
+عارف إبراهيم معايا؟ طيب
+
+221
+00:20:15,860 --> 00:20:23,000
+أي سؤال؟ أعيد؟ الآن لـ "برايم" b أكبر ويساوي
+
+222
+00:20:23,000 --> 00:20:28,480
+الخمسة مدام الـ "برايم" وبدأ أقسم على ستة ستة ستة
+
+223
+00:20:28,480 --> 00:20:31,440
+ستة ستة ستة ستة b بتساوي 6k لأن b بتساوي
+
+224
+00:20:31,440 --> 00:20:36,080
+6k مش برايم الآن 6k زيادة واحد ممكن يكون
+
+225
+00:20:36,080 --> 00:20:39,940
+6k زيادة اثنين برضه مش برايم 6k زيادة 
+
+226
+00:20:39,940 --> 00:20:43,340
+تلاتة برضه مش برايم 6k زيادة أربعة برضه مش
+
+227
+00:20:43,340 --> 00:20:50,060
+برايم 6K زيادة خمسة ممكن 6K
+
+228
+00:20:50,060 --> 00:20:54,520
+زيادة اثنين إيش هي؟ اثنين في تلاتة K زيادة مين
+
+229
+00:20:54,520 --> 00:21:00,620
+زيادة واحد يعني مش برايم even غير اثنين و 6K زيادة
+
+230
+00:21:00,620 --> 00:21:07,300
+تلاتة و 6K زيادة أربعة و 6K كل هدولة مش برايم الآن 
+
+231
+00:21:07,300 --> 00:21:10,480
+عندي بدي أثبت لك إن b تربيع زائد اثنين أشمالها
+
+232
+00:21:10,480 --> 00:21:16,980
+composite ما عليّ إلا أجيب هاي b تربيع زائد اثنين
+
+233
+00:21:16,980 --> 00:21:24,440
+و أعوض بـ b بـ 6K زائد واحد و المرة الثانية بـ 6K
+
+234
+00:21:24,440 --> 00:21:29,180
+زائد خمسة هاي معوضة طلعت تلاتة في رقم و تلاتة في
+
+235
+00:21:29,180 --> 00:21:32,460
+رقم في الثانية في الحل الثانية طلعت أشمالها is
+
+236
+00:21:32,460 --> 00:21:41,380
+composite والتفاصيل موجودة في الحل اللي بعده خمسة
+
+237
+00:21:41,380 --> 00:21:49,880
+K ال b تأخذ خمسة K لـ prime خمسة
+
+238
+00:21:49,880 --> 00:21:56,000
+K زائد واحد ممكن تكون prime زي الواحد تلاتين مثلاً 
+
+239
+00:21:56,000 --> 00:21:59,680
+خمسة K زائد اثنين برضه مقدرش اجزم إنّه مش برايم خمسة 
+
+240
+00:21:59,680 --> 00:22:03,040
+K زائد التلاتة مقدرش وخمسة K زائد الأربعة مقدرش اجزم 
+
+241
+00:22:03,040 --> 00:22:10,590
+إنها برايم معايا اللي بعده؟ بنفع 
+
+242
+00:22:10,590 --> 00:22:15,470
+تروح بالتجاه مثلاً تمانية K زي تمانية K الجسم على 
+
+243
+00:22:15,470 --> 00:22:20,810
+تمانية آه بنفع بس هتكون إيه؟ هتكون بتغلبك أكثر سبعة 
+
+244
+00:22:20,810 --> 00:22:25,930
+هتعمل لي مشكلة زي مين؟ زي الخمسة واحد بنفع يقول
+
+245
+00:22:25,930 --> 00:22:30,170
+الجسم اعمل بالنسبالي مين؟ آه بنفع بس يضحكوا علينا
+
+246
+00:22:30,170 --> 00:22:34,390
+الناس طيب
+
+247
+00:22:37,800 --> 00:22:44,320
+النجلة السؤال اللي بعده if
+
+248
+00:22:44,320 --> 00:22:47,740
+b أكبر أو يساوي q أكبر أو يساوي خمسة and b and q
+
+249
+00:22:47,740 --> 00:22:51,520
+are both prime then من الأربعة و عشرين تقسم ال b
+
+250
+00:22:51,520 --> 00:22:56,880
+تربيع زائد q تربيع نفس الفكرة نفس الفكرة عندي اللي
+
+251
+00:22:56,880 --> 00:23:05,440
+هو ال b الـ B يا إما 6K زائد 1 يا 6K زائد 5
+
+252
+00:23:05,440 --> 00:23:10,540
+ونفس الشيء ميم هي الـ Q يا إما 6K زائد 1 يا 
+
+253
+00:23:10,540 --> 00:23:17,280
+6K زائد 5 اللي أنا غرضي أحسب مين؟ الـ B تربيع مع 
+
+254
+00:23:17,280 --> 00:23:22,280
+تصميم لـ Q تربيع عندي الآن بناء على هذا الحديث في 
+
+255
+00:23:22,280 --> 00:23:28,560
+عندي three cases يا إما الـ B و الـ Q على صورة 
+
+256
+00:23:28,560 --> 00:23:37,360
+6K زائد 1 و 6N زائد 1 اثنين على صورة 6k زائد خمسة
+
+257
+00:23:37,360 --> 00:23:42,980
+و 6m زائد خمسة أو واحدة منهن على صورة 6k زائد واحد
+
+258
+00:23:42,980 --> 00:23:49,560
+والتاني على صورة 6m زائد خمسة واضح لأن بعوض في كل
+
+259
+00:23:49,560 --> 00:23:56,380
+حالة b تربيع ناقص q تربيع حالجيها بتطلع لي اللي هو
+
+260
+00:23:56,380 --> 00:24:01,120
+ال 12 في الحالة الأولى مثلاً بتطلع 12 في هذا المقدر
+
+261
+00:24:01,120 --> 00:24:08,870
+المربع واطرح معايا؟ اعمل لكم حالة؟ اللي عندي b تربيع
+
+262
+00:24:08,870 --> 00:24:13,450
+ناقص q تربيع إيش بتساوي؟ 6K زائد واحد معايا يا
+
+263
+00:24:13,450 --> 00:24:20,990
+شباب لكل تربيع ناقص 6M زائد واحد لكل تربيع أنا غير
+
+264
+00:24:20,990 --> 00:24:25,450
+بإن أثبت مين ال 24 اللي بتجسم ال b تربيع ناقص مين؟
+
+265
+00:24:25,450 --> 00:24:32,810
+ال q تربيع ويساوي هذا يصبح لديه 36K تربيع زائد 12K
+
+266
+00:24:32,810 --> 00:24:40,230
+زائد 1 ناقص نفس الشيء 36M تربيع ناقص 12M ناقص 1
+
+267
+00:24:42,320 --> 00:24:46,340
+الواحد هيروح مع مين؟ مع السالب واحد، إذا ظهرت عندي
+
+268
+00:24:46,340 --> 00:24:49,760
+مين؟ العوامل المشتركة
+
+269
+00:24:49,760 --> 00:24:57,320
+العوامل المشتركة بيصير فيك ستة تلاتة في K تربيع ناقص K ناقص 
+
+270
+00:24:57,320 --> 00:25:07,150
+M تربيع زائد اللي هو K ناقص M ماشي الحال الآن هذه
+
+271
+00:25:07,150 --> 00:25:17,170
+فيها هتظهر الاثنين كيف هتظهر الاثنين عند الـ K و الـ M 
+
+272
+00:25:17,170 --> 00:25:23,870
+إما اثنين قديمة اثنين even يا واحدة odd واحدة even 
+
+273
+00:25:23,870 --> 00:25:28,430
+لو الاثنين even معناته صار هذا even وهذا even 
+
+274
+00:25:28,430 --> 00:25:32,370
+مجمعهم even إذا ظهرت الاثنين إذا ظهرت مين؟
+
+275
+00:25:32,370 --> 00:25:37,950
+الأربع والعشرين معايا لو الاثنين odd معناته صار هذا 
+
+276
+00:25:37,950 --> 00:25:44,690
+even وهذا even مجمعهم even إذا حيظهر كمان مرة اثنين
+
+277
+00:25:45,700 --> 00:25:50,480
+لو كانت واحدة even واحدة odd معناته واحدة طلعت odd
+
+278
+00:25:50,480 --> 00:25:54,920
+وهذه واحدة odd مع بعض إيش؟ ما مجمعنيهاش even إذا في
+
+279
+00:25:54,920 --> 00:26:00,320
+كل الأحوال هذه فيها اثنين إذا صار الأربعة و العشرين
+
+280
+00:26:00,320 --> 00:26:05,860
+بتجسم b تربيع ناقص q تربيع اللي هو في حالة اللي 
+
+281
+00:26:05,860 --> 00:26:08,080
+هو هذا similarly وهذا نفس الشيء
+
+282
+00:26:17,410 --> 00:26:31,430
+بيصير K زي 3 في K زي 1 برضه
+
+283
+00:26:31,430 --> 00:26:36,650
+بدك تأخذ cases نعم لكن مش طرق أخرى ممكن تكون طرق
+
+284
+00:26:36,650 --> 00:26:41,710
+أخرى فيه صلى
+
+285
+00:26:41,710 --> 00:26:46,110
+الله عليه الصلاة والسلام الآن
+
+286
+00:26:46,110 --> 00:26:55,890
+عندي إذا B لا تساوي 5، B تربيع ناقص 1 أو B
+
+287
+00:26:55,890 --> 00:26:57,910
+تربيع زائد 1، فهو ممكن أن يتم قسمته على
+
+288
+00:26:57,910 --> 00:27:01,090
+العشرة. لسه معلوماتنا في نظرية الأعداد في
+
+289
+00:27:01,090 --> 00:27:06,010
+بدايتها، ماشي الحال، لسه ما أخذنا التطابقات ولا
+
+290
+00:27:06,010 --> 00:27:09,430
+أخذنا غيره لأن إحنا بنحكي عن الـ Fundamental
+
+291
+00:27:09,430 --> 00:27:13,370
+Theorem of Arithmetic و تعريف الـPrime في هذه
+
+292
+00:27:13,370 --> 00:27:17,940
+المعلومات بدنا نحل الأسئلة هذه ماشي الحال بقى فترة
+
+293
+00:27:17,940 --> 00:27:22,440
+هتلاقوا اللي هو كثير من الحلول بتسهل في اللي هو مع
+
+294
+00:27:22,440 --> 00:27:27,700
+أننا نأخذ نظريات أو اللي هو مادة فوق المادة اللي
+
+295
+00:27:27,700 --> 00:27:35,020
+أخذناها طيب شوفوا سؤالنا كالتالي إذا كانت B لا
+
+296
+00:27:35,020 --> 00:27:41,360
+تساوي 5 is an odd prime إيش ماله odd prime و
+
+297
+00:27:41,360 --> 00:27:46,740
+بيساوي 5 يعني هو هذا اللي بيحكي عنه 3 أو
+
+298
+00:27:46,740 --> 00:27:52,340
+7 أو 11 أو طالع ماشي مستفيدين من هذه الخمسة
+
+299
+00:27:52,340 --> 00:27:58,660
+من الحديث بقول أثبت أنه دائماً هذا الـ B لو
+
+300
+00:27:58,660 --> 00:28:02,000
+حسبت له الـ B تربيع ناقص 1 أو الـ B تربيع زائد 1
+
+301
+00:28:02,000 --> 00:28:08,240
+هتلاقي إيش ما قال واحد منهم بيكسب العشرة ماشي يعني
+
+302
+00:28:08,240 --> 00:28:13,420
+دائماً هتلاقي العشرة بتقسم بـ تربيع ناقص 1 or
+
+303
+00:28:13,420 --> 00:28:19,980
+العشرة بتقسم بـ تربيع زائد 1 الآن عشان اللي هو
+
+304
+00:28:19,980 --> 00:28:24,240
+الحديث عن القسمة على 10 بدي أتكلم عن القسمة على
+
+305
+00:28:24,240 --> 00:28:28,060
+10 مادام بدي أتكلم عن القسمة على 10 خليني
+
+306
+00:28:28,060 --> 00:28:32,200
+أستثني من بينهم الـ 3 والـ 7 لأنه كيف بدك تبيّن
+
+307
+00:28:32,200 --> 00:28:37,000
+الآن الـ 3 والـ 7 حساب بسيط قد برايم هو طالب قد
+
+308
+00:28:37,000 --> 00:28:44,040
+برايم قد برايم لأن في حالة الـ B بتساوي 3 واضح
+
+309
+00:28:44,040 --> 00:28:48,980
+الـ B تربيع زائد الـ 1 هي الـ 10 يعني هي اللي
+
+310
+00:28:48,980 --> 00:28:55,660
+بتقسم الـ 10 بتقسمها في حالة الـ B بتساوي 7 برضه
+
+311
+00:28:55,660 --> 00:29:00,100
+الـ B تربيع زائد 1 لهاش بتساوي 50 الـ 10
+
+312
+00:29:00,100 --> 00:29:07,660
+بتقسمها إذن هذول الحالتين بينطبق عليهن الآن بدنا
+
+313
+00:29:07,660 --> 00:29:11,640
+نأخذ اللي هو القسمة على 10 by division algorithm
+
+314
+00:29:11,640 --> 00:29:18,840
+الأعداد عموماً هي صورة 10 K زائد 1، 10 K مش
+
+315
+00:29:18,840 --> 00:29:26,980
+واردة ليش؟ لأنه prime قد prime 10 K زائد
+
+316
+00:29:26,980 --> 00:29:34,370
+2 مش واردة 3 مش واردة 4 مش واردة 5 مش 
+
+317
+00:29:34,370 --> 00:29:41,030
+واردة 6 مش واردة 7 مش واردة 8 مش
+
+318
+00:29:41,030 --> 00:29:48,170
+واردة 9 ممكن 10
+
+319
+00:29:48,170 --> 00:29:52,650
+الآن صار عند القسمة على 10 واحدة تنتهي بـ 1، 3، 4،
+
+320
+00:29:53,320 --> 00:29:57,800
+4، الآن اللي .. اللي .. اللي بدنا هي بس لحالكم
+
+321
+00:29:57,800 --> 00:30:02,240
+عوضوا على P تربيع ناقص 1 و P تربيع زائد 1 في
+
+322
+00:30:02,240 --> 00:30:07,040
+كل حالة تغلب شوية و هتلاقي العشرة هتلاقي العشرة
+
+323
+00:30:07,040 --> 00:30:10,340
+بتقسم يا الـ P تربيع زائد 1 يا الـ P تربيع ناقص
+
+324
+00:30:10,340 --> 00:30:14,720
+1 في كل واحدة ده اللي بعده
+
+325
+00:30:19,530 --> 00:30:23,870
+السؤال اللي بعده هو prove that a positive integer a
+
+326
+00:30:23,870 --> 00:30:33,170
+أكبر من صفر is a square if and only if its
+
+327
+00:30:33,170 --> 00:30:37,730
+form in the canonical form أو its representation
+
+328
+00:30:37,730 --> 00:30:42,490
+in the canonical form of
+
+329
+00:30:42,490 --> 00:30:46,930
+all exponents of the primes are even integers أيش
+
+330
+00:30:46,930 --> 00:30:48,890
+اللي بيقول السؤال؟ بيقول ما يا ليه؟
+
+331
+00:30:53,190 --> 00:30:58,010
+السؤال سهل بيقول
+
+332
+00:30:58,010 --> 00:31:07,170
+أنه a هيكون اللي هو perfect square a طبعاً بيساوي
+
+333
+00:31:07,170 --> 00:31:12,410
+P1 α1 لعند P r α r هذا بيكون
+
+334
+00:31:12,410 --> 00:31:22,200
+perfect square if and only if اللي هو α1 أو
+
+335
+00:31:22,200 --> 00:31:35,460
+α2 لعند αr are even integers ماشي؟ بنقول أنه اللي
+
+336
+00:31:35,460 --> 00:31:39,460
+هو العدد
+
+337
+00:31:39,460 --> 00:31:43,620
+هيكون إيه؟ is a perfect square إيه ده؟ وفقط إيه
+
+338
+00:31:43,620 --> 00:31:48,760
+ده؟ اللي هو الـ exponents لـ its prime factorization
+
+339
+00:31:48,760 --> 00:31:56,070
+is even الكلام سهل يعني بنقول suppose that اللي هو
+
+340
+00:31:56,070 --> 00:32:06,690
+a suppose that a is a perfect square بجان perfect
+
+341
+00:32:06,690 --> 00:32:14,650
+square then there exist اللي هو مثلًا P element in
+
+342
+00:32:14,650 --> 00:32:20,850
+Z such that a بتساوي P تربيع معايا يا شباب
+
+343
+00:32:23,980 --> 00:32:30,840
+الآن الـ P عندي الـ P عندي اللي هو أكبر من 1
+
+344
+00:32:30,840 --> 00:32:34,100
+لأن الـ A أكبر من 1 إذن في لـ Factorization
+
+345
+00:32:34,100 --> 00:32:37,980
+لأن الـ Factorization للـ P نفترض إنه عبارة عن Q
+
+346
+00:32:37,980 --> 00:32:44,860
+1 α1 لعند Q r αr أو P زي ما بدك
+
+347
+00:32:44,860 --> 00:32:48,100
+وهذا إيش ماله؟ هذا مين؟ هو الـ Prime Factorization
+
+348
+00:32:48,100 --> 00:32:52,800
+مين؟ للـ P by unique factorization theorem أو
+
+349
+00:32:52,800 --> 00:32:56,880
+fundamental theorem of arithmetic اللي هنرفعه على
+
+350
+00:32:56,880 --> 00:33:03,000
+القوة 2 هيطلع عبارة عن Q1 تربيع α1 لعند Qr تربيع  
+
+351
+00:33:03,000 --> 00:33:08,900
+إذن حصلنا على مين؟ كل الـ exponents اليمين are
+
+352
+00:33:08,900 --> 00:33:14,520
+even conversely .. conversely سبق conversely
+
+353
+00:33:16,290 --> 00:33:23,070
+البرنامج موجود كامل يا جماعة Suppose that A is
+
+354
+00:33:23,070 --> 00:33:30,830
+written as P1 α1 لعند Pr αr where
+
+355
+00:33:30,830 --> 00:33:35,050
+α1 لعند αr are even
+
+356
+00:33:39,990 --> 00:33:44,150
+بتساوي P1 α1 على 2 لها معنى أنها
+
+357
+00:33:44,150 --> 00:33:49,370
+صارت even لأن عند Pr αr على 2 لها معنى
+
+358
+00:33:49,370 --> 00:33:55,770
+أنها even αr فاهمين؟ مش بحكي الكل إيش ماله قس
+
+359
+00:33:55,770 --> 00:34:02,550
+2 وهذا إيش ماله is integer say مثلًا P إذن صارت
+
+360
+00:34:02,550 --> 00:34:08,210
+الـ a على صورة P تربيع إذن is a perfect square إيش
+
+361
+00:34:08,210 --> 00:34:17,640
+يا محمد واضح؟ اه مجدداً أنا
+
+362
+00:34:17,640 --> 00:34:24,280
+بيكون الأساس نفس الشيء ماشي
+
+363
+00:34:24,280 --> 00:34:24,980
+أي سؤال
+
+364
+00:34:45,210 --> 00:34:52,010
+نجي لـ 3.2 نمر سريع برضه على الأسئلة في 3.2
+
+365
+00:34:52,010 --> 00:34:57,590
+الـ
+
+366
+00:34:57,590 --> 00:35:00,730
+N خلينا نمر بشكل سريع على الأسئلة عشان بالك أن
+
+367
+00:35:00,730 --> 00:35:06,790
+طلعنا كل الأسئلة given B لا تقسم N الـ B مش من
+
+368
+00:35:06,790 --> 00:35:12,290
+عوامل مين؟ N for all primes أصغر أو يساوي من جذر
+
+369
+00:35:12,290 --> 00:35:20,300
+التكعيب للـ N نفترض إن كل الـ Primes اللي أجل أو
+
+370
+00:35:20,300 --> 00:35:26,220
+تساوي جذر التكعيب للـ N ليست من عوامل الـ N
+
+371
+00:35:26,220 --> 00:35:32,480
+معايا بدنا نفترض هيك إن الـ N عبارة عن عدد بحيث إن
+
+372
+00:35:32,480 --> 00:35:39,700
+كل الـ Primes اللي أجل من جذر التكعيب له شاملها
+
+373
+00:35:39,700 --> 00:35:46,580
+لا تقسم الـ N show that n أكبر من 1 لما تكون n
+
+374
+00:35:46,580 --> 00:35:51,540
+أكبر من 1 is either a prime or إيش ماله a
+
+375
+00:35:51,540 --> 00:35:57,680
+product of two primes أعطيك
+
+376
+00:35:57,680 --> 00:36:10,700
+مثال عددي خليني أعطيك مثال عددي مثلًا
+
+377
+00:36:10,700 --> 00:36:17,640
+مثال بسيط الـ 15 بتساوي 3 في مين؟ في 5
+
+378
+00:36:17,640 --> 00:36:24,080
+الآن الشروط اللي هو المعطيات اللي هي السؤال أو
+
+379
+00:36:24,080 --> 00:36:29,820
+شروط السؤال متحققة ليش؟ لأن جذر التكعيب
+
+380
+00:36:29,820 --> 00:36:40,120
+للـ 15 اللي هو أجل من 3 أكيد أجل من 3
+
+381
+00:36:40,120 --> 00:36:47,180
+ماشي الحال إذا .. إذا .. إذا عند ال .. ال .. ال ..
+
+382
+00:36:47,180 --> 00:36:47,700
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+383
+00:36:47,700 --> 00:36:48,980
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+384
+00:36:48,980 --> 00:36:50,260
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+385
+00:36:50,260 --> 00:36:50,980
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+386
+00:36:50,980 --> 00:36:51,040
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+387
+00:36:51,040 --> 00:36:56,080
+.. ال .. ال .. ال .. ال .. ال ..
+
+388
+00:36:56,080 --> 00:36:56,220
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+389
+00:36:56,220 --> 00:36:56,400
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+390
+00:36:56,400 --> 00:36:56,500
+.. ال .. ال .. ال .. ال .. ال .. ال
+
+391
+00:37:09,410 --> 00:37:14,730
+معايا ومن طلع عندي هنا اللي هو product of two
+
+392
+00:37:14,730 --> 00:37:19,130
+primes الآن
+
+393
+00:37:19,130 --> 00:37:27,250
+بدنا .. بدنا نثبت اللي هو أنه تحت الشروط هذه أنه
+
+394
+00:37:27,250 --> 00:37:35,590
+ما فيش ولا prime أجل من جذر التكعيب للـ n بيقسم n الآن
+
+395
+00:37:35,590 --> 00:37:44,390
+يؤدي إلى أن هذه الـ n يا هتكون product of إيش؟ of
+
+396
+00:37:44,390 --> 00:37:54,010
+two primes الآن نفترض أن n بتحتوي على الأقل إيش؟
+
+397
+00:37:54,010 --> 00:38:01,450
+three distinct prime factors ماشي الحال نفترض أن
+
+398
+00:38:01,450 --> 00:38:07,600
+في إيش؟ 3 say that وهو بيحقق إن هذا عشان نصل لـ
+
+399
+00:38:07,600 --> 00:38:10,420
+contradiction بيحقق إن الـ first three prime
+
+400
+00:38:10,420 --> 00:38:16,440
+factors of N P1 و P2 و مين؟ و P3 ماشي
+
+401
+00:38:16,440 --> 00:38:20,460
+الحال إذا عندي الـ P1 بتقسم الـ N و P2
+
+402
+00:38:20,460 --> 00:38:26,760
+بتقسم الـ N و P3 إيش ماله بتقسم الـ N إذن من هنا
+
+403
+00:38:26,760 --> 00:38:31,720
+أكيد الـ N إيش ماله بدون أصل contradiction أكبر و
+
+404
+00:38:31,720 --> 00:38:34,460
+سوى P1 في P2 في مين؟ P3 حصل الـ
+
+405
+00:38:34,460 --> 00:38:39,620
+contradiction بشكل آخر واضح إيش اللي سويته؟ فرضت أن
+
+406
+00:38:39,620 --> 00:38:44,960
+الـ N تبعتنا هذه الـ N بتحتوي على الأقل three
+
+407
+00:38:44,960 --> 00:38:49,560
+prime factors مين هنسميهم بالظبط P1 و P
+
+408
+00:38:49,560 --> 00:38:53,580
+2 و P إيش؟ 3 صارت P1 بتقسم N و P2
+
+409
+00:38:53,580 --> 00:38:59,090
+بتقسم N و P3 بتقسم N إذن الأكيد N تبعتنا لأنها
+
+410
+00:38:59,090 --> 00:39:04,310
+أصلًا الـ P1 والـ P2 والـ P3 منها ويمكن في غيرها N
+
+411
+00:39:04,310 --> 00:39:08,830
+هتكون أكبر أو تساوي P1 في P2 في P3 الآن في سؤالنا
+
+412
+00:39:08,830 --> 00:39:16,070
+بما أن الـ P لا تقسم الـ N for all primes P أصغر أو
+
+413
+00:39:16,070 --> 00:39:21,290
+يساوي جذر التكعيب للـ N إذن الـ P1 هذه اللي قسمت
+
+414
+00:39:21,290 --> 00:39:25,870
+و الـ P2 اللي قسمت و الـ P3 اللي قسمت كلهم
+
+415
+00:39:25,870 --> 00:39:34,510
+أكبر من مين؟ من جذر التكعيب أه إذن أضحى الصورة
+
+416
+00:39:34,510 --> 00:39:38,910
+إذا صار عند الـ P1 في الـ P2 في الـ P3 إيش ماله
+
+417
+00:39:38,910 --> 00:39:46,870
+أكبر من الـ N Contradiction إذن يستحيل أنه يكون في
+
+418
+00:39:46,870 --> 00:39:53,250
+عوامل اللي هو 3 أو أكثر من الـ primes بيقسموا الـ N
+
+419
+00:39:53,250 --> 00:40:00,330
+الـ N وفي نفس الوقت هذا الـ condition إيش ماله متحقق
+
+420
+00:40:00,330 --> 00:40:11,230
+Therefore عندي الـ n الـ factors لها يا one
+
+421
+00:40:11,230 --> 00:40:20,240
+prime factor يا two primes as a factors Fine اللي
+
+422
+00:40:20,240 --> 00:40:34,540
+بعده Show
+
+423
+00:40:34,540 --> 00:40:44,320
+that
+
+424
+00:40:48,380 --> 00:40:54,800
+أي عدد كومبوزيت ثلاث أرقام يجب أن يكون لديه عدد
+
+425
+00:40:54,800 --> 00:41:05,000
+كومبوزيت أقل من أو أصغر من 31 أي عدد
+
+426
+00:41:05,000 --> 00:41:14,360
+كومبوزيت من ثلاث أرقام يجب أن يحتوي على عدد كومبوزيت 
+
+427
+00:41:14,360 --> 00:41:24,440
+أقل من أو أصغر من 31 يعني الـ 31 ما في سؤال
+
+428
+00:41:24,440 --> 00:41:27,800
+أو من دون الحكاية أكبر رقم من الـ three digits اللي
+
+429
+00:41:27,800 --> 00:41:33,780
+هو 999 نعم جذرها اللي هو 33 في 32 أو شيء زي ذلك الـ
+
+430
+00:41:33,780 --> 00:41:37,600
+33 و 32 مش برايم إن إن اللي تحكي مباشرة الـ 31 
+
+431
+00:41:37,600 --> 00:41:42,000
+أيه ده في هنا صح ولا ده؟ ده في هنا نعم إن أنت بدك
+
+432
+00:41:42,000 --> 00:41:50,070
+تستثني، بدك تستثني اللي هو عندك الـ 32 وبيظل الـ
+
+433
+00:41:50,070 --> 00:41:54,910
+100 عندك طبيعي لازم تستثني الـ 32 فما بعدها لو 
+
+434
+00:41:54,910 --> 00:41:59,860
+دلنا أصلاً بيطلع عن الـ 100 بتطلع عن الـ 1000 اه
+
+435
+00:41:59,860 --> 00:42:04,820
+صحيح اه الآن عندي وهذه الفكرة بناء على ايش؟ على
+
+436
+00:42:04,820 --> 00:42:10,240
+إن اللي أخذناها المرة الماضية إن في بي أصغر أو
+
+437
+00:42:10,240 --> 00:42:13,720
+أصغر من جذر الـ A بدون ما نحتاج من الله مدان بي هو
+
+438
+00:42:13,720 --> 00:42:16,980
+أنت ليه احتجت؟ مين قال لك احتجت؟ أنت حديثك أنت
+
+439
+00:42:16,980 --> 00:42:22,880
+احتجتها ليه؟ أنت احتجت في حديثك أصلاً على أساس الآن
+
+440
+00:42:22,880 --> 00:42:26,780
+احنا بنقول كومبوزيت ماشي الحال ما دام كومبوزيت
+
+441
+00:42:26,780 --> 00:42:31,360
+إذا فيه برايم فاكتور مضمون مضمون مضمون واحد من
+
+442
+00:42:31,360 --> 00:42:35,540
+الـ برايم فاكتور زي أصغر من مين؟ من جذر الـ A ماشي
+
+443
+00:42:35,540 --> 00:42:39,020
+اللي هو جذر مين؟ اللي الـ تلات أرقام على واحد اللي قلت 
+
+444
+00:42:39,020 --> 00:42:43,440
+عنه مين؟ هو تسعة تسعة تسعة مظبوط اللي هو أصغر ..
+
+445
+00:42:43,440 --> 00:42:46,480
+اللي هو الـ .. الـ B اللي أصغر أو يساوي اللي هو الـ S
+
+446
+00:42:46,480 --> 00:42:50,120
+بتكون اللي هو الواحد والثلاثين لأن اثنين والثلاثين 
+
+447
+00:42:50,120 --> 00:42:55,240
+هيعدّى الثلاث أرقام عشان ألف وأربع وعشرين إذاً
+
+448
+00:42:55,240 --> 00:43:03,540
+هيكون أصغر أو يساوي مين؟ واحد وثلاثين واضح؟ لأ لأ
+
+449
+00:43:03,540 --> 00:43:08,260
+طبيعي طبيعي أصغر أو يساوي واحد وثلاثين أي سؤال؟
+
+450
+00:43:13,870 --> 00:43:18,910
+السهل السؤال هذا if
+
+451
+00:43:18,910 --> 00:43:23,510
+PN is the nth prime number prove that none of the
+
+452
+00:43:23,510 --> 00:43:32,090
+integers is a perfect square أثبتنا
+
+453
+00:43:32,090 --> 00:43:37,370
+قبل هيك أن الـ perfect square معايا يا شباب الـ
+
+454
+00:43:37,370 --> 00:43:44,660
+perfect square أثبتنا أثبتناها أن مع صورة 4M أو
+
+455
+00:43:44,660 --> 00:43:48,680
+أربعة N زائد واحد صح؟ أربعة K أو أربعة K زائد واحد
+
+456
+00:43:48,680 --> 00:43:54,080
+بتثبت لك اللي هو الـ BN في هذه الحالة ايش ماله؟ ع
+
+457
+00:43:54,080 --> 00:43:59,920
+صورة اللي هو لا هذه ولا هذه يعني ع صورة أربعة K
+
+458
+00:43:59,920 --> 00:44:07,500
+زائد مين؟ لا أربعة K ولا أربعة K زائد واحد يا اثنين 
+
+459
+00:44:07,500 --> 00:44:11,740
+يا تلاتة واحنا بنحكي عن مين؟ اللي هو B1
+
+460
+00:44:14,760 --> 00:44:23,540
+B1 وهو 2 وB2 عند الـ BN Odd إذا صار عندي B1 في B2
+
+461
+00:44:23,540 --> 00:44:30,220
+في BN اثنين في something اثنين في اللي هو اثنين
+
+462
+00:44:30,220 --> 00:44:34,220
+ك زائد واحد عارفين ليش اثنين ك زائد واحد؟ لأنه Odd لأن
+
+463
+00:44:34,220 --> 00:44:39,580
+حصل ضرب وده Primes هذول هذول اللي بضلوا B2 وB3 عن 
+
+464
+00:44:39,580 --> 00:44:44,460
+الـ VR هذول Primes يا جماعة وكل نقض حصل ضرب نقض
+
+465
+00:44:44,460 --> 00:44:49,600
+إذا نسامر على صورة 2K زائد 1 والـ 8 في الأصل فصارت
+
+466
+00:44:49,600 --> 00:44:54,560
+2×2K زائد 1 يعني على صورة 4K زائد مين؟ 2 مش على 
+
+467
+00:44:54,560 --> 00:45:01,140
+الصورة مين؟ الآن BM ليهادي زائد هادي زائد 1 ع صورة
+
+468
+00:45:01,140 --> 00:45:07,200
+ايش؟ 4K زائد 3 مش على الصورة مين؟ 4K زائد 1 أو مين؟ أو
+
+469
+00:45:07,200 --> 00:45:13,930
+4K إذا مش Perfect Square كمان
+
+470
+00:45:13,930 --> 00:45:22,290
+مرة هذا العدد اللي هو فش ي prove that none of the
+
+471
+00:45:22,290 --> 00:45:27,930
+integers هذول is a perfect square الفكرة أن تثبت
+
+472
+00:45:27,930 --> 00:45:31,070
+هذا إنه مش perfect square إنك تكتب لك اياه على صورة
+
+473
+00:45:31,070 --> 00:45:39,780
+مين؟ اللي هو أربعة K زائد تلاتة مش أربعة K ولا أربعة
+
+474
+00:45:39,780 --> 00:45:46,120
+K زائد واحد والفكرة سهلة أول عدد اثنين و هذول ع
+
+475
+00:45:46,120 --> 00:45:50,080
+صورة اثنين K زائد واحد لأن الـ Odd حصل ضربهم فبصير 
+
+476
+00:45:50,080 --> 00:45:54,140
+هذول مع بعض عبارة عن أربعة K زائد اثنين وفي كمان 
+
+477
+00:45:54,140 --> 00:45:58,200
+واحد إذا صار أربعة K زائد ايش؟ تلاتة إذا is not a
+
+478
+00:45:58,200 --> 00:46:00,120
+perfect square
+
+479
+00:46:05,880 --> 00:46:13,200
+أي Perfect Square ايش صورته؟ يا 4k يا 4k زائد 1 هذا
+
+480
+00:46:13,200 --> 00:46:17,820
+الـ perfect square المربع الكامل الـ N بتثبت لك إن الـ
+
+481
+00:46:17,820 --> 00:46:24,940
+BN هذا اللي هو عبارة عن B1 في B2 لعند الـ BR زائد 
+
+482
+00:46:24,940 --> 00:46:30,580
+1 أو BN زائد 1 بتثبت لك إنه مش Perfect Square يعني
+
+483
+00:46:30,580 --> 00:46:34,620
+لو أثبتت صورته مش على الصورة لا هذه ولا هذه معناته
+
+484
+00:46:34,620 --> 00:46:39,940
+مش Perfect Square طيب، الـ N كيف؟ عند الـ B1 هو
+
+485
+00:46:39,940 --> 00:46:44,200
+أول الـ Prime أحد دول الـ Primes المعتمدة إذا هذا 
+
+486
+00:46:44,200 --> 00:46:48,960
+صار 2 هذا مضروب في إن كل هذول الدولة حاصل ضربهم Odd
+
+487
+00:46:48,960 --> 00:46:54,740
+لأن كلها Odd فصار عبارة عن ايش شكله هذا؟ اثنين ك 
+
+488
+00:46:54,740 --> 00:47:00,240
+زائد واحد مظبوط ومضروبات في اثنين صار اثنين في 
+
+489
+00:47:00,240 --> 00:47:05,920
+اثنين ك أربعة ك وزائد اثنين وفي عندي كمان واحد
+
+490
+00:47:05,920 --> 00:47:11,040
+مضروبة إنزاداش إذا هذه مش على الصورة لا هذه ولا هذه
+
+491
+00:47:11,040 --> 00:47:16,820
+إذا صار البيئة is not a perfect square is not a
+
+492
+00:47:16,820 --> 00:47:24,560
+perfect square معنى على تلاتة تلاتة تلاتة تلاتة
+
+493
+00:47:24,560 --> 00:47:41,620
+نشوف إذا كان ضل وجت سهلة
+
+494
+00:47:41,620 --> 00:47:46,800
+السؤال هذا على السريع المهم الأسئلة هي المحلولة
+
+495
+00:47:46,800 --> 00:47:52,340
+لإنتهى الوقت لكن السؤال الأول سهل show that the
+
+496
+00:47:52,340 --> 00:47:59,700
+integers n و n زائد تلاتة و n زائد أربعة can't all
+
+497
+00:47:59,700 --> 00:48:01,320
+be prime
+
+498
+00:48:07,400 --> 00:48:11,740
+الآن خذ اللي هو N يا تلاتة K يا تلاتة K زائد واحد
+
+499
+00:48:11,740 --> 00:48:15,300
+يا تلاتة K زائد اثنين في حالتي الـ N بيساوي تلاتة
+
+500
+00:48:15,300 --> 00:48:19,840
+K هتلاقي هذا مش الـ Prime في حالتي تلاتة K زائد
+
+501
+00:48:19,840 --> 00:48:24,200
+واحد هتلاقي اللي هو مين؟ تلاتة K زائد اللي هو تلاتة
+
+502
+00:48:24,200 --> 00:48:28,500
+مش الـ Prime أو تلاتة K زائد اثنين مش الـ Prime أو
+
+503
+00:48:28,500 --> 00:48:32,180
+N زائد اثنين أسف وN زائد أربعة في حالتي تلاتة K
+
+504
+00:48:32,180 --> 00:48:34,820
+زائد اثنين هتلاقي الـ N أربعة زائد أربعة مش الـ
+
+505
+00:48:34,820 --> 00:48:34,980
+Prime
+
+506
+00:48:37,850 --> 00:48:44,930
+اللي عندي التلاتة لو جربت أول حاجة ايش عندك الآن؟
+
+507
+00:48:44,930 --> 00:48:49,090
+أنا أكبر من مين؟ من تلاتة ماشي بتدقق لغة التلاتة 
+
+508
+00:48:49,090 --> 00:48:57,290
+أسهل شيء مين؟ هي القسمة على التلاتة هو كل عدد اللي 
+
+509
+00:48:57,290 --> 00:49:01,930
+أكبر من تلاتة بقدر أكثر ع صورة تلاتة بقدر أقسمها
+
+510
+00:49:01,930 --> 00:49:02,370
+تلاتة
+
+511
+00:49:08,010 --> 00:49:13,990
+ركز شوية أي عدد في الدنيا اللي هو من تلاتة وطالع
+
+512
+00:49:13,990 --> 00:49:17,910
+بقدر أقسمه عالنين ع تلاتة بحيث إن المتبقي يكون 
+
+513
+00:49:17,910 --> 00:49:23,110
+موجب ماشي الحال أكبر أي عدد في الدنيا أكبر من 
+
+514
+00:49:23,110 --> 00:49:25,710
+التلاتة بقدر أقسمها تلاتة ولا لأ؟
+
+515
+00:49:29,170 --> 00:49:32,870
+احنا كل شيء هنبقى الـ Dividing Algorithm يا تلاتة
+
+516
+00:49:32,870 --> 00:49:36,890
+K يا تلاتة K زائد واحد يا تلاتة K زائد مين؟ اثنين،
+
+517
+00:49:36,890 --> 00:49:40,670
+ماشي الحال أسهل شيء ما أقسم على تلاتة الآن أول
+
+518
+00:49:40,670 --> 00:49:46,950
+واحد بدي أحكي فيه إن هو التلاتة بنفع غيره؟ بنفع، 
+
+519
+00:49:46,950 --> 00:49:50,750
+اه طبعا، مش هتقسم على الأسهل، طب الأبسط والأسهل 
+
+520
+00:49:50,750 --> 00:49:54,110
+المرة
+
+521
+00:49:54,110 --> 00:50:00,120
+الجاية بنكمل، اللي هو إن شاء الله كما نكون احنا
+
+522
+00:50:00,120 --> 00:50:07,900
+أنهينا اللي هو Chapter تلاتة وراجعنا اللي هي بقدر
+
+523
+00:50:07,900 --> 00:50:12,700
+الإمكان اللي هو بعض الأسئلة اللي مطلوبة واللي 
+
+524
+00:50:12,700 --> 00:50:18,600
+بظل من الأسئلة بتحلها أنت ما عرفش تحلها في حلول 
+
+525
+00:50:18,600 --> 00:50:21,520
+موجودة على الصفحة مبارك الله فيكم 
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/PxxuZS1skY0_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/PxxuZS1skY0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f45ba7316903dd0a292ee16ab6fc7eb4fbb5cb87
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/PxxuZS1skY0_raw.json
@@ -0,0 +1 @@
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51.56, "end": 52.52, "word": " دُرست", "probability": 0.803955078125}, {"start": 52.52, "end": 53.18, "word": " قديما", "probability": 0.9334309895833334}, {"start": 53.18, "end": 53.42, "word": " من", "probability": 0.78466796875}, {"start": 53.42, "end": 53.98, "word": " القدم", "probability": 0.897216796875}, {"start": 53.98, "end": 55.1, "word": " ولها", "probability": 0.8037109375}, {"start": 55.1, "end": 56.16, "word": " أهميتها", "probability": 0.9931640625}, {"start": 56.16, "end": 57.24, "word": " وكثير", "probability": 0.920166015625}, {"start": 57.24, "end": 57.42, "word": " من", "probability": 0.9921875}, {"start": 57.42, "end": 57.7, "word": " هذه", "probability": 0.94091796875}, {"start": 57.7, "end": 58.52, "word": " الأعداد", "probability": 0.9811197916666666}, {"start": 58.52, "end": 59.02, "word": " اللي", "probability": 0.889892578125}, {"start": 59.02, "end": 59.46, "word": " هو", "probability": 0.95068359375}, {"start": 59.46, "end": 61.2, "word": " وضع", "probability": 0.9620768229166666}, {"start": 61.2, "end": 61.66, "word": " أسئلة", "probability": 0.9827880859375}, {"start": 61.66, "end": 62.06, "word": " كثير", "probability": 0.8616536458333334}, {"start": 62.06, "end": 62.58, "word": " حولها", "probability": 0.9855143229166666}, {"start": 62.58, "end": 63.24, "word": " بعضها", "probability": 0.9148763020833334}, {"start": 63.24, "end": 63.72, "word": " حل", "probability": 0.938720703125}, {"start": 63.72, "end": 64.8, "word": " وبعضها", "probability": 0.927001953125}, {"start": 64.8, "end": 65.02, "word": " ما", "probability": 0.794921875}, {"start": 65.02, "end": 65.48, "word": " زال", "probability": 0.992919921875}, {"start": 65.48, "end": 66.1, "word": " قائما", "probability": 0.8938802083333334}, {"start": 66.1, "end": 66.6, "word": " بدون", "probability": 0.987060546875}, {"start": 66.6, "end": 66.94, "word": " حل", "probability": 0.990478515625}], "temperature": 1.0}, {"id": 4, "seek": 8147, "start": 67.51, "end": 81.47, "text": "نبدأ في أول نوع من أنواع هذه الأعداد اللي هو اللي بنسميه الـ Perfect Numbers شبط الـ 11 هو عبارة عن Numbers of Special Forms", "tokens": [1863, 44510, 10721, 8978, 5551, 12610, 8717, 45367, 9154, 14739, 14407, 3615, 29538, 16247, 22488, 18513, 13672, 1829, 31439, 13672, 1829, 44945, 38251, 1829, 3224, 2423, 39184, 10246, 22592, 1616, 13412, 3555, 9566, 2423, 39184, 2975, 31439, 6225, 3555, 9640, 3660, 18871, 22592, 1616, 295, 11863, 10126, 82], "avg_logprob": -0.24952169340483996, "compression_ratio": 1.2808219178082192, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 67.51, "end": 68.19, "word": "نبدأ", "probability": 0.8047688802083334}, {"start": 68.19, "end": 68.31, "word": " في", "probability": 0.63623046875}, {"start": 68.31, "end": 68.75, "word": " أول", "probability": 0.954833984375}, {"start": 68.75, "end": 69.21, "word": " نوع", "probability": 0.915771484375}, {"start": 69.21, "end": 69.51, "word": " من", "probability": 0.9599609375}, {"start": 69.51, "end": 70.15, "word": " أنواع", "probability": 0.93798828125}, {"start": 70.15, "end": 70.43, "word": " هذه", "probability": 0.95947265625}, {"start": 70.43, "end": 71.23, "word": " الأعداد", "probability": 0.953125}, {"start": 71.23, "end": 71.99, "word": " اللي", "probability": 0.7421875}, {"start": 71.99, "end": 72.29, "word": " هو", "probability": 0.67041015625}, {"start": 72.29, "end": 73.15, "word": " اللي", "probability": 0.857177734375}, {"start": 73.15, "end": 73.99, "word": " بنسميه", "probability": 0.8629150390625}, {"start": 73.99, "end": 74.21, "word": " الـ", "probability": 0.650634765625}, {"start": 74.21, "end": 74.57, "word": " Perfect", "probability": 0.5029296875}, {"start": 74.57, "end": 75.35, "word": " Numbers", "probability": 0.7255859375}, {"start": 75.35, "end": 77.05, "word": " شبط", "probability": 0.635009765625}, {"start": 77.05, "end": 77.35, "word": " الـ", "probability": 0.6463623046875}, {"start": 77.35, "end": 77.37, "word": " 11", "probability": 0.720703125}, {"start": 77.37, "end": 77.75, "word": " هو", "probability": 0.86083984375}, {"start": 77.75, "end": 78.05, "word": " عبارة", "probability": 0.9573974609375}, {"start": 78.05, "end": 78.21, "word": " عن", "probability": 0.9892578125}, {"start": 78.21, "end": 78.93, "word": " Numbers", "probability": 0.58447265625}, {"start": 78.93, "end": 79.61, "word": " of", "probability": 0.9462890625}, {"start": 79.61, "end": 79.99, "word": " Special", "probability": 0.77392578125}, {"start": 79.99, "end": 81.47, "word": " Forms", "probability": 0.94287109375}], "temperature": 1.0}, {"id": 5, "seek": 10230, "start": 82.2, "end": 102.3, "text": "احد عاش اتنين اللي هو عبارة عن perfect numbers perfect numbers نيجي نعرف شو معناه perfect number بنقول عن العدد ال positive number اللي اكبر من سفر انه perfect number اذا كان مجموع ال divisors إله بدونه", "tokens": [995, 24401, 6225, 33599, 1975, 2655, 1863, 9957, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 2176, 3547, 2176, 3547, 8717, 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0.99169921875}, {"start": 84.76, "end": 85.28, "word": " perfect", "probability": 0.7197265625}, {"start": 85.28, "end": 86.36, "word": " numbers", "probability": 0.755859375}, {"start": 86.36, "end": 86.82, "word": " perfect", "probability": 0.65283203125}, {"start": 86.82, "end": 87.34, "word": " numbers", "probability": 0.59033203125}, {"start": 87.34, "end": 88.16, "word": " نيجي", "probability": 0.8179931640625}, {"start": 88.16, "end": 88.44, "word": " نعرف", "probability": 0.869140625}, {"start": 88.44, "end": 88.7, "word": " شو", "probability": 0.768310546875}, {"start": 88.7, "end": 88.94, "word": " معناه", "probability": 0.8727213541666666}, {"start": 88.94, "end": 89.28, "word": " perfect", "probability": 0.9111328125}, {"start": 89.28, "end": 89.7, "word": " number", "probability": 0.9052734375}, {"start": 89.7, "end": 90.92, "word": " بنقول", "probability": 0.5712483723958334}, {"start": 90.92, "end": 91.36, "word": " عن", "probability": 0.97216796875}, {"start": 91.36, "end": 91.98, "word": " العدد", "probability": 0.98291015625}, {"start": 91.98, "end": 93.1, "word": " ال", "probability": 0.87060546875}, {"start": 93.1, "end": 93.68, "word": " positive", "probability": 0.79150390625}, {"start": 93.68, "end": 94.24, "word": " number", "probability": 0.9814453125}, {"start": 94.24, "end": 94.44, "word": " اللي", "probability": 0.9716796875}, {"start": 94.44, "end": 94.88, "word": " اكبر", "probability": 0.8064778645833334}, {"start": 94.88, "end": 95.08, "word": " من", "probability": 0.9892578125}, {"start": 95.08, "end": 95.4, "word": " سفر", "probability": 0.7222493489583334}, {"start": 95.4, "end": 95.74, "word": " انه", "probability": 0.888427734375}, {"start": 95.74, "end": 96.14, "word": " perfect", "probability": 0.947265625}, {"start": 96.14, "end": 96.92, "word": " number", "probability": 0.98193359375}, {"start": 96.92, "end": 98.14, "word": " اذا", "probability": 0.877685546875}, {"start": 98.14, "end": 98.62, "word": " كان", "probability": 0.99560546875}, {"start": 98.62, "end": 99.36, "word": " مجموع", "probability": 0.91162109375}, {"start": 99.36, "end": 99.56, "word": " ال", "probability": 0.97119140625}, {"start": 99.56, "end": 100.66, "word": " divisors", "probability": 0.833251953125}, {"start": 100.66, "end": 101.34, "word": " إله", "probability": 0.24688720703125}, {"start": 101.34, "end": 102.3, "word": " بدونه", "probability": 0.9752604166666666}], "temperature": 1.0}, {"id": 6, "seek": 13244, "start": 105.03, "end": 132.45, "text": "مجموع الـ divisors اللي إله بدون و N لأن أي عدد بيقسم نفسه لأن أنا بدي أخد مجموع ال divisors اللي إله مع ده هو إذا طلع بساوة N بسميه perfect number أو بمفهوم آخر أو بمعنى آخر بنقول N is a perfect number إذا كان sigma of N يعني مجموع ال divisors كلهم بما فيه هو إيش حساوة؟", "tokens": [2304, 7435, 2304, 45367, 2423, 39184, 25974, 830, 13672, 1829, 11933, 43761, 47525, 11536, 4032, 426, 5296, 33456, 36632, 6225, 3215, 3215, 4724, 1829, 4587, 38251, 8717, 36178, 3224, 5296, 33456, 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"word": " اللي", "probability": 0.89892578125}, {"start": 107.11, "end": 107.49, "word": " إله", "probability": 0.5521240234375}, {"start": 107.49, "end": 108.35, "word": " بدون", "probability": 0.96240234375}, {"start": 108.35, "end": 108.53, "word": " و", "probability": 0.61083984375}, {"start": 108.53, "end": 108.75, "word": " N", "probability": 0.1011962890625}, {"start": 108.75, "end": 109.23, "word": " لأن", "probability": 0.810302734375}, {"start": 109.23, "end": 109.51, "word": " أي", "probability": 0.65966796875}, {"start": 109.51, "end": 109.93, "word": " عدد", "probability": 0.9884440104166666}, {"start": 109.93, "end": 110.63, "word": " بيقسم", "probability": 0.8824462890625}, {"start": 110.63, "end": 111.25, "word": " نفسه", "probability": 0.9972330729166666}, {"start": 111.25, "end": 111.79, "word": " لأن", "probability": 0.74169921875}, {"start": 111.79, "end": 111.95, "word": " أنا", "probability": 0.81982421875}, {"start": 111.95, "end": 112.19, "word": " بدي", "probability": 0.6031494140625}, {"start": 112.19, "end": 112.43, "word": " أخد", "probability": 0.9381510416666666}, {"start": 112.43, "end": 112.87, "word": " مجموع", "probability": 0.9754638671875}, {"start": 112.87, "end": 112.99, "word": " ال", "probability": 0.98876953125}, {"start": 112.99, "end": 113.51, "word": " divisors", "probability": 0.841552734375}, {"start": 113.51, "end": 113.83, "word": " اللي", "probability": 0.992431640625}, {"start": 113.83, "end": 114.17, "word": " إله", "probability": 0.92919921875}, {"start": 114.17, "end": 114.73, "word": " مع", "probability": 0.95166015625}, {"start": 114.73, "end": 115.09, "word": " ده", "probability": 0.84228515625}, {"start": 115.09, "end": 115.39, "word": " هو", "probability": 0.9853515625}, {"start": 115.39, "end": 116.17, "word": " إذا", "probability": 0.933349609375}, {"start": 116.17, "end": 116.47, "word": " طلع", "probability": 0.9261067708333334}, {"start": 116.47, "end": 116.85, "word": " بساوة", "probability": 0.68017578125}, {"start": 116.85, "end": 116.99, "word": " N", "probability": 0.6904296875}, {"start": 116.99, "end": 117.59, "word": " بسميه", "probability": 0.9315185546875}, {"start": 117.59, "end": 117.97, "word": " perfect", "probability": 0.72119140625}, {"start": 117.97, "end": 118.73, "word": " number", "probability": 0.98193359375}, {"start": 118.73, "end": 119.77, "word": " أو", "probability": 0.84814453125}, {"start": 119.77, "end": 120.71, "word": " بمفهوم", "probability": 0.97666015625}, {"start": 120.71, "end": 121.29, "word": " آخر", "probability": 0.854736328125}, {"start": 121.29, "end": 121.57, "word": " أو", "probability": 0.89501953125}, {"start": 121.57, "end": 122.03, "word": " بمعنى", "probability": 0.9822265625}, {"start": 122.03, "end": 122.63, "word": " آخر", "probability": 0.974853515625}, {"start": 122.63, "end": 123.97, "word": " بنقول", "probability": 0.903564453125}, {"start": 123.97, "end": 124.29, "word": " N", "probability": 0.810546875}, {"start": 124.29, "end": 124.47, "word": " is", "probability": 0.94970703125}, {"start": 124.47, "end": 124.59, "word": " a", "probability": 0.9814453125}, {"start": 124.59, "end": 124.91, "word": " perfect", "probability": 0.92578125}, {"start": 124.91, "end": 125.41, "word": " number", "probability": 0.97314453125}, {"start": 125.41, "end": 125.73, "word": " إذا", "probability": 0.9755859375}, {"start": 125.73, "end": 126.03, "word": " كان", "probability": 0.99658203125}, {"start": 126.03, "end": 126.57, "word": " sigma", "probability": 0.306884765625}, {"start": 126.57, "end": 126.93, "word": " of", "probability": 0.9501953125}, {"start": 126.93, "end": 127.39, "word": " N", "probability": 0.92529296875}, {"start": 127.39, "end": 128.27, "word": " يعني", "probability": 0.960693359375}, {"start": 128.27, "end": 128.75, "word": " مجموع", "probability": 0.9527587890625}, {"start": 128.75, "end": 128.89, "word": " ال", "probability": 0.990234375}, {"start": 128.89, "end": 129.53, "word": " divisors", "probability": 0.982421875}, {"start": 129.53, "end": 130.11, "word": " كلهم", "probability": 0.97509765625}, {"start": 130.11, "end": 130.43, "word": " بما", "probability": 0.9794921875}, {"start": 130.43, "end": 130.71, "word": " فيه", "probability": 0.905029296875}, {"start": 130.71, "end": 131.11, "word": " هو", "probability": 0.9794921875}, {"start": 131.11, "end": 131.65, "word": " إيش", "probability": 0.8141276041666666}, {"start": 131.65, "end": 132.45, "word": " حساوة؟", "probability": 0.7821858723958334}], "temperature": 1.0}, {"id": 7, "seek": 15937, "start": 133.79, "end": 159.37, "text": "2n إذاً n أكبر من 0 is called a perfect number if sigma of n بيساوي إيش؟ 2n أو زي ما قلنا في البداية positive integer n is said to be perfect if n is equal to the sum of all its positive divisors excluding n itself i.e. n is perfect if and only if sigma of n بيساوي 2n", "tokens": [17, 77, 11933, 15730, 14111, 297, 5551, 4117, 26890, 9154, 1958, 307, 1219, 257, 2176, 1230, 498, 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150.99, "end": 151.77, "word": " divisors", "probability": 0.98974609375}, {"start": 151.77, "end": 153.09, "word": " excluding", "probability": 0.6826171875}, {"start": 153.09, "end": 153.73, "word": " n", "probability": 0.86865234375}, {"start": 153.73, "end": 154.29, "word": " itself", "probability": 0.6572265625}, {"start": 154.29, "end": 154.63, "word": " i", "probability": 0.2005615234375}, {"start": 154.63, "end": 154.93, "word": ".e.", "probability": 0.988525390625}, {"start": 154.97, "end": 155.29, "word": " n", "probability": 0.83740234375}, {"start": 155.29, "end": 155.55, "word": " is", "probability": 0.96484375}, {"start": 155.55, "end": 156.05, "word": " perfect", "probability": 0.90966796875}, {"start": 156.05, "end": 156.25, "word": " if", "probability": 0.39697265625}, {"start": 156.25, "end": 156.43, "word": " and", "probability": 0.5048828125}, {"start": 156.43, "end": 156.63, "word": " only", "probability": 0.5634765625}, {"start": 156.63, "end": 156.79, "word": " if", "probability": 0.96875}, {"start": 156.79, "end": 157.05, "word": " sigma", "probability": 0.9091796875}, {"start": 157.05, "end": 157.21, "word": " of", "probability": 0.95947265625}, {"start": 157.21, "end": 157.35, "word": " n", "probability": 0.990234375}, {"start": 157.35, "end": 157.93, "word": " بيساوي", "probability": 0.94873046875}, {"start": 157.93, "end": 159.37, "word": " 2n", "probability": 0.964111328125}], "temperature": 1.0}, {"id": 8, "seek": 18620, "start": 161.06, "end": 186.2, "text": "الأعداد الـ Perfect Numbers عزيزة شوية يعني لأ لأن لما نحكي عن الأعداد من واحد لعشر هنلاجينا عدد اللي هو الستة من اللي هو المكوّن من رقمين هنلاجينا التمانية وعشرين تلت أرقام فيه كمان عدد إلى آخره الآن هذه الأعداد اللي هي بدنا نتعرف الآن", "tokens": [6027, 10721, 22488, 18513, 2423, 39184, 10246, 22592, 1616, 6225, 11622, 1829, 11622, 3660, 13412, 2407, 10632, 37495, 22653, 5296, 10721, 5296, 10721, 1863, 5296, 15042, 8717, 5016, 4117, 1829, 18871, 16247, 22488, 18513, 9154, 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{"start": 164.0, "end": 164.86, "word": " عزيزة", "probability": 0.982421875}, {"start": 164.86, "end": 165.34, "word": " شوية", "probability": 0.89453125}, {"start": 165.34, "end": 166.38, "word": " يعني", "probability": 0.8515625}, {"start": 166.38, "end": 166.82, "word": " لأ", "probability": 0.540283203125}, {"start": 166.82, "end": 167.18, "word": " لأن", "probability": 0.5312906901041666}, {"start": 167.18, "end": 167.36, "word": " لما", "probability": 0.75}, {"start": 167.36, "end": 168.2, "word": " نحكي", "probability": 0.98291015625}, {"start": 168.2, "end": 168.4, "word": " عن", "probability": 0.98388671875}, {"start": 168.4, "end": 168.82, "word": " الأعداد", "probability": 0.9812825520833334}, {"start": 168.82, "end": 169.0, "word": " من", "probability": 0.984375}, {"start": 169.0, "end": 169.32, "word": " واحد", "probability": 0.785888671875}, {"start": 169.32, "end": 169.66, "word": " لعشر", "probability": 0.8416341145833334}, {"start": 169.66, "end": 170.28, "word": " هنلاجينا", "probability": 0.6863606770833334}, {"start": 170.28, "end": 170.7, "word": " عدد", "probability": 0.9903971354166666}, {"start": 170.7, "end": 170.84, "word": " اللي", "probability": 0.947509765625}, {"start": 170.84, "end": 171.0, "word": " هو", "probability": 0.98828125}, {"start": 171.0, "end": 171.7, "word": " الستة", "probability": 0.7918294270833334}, {"start": 171.7, "end": 172.62, "word": " من", "probability": 0.947265625}, {"start": 172.62, "end": 173.16, "word": " اللي", "probability": 0.98779296875}, {"start": 173.16, "end": 173.5, "word": " هو", "probability": 0.99267578125}, {"start": 173.5, "end": 174.36, "word": " المكوّن", "probability": 0.82861328125}, {"start": 174.36, "end": 174.52, "word": " من", "probability": 0.99267578125}, {"start": 174.52, "end": 175.1, "word": " رقمين", "probability": 0.9656982421875}, {"start": 175.1, "end": 175.7, "word": " هنلاجينا", "probability": 0.9747721354166666}, {"start": 175.7, "end": 176.14, "word": " التمانية", "probability": 0.78662109375}, {"start": 176.14, "end": 176.76, "word": " وعشرين", "probability": 0.909912109375}, {"start": 176.76, "end": 177.3, "word": " تلت", "probability": 0.8518880208333334}, {"start": 177.3, "end": 177.66, "word": " أرقام", "probability": 0.9913330078125}, {"start": 177.66, "end": 177.92, "word": " فيه", "probability": 0.720458984375}, {"start": 177.92, "end": 178.1, "word": " كمان", "probability": 0.9742838541666666}, {"start": 178.1, "end": 178.5, "word": " عدد", "probability": 0.98876953125}, {"start": 178.5, "end": 178.7, "word": " إلى", "probability": 0.88671875}, {"start": 178.7, "end": 179.22, "word": " آخره", "probability": 0.80517578125}, {"start": 179.22, "end": 180.48, "word": " الآن", "probability": 0.698974609375}, {"start": 180.48, "end": 182.16, "word": " هذه", "probability": 0.8505859375}, {"start": 182.16, "end": 183.04, "word": " الأعداد", "probability": 0.97998046875}, {"start": 183.04, "end": 183.74, "word": " اللي", "probability": 0.984130859375}, {"start": 183.74, "end": 184.12, "word": " هي", "probability": 0.93505859375}, {"start": 184.12, "end": 184.92, "word": " بدنا", "probability": 0.95849609375}, {"start": 184.92, "end": 185.6, "word": " نتعرف", "probability": 0.965576171875}, {"start": 185.6, "end": 186.2, "word": " الآن", "probability": 0.72021484375}], "temperature": 1.0}, {"id": 9, "seek": 20676, "start": 187.16, "end": 206.76, "text": "بقدر الإمكان على طبيعة هذه الأعداد وعلى كيف نودت بعضها أو بعض هذه الأعداد وكيف شكل العدد ال perfect لو كان even لو كان even number", "tokens": [3555, 28543, 2288, 33688, 2304, 41361, 15844, 23032, 21292, 27884, 29538, 16247, 22488, 18513, 4032, 3615, 23942, 9122, 33911, 8717, 23328, 2655, 45030, 11242, 11296, 34051, 45030, 11242, 29538, 16247, 22488, 18513, 4032, 4117, 33911, 13412, 28820, 18863, 3215, 3215, 2423, 2176, 45164, 25961, 754, 45164, 25961, 754, 1230], "avg_logprob": -0.10171874895691872, "compression_ratio": 1.6090225563909775, "no_speech_prob": 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"probability": 0.990478515625}, {"start": 196.66, "end": 197.18, "word": " هذه", "probability": 0.95458984375}, {"start": 197.18, "end": 198.24, "word": " الأعداد", "probability": 0.9806315104166666}, {"start": 198.24, "end": 200.44, "word": " وكيف", "probability": 0.90185546875}, {"start": 200.44, "end": 200.94, "word": " شكل", "probability": 0.97607421875}, {"start": 200.94, "end": 201.8, "word": " العدد", "probability": 0.90087890625}, {"start": 201.8, "end": 202.78, "word": " ال", "probability": 0.96875}, {"start": 202.78, "end": 203.26, "word": " perfect", "probability": 0.515625}, {"start": 203.26, "end": 203.64, "word": " لو", "probability": 0.95849609375}, {"start": 203.64, "end": 203.96, "word": " كان", "probability": 0.99560546875}, {"start": 203.96, "end": 204.44, "word": " even", "probability": 0.818359375}, {"start": 204.44, "end": 205.54, "word": " لو", "probability": 0.7138671875}, {"start": 205.54, "end": 205.82, "word": " كان", "probability": 0.9951171875}, {"start": 205.82, "end": 206.26, "word": " even", "probability": 0.8251953125}, {"start": 206.26, "end": 206.76, "word": " number", "probability": 0.9765625}], "temperature": 1.0}, {"id": 10, "seek": 21957, "start": 207.47, "end": 219.57, "text": "لو جربنا الـ 6 حسبنا الـ sigma of 6 سنسوى ما هو sigma of 2 أسهل لك في sigma of 3", "tokens": [1211, 2407, 10874, 25513, 8315, 2423, 39184, 1386, 11331, 35457, 8315, 2423, 39184, 12771, 295, 1386, 8608, 1863, 3794, 2407, 7578, 19446, 31439, 12771, 295, 568, 5551, 3794, 3224, 1211, 5296, 4117, 8978, 12771, 295, 805], "avg_logprob": -0.4451013642388421, "compression_ratio": 1.2637362637362637, "no_speech_prob": 2.6226043701171875e-06, "words": [{"start": 207.47, "end": 208.15, "word": "لو", "probability": 0.6641845703125}, {"start": 208.15, "end": 208.71, "word": " جربنا", "probability": 0.833984375}, {"start": 208.71, "end": 209.05, "word": " الـ", "probability": 0.43597412109375}, {"start": 209.05, "end": 209.35, "word": " 6", "probability": 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218.51, "word": " لك", "probability": 0.5947265625}, {"start": 218.51, "end": 218.63, "word": " في", "probability": 0.71142578125}, {"start": 218.63, "end": 218.91, "word": " sigma", "probability": 0.92041015625}, {"start": 218.91, "end": 219.11, "word": " of", "probability": 0.9677734375}, {"start": 219.11, "end": 219.57, "word": " 3", "probability": 0.9833984375}], "temperature": 1.0}, {"id": 11, "seek": 24854, "start": 224.26, "end": 248.54, "text": "والتلاتة اللي هي إياش أربعة بساوية أداش ماعشر واثنين في ستة إذا فعلا اللي هو الستة is a perfect number نجي الآن لنظريتنا الأولى اللي بتتحدث برضه حنتحدث حديثنا عن اللي هو even perfect number if two to the k minus one", "tokens": [2407, 6027, 2655, 1211, 9307, 3660, 13672, 1829, 39896, 11933, 1829, 33599, 5551, 25513, 27884, 4724, 3794, 995, 2407, 10632, 5551, 3215, 33599, 19446, 3615, 46309, 4032, 5718, 104, 1863, 9957, 8978, 8608, 2655, 3660, 11933, 15730, 6156, 3615, 15040, 13672, 1829, 31439, 21136, 2655, 3660, 307, 257, 2176, 1230, 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بسوء 2K-1×2K-1 is perfect و أي even perfect number هيكون على هذه الصورة نشوف أيش النظرية اللي بتقوله بالظبط و نبهن النظرية theorem أحد عشر واحد عندي", "tokens": [271, 5835, 4032, 2423, 39184, 591, 5551, 4117, 26890, 9154, 36764, 24401, 48812, 27842, 426, 4724, 3794, 2407, 38207, 568, 42, 12, 16, 37550, 17, 42, 12, 16, 307, 2176, 4032, 36632, 754, 2176, 1230, 8032, 1829, 30544, 15844, 29538, 31767, 13063, 3660, 8717, 8592, 38688, 36632, 8592, 28239, 19913, 2288, 10632, 13672, 1829, 39894, 39648, 3224, 20666, 19913, 3555, 9566, 4032, 8717, 3555, 3224, 1863, 28239, 19913, 2288, 10632, 20904, 5551, 24401, 6225, 46309, 36764, 24401, 18871, 16254], "avg_logprob": -0.2974609300494194, "compression_ratio": 1.41, "no_speech_prob": 3.6954879760742188e-06, "words": [{"start": 249.41, "end": 249.77, "word": "is", "probability": 0.408203125}, {"start": 249.77, "end": 250.43, "word": " prime", "probability": 0.814453125}, {"start": 250.43, "end": 251.69, "word": " و", "probability": 0.471923828125}, 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303.07, "text": "ف إتنين أس كي ناقص واحد is a prime ويعني بالكي نفسها أكبر أو يساوي اتنين او أكبر strictly من واحد then .. then اللي هو ال N بتساوي اتنين أس كي minus واحد", "tokens": [5172, 11933, 2655, 1863, 9957, 5551, 3794, 9122, 1829, 8717, 995, 4587, 9381, 36764, 24401, 307, 257, 5835, 4032, 40228, 22653, 20666, 4117, 1829, 8717, 36178, 11296, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 1975, 2407, 5551, 4117, 26890, 20792, 9154, 36764, 24401, 550, 4386, 550, 13672, 1829, 31439, 2423, 426, 39894, 3794, 995, 45865, 1975, 2655, 1863, 9957, 5551, 3794, 9122, 1829, 3175, 36764, 24401], "avg_logprob": -0.3005642311440574, "compression_ratio": 1.535031847133758, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 279.78999999999996, "end": 280.65, "word": "ف", "probability": 0.380126953125}, {"start": 280.65, "end": 281.51, "word": " إتنين", "probability": 0.571075439453125}, {"start": 281.51, "end": 281.79, "word": " أس", "probability": 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289.05, "end": 289.45, "word": " اتنين", "probability": 0.919677734375}, {"start": 289.45, "end": 289.65, "word": " او", "probability": 0.775634765625}, {"start": 289.65, "end": 289.95, "word": " أكبر", "probability": 0.8712565104166666}, {"start": 289.95, "end": 290.41, "word": " strictly", "probability": 0.69384765625}, {"start": 290.41, "end": 290.57, "word": " من", "probability": 0.994140625}, {"start": 290.57, "end": 291.19, "word": " واحد", "probability": 0.990478515625}, {"start": 291.19, "end": 293.93, "word": " then", "probability": 0.619140625}, {"start": 293.93, "end": 294.21, "word": " ..", "probability": 0.1485595703125}, {"start": 294.21, "end": 296.25, "word": " then", "probability": 0.544921875}, {"start": 296.25, "end": 297.93, "word": " اللي", "probability": 0.93408203125}, {"start": 297.93, "end": 298.33, "word": " هو", "probability": 0.98583984375}, {"start": 298.33, "end": 299.69, "word": " ال", "probability": 0.89892578125}, {"start": 299.69, "end": 300.03, "word": " N", "probability": 0.244140625}, {"start": 300.03, "end": 301.13, "word": " بتساوي", "probability": 0.9293212890625}, {"start": 301.13, "end": 301.53, "word": " اتنين", "probability": 0.926025390625}, {"start": 301.53, "end": 301.81, "word": " أس", "probability": 0.9384765625}, {"start": 301.81, "end": 302.05, "word": " كي", "probability": 0.971923828125}, {"start": 302.05, "end": 302.41, "word": " minus", "probability": 0.65478515625}, {"start": 302.41, "end": 303.07, "word": " واحد", "probability": 0.98779296875}], "temperature": 1.0}, {"id": 14, "seek": 33098, "start": 303.78, "end": 330.98, "text": "في الـ 2 أُس K ناقص 1 هذا الـ prime is perfect فهي أول جزء من النظرية لو كان هذا المقدار الـ prime طبعا الـ K تبعتنا أكبر أو سوى 2 بيكون العصور الـ 2 أس K ماينس واحد في 2K ناقص واحد اشمله is a perfect number", "tokens": [41185, 2423, 39184, 568, 5551, 10859, 3794, 591, 8717, 995, 4587, 9381, 502, 23758, 2423, 39184, 5835, 307, 2176, 6156, 3224, 1829, 5551, 12610, 10874, 11622, 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{"start": 313.66, "end": 314.1, "word": " كان", "probability": 0.99609375}, {"start": 314.1, "end": 315.48, "word": " هذا", "probability": 0.9658203125}, {"start": 315.48, "end": 316.38, "word": " المقدار", "probability": 0.9781901041666666}, {"start": 316.38, "end": 317.12, "word": " الـ", "probability": 0.6480712890625}, {"start": 317.12, "end": 317.6, "word": " prime", "probability": 0.83447265625}, {"start": 317.6, "end": 318.62, "word": " طبعا", "probability": 0.9058837890625}, {"start": 318.62, "end": 318.74, "word": " الـ", "probability": 0.46240234375}, {"start": 318.74, "end": 318.84, "word": " K", "probability": 0.8447265625}, {"start": 318.84, "end": 319.28, "word": " تبعتنا", "probability": 0.8624267578125}, {"start": 319.28, "end": 319.56, "word": " أكبر", "probability": 0.9739583333333334}, {"start": 319.56, "end": 319.72, "word": " أو", "probability": 0.94580078125}, {"start": 319.72, "end": 319.96, "word": " سوى", "probability": 0.7275390625}, {"start": 319.96, "end": 320.38, "word": " 2", "probability": 0.91748046875}, {"start": 320.38, "end": 324.08, "word": " بيكون", "probability": 0.7062174479166666}, {"start": 324.08, "end": 325.68, "word": " العصور", "probability": 0.8116861979166666}, {"start": 325.68, "end": 325.86, "word": " الـ", "probability": 0.751953125}, {"start": 325.86, "end": 326.02, "word": " 2", "probability": 0.89990234375}, {"start": 326.02, "end": 326.18, "word": " أس", "probability": 0.772216796875}, {"start": 326.18, "end": 326.3, "word": " K", "probability": 0.97216796875}, {"start": 326.3, "end": 326.62, "word": " ماينس", "probability": 0.7108561197916666}, {"start": 326.62, "end": 326.96, "word": " واحد", "probability": 0.7042236328125}, {"start": 326.96, "end": 327.1, "word": " في", "probability": 0.67822265625}, {"start": 327.1, "end": 327.56, "word": " 2K", "probability": 0.770263671875}, {"start": 327.56, "end": 327.86, "word": " ناقص", "probability": 0.9783935546875}, {"start": 327.86, "end": 328.08, "word": " واحد", "probability": 0.84619140625}, {"start": 328.08, "end": 328.64, "word": " اشمله", "probability": 0.68206787109375}, {"start": 328.64, "end": 329.5, "word": " is", "probability": 0.8564453125}, {"start": 329.5, "end": 329.66, "word": " a", "probability": 0.9658203125}, {"start": 329.66, "end": 330.04, "word": " perfect", "probability": 0.9404296875}, {"start": 330.04, "end": 330.98, "word": " number", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 15, "seek": 35926, "start": 331.9, "end": 359.26, "text": "هذه أول جزء الجزء الثاني بقول لك if N is an even perfect number then N has this form يعني N هتكون على صورة 2ك-1×2k-1", "tokens": [3224, 24192, 5551, 12610, 10874, 11622, 38207, 2423, 7435, 11622, 38207, 6024, 104, 7649, 1829, 4724, 39648, 5296, 4117, 498, 426, 307, 364, 754, 2176, 1230, 550, 426, 575, 341, 1254, 37495, 22653, 426, 8032, 2655, 30544, 15844, 20328, 13063, 3660, 568, 4117, 12, 16, 37550, 17, 74, 12, 16], "avg_logprob": -0.2896752427606022, "compression_ratio": 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0.971923828125}], "temperature": 1.0}, {"id": 24, "seek": 58210, "start": 553.36, "end": 582.1, "text": "بنقول suppose that n is an even perfect number فرضنا انه ايش ماله؟ an even perfect", "tokens": [3555, 1863, 39648, 7297, 300, 297, 307, 364, 754, 2176, 1230, 6156, 43042, 8315, 16472, 3224, 1975, 1829, 8592, 3714, 6027, 3224, 22807, 364, 754, 2176], "avg_logprob": -0.39901619045822706, "compression_ratio": 1.10752688172043, "no_speech_prob": 0.0, "words": [{"start": 553.36, "end": 554.22, "word": "بنقول", "probability": 0.5764973958333334}, {"start": 554.22, "end": 555.98, "word": " suppose", "probability": 0.5654296875}, {"start": 555.98, "end": 560.44, "word": " that", "probability": 0.818359375}, {"start": 560.44, "end": 562.02, "word": " n", "probability": 0.416259765625}, {"start": 562.02, "end": 563.46, "word": " is", "probability": 0.93115234375}, {"start": 563.46, "end": 566.02, "word": " an", "probability": 0.8154296875}, {"start": 566.02, "end": 567.32, "word": " even", 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"word": " اللي", "probability": 0.953369140625}, {"start": 1558.17, "end": 1558.17, "word": " اللي", "probability": 0.952880859375}, {"start": 1558.17, "end": 1558.17, "word": " اللي", "probability": 0.95166015625}, {"start": 1558.17, "end": 1558.31, "word": " اللي", "probability": 0.9521484375}, {"start": 1558.31, "end": 1558.31, "word": " اللي", "probability": 0.95068359375}, {"start": 1558.31, "end": 1558.31, "word": " اللي", "probability": 0.950439453125}, {"start": 1558.31, "end": 1558.31, "word": " اللي", "probability": 0.9482421875}, {"start": 1558.31, "end": 1558.31, "word": " اللي", "probability": 0.947265625}, {"start": 1558.31, "end": 1558.31, "word": " اللي", "probability": 0.9462890625}, {"start": 1558.31, "end": 1558.31, "word": " اللي", "probability": 0.946044921875}, {"start": 1558.31, "end": 1558.31, "word": " اللي", "probability": 0.9453125}, {"start": 1558.31, "end": 1561.81, "word": " اللي", "probability": 0.9443359375}, {"start": 1561.81, "end": 1564.65, "word": " اللي", "probability": 0.94384765625}, {"start": 1564.65, "end": 1564.65, "word": " اللي", "probability": 0.94287109375}, {"start": 1564.65, "end": 1564.65, "word": " اللي", "probability": 0.94189453125}, {"start": 1564.65, "end": 1564.65, "word": " اللي", "probability": 0.94091796875}, {"start": 1564.65, "end": 1564.69, "word": " اللي", "probability": 0.939697265625}, {"start": 1564.69, "end": 1564.71, "word": " اللي", "probability": 0.93896484375}, {"start": 1564.71, "end": 1565.73, "word": " اللي", "probability": 0.9375}, {"start": 1565.73, "end": 1569.85, "word": " اللي", "probability": 0.935791015625}, {"start": 1569.85, "end": 1570.31, "word": " اللي", "probability": 0.933837890625}, {"start": 1570.31, "end": 1570.31, "word": " الل", "probability": 0.8623046875}], "temperature": 1.0}, {"id": 62, "seek": 159823, "start": 1570.33, "end": 1598.23, "text": "الان الجزء الثاني من النظرية اللي هو المعلومة التانية ان اي even perfect number لازم يكون على الصورة هذه حيث هذا سيظهر عند ايه الـ Z' والـK أكبر وسوء اتنين وهذا لاتبتناه في النظرية الان هنروح باتجاه نتيجة اكتر دقة او اكتر التساقر بطبيعة العدد ان اي even perfect number", "tokens": [6027, 7649, 25724, 11622, 38207, 6024, 104, 7649, 1829, 9154, 28239, 19913, 2288, 10632, 13672, 1829, 31439, 9673, 30241, 20498, 3660, 16712, 7649, 10632, 16472, 1975, 1829, 754, 2176, 1230, 5296, 31377, 2304, 7251, 30544, 15844, 31767, 13063, 3660, 29538, 11331, 1829, 12984, 23758, 8608, 1829, 19913, 3224, 2288, 43242, 1975, 1829, 3224, 2423, 39184, 1176, 6, 16070, 39184, 42, 5551, 4117, 26890, 46952, 2407, 38207, 1975, 2655, 1863, 9957, 37037, 15730, 5296, 9307, 3555, 2655, 8315, 3224, 8978, 28239, 19913, 2288, 10632, 2423, 7649, 8032, 1863, 32887, 5016, 4724, 9307, 7435, 40294, 8717, 31371, 7435, 3660, 1975, 4117, 2655, 2288, 11778, 28671, 1975, 2407, 1975, 4117, 2655, 2288, 16712, 3794, 995, 4587, 2288, 4724, 9566, 21292, 27884, 18863, 3215, 3215, 16472, 1975, 1829, 754, 2176, 1230], "avg_logprob": -0.23767089599277824, "compression_ratio": 1.8442622950819672, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1570.33, "end": 1570.83, "word": "الان", "probability": 0.6224365234375}, {"start": 1570.83, "end": 1571.31, "word": " الجزء", "probability": 0.7788899739583334}, {"start": 1571.31, "end": 1571.71, "word": " الثاني", "probability": 0.9158935546875}, {"start": 1571.71, "end": 1571.83, "word": " من", "probability": 0.9716796875}, {"start": 1571.83, "end": 1572.39, "word": " النظرية", "probability": 0.930908203125}, {"start": 1572.39, "end": 1572.61, "word": " اللي", "probability": 0.709716796875}, {"start": 1572.61, "end": 1572.71, "word": " هو", "probability": 0.9541015625}, {"start": 1572.71, "end": 1573.17, "word": " المعلومة", "probability": 0.9771728515625}, {"start": 1573.17, "end": 1573.65, "word": " التانية", "probability": 0.9580078125}, {"start": 1573.65, "end": 1574.55, "word": " ان", "probability": 0.6171875}, {"start": 1574.55, "end": 1575.59, "word": " اي", "probability": 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"probability": 0.741943359375}, {"start": 1586.57, "end": 1587.11, "word": " هنروح", "probability": 0.9017333984375}, {"start": 1587.11, "end": 1587.65, "word": " باتجاه", "probability": 0.8984375}, {"start": 1587.65, "end": 1589.37, "word": " نتيجة", "probability": 0.9871826171875}, {"start": 1589.37, "end": 1590.03, "word": " اكتر", "probability": 0.91552734375}, {"start": 1590.03, "end": 1590.47, "word": " دقة", "probability": 0.889892578125}, {"start": 1590.47, "end": 1591.89, "word": " او", "probability": 0.859130859375}, {"start": 1591.89, "end": 1592.39, "word": " اكتر", "probability": 0.9730224609375}, {"start": 1592.39, "end": 1593.13, "word": " التساقر", "probability": 0.8798828125}, {"start": 1593.13, "end": 1593.63, "word": " بطبيعة", "probability": 0.881591796875}, {"start": 1593.63, "end": 1594.39, "word": " العدد", "probability": 0.9558919270833334}, {"start": 1594.39, "end": 1595.37, "word": " ان", "probability": 0.88330078125}, {"start": 1595.37, "end": 1596.23, "word": " اي", "probability": 0.943603515625}, {"start": 1596.23, "end": 1596.89, "word": " even", "probability": 0.86328125}, {"start": 1596.89, "end": 1597.61, "word": " perfect", "probability": 0.9091796875}, {"start": 1597.61, "end": 1598.23, "word": " number", "probability": 0.97314453125}], "temperature": 1.0}, {"id": 63, "seek": 161552, "start": 1599.66, "end": 1615.52, "text": "هيكون نهايته يا ستة يا تمانية يعني أي عدد اللي نهايته سفر أو اتنين أو اربعة قطعاً هتقول ليه اشماله is not a perfect number", "tokens": [3224, 1829, 30544, 8717, 11296, 36081, 3224, 35186, 8608, 2655, 3660, 35186, 46811, 7649, 10632, 37495, 22653, 36632, 6225, 3215, 3215, 13672, 1829, 8717, 11296, 36081, 3224, 8608, 5172, 2288, 34051, 1975, 2655, 1863, 9957, 34051, 1975, 25513, 27884, 12174, 9566, 3615, 995, 14111, 8032, 2655, 39648, 32239, 3224, 1975, 8592, 2304, 6027, 3224, 307, 406, 257, 2176, 1230], "avg_logprob": -0.1640625002483527, "compression_ratio": 1.3862068965517242, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1599.66, "end": 1600.52, "word": "هيكون", "probability": 0.8644205729166666}, {"start": 1600.52, "end": 1601.72, "word": " نهايته", "probability": 0.9578857421875}, {"start": 1601.72, "end": 1602.02, "word": " يا", "probability": 0.67578125}, {"start": 1602.02, "end": 1602.8, "word": " ستة", "probability": 0.7499186197916666}, {"start": 1602.8, "end": 1603.56, "word": " يا", "probability": 0.63818359375}, {"start": 1603.56, "end": 1604.1, "word": " تمانية", "probability": 0.9850260416666666}, {"start": 1604.1, "end": 1605.62, "word": " يعني", "probability": 0.888916015625}, {"start": 1605.62, "end": 1605.86, "word": " أي", "probability": 0.79931640625}, {"start": 1605.86, "end": 1606.52, "word": " عدد", "probability": 0.9817708333333334}, {"start": 1606.52, "end": 1608.18, "word": " اللي", "probability": 0.922119140625}, {"start": 1608.18, "end": 1608.74, "word": " نهايته", "probability": 0.94677734375}, {"start": 1608.74, "end": 1609.16, 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not a prime say that إن الـ K is composite إيش معناه composite؟ إنه في R و S such that الـ K بتساوي R في S و الـ R و الـ S أكبر من 1 وأصغر من مين؟ من الـ K", "tokens": [9778, 1211, 11703, 9381, 8315, 25724, 11622, 38207, 16247, 12610, 47525, 8315, 8717, 12984, 3555, 2655, 5296, 24793, 36145, 2423, 39184, 591, 5551, 8592, 2304, 6027, 11296, 318, 6, 8717, 5172, 2655, 43042, 36145, 2423, 39184, 591, 307, 406, 257, 5835, 584, 300, 36145, 2423, 39184, 591, 307, 25557, 11933, 1829, 8592, 20449, 8315, 3224, 25557, 22807, 36145, 3224, 8978, 497, 4032, 318, 1270, 300, 2423, 39184, 591, 39894, 3794, 995, 45865, 497, 8978, 318, 4032, 2423, 39184, 497, 4032, 2423, 39184, 318, 5551, 4117, 26890, 9154, 502, 36725, 9381, 17082, 2288, 9154, 3714, 9957, 22807, 9154, 2423, 39184, 591], "avg_logprob": -0.2530940688482606, "compression_ratio": 1.6153846153846154, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1830.97, "end": 1831.45, "word": "خلّصنا", "probability": 0.831103515625}, 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"probability": 0.93408203125}, {"start": 1970.86, "end": 1970.86, "word": " تلاتة", "probability": 0.976806640625}, {"start": 1970.86, "end": 1971.04, "word": " او", "probability": 0.915283203125}, {"start": 1971.04, "end": 1971.04, "word": " تلاتة", "probability": 0.98193359375}, {"start": 1971.04, "end": 1972.12, "word": " او", "probability": 0.903564453125}, {"start": 1972.12, "end": 1972.5, "word": " تلاتة", "probability": 0.9844970703125}, {"start": 1972.5, "end": 1974.12, "word": " او", "probability": 0.901123046875}, {"start": 1974.12, "end": 1974.14, "word": " ت", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 77, "seek": 200412, "start": 1976.4, "end": 2004.12, "text": "من واحد ماشي الحال و هذا عندي نفسه أكيد أكبر من مين من واحد عارفين ليش أكبر من واحد لأن هذا أكبر من ايه و أصار زائد واحد زي ما عملنا فوق اللي هو أكبر strictly من مين من واحد إذا صار هذا أكبر من واحد و هذا أكبر من واحد و هذا prime إذا صار contradiction واضح therefore K", "tokens": [27842, 36764, 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"word": " واحد", "probability": 0.993408203125}, {"start": 1996.46, "end": 1997.42, "word": " و", "probability": 0.89208984375}, {"start": 1997.42, "end": 1997.72, "word": " هذا", "probability": 0.91943359375}, {"start": 1997.72, "end": 1998.28, "word": " prime", "probability": 0.62646484375}, {"start": 1998.28, "end": 1998.98, "word": " إذا", "probability": 0.95654296875}, {"start": 1998.98, "end": 1999.24, "word": " صار", "probability": 0.9677734375}, {"start": 1999.24, "end": 1999.84, "word": " contradiction", "probability": 0.8779296875}, {"start": 1999.84, "end": 2001.6, "word": " واضح", "probability": 0.8518880208333334}, {"start": 2001.6, "end": 2003.34, "word": " therefore", "probability": 0.44580078125}, {"start": 2003.34, "end": 2004.12, "word": " K", "probability": 0.50390625}], "temperature": 1.0}, {"id": 78, "seek": 203501, "start": 2005.59, "end": 2035.01, "text": "Can't be positive يعني K is a prime يعني إن اللي ما بتقولك أو اللي وصلنا إله لما الـ A K minus واحد is prime والـ A أكبر من سفر والـ K أكبر سوا اتنين لازم يطلع عند الـ A بسوا اتنين والـ K نفسهاش is prime أي سؤال طيب يا شباب", "tokens": [11531, 380, 312, 3353, 37495, 22653, 591, 307, 257, 5835, 37495, 22653, 36145, 13672, 1829, 19446, 39894, 39648, 4117, 34051, 13672, 1829, 4032, 36520, 8315, 11933, 43761, 5296, 15042, 2423, 39184, 316, 591, 3175, 36764, 24401, 307, 5835, 16070, 39184, 316, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 16070, 39184, 591, 5551, 4117, 26890, 8608, 14407, 1975, 2655, 1863, 9957, 5296, 31377, 2304, 7251, 9566, 1211, 3615, 43242, 2423, 39184, 316, 4724, 3794, 14407, 1975, 2655, 1863, 9957, 16070, 39184, 591, 8717, 36178, 3224, 33599, 307, 5835, 36632, 8608, 33604, 6027, 23032, 1829, 3555, 35186, 13412, 3555, 16758], "avg_logprob": -0.23595328463448417, "compression_ratio": 1.6878048780487804, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2005.59, "end": 2005.99, "word": "Can't", "probability": 0.61376953125}, {"start": 2005.99, "end": 2006.15, "word": " be", "probability": 0.8759765625}, {"start": 2006.15, "end": 2006.77, "word": " positive", "probability": 0.8984375}, {"start": 2006.77, "end": 2007.17, "word": " يعني", "probability": 0.927978515625}, {"start": 2007.17, "end": 2007.65, "word": " K", "probability": 0.228759765625}, {"start": 2007.65, "end": 2009.13, "word": " is", "probability": 0.87548828125}, {"start": 2009.13, "end": 2009.55, "word": " a", "probability": 0.44677734375}, {"start": 2009.55, "end": 2009.85, "word": " prime", "probability": 0.76806640625}, {"start": 2009.85, "end": 2010.49, "word": " يعني", "probability": 0.891845703125}, {"start": 2010.49, "end": 2011.43, "word": " إن", "probability": 0.19873046875}, {"start": 2011.43, "end": 2011.89, "word": " اللي", "probability": 0.78759765625}, {"start": 2011.89, "end": 2012.05, "word": " ما", "probability": 0.32080078125}, {"start": 2012.05, "end": 2012.87, "word": " بتقولك", "probability": 0.9430338541666666}, {"start": 2012.87, "end": 2013.83, "word": " أو", "probability": 0.900390625}, {"start": 2013.83, "end": 2013.99, "word": " اللي", "probability": 0.98486328125}, {"start": 2013.99, "end": 2014.37, "word": " وصلنا", "probability": 0.98095703125}, {"start": 2014.37, "end": 2014.71, "word": " إله", "probability": 0.603271484375}, {"start": 2014.71, "end": 2015.09, "word": " لما", "probability": 0.87353515625}, {"start": 2015.09, "end": 2015.25, "word": " الـ", "probability": 0.5084228515625}, {"start": 2015.25, "end": 2015.31, "word": " A", "probability": 0.314208984375}, {"start": 2015.31, "end": 2015.47, "word": " K", "probability": 0.7392578125}, {"start": 2015.47, "end": 2015.77, "word": " minus", "probability": 0.371826171875}, {"start": 2015.77, "end": 2016.03, "word": " واحد", "probability": 0.93896484375}, {"start": 2016.03, "end": 2016.17, "word": " is", "probability": 0.951171875}, {"start": 2016.17, "end": 2016.65, "word": " prime", "probability": 0.54248046875}, {"start": 2016.65, "end": 2017.43, "word": " والـ", "probability": 0.641357421875}, {"start": 2017.43, "end": 2017.51, "word": " A", "probability": 0.83544921875}, {"start": 2017.51, "end": 2017.79, "word": " أكبر", "probability": 0.970703125}, {"start": 2017.79, "end": 2017.95, "word": " من", "probability": 0.98291015625}, {"start": 2017.95, "end": 2018.27, "word": " سفر", "probability": 0.7122395833333334}, {"start": 2018.27, "end": 2018.43, "word": " والـ", "probability": 0.705810546875}, {"start": 2018.43, "end": 2018.53, "word": " K", "probability": 0.86376953125}, {"start": 2018.53, "end": 2018.73, "word": " أكبر", "probability": 0.9856770833333334}, {"start": 2018.73, "end": 2018.95, "word": " سوا", "probability": 0.453125}, {"start": 2018.95, "end": 2019.35, "word": " اتنين", "probability": 0.9200439453125}, {"start": 2019.35, "end": 2020.11, "word": " لازم", "probability": 0.9869791666666666}, {"start": 2020.11, "end": 2020.37, "word": " يطلع", "probability": 0.988037109375}, {"start": 2020.37, "end": 2020.55, "word": " عند", "probability": 0.82666015625}, {"start": 2020.55, "end": 2020.69, "word": " الـ", "probability": 0.74853515625}, {"start": 2020.69, "end": 2020.81, "word": " A", "probability": 0.9189453125}, {"start": 2020.81, "end": 2021.15, "word": " بسوا", "probability": 0.76611328125}, {"start": 2021.15, "end": 2021.73, "word": " اتنين", "probability": 0.97802734375}, {"start": 2021.73, "end": 2022.55, "word": " والـ", "probability": 0.76953125}, {"start": 2022.55, "end": 2022.75, "word": " K", "probability": 0.91650390625}, {"start": 2022.75, "end": 2024.15, "word": " نفسهاش", "probability": 0.73590087890625}, {"start": 2024.15, "end": 2025.07, "word": " is", "probability": 0.90185546875}, {"start": 2025.07, "end": 2025.45, "word": " prime", "probability": 0.8994140625}, {"start": 2025.45, "end": 2026.69, "word": " أي", "probability": 0.71337890625}, {"start": 2026.69, "end": 2027.27, "word": " سؤال", "probability": 0.9959309895833334}, {"start": 2027.27, "end": 2034.63, "word": " طيب", "probability": 0.9075520833333334}, {"start": 2034.63, "end": 2034.75, "word": " يا", "probability": 0.986328125}, {"start": 2034.75, "end": 2035.01, "word": " شباب", "probability": 0.9928385416666666}], "temperature": 1.0}, {"id": 79, "seek": 205767, "start": 2037.82, "end": 2057.68, "text": "نجي لآخر نظرية في الـ Section اللي هي theorem 11-2 بتقولّي أن an even perfect number an ends in the digits 6 or 8 بيقولّي أن اللي هو الـ even perfect number", "tokens": [1863, 7435, 1829, 5296, 148, 95, 34740, 8717, 19913, 2288, 10632, 8978, 2423, 39184, 1100, 882, 13672, 1829, 39896, 20904, 2975, 12, 17, 39894, 39648, 11703, 1829, 14739, 364, 754, 2176, 1230, 364, 5314, 294, 264, 27011, 1386, 420, 1649, 4724, 1829, 39648, 11703, 1829, 14739, 13672, 1829, 31439, 2423, 39184, 754, 2176, 1230], "avg_logprob": -0.37471591342579236, "compression_ratio": 1.355263157894737, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2037.82, "end": 2038.2, "word": "نجي", "probability": 0.4649251302083333}, {"start": 2038.2, "end": 2038.5, "word": " لآخر", "probability": 0.72821044921875}, {"start": 2038.5, "end": 2038.94, "word": " نظرية", "probability": 0.9608154296875}, {"start": 2038.94, "end": 2039.1, "word": " في", "probability": 0.91552734375}, {"start": 2039.1, "end": 2039.2, "word": " الـ", "probability": 0.64697265625}, {"start": 2039.2, "end": 2039.6, "word": " Section", "probability": 0.614990234375}, {"start": 2039.6, "end": 2041.36, "word": " اللي", "probability": 0.594970703125}, {"start": 2041.36, "end": 2041.76, "word": " هي", "probability": 0.962890625}, {"start": 2041.76, "end": 2042.36, "word": " theorem", "probability": 0.51904296875}, {"start": 2042.36, "end": 2042.88, "word": " 11", "probability": 0.81591796875}, {"start": 2042.88, "end": 2043.32, "word": "-2", "probability": 0.7734375}, {"start": 2043.32, "end": 2044.8, "word": " بتقولّي", "probability": 0.719451904296875}, {"start": 2044.8, "end": 2045.06, "word": " أن", "probability": 0.452880859375}, {"start": 2045.06, "end": 2045.66, "word": " an", "probability": 0.11480712890625}, {"start": 2045.66, "end": 2046.3, "word": " even", "probability": 0.89013671875}, {"start": 2046.3, "end": 2047.08, "word": " perfect", "probability": 0.77392578125}, {"start": 2047.08, "end": 2047.78, "word": " number", "probability": 0.97802734375}, {"start": 2047.78, "end": 2048.22, "word": " an", "probability": 0.505859375}, {"start": 2048.22, "end": 2049.92, "word": " ends", "probability": 0.63525390625}, {"start": 2049.92, "end": 2050.66, "word": " in", "probability": 0.9560546875}, {"start": 2050.66, "end": 2050.9, "word": " the", "probability": 0.86181640625}, {"start": 2050.9, "end": 2051.48, "word": " digits", "probability": 0.9384765625}, {"start": 2051.48, "end": 2052.4, "word": " 6", "probability": 0.74658203125}, {"start": 2052.4, "end": 2053.04, "word": " or", "probability": 0.90283203125}, {"start": 2053.04, "end": 2053.66, "word": " 8", "probability": 0.98095703125}, {"start": 2053.66, "end": 2055.24, "word": " بيقولّي", "probability": 0.779931640625}, {"start": 2055.24, "end": 2055.54, "word": " أن", "probability": 0.70458984375}, {"start": 2055.54, "end": 2055.96, "word": " اللي", "probability": 0.782958984375}, {"start": 2055.96, "end": 2056.18, "word": " هو", "probability": 0.986328125}, {"start": 2056.18, "end": 2056.36, "word": " الـ", "probability": 0.681640625}, {"start": 2056.36, "end": 2056.56, "word": " even", "probability": 0.76220703125}, {"start": 2056.56, "end": 2057.04, "word": " perfect", "probability": 0.900390625}, {"start": 2057.04, "end": 2057.68, "word": " number", "probability": 0.982421875}], "temperature": 1.0}, {"id": 80, "seek": 208196, "start": 2058.77, "end": 2081.97, "text": "أخر اللي هو digit فيه يا ستة يا تمانية يعني خانة العشرات خانة الأحد يا ستة يا تمانية يعني بمعنى أخر حيكون عنده الأن يا بطابق الستة مضله عشرة يا بطابق التمانية ايش مضله عشرة واضح؟ إذا بدنا الآن نثبت ما يليه", "tokens": [10721, 34740, 13672, 1829, 31439, 14293, 8978, 3224, 35186, 8608, 2655, 3660, 35186, 46811, 7649, 10632, 37495, 22653, 16490, 7649, 3660, 18863, 46309, 9307, 16490, 7649, 3660, 16247, 24401, 35186, 8608, 2655, 3660, 35186, 46811, 7649, 10632, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 11331, 1829, 30544, 43242, 3224, 16247, 1863, 35186, 4724, 9566, 16758, 4587, 21136, 2655, 3660, 3714, 11242, 43761, 6225, 8592, 25720, 35186, 4724, 9566, 16758, 4587, 16712, 2304, 7649, 10632, 1975, 1829, 8592, 3714, 11242, 43761, 6225, 8592, 25720, 4032, 46958, 5016, 22807, 11933, 15730, 47525, 8315, 6024, 48506, 8717, 12984, 3555, 2655, 19446, 7251, 20292, 3224], "avg_logprob": -0.20357572717162278, "compression_ratio": 2.022222222222222, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2058.77, "end": 2059.47, "word": "أخر", "probability": 0.6866455078125}, {"start": 2059.47, "end": 2060.47, "word": " اللي", "probability": 0.829345703125}, {"start": 2060.47, "end": 2060.81, "word": " هو", "probability": 0.97412109375}, {"start": 2060.81, "end": 2061.23, "word": " digit", "probability": 0.54541015625}, {"start": 2061.23, "end": 2061.67, "word": " فيه", "probability": 0.9609375}, {"start": 2061.67, "end": 2061.79, "word": " يا", "probability": 0.7080078125}, {"start": 2061.79, "end": 2062.51, "word": " ستة", "probability": 0.7437337239583334}, {"start": 2062.51, "end": 2063.45, "word": " يا", "probability": 0.82080078125}, {"start": 2063.45, "end": 2063.95, "word": " تمانية", "probability": 0.9529622395833334}, {"start": 2063.95, "end": 2064.19, "word": " يعني", "probability": 0.75048828125}, {"start": 2064.19, "end": 2064.53, "word": " خانة", "probability": 0.845703125}, {"start": 2064.53, "end": 2065.33, "word": " العشرات", "probability": 0.8583984375}, {"start": 2065.33, "end": 2065.75, "word": " خانة", "probability": 0.8330078125}, {"start": 2065.75, "end": 2066.15, "word": " الأحد", "probability": 0.787841796875}, {"start": 2066.15, "end": 2066.35, "word": " يا", "probability": 0.82275390625}, {"start": 2066.35, "end": 2067.03, "word": " ستة", "probability": 0.9736328125}, {"start": 2067.03, "end": 2067.57, "word": " يا", "probability": 0.96826171875}, {"start": 2067.57, "end": 2067.99, "word": " تمانية", "probability": 0.9920247395833334}, {"start": 2067.99, "end": 2068.25, "word": " يعني", "probability": 0.914794921875}, {"start": 2068.25, "end": 2068.63, "word": " بمعنى", "probability": 0.987890625}, {"start": 2068.63, "end": 2069.07, "word": " أخر", "probability": 0.7149658203125}, {"start": 2069.07, "end": 2069.97, "word": " حيكون", "probability": 0.7223714192708334}, {"start": 2069.97, "end": 2070.37, "word": " عنده", "probability": 0.7998046875}, {"start": 2070.37, "end": 2070.71, "word": " الأن", "probability": 0.6632080078125}, {"start": 2070.71, "end": 2070.97, "word": " يا", "probability": 0.74462890625}, {"start": 2070.97, "end": 2071.45, "word": " بطابق", "probability": 0.8758544921875}, {"start": 2071.45, "end": 2072.17, "word": " الستة", "probability": 0.8453776041666666}, {"start": 2072.17, "end": 2072.41, "word": " مضله", "probability": 0.7703450520833334}, {"start": 2072.41, "end": 2072.89, "word": " عشرة", "probability": 0.9388020833333334}, {"start": 2072.89, "end": 2073.55, "word": " يا", "probability": 0.87060546875}, {"start": 2073.55, "end": 2074.01, "word": " بطابق", "probability": 0.98095703125}, {"start": 2074.01, "end": 2074.47, "word": " التمانية", "probability": 0.8978271484375}, {"start": 2074.47, "end": 2075.05, "word": " ايش", "probability": 0.745849609375}, {"start": 2075.05, "end": 2075.81, "word": " مضله", "probability": 0.8751627604166666}, {"start": 2075.81, "end": 2076.39, "word": " عشرة", "probability": 0.9397786458333334}, {"start": 2076.39, "end": 2077.65, "word": " واضح؟", "probability": 0.80328369140625}, {"start": 2077.65, "end": 2078.15, "word": " إذا", "probability": 0.63671875}, {"start": 2078.15, "end": 2078.49, "word": " بدنا", "probability": 0.892578125}, {"start": 2078.49, "end": 2078.93, "word": " الآن", "probability": 0.81201171875}, {"start": 2078.93, "end": 2080.71, "word": " نثبت", "probability": 0.990966796875}, {"start": 2080.71, "end": 2081.03, "word": " ما", "probability": 0.93603515625}, {"start": 2081.03, "end": 2081.97, "word": " يليه", "probability": 0.6410319010416666}], "temperature": 1.0}, {"id": 81, "seek": 211937, "start": 2090.91, "end": 2119.37, "text": "Theorem Theorem 11-2 if n is an even perfect number then n is congruent to 6 modulo 10 or n is congruent to 8 modulo 10 proof", "tokens": [2278, 37956, 440, 37956, 2975, 12, 17, 498, 297, 307, 364, 754, 2176, 1230, 550, 297, 307, 8882, 19226, 281, 1386, 1072, 13455, 1266, 420, 297, 307, 8882, 19226, 281, 1649, 1072, 13455, 1266, 8177], "avg_logprob": -0.2727864724066522, "compression_ratio": 1.358695652173913, "no_speech_prob": 0.0, "words": [{"start": 2090.91, "end": 2092.29, "word": "Theorem", "probability": 0.6087646484375}, {"start": 2092.29, "end": 2093.67, "word": " Theorem", "probability": 0.5716552734375}, {"start": 2093.67, "end": 2095.65, "word": " 11", "probability": 0.50341796875}, {"start": 2095.65, "end": 2096.35, "word": "-2", "probability": 0.71142578125}, {"start": 2096.35, "end": 2098.11, "word": " if", "probability": 0.27099609375}, {"start": 2098.11, "end": 2099.55, "word": " n", "probability": 0.552734375}, {"start": 2099.55, "end": 2100.23, "word": " is", "probability": 0.953125}, {"start": 2100.23, "end": 2101.09, "word": " an", "probability": 0.8720703125}, {"start": 2101.09, "end": 2101.85, "word": " even", "probability": 0.89453125}, {"start": 2101.85, "end": 2104.01, "word": " perfect", "probability": 0.716796875}, {"start": 2104.01, "end": 2106.45, "word": " number", "probability": 0.96533203125}, {"start": 2106.45, "end": 2108.69, "word": " then", "probability": 0.671875}, {"start": 2108.69, "end": 2110.11, "word": " n", "probability": 0.88427734375}, {"start": 2110.11, "end": 2110.63, "word": " is", "probability": 0.927734375}, {"start": 2110.63, "end": 2111.29, "word": " congruent", "probability": 0.97705078125}, {"start": 2111.29, "end": 2111.51, "word": " to", "probability": 0.76904296875}, {"start": 2111.51, "end": 2112.17, "word": " 6", "probability": 0.9267578125}, {"start": 2112.17, "end": 2112.63, "word": " modulo", "probability": 0.682861328125}, {"start": 2112.63, "end": 2113.01, "word": " 10", "probability": 0.95849609375}, {"start": 2113.01, "end": 2114.21, "word": " or", "probability": 0.87451171875}, {"start": 2114.21, "end": 2114.75, "word": " n", "probability": 0.96142578125}, {"start": 2114.75, "end": 2115.25, "word": " is", "probability": 0.94580078125}, {"start": 2115.25, "end": 2115.75, "word": " congruent", "probability": 0.966796875}, {"start": 2115.75, "end": 2115.95, "word": " to", "probability": 0.9794921875}, {"start": 2115.95, "end": 2116.35, "word": " 8", "probability": 0.97900390625}, {"start": 2116.35, "end": 2117.61, "word": " modulo", "probability": 0.939453125}, {"start": 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"end": 2795.81, "word": " الله", "probability": 0.97314453125}, {"start": 2795.81, "end": 2796.17, "word": " فيكم", "probability": 0.931884765625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2796.49525, "duration_after_vad": 2660.3462499999914}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/Q3tp1nfGrIU.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/Q3tp1nfGrIU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..cdbf94ec6a87e2b04c769444a2eabdbffb649d3a
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/Q3tp1nfGrIU.srt
@@ -0,0 +1,1435 @@
+1
+00:00:19,710 --> 00:00:25,610
+بسم الله الرحمن الرحيم كل عام وأنتم بخير ومناسبة 
+
+2
+00:00:25,610 --> 00:00:33,330
+حلول شهر رمضان المبارك والحمد لله سلامتكم، هنكمل 
+
+3
+00:00:33,330 --> 00:00:38,770
+اليوم إن شاء الله شابتر 11، اليوم المحاضرة رقم
+
+4
+00:00:38,770 --> 00:00:43,550
+30 هنحكي
+
+5
+00:00:43,550 --> 00:00:48,520
+عن الـ Mersenne non-primes،  دبل ما نحكي عن الـ Mersenne
+
+6
+00:00:48,520 --> 00:00:53,280
+Primes أو الـ Mersenne Numbers، نذكركم باللي حكيناه 
+
+7
+00:00:53,280 --> 00:00:57,280
+المرة الماضية عن الـ Perfect Numbers، حكينا عن الـ
+
+8
+00:00:57,280 --> 00:01:02,660
+Even Perfect Numbers، وقلنا إنه الـ .. بنقول عن الـ
+
+9
+00:01:02,660 --> 00:01:05,840
+.. الـ perfect .. عن الـ number n إنه perfect إذا
+
+10
+00:01:05,840 --> 00:01:11,660
+كان sigma of n بيساوي 2n، واخدنا قلنا لو كان عندي 2
+
+11
+00:01:11,660 --> 00:01:18,550
+أس k ناقص واحد is prime هيعطيني اللي هو اثنين أس
+
+12
+00:01:18,550 --> 00:01:22,470
+k ناقص واحد في اثنين أس k ناقص واحد is a perfect
+
+13
+00:01:22,470 --> 00:01:28,090
+number، طبعًا هذا even perfect number، وقلنا إن الـ
+
+14
+00:01:28,090 --> 00:01:36,890
+even perfect number في نظرية، لو كان عندي اللي هو n
+
+15
+00:01:36,890 --> 00:01:44,860
+is an even perfect number هيكون الـ n الخانة الأحد
+
+16
+00:01:44,860 --> 00:01:51,280
+في يا ستة يا إيش يا ثمانية، إذا كان an even perfect
+
+17
+00:01:51,280 --> 00:01:55,920
+number هيكون لو خانة الأحد يا ستة يا ثمانية، يعني 
+
+18
+00:01:55,920 --> 00:01:59,360
+معناته أنتوا طابق اللي هو الستة، وأنتوا طابق
+
+19
+00:01:59,360 --> 00:02:05,200
+الثمانية، نضله عشرة هذا
+
+20
+00:02:05,200 --> 00:02:10,000
+اللي حكيناه المرة الماضية عن الـ Even Perfect
+
+21
+00:02:10,000 --> 00:02:15,560
+Numbers، اليوم هنكمل الحديث عن المرسين بـ Numbers 
+
+22
+00:02:15,560 --> 00:02:23,700
+وإنّ اللي هو هنعرج على اللي هو الـ Odd Perfect 
+
+23
+00:02:23,700 --> 00:02:30,180
+Number إذا كانت موجودة، فهي موجودة بالشكل اللي
+
+24
+00:02:30,180 --> 00:02:32,980
+سنحكي عنه، الشكل اللي سنشوفه إن شاء الله، ندى
+
+25
+00:02:32,980 --> 00:02:38,400
+لنرسيني برايمز، هنحكي عن اللي هو الوعية الجديدة من 
+
+26
+00:02:38,400 --> 00:02:45,310
+الأرقام اللي هي اسمها مرسين numbers، بنقول إن الرقم
+
+27
+00:02:45,310 --> 00:02:48,930
+اللي على الصورة اللي هي اثنين أس m ناقص واحد
+
+28
+00:02:48,930 --> 00:02:53,750
+بنسميها ده إيش ماله؟ مرسين number، مرسين number على
+
+29
+00:02:53,750 --> 00:02:59,910
+اسم حالة، اسمه مرسين، الآن m = 1، m = 1 بيساوي
+
+30
+00:02:59,910 --> 00:03:06,730
+اثنين أس واحد ناقص واحد، ويساوي واحد، m = 2، 2 أس
+
+31
+00:03:06,730 --> 00:03:12,850
+2 ناقص 1 = 3، إن 3 بيساوي 2 أس 3 ناقص 1 =
+
+32
+00:03:12,850 --> 00:03:21,790
+7، إن 4 بيساوي 2 أس 4 ناقص 1 = 15، وهكذا
+
+33
+00:03:22,510 --> 00:03:26,810
+واضح أنه في الـ Mersenne numbers اللي هي Primes
+
+34
+00:03:26,810 --> 00:03:32,990
+وفي composite، معايا؟ إذا الآن لو كان هذا الـ
+
+35
+00:03:32,990 --> 00:03:36,430
+Mersenne number is a prime بنسميه Mersenne prime
+
+36
+00:03:36,430 --> 00:03:40,910
+بُسمّي أشماله Mersenne prime، إذا الـ n integer، mn 
+
+37
+00:03:40,910 --> 00:03:44,750
+بيساوي 2 أس n ناقص 1 is called Mersenne number if
+
+38
+00:03:44,750 --> 00:03:49,150
+this mn is a prime then it is called أشماله
+
+39
+00:03:49,150 --> 00:03:56,530
+Mersenne prime، نأتي الآن ناخذ خصائص اللي هو حول
+
+40
+00:03:56,530 --> 00:04:03,290
+الـ Mersenne numbers أو الـ Mersenne primes، خلّينا نشوف 
+
+41
+00:04:03,290 --> 00:04:08,890
+الأول نظرية اللي هي theorem 11-3 بتقول مالي
+
+42
+00:04:08,890 --> 00:04:18,090
+theorem 11-3 if b and
+
+43
+00:04:19,570 --> 00:04:29,330
+q على صورة 2b زائد 1 primes، ثم نفترض أنّ p وq 
+
+44
+00:04:29,330 --> 00:04:36,330
+بيساوي 2m أو 2b زائد 1 primes number أو r
+
+45
+00:04:36,330 --> 00:04:41,350
+primes number، ثم ثم
+
+46
+00:04:41,350 --> 00:04:58,390
+هيكون q بتجسم الـ mb or لـ q تجسم m ب زائد اثنين 
+
+47
+00:04:58,390 --> 00:05:12,650
+but not both، أبروف كمان مرة، كمان مرة، إذا كانت b 
+
+48
+00:05:13,520 --> 00:05:19,300
+الـ q بيساوي 2b زائد 1 primes، ماشي؟ إذا، هيكون
+
+49
+00:05:19,300 --> 00:05:24,700
+عند الـ q بتكسب الـ mb، قريب الـ q بتكسب مين؟ الـ
+
+50
+00:05:24,700 --> 00:05:29,380
+mb زائد 2، but not both، يعني مستحيل تكسب التنين مع
+
+51
+00:05:29,380 --> 00:05:36,680
+بعض، يعني بس هتكسب exactly one of them، الـ 
+
+52
+00:05:36,680 --> 00:05:46,430
+q أسوأ تتنين بيزايد واحد، بيز برايم، b is prime، لأن
+
+53
+00:05:46,430 --> 00:05:53,690
+المقطع عنده إش إنّ b and q are primes، والـ q على
+
+54
+00:05:53,690 --> 00:06:05,510
+صورة 2 بيزايد واحد، واضح؟ طيب، نجي للبرهان، proof عندي
+
+55
+00:06:05,510 --> 00:06:12,850
+واضح أنّ الـ q لا تقسم الاثنين 
+
+56
+00:06:14,820 --> 00:06:18,220
+أو الـ Greatest Common Divisor بين الـ q والاثنين 
+
+57
+00:06:18,220 --> 00:06:27,220
+بيساوي واحد، إذا أكيد by Fermat theorem، اثنين الـ q
+
+58
+00:06:27,220 --> 00:06:36,560
+ناقص واحد، مظبوط؟ تطابق الواحد مدولوا مين؟ مدولوا الـ q
+
+59
+00:06:36,560 --> 00:06:45,710
+واضح أه؟ هذه by Fermat's theorem، 2sq-1 تطابق الواحد
+
+60
+00:06:45,710 --> 00:06:58,650
+modulo q، لاحظ عندي الـ q-1 عبارة عن عدد زوجي، وكأنه
+
+61
+00:06:58,650 --> 00:07:07,510
+بيقدر يقول إنّ 2sq-1 على 2 لكل تربيع ناقص واحد
+
+62
+00:07:07,510 --> 00:07:14,740
+تطابق الـ 0 مدولوا مين؟ مدولوا q، نجرت العدين هذه 
+
+63
+00:07:14,740 --> 00:07:20,400
+وكتبت 2q 2 على صورة q ناقص واحد على اثنين تربيع، هل
+
+64
+00:07:20,400 --> 00:07:25,340
+هذه Integer؟ اه Integer، لأن q ناقص واحد بيساوي 2b 
+
+65
+00:07:25,340 --> 00:07:30,820
+يعني q ناقص واحد على اثنين عبارة عن عدد، واضح؟
+
+66
+00:07:30,820 --> 00:07:42,000
+ويساوي هذا بيساوي 2 أس b تربيع ناقص واحد لأن عندي
+
+67
+00:07:42,000 --> 00:07:49,060
+الـ q بيساوي 2b زائد 1، يعني q ناقص 1 على 2 مش
+
+68
+00:07:49,060 --> 00:07:57,880
+متساوي بيساوي b، واضح؟ طيب الآن هذا فرق بين مربعين
+
+69
+00:07:57,880 --> 00:08:04,360
+بقدر أحلله، هو عبارة عن 2 أس b ناقص 1 في 2 أس b
+
+70
+00:08:04,360 --> 00:08:09,760
+زائد 1، وهذا مين هو؟
+
+71
+00:08:15,940 --> 00:08:26,640
+وهذا عبارة عن mb زائد 2، إذن سعر عندي اللي هو mb
+
+72
+00:08:26,640 --> 00:08:32,600
+في mb زائد 2 بقادر الصفر مدولوا من كله مدولوا q، إيش
+
+73
+00:08:32,600 --> 00:08:37,460
+معناته هذا؟ معناته إنّ سعر عندي q تقسم الـ mb في 
+
+74
+00:08:37,460 --> 00:08:43,570
+الـ mb زائد 2، ماذا يعني هذا؟ لدي الـ q زبرايا مدام
+
+75
+00:08:43,570 --> 00:08:49,430
+الـ q زبرايا، إذن إذا الـ q تجسم الـ mb أو الـ q
+
+76
+00:08:49,430 --> 00:08:54,850
+تجسم الـ mb زائد اثنين، اللي نريد أن نثبت هو but not
+
+77
+00:08:54,850 --> 00:09:01,590
+both، but not both، سببه not يعني سببه إنّ الـ q تجسم
+
+78
+00:09:01,590 --> 00:09:08,700
+هذا وهذا مع بعض، مفترض أنّ الـ q تجسم الـ mb and الـ 
+
+79
+00:09:08,700 --> 00:09:13,460
+q تجسم الـ mb زائد 2، إذاً هتجسم أي Linear combination
+
+80
+00:09:13,460 --> 00:09:19,040
+بينهم، إذاً أكيد هتصير then الـ q هتجسم الـ mb زائد
+
+81
+00:09:19,040 --> 00:09:25,720
+2 ناقص الـ mb اللي هو كل جدّش هذا اثنين، صارت الـ q
+
+82
+00:09:25,720 --> 00:09:29,820
+تجسم اثنين، وهذا Contradiction، لأنّ الـ q أشماله is 
+
+83
+00:09:29,820 --> 00:09:38,370
+an odd prime، Therefore الـ q تجسم mb or q تجسم 
+
+84
+00:09:38,370 --> 00:09:45,070
+mb زائد اثنين but not both، but not both، اطلع
+
+85
+00:09:45,070 --> 00:09:55,990
+على فوق، نيجي للنظرية 11-4، 11-4 تقول ما يلي
+
+86
+00:09:55,990 --> 00:10:00,450
+theorem 11-4 
+
+87
+00:10:01,950 --> 00:10:08,390
+عندي الـ q عبارة عن odd prime if الـ q بتساوي 2 
+
+88
+00:10:08,390 --> 00:10:14,630
+and b زي 1 then الـ
+
+89
+00:10:14,630 --> 00:10:22,330
+q بتساوي 2 and b زي 1 مجرد odd prime، عبارة عن if الـ
+
+90
+00:10:22,330 --> 00:10:31,110
+q بتساوي 2 and b زي 1 is prime then الـ q بتجسم n n
+
+91
+00:10:31,110 --> 00:10:42,710
+في حال provided that الـ b على صورة 8k زائد 1، يعني 
+
+92
+00:10:42,710 --> 00:10:48,430
+b تطابق الواحد، الـ q تطابق الواحد modulo ثمانية أو
+
+93
+00:10:48,430 --> 00:10:56,760
+الـ q تطابق السبعة modulo إيش؟ ثمانية، اثنين، الـ q
+
+94
+00:10:56,760 --> 00:11:04,120
+بتجسم الـ n n زي 2، في حال كانت الـ q بالطابق
+
+95
+00:11:04,120 --> 00:11:12,520
+الثلاثة modulo 8 أو الـ q بالطابق الخمسة modulo 8
+
+96
+00:11:12,520 --> 00:11:19,590
+ماشي الحال تمام، مرة إذا كان الـ q عبارة عن إبراهيم
+
+97
+00:11:19,590 --> 00:11:24,910
+الـ q هذا مدام إبراهيم، قد إبراهيم إذا هو على صورة
+
+98
+00:11:24,910 --> 00:11:30,570
+أحد الصور الأربعة التالية، يا ثمانية ك زائد واحد يا 
+
+99
+00:11:30,570 --> 00:11:35,130
+ثمانية ك زائد ثلاثة يا ثمانية ك زائد خمسة يا ثمانية
+
+100
+00:11:35,130 --> 00:11:40,380
+ك زائد سبعة ماشي الحال، عندي إذا كان كيوب تكسب الام
+
+101
+00:11:40,380 --> 00:11:45,960
+إنّ هذا بيحدث متى؟ بس للأرقام اللي بتكون b كيوب 
+
+102
+00:11:45,960 --> 00:11:51,480
+الطابق الواحد أو كيوب الطابق مين؟ السبعة الآن، وإذا 
+
+103
+00:11:51,480 --> 00:11:54,320
+كانت الأرقام ع صورة كيوب تكسب ثلاثة أو كيوب تكسب
+
+104
+00:11:54,320 --> 00:11:59,960
+خمسة، هذا هيكون أشماله، وكيوب تكسب n، الام زائد واحد
+
+105
+00:11:59,960 --> 00:12:06,470
+زائد اثنين، الآن المظلة بتطلب اللي هو شابتر 9 عشان
+
+106
+00:12:06,470 --> 00:12:09,430
+هيك احنا ماخذنا الشابتر 9 أو مش هناخد شابتر 9
+
+107
+00:12:09,430 --> 00:12:14,170
+فالبرنامج مش مطلوب، نفي للـ Corollary اللي بقتها
+
+108
+00:12:14,170 --> 00:12:23,590
+الـ Corollary بتقول ما يلي، b and q على صورة 2b زي 
+
+109
+00:12:23,590 --> 00:12:28,250
+1 are both primes، يعني الباقي لأن الـ b هذه برضه
+
+110
+00:12:28,250 --> 00:12:34,850
+أشماله برايم هناك q مجرد عصورة 2n زي 1، هنا الـ b is
+
+111
+00:12:34,850 --> 00:12:40,070
+prime ومع تيني الـ b أشماله بالثلاثة مدولوا مين؟
+
+112
+00:12:40,070 --> 00:12:47,090
+مدولوا أربعة، الـ Corollary، الـ Corollary بتقول مالي
+
+113
+00:12:47,090 --> 00:12:57,130
+if b وq بيساوي 2b زي 1 are odd primes، هاي واحد اثنين
+
+114
+00:12:57,130 --> 00:13:04,000
+قال لك إنّه b تطابق الثلاثة modulo أربعة، يعني الـ b
+
+115
+00:13:04,000 --> 00:13:09,280
+على صورة أربعة k زائد ثلاثة، b تطابق الثلاثة modulo
+
+116
+00:13:09,280 --> 00:13:12,360
+أربعة، يعني الـ b أشماله على صورة أربعة k زائد 
+
+117
+00:13:12,360 --> 00:13:20,520
+ثلاثة، then هذا بأكد لك إنّ الـ q هتجسم مين؟ الـ mb
+
+118
+00:13:20,520 --> 00:13:27,980
+الـ q هتجسم الـ mb، البروف صغير، البروف مباشر، البروف
+
+119
+00:13:29,590 --> 00:13:34,430
+إنّ الـ b تُطابق الثلاثة مدونة مين؟ مدونة أربعة
+
+120
+00:13:34,430 --> 00:13:39,970
+يعني الـ b هتساوي أربعة k زائد ثلاثة for some k
+
+121
+00:13:39,970 --> 00:13:46,690
+element in z، معايا منه إيش هتطلع الـ q؟ then الـ q 
+
+122
+00:13:46,690 --> 00:13:54,590
+هتساوي اثنين في أربعة k زائد ثلاثة زائد واحد 
+
+123
+00:13:54,590 --> 00:14:01,920
+ويساوي ثمانية k زائد سبعة، ما هو معناته هذا؟ معناته
+
+124
+00:14:01,920 --> 00:14:09,040
+أنّه تقع عندك q تطابق السبعة modulo ثمانية، إذا
+
+125
+00:14:09,040 --> 00:14:16,220
+الحسب اللي هو واحد، إذا عندي hence الـ q هتجسم من
+
+126
+00:14:16,220 --> 00:14:26,060
+الـ m أنا اللي في هذا الحال اللي هي b، q بتجسم الـ mb
+
+127
+00:14:30,290 --> 00:14:39,630
+أي سؤال؟ نجي لنظرية 11-5، نظرية 11-5 برهانة بيتمد
+
+128
+00:14:39,630 --> 00:14:44,690
+على chapter 8، هناخد 
+
+129
+00:14:44,690 --> 00:14:49,750
+chapter 8 احنا إن شاء الله بس هأحكي معلومتين في
+
+130
+00:14:49,750 --> 00:14:54,110
+chapter 8 على أساس الاستخدام من الآن في إثبات
+
+131
+00:14:54,110 --> 00:14:58,690
+النظرية، خلينا نشوف إيش المعلومتين وبناء عليهم اللي 
+
+132
+00:14:58,690 --> 00:15:12,760
+هوانبهر النظرية الـ 
+
+133
+00:15:12,760 --> 00:15:22,900
+Definition موجود في Chapter 8، الـ Definition، k
+
+134
+00:15:22,900 --> 00:15:36,940
+is called the order of two modulo q in
+
+135
+00:15:36,940 --> 00:15:46,360
+the case that واحد اللي هو اثنين to the k تطابق 
+
+136
+00:15:46,360 --> 00:15:55,500
+الواحد modulo q، اثنين k is the smallest 
+
+137
+00:15:58,530 --> 00:16:05,850
+such that it means to the end طبق الواحد modulo q 
+
+138
+00:16:05,850 --> 00:16:12,350
+أو modulo b زي ما بدكم، إذا الآن الـ Definition هذا 
+
+139
+00:16:12,350 --> 00:16:18,770
+بدنا نعرف شو معناته k، أي عبارة عن الـ order لـ two
+
+140
+00:16:18,770 --> 00:16:22,850
+modulo mean modulo q، هذا الـ Definition من شرط 
+
+141
+00:16:22,850 --> 00:16:28,400
+التمانية نحتاجينه عشان نبرهن النظرية الآن K is
+
+142
+00:16:28,400 --> 00:16:32,940
+called the order of 2 modulo Q في حال ما يلي Q
+
+143
+00:16:32,940 --> 00:16:39,770
+طبعا اللي هنستخدمها هنا عبارة عن 2 to 
+
+144
+00:16:39,770 --> 00:16:44,670
+the K  تطابق الواحد modulo Q  هذا أول شرط الشرط
+
+145
+00:16:44,670 --> 00:16:49,810
+الثاني أنه لو كان عند أي 2 أس M تطابق الواحد 
+
+146
+00:16:49,810 --> 00:16:55,070
+modulo Q  هتكون الـ K أصغر منها أو تساوي M يعني 
+
+147
+00:16:55,070 --> 00:16:59,470
+الـ K شرطين عليها أن 2 to the K تطابق الواحد شرط
+
+148
+00:16:59,470 --> 00:17:03,670
+الثاني K is the smallest such M بحيث أن 2 to the M
+
+149
+00:17:03,670 --> 00:17:10,100
+تطابق الواحد modulo Q  في نظرية برضه هستخدمها
+
+150
+00:17:10,100 --> 00:17:14,220
+theorem 8-1 هنجيها بالتفصيل لما ناخد Chapter 8
+
+151
+00:17:14,220 --> 00:17:27,320
+theorem 8-1 بتقول if K is the order of 2 modulo
+
+152
+00:17:27,320 --> 00:17:39,000
+Q and 2 to the B مثلا تطابق الواحد modulo Q ثم
+
+153
+00:17:39,000 --> 00:17:46,020
+الـ K  تقسم B  هذا ما تعلمناه دولة بديها من 
+
+154
+00:17:46,020 --> 00:17:49,800
+chapter ثمانية  عينيها بستخدمها في برهان النظرية
+
+155
+00:17:49,800 --> 00:17:59,610
+كمان مرة if K is the order of 2 Modulo Q وكان
+
+156
+00:17:59,610 --> 00:18:04,090
+عندي 2 to the B تطابق الواحد Modulo Q هتكون الـ 
+
+157
+00:18:04,090 --> 00:18:07,550
+K  طبعا هي smallest  مش عدد  smallest  النظرية
+
+158
+00:18:07,550 --> 00:18:13,750
+بتقول لك لأ هتكون الـ K بتقسم الـ B K عامل من عوامل 
+
+159
+00:18:13,750 --> 00:18:22,170
+الـ B طيب نجي لنظريتنا اللي في شبترنا في Chapter 11
+
+160
+00:18:22,170 --> 00:18:31,060
+النظرية بتقول ماليها نمرة 11.5 بتقول if B
+
+161
+00:18:31,060 --> 00:18:47,840
+if B is an odd prime then then any divisor
+
+162
+00:18:47,840 --> 00:18:50,960
+of M is 
+
+163
+00:18:55,160 --> 00:19:03,520
+of the form of the
+
+164
+00:19:03,520 --> 00:19:07,960
+form 2K زائد 1
+
+165
+00:19:21,100 --> 00:19:29,340
+أن أي برايم فايزر من 
+
+166
+00:19:29,340 --> 00:19:30,120
+أي برايم 
+
+167
+00:19:36,590 --> 00:19:42,570
+of m,b is of the form 2a,b,z,1  إيش الـ m,b يا 
+
+168
+00:19:42,570 --> 00:19:46,810
+جماعة؟ موضوعنا للذين متأخرين هو عبارة عن مرسيل 
+
+169
+00:19:46,810 --> 00:19:51,270
+number  الـ Mersenne number، العدد العصور 2، m ناقص
+
+170
+00:19:51,270 --> 00:19:56,830
+واحد، بنسميه m,m، بنسميه مرسيل number لو هذا الـ MN
+
+171
+00:19:56,830 --> 00:20:01,550
+طلع برايم لو هذا طلع برايم بنسميه مرسين برايم
+
+172
+00:20:01,550 --> 00:20:05,310
+ماشي الحال و بدنا ناخد خواصه الآن أخذنا خواص واين
+
+173
+00:20:05,310 --> 00:20:11,650
+بنكمل على الخواص الأخرى الآن المظلة اللي عندنا
+
+174
+00:20:11,650 --> 00:20:16,210
+بتقول إن إذا كانت B is an odd prime then any prime
+
+175
+00:20:16,210 --> 00:20:24,610
+divisor of MB is of the form 2KB زائد 1 معايا؟ طيب
+
+176
+00:20:25,630 --> 00:20:33,050
+الآن بدنا نرهم بدي أخد الـ Q الآن بقول let Q be
+
+177
+00:20:33,050 --> 00:20:39,450
+any prime divisor لمين؟ لـ NB الـ Q بتكسب مين؟ الـ
+
+178
+00:20:39,450 --> 00:20:47,310
+NB الآن مدام الـ Q بتكسب الـ NB then الـ NB تطابق
+
+179
+00:20:47,310 --> 00:20:53,030
+الصفر modulo مين؟ modulo Q الـ Q بتكسب من الـ NB
+
+180
+00:20:53,030 --> 00:20:55,550
+إذا الـ NB تطابق اللي هو الـ Zero modulo N modulo
+
+181
+00:20:55,550 --> 00:21:01,410
+Q الـ NB إيش اسمها؟ 2 أس بي ناقص واحد هي
+
+182
+00:21:01,410 --> 00:21:05,850
+بتعريف الـ Mersenne number 2 أس بي ناقص واحد إيش
+
+183
+00:21:05,850 --> 00:21:12,190
+معناته هذا الكلام؟ معناته أنه then 2 أس بي
+
+184
+00:21:12,190 --> 00:21:20,230
+تطابق الواحد modulo Q  ماشي الحال؟ طيب اللي هبقى 
+
+185
+00:21:20,230 --> 00:21:21,070
+أقول لك مت
+
+186
+00:21:41,940 --> 00:21:43,340
+كيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكي
+
+187
+00:21:44,000 --> 00:21:49,080
+الآن عندي 2 أس بي تطابق الواحد بدون الـQ إذا من
+
+188
+00:21:49,080 --> 00:21:53,680
+النتيجة اللي جابني بشوية مدام الـK of order 2
+
+189
+00:21:53,680 --> 00:21:57,520
+بدون الـQ و2 أس بي تطابق الواحد بدون الـQ إذا
+
+190
+00:21:57,520 --> 00:22:05,760
+الـK هتكسب من هذا الـB إذا then الـK تقسم الـB
+
+191
+00:22:05,760 --> 00:22:13,840
+مدام الـK هذه بقى theorem 8.1 الآن الـ B زوجي والـ 
+
+192
+00:22:13,840 --> 00:22:18,140
+K بتقسم الـ B إذا الـ K يا بتساوي واحد يا B إذا
+
+193
+00:22:18,140 --> 00:22:22,580
+الـ K عندي يا بتساوي واحد يا الـ K بتساوي B
+
+194
+00:22:22,580 --> 00:22:29,200
+بقول لك K بتساوي واحد مستحيل ليش؟ لإن إيش معنى الـ 
+
+195
+00:22:29,200 --> 00:22:33,100
+K هي الأرض الـ 2 modulo Q؟ معناته إن 2 ..
+
+196
+00:22:33,100 --> 00:22:36,600
+إيش معنى هذه؟ معناته إن 2 أس K أو بتعطي
+
+197
+00:22:36,600 --> 00:22:45,020
+تطابق الواحد modulo Q معنى هذا أن
+
+198
+00:22:45,020 --> 00:22:49,800
+K تكسب 2 أس K ناقص؟ لو كانت K واحد
+
+199
+00:22:49,800 --> 00:22:54,240
+بيصير K تكسب مين 1؟ يعني معناه K تساوي
+
+200
+00:22:54,240 --> 00:22:59,690
+واحد كون K زوجية إذا الـ K أصغر منها قطعًا لا 
+
+201
+00:22:59,690 --> 00:23:04,950
+تساوي الواحد إذا we must have K إيش بتساوي بتساوي B
+
+202
+00:23:04,950 --> 00:23:10,610
+إذا احفظ في الذاكرة إن الـ K إن إيش بتساوي بتساوي 
+
+203
+00:23:10,610 --> 00:23:15,230
+الـ B الآن
+
+204
+00:23:15,230 --> 00:23:21,730
+الـ clue الـ clue is N of the prime يعني لا الـ 2
+
+205
+00:23:21,730 --> 00:23:26,130
+بتقسم بـQ ولا الـQ بيقسم 2 يعني العامل المشترك
+
+206
+00:23:26,130 --> 00:23:30,230
+اللي على بين الـQ والـ2 مش بيساوي يعني by Fermat's
+
+207
+00:23:30,230 --> 00:23:35,710
+theorem بيصير 2 Q minus 1 تطابق الواحد
+
+208
+00:23:35,710 --> 00:23:43,590
+modulo Q كم مرة؟ طيب صلوا على النبي عليه الصلاة
+
+209
+00:23:43,590 --> 00:23:52,670
+والسلام الآن بالبرهان إنه الـ 2 و الـ Q العامل
+
+210
+00:23:52,670 --> 00:23:57,990
+المشترك الأعلى بينهما 1 لأن Q is odd if I divide
+
+211
+00:23:57,990 --> 00:24:02,870
+by Fermat's theorem 2 to the Q minus .. و Q برقم
+
+212
+00:24:02,870 --> 00:24:06,630
+طبعًا .. 2 to the Q .. و 2 كمان برقم بالمرة 2 to
+
+213
+00:24:06,630 --> 00:24:10,830
+the Q minus 1 تطابق الواحد بدون مين؟ by Fermat's
+
+214
+00:24:10,830 --> 00:24:16,130
+theorem طيب، احنا بنقول الـ K هي مين؟ الـ order لـ
+
+215
+00:24:16,130 --> 00:24:20,790
+2 modulo Q معناه بنطبق 8.1 كمان مرة لإن
+
+216
+00:24:20,790 --> 00:24:25,090
+الساعة عندي 2 نص Q مانس 1 تطابق 1 modulo Q إذا
+
+217
+00:24:25,090 --> 00:24:33,450
+.. إذا أكيد .. إذا K تقسم Q مانس 1 واضح أه؟
+
+218
+00:24:33,450 --> 00:24:36,650
+كامل هي أصلاً .. احنا لازم نهلش فوق اللي عملنا كمية
+
+219
+00:24:36,650 --> 00:24:43,730
+مين الـ B معناه أنه hence الـ B يقسم الـ Q مانس
+
+220
+00:24:43,730 --> 00:24:53,400
+1 معايا؟ إذا صار عندك الـ Q Q minus 1 بساوي T
+
+221
+00:24:53,400 --> 00:25:01,760
+في B for some T element in Z إيش معنى هذا؟ هذا
+
+222
+00:25:01,760 --> 00:25:10,900
+بيعطيني إن الـ Q بتساوي T في B زائد 1 معايا؟
+
+223
+00:25:10,900 --> 00:25:12,320
+طيب
+
+224
+00:25:16,380 --> 00:25:25,460
+عندي الـ B عدد برايم صح ولا لأ؟ و هذا الـ T في B
+
+225
+00:25:25,460 --> 00:25:33,520
+زائد مين؟ زائد 1 الـ Q عدد برايم الآن الـ T لو
+
+226
+00:25:33,520 --> 00:25:38,420
+كانت عدد فردي بيصير هذا على هذا عدد فردي فأي عدد فردي بيطلع إيش زائد 
+
+227
+00:25:38,420 --> 00:25:42,760
+واحد بيطلع زوجي تناقض إذا الـ T لازم تطلع
+
+228
+00:25:42,760 --> 00:25:48,810
+إيش زوجي عدد فردي زائد عدد فردي زائد عدد فردي بيطلع زوجي 
+
+229
+00:25:48,810 --> 00:25:54,450
+تناقض إذا الـ T must be even الآن إذا T
+
+230
+00:25:54,450 --> 00:26:01,910
+بتساوي 2M for some M يعني صارت الـ Q لازم تطلع
+
+231
+00:26:01,910 --> 00:26:09,590
+صورتها 2MB زائد 1 for some m element in Z وهي
+
+232
+00:26:09,590 --> 00:26:12,810
+الصورة المطلوبة 2KB زائد 1 طبعا الـ K هذه
+
+233
+00:26:12,810 --> 00:26:16,710
+مش هي الـ K اللي انا فايد معاها أه إنّها دي for some 
+
+234
+00:26:16,710 --> 00:26:23,310
+k element in Z إذا اللي أثبتناه أنه لو كانت B of
+
+235
+00:26:23,310 --> 00:26:27,310
+the prime إذا أي prime divisor of MB is of the
+
+236
+00:26:27,310 --> 00:26:33,690
+form 2KB زائد 1 أي
+
+237
+00:26:33,690 --> 00:26:38,770
+سؤال اللي بعده يلا اطلعنا على اللي بعدها بخليها في
+
+238
+00:26:38,770 --> 00:26:44,450
+الأخر على سريع قبل ما نحكي عن نظرية الـ 11.6 نيجي
+
+239
+00:26:44,450 --> 00:26:53,130
+على 11.7 11.7 مش هنبرهنها 11.7 إذا بتتذكر المرة
+
+240
+00:26:53,130 --> 00:26:58,690
+الماضية المرة الماضية حكينا عن مين عن perfect 
+
+241
+00:26:58,690 --> 00:27:03,010
+numbers في الواقع اللي حكينا عنه عن الـ even
+
+242
+00:27:03,010 --> 00:27:07,620
+perfect numbers معايا الـ even perfect numbers
+
+243
+00:27:07,620 --> 00:27:12,640
+وآخرنا إنّه لا concrete examples ستة وثمانية
+
+244
+00:27:12,640 --> 00:27:17,850
+عشرين وفي أرقام أخرى مذكورة في الكتاب وقلنا 
+
+245
+00:27:17,850 --> 00:27:23,890
+الأرقام الـ Perfect Numbers عزيزة إنّها كل فترة
+
+246
+00:27:23,890 --> 00:27:28,290
+بيظهر اللي هو يعني كل زيادة خانة بيظهر وأحيانًا 
+
+247
+00:27:28,290 --> 00:27:33,650
+خانة بتزيد لكن ما بيظهرش فيها في كل اللي هو يعني
+
+248
+00:27:33,650 --> 00:27:36,570
+الأرقام اللي بالأربع خانات أو الخمس خانات ممكن
+
+249
+00:27:36,570 --> 00:27:41,860
+ما يظهرش ممكن يظهر كل بعدين ما حكيناش عن الـ odd 
+
+250
+00:27:41,860 --> 00:27:46,240
+number الـ odd perfect number ما حكيناش فيش
+
+251
+00:27:46,240 --> 00:27:50,220
+concrete example لحد الآن إنّ واحد يقولنا هذا هو odd
+
+252
+00:27:50,220 --> 00:27:55,120
+number وهو الـ perfect number ما حدش لحد الآن 
+
+253
+00:27:55,120 --> 00:28:01,380
+أعطاه لكن الآن هذه النظرية بتقول لك إنّ لو في .. لو في
+
+254
+00:28:01,380 --> 00:28:05,900
+odd perfect number هيكون صورته على الصورة التالية
+
+255
+00:28:05,900 --> 00:28:10,460
+بس هي اللي بتحكي النظرية .. أه؟ الآن بتقول if N is
+
+256
+00:28:10,460 --> 00:28:14,140
+an odd perfect number if N is an odd perfect 
+
+257
+00:28:14,140 --> 00:28:19,740
+number then this N must be of the form بـ1K1 يعني
+
+258
+00:28:19,740 --> 00:28:25,880
+ما تفكروش تدوروا في الـOdd Perfect Numbers في غير
+
+259
+00:28:25,880 --> 00:28:29,020
+هذه العائلة يعني اللي بده يفكر يروح يدور على
+
+260
+00:28:29,020 --> 00:28:31,800
+الـOdd Perfect Number اللي هو إذا بده يلاقي
+
+261
+00:28:31,800 --> 00:28:36,370
+بناديه عدد برايم مش هيلاقيه لأن if n is an odd 
+
+262
+00:28:36,370 --> 00:28:40,110
+perfect number then n can be written على صورة بي
+
+263
+00:28:40,110 --> 00:28:45,070
+واحد أس كي واحد بي 2 أس 2 J 2 لعين
+
+264
+00:28:45,070 --> 00:28:51,590
+بي ار أس 2 ج ار واضح إنّ هدول كل واحد فيه
+
+265
+00:28:51,590 --> 00:28:59,170
+مربع كامل يعني مرفوع لـ 2 Alpha أو 2 J أو 
+
+266
+00:28:59,170 --> 00:29:02,910
+2 اللي بدك إياه هذول بي 1 بي 2 بي ار ار 
+
+267
+00:29:02,910 --> 00:29:07,620
+Distant Primes معايا يا شباب؟ اللي يعمل مش هذا
+
+268
+00:29:07,620 --> 00:29:13,120
+ويحدّبك أكثر بيقول لك الرقم الأول فيه، هذا الـB1 
+
+269
+00:29:13,120 --> 00:29:19,920
+هتلاقي اللي هو على صورة 4K زائد 1 الـB1 على صورة 
+
+270
+00:29:19,920 --> 00:29:24,720
+مين؟ 4K زائد 1، هتفاجأ نقض يعني مش هيكون زوجي، مش 
+
+271
+00:29:24,720 --> 00:29:30,120
+هيبقى أحد even على صورة مين؟ 4K زائد 1 والأس تبعه 
+
+272
+00:29:30,120 --> 00:29:35,990
+برضه على صورة 4M زائد 1 واضح؟ إذا بيقول لك إذا كانت n 
+
+273
+00:29:35,990 --> 00:29:42,070
+is an odd perfect number then it must has the form
+
+274
+00:29:42,070 --> 00:29:46,070
+n بيساوي بي 1 ك 1 بي 2 ج 2 و بي 2
+
+275
+00:29:46,070 --> 00:29:48,930
+ج 2 و بي 2 ج 2 و بي 2 ج 2 و بي 2
+
+276
+00:29:48,930 --> 00:29:50,690
+ج 2 و بي 2 ج 2 و بي 2 ج 2 و بي 2
+
+277
+00:29:50,690 --> 00:29:58,530
+ج 2 و بي 2 ج 2 و بي 2 ج 2 و بي 2
+
+278
+00:29:58,530 --> 00:30:07,270
+ج 2 واللي هي الأس تبعه برضه على صورة 4M تساوي
+
+279
+00:30:07,270 --> 00:30:13,230
+الواحد أي شوية انزل لتحت بقول لك اللي هو الـ 
+
+280
+00:30:13,230 --> 00:30:18,730
+Corollary اللي هي بتقول لك if M is an odd perfect 
+
+281
+00:30:18,730 --> 00:30:25,470
+number then M has the form M بتساوي بيقص K في مين
+
+282
+00:30:25,470 --> 00:30:33,630
+في M تربيع where B is an odd prime وB مش من عامل
+
+283
+00:30:33,630 --> 00:30:37,670
+أمتَر بيعي يعني بقى إن الـ B أشمَع من مصحوبة كل الـ
+
+284
+00:30:37,670 --> 00:30:43,430
+value برا وعلى صورة B كفي المربع كامل حيث الـ B
+
+285
+00:30:43,430 --> 00:30:48,730
+عبارة على صورة 4K زيادة واحد والـ K على صورة 8 4K
+
+286
+00:30:48,730 --> 00:30:52,600
+زيادة واحدة. هذا اللي بتعرفوه عن الـOdd Prime. أو
+
+287
+00:30:52,600 --> 00:30:55,960
+Odd Perfect Number. عموماً في كلام كثير في الكتاب
+
+288
+00:30:55,960 --> 00:31:00,880
+حول تاريخ الـMerced Number وتاريخ الـPerfect
+
+289
+00:31:00,880 --> 00:31:05,100
+Numbers وحتى صار حديث عن بعض اللي هي مسائل مش
+
+290
+00:31:05,100 --> 00:31:08,460
+محلولة و Open Problems وآخري. أنا منصح بقراءة
+
+291
+00:31:08,460 --> 00:31:15,820
+الكتاب في هذا يعني جيداً بتعطيك صورة اللي هي يعني
+
+292
+00:31:15,820 --> 00:31:20,410
+خلفية منيحة عن اللي هو الموضوع. نجي للاخر نظرية
+
+293
+00:31:20,410 --> 00:31:31,350
+عندنا رجعلي ال 11 6 فيون 11 6 if
+
+294
+00:31:31,350 --> 00:31:41,490
+B is an odd prime
+
+295
+00:31:41,490 --> 00:31:45,110
+then
+
+296
+00:31:45,110 --> 00:31:47,390
+أي
+
+297
+00:31:51,400 --> 00:32:05,020
+prime divisor Q of MB is
+
+298
+00:32:05,020 --> 00:32:13,160
+of the form Q
+
+299
+00:32:13,160 --> 00:32:17,900
+بالطابق الواحد زي ذا ناقص واحد modulo
+
+300
+00:32:37,210 --> 00:32:47,530
+800 حضارة يعني الحضارة الأشياء وسيطة فيها لكم نشوف
+
+301
+00:32:47,530 --> 00:32:54,940
+أشياء نظرية بتقول FB is an odd prime then any prime
+
+302
+00:32:54,940 --> 00:33:02,620
+divisor Q of M B is of the form Q تطابق الواحد أو
+
+303
+00:33:02,620 --> 00:33:06,660
+ناقص واحد مضله تمانية يعني يعني الـ Q يا إن الطابق
+
+304
+00:33:06,660 --> 00:33:11,380
+الواحد أو الطابق السبعة يعني فالاخر الـ Q هتكون
+
+305
+00:33:11,380 --> 00:33:15,320
+على صورة تمانية K أو إيش أو سبعة K
+
+306
+00:33:22,200 --> 00:33:34,260
+طبعاً ال .. ال .. ال odd prime ال odd prime أو .. و
+
+307
+00:33:34,260 --> 00:33:43,240
+ال .. و ال prime divisor ال q لل mb ال q هذه أكيد 
+
+308
+00:33:43,240 --> 00:33:49,960
+صورتها مدام تبرايم قد برايم الـ Q هتكون على صورة يا
+
+309
+00:33:49,960 --> 00:33:54,620
+تمانية K زائد واحد يا تمانية K زائد ثلاثة يا
+
+310
+00:33:54,620 --> 00:33:58,940
+تمانية K زائد خمسة يا تمانية K زائد إيش زائد سبعة
+
+311
+00:33:58,940 --> 00:34:08,000
+ماشي الحل الآن تمانية K زائد ثلاثة و تمانية K زائد
+
+312
+00:34:08,000 --> 00:34:15,370
+خمسة بأهلنه حسب النظرية اللي فاتت بأهلنه إنه يقسم
+
+313
+00:34:15,370 --> 00:34:18,810
+الـ
+
+314
+00:34:18,810 --> 00:34:28,290
+NB زائد 2 إذا
+
+315
+00:34:28,290 --> 00:34:36,130
+هدولة مش هيكون الورداتلأن ما دام الـ Q قسم الـ NP
+
+316
+00:34:36,130 --> 00:34:40,790
+أكيد مش هيجسم الـ NP زاد اثنين. اتفجنا عليه إنه
+
+317
+00:34:40,790 --> 00:34:46,130
+قلنا الـ Q هتجسم هذه أو هذه. إذا نضل اللي هو إن الـ
+
+318
+00:34:46,130 --> 00:34:53,590
+Q تجسم اللي هو الـ Q على صورة واحد أو إيه أو سالب
+
+319
+00:34:53,590 --> 00:35:00,750
+واحد. نشوف كيف إن الـ Q تكسب الـ NP ستجعل الـ Q
+
+320
+00:35:00,750 --> 00:35:07,730
+بالطابق الذئب أو ناقص واحد اللي هو المدل و ثمانية
+
+321
+00:35:07,730 --> 00:35:14,330
+نجي للأمر هنا. ال proof نفترض 
+
+322
+00:35:14,330 --> 00:35:24,510
+الآن suppose that Q is an odd prime اللي هو الـ 
+
+323
+00:35:24,510 --> 00:35:29,250
+device mean الـ NB هيكون على صورة الـ Q يعيش 2N
+
+324
+00:35:29,250 --> 00:35:43,010
+زائد 1 is a prime divisor of mean of NB. فرضنا إيش
+
+325
+00:35:43,010 --> 00:35:50,860
+إحنا إنه الـ Q بتبسم صورته على 2N زائد 1 وهو الـ
+
+326
+00:35:50,860 --> 00:35:58,040
+Grand Divisor لمن؟ للـ N بيه شوف الـ N خذها
+
+327
+00:35:58,040 --> 00:36:05,680
+الأدالة اللي بديها let A بساوي 2 أُس B زائد 1 على
+
+328
+00:36:05,680 --> 00:36:10,760
+2 ربيع
+
+329
+00:36:10,760 --> 00:36:13,640
+للـ A بصير الـ A تربيع
+
+330
+00:36:16,250 --> 00:36:22,990
+الـ letter دي بيساوي اثنين أُس بي زائد واحد معايا
+
+331
+00:36:22,990 --> 00:36:30,530
+اترحلي من هنا إلى اثنين ومن هنا مين اثنين واضح
+
+332
+00:36:30,530 --> 00:36:38,190
+اه؟ الان هذه بتساوي اثنين
+
+333
+00:36:38,190 --> 00:36:51,280
+خذ عامل مشترك بيصير 2B-1 ويساوي مين
+
+334
+00:36:51,280 --> 00:37:02,240
+هي 2NB. نفترض أن الـ Q بتكسب مين الـ NB إذا صارت
+
+335
+00:37:02,240 --> 00:37:10,720
+هذه أشمالها مطابق السفر Modulo مين Modulo Q. من أين
+
+336
+00:37:10,720 --> 00:37:18,500
+جبتها؟ اللي هو الـ Q بتكسب مين الـ N بيه إيش معناه
+
+337
+00:37:18,500 --> 00:37:26,400
+هذا؟ معناته أن A تربيع تطابق 2 مضله مين؟ مضله Q صح
+
+338
+00:37:26,400 --> 00:37:34,300
+ولا لأ؟ الآن ارفعلي الجهتين للـ أُس N. هذا الـ N
+
+339
+00:37:34,300 --> 00:37:47,280
+بصير A أُس 2N تطابق 2 أُس N مضله مين؟ مضله Q واضح
+
+340
+00:37:47,280 --> 00:37:57,360
+أه؟ أي سؤال؟ طيب الآن اثنين أُس N اثنين
+
+341
+00:37:57,360 --> 00:38:05,800
+أن عبارة عن الـ Q ناقص واحد واضح أه؟ اثنين أن هي
+
+342
+00:38:05,800 --> 00:38:13,520
+عبارة عن الـ Q. إذا اللي هذي بتصير عبارة عن A SQ-1
+
+343
+00:38:13,520 --> 00:38:22,360
+وده
+
+344
+00:38:22,360 --> 00:38:32,640
+صار عندي الـ A واضحة. صار عندي الـ A SQ-1 تطابق 2N
+
+345
+00:38:32,640 --> 00:38:40,820
+Modulo EQ الآن
+
+346
+00:38:42,930 --> 00:38:47,830
+إيش العلاقة بين الـ A و بين الـ Q؟ الـ A عبارة عن
+
+347
+00:38:47,830 --> 00:38:54,670
+power of two يعني اثنين، أربعة، ثمانية، ستة عشر،
+
+348
+00:38:54,670 --> 00:38:58,910
+الاخرين إذاً أكيد العامل المشترك اللي على بين الـ
+
+349
+00:38:58,910 --> 00:39:03,690
+A و بين الـ Q أيش مساعد؟ واحد إذاً بإمكانك تطبيق
+
+350
+00:39:03,690 --> 00:39:08,010
+مين في الـ Math's theorem يعني اثنين يعني إيه؟ to
+
+351
+00:39:08,010 --> 00:39:15,820
+the Q minus واحد تطابق الواحد modulo a cube by
+
+352
+00:39:15,820 --> 00:39:22,880
+Fermat's theorem من التنتين مع بعض بس يعني عندي
+
+353
+00:39:22,880 --> 00:39:29,100
+اثنين أُس أن تطابق الواحد modulo. معناته إن الـ Q إيش
+
+354
+00:39:29,100 --> 00:39:38,580
+بتيب سن اثنين أُس أن ماقص واحد. طيب الـ Q بتكسب 2 أُس
+
+355
+00:39:38,580 --> 00:39:45,420
+N ناقص 1. يعني الـ Q بتكسب 2 الـ M N الـ Q بتكسب 2
+
+356
+00:39:45,420 --> 00:39:58,060
+الـ M N إذا الـ Q هتكون صورتها يا إما 1 يا إما 7
+
+357
+00:39:58,060 --> 00:40:05,700
+Modulo 8 Modulo 8
+
+358
+00:40:06,930 --> 00:40:12,490
+وانتوا بتقولوا ليش و الله يعطيكم العافية مرة
+
+359
+00:40:12,490 --> 00:40:13,650
+إجابة نكمل إن شاء الله 
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/Q3tp1nfGrIU_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/Q3tp1nfGrIU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b993011735610963fe8e846e2ddb5bac4ff0ba34
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/Q3tp1nfGrIU_raw.srt
@@ -0,0 +1,1444 @@
+1
+00:00:19,710 --> 00:00:25,610
+بسم الله الرحمن الرحيم كل عام انتوا بخير و مناسبة
+
+2
+00:00:25,610 --> 00:00:33,330
+حلول شهر رمضان المبارك و الحمد لله سلامتكم هنكمل
+
+3
+00:00:33,330 --> 00:00:38,770
+اليوم ان شاء الله شبتر احداشر اليوم المحاضرة رقم
+
+4
+00:00:38,770 --> 00:00:43,550
+تلاتين هنحكي
+
+5
+00:00:43,550 --> 00:00:48,520
+عن ال mercy non-primesدبل ما نحكي عن الـ Mercian
+
+6
+00:00:48,520 --> 00:00:53,280
+Primes أو الـ Mercian Numbers نذكركم باللي حكيناه
+
+7
+00:00:53,280 --> 00:00:57,280
+المرة الماضية عن الـ Perfect Numbers حكينا عن الـ
+
+8
+00:00:57,280 --> 00:01:02,660
+Even Perfect Numbers وقلنا إنه ال .. بنقول عن ال
+
+9
+00:01:02,660 --> 00:01:05,840
+.. ال perfect .. عن ال number n إنه perfect إذا
+
+10
+00:01:05,840 --> 00:01:11,660
+كان sigma of n بساوة 2n واخدنا قلنا لو كان عندي 2
+
+11
+00:01:11,660 --> 00:01:18,550
+أس Kناقص واحد is prime هيعطيني اللي هو اتنين اث
+
+12
+00:01:18,550 --> 00:01:22,470
+كناقص واحد في اتنين اث كناقص واحد is a perfect
+
+13
+00:01:22,470 --> 00:01:28,090
+number طبعا هذا even perfect number وقلنا ان ال
+
+14
+00:01:28,090 --> 00:01:36,890
+even perfect number في نظرية لو كان عندي اللي هو n
+
+15
+00:01:36,890 --> 00:01:44,860
+is an even perfect number هيكون ال nالخانة الأحد
+
+16
+00:01:44,860 --> 00:01:51,280
+في يا ستة يا إيش يا تمانية إذا كان un even perfect
+
+17
+00:01:51,280 --> 00:01:55,920
+number هيكون لو خانة الأحد يا ستة يا تمانية يعني
+
+18
+00:01:55,920 --> 00:01:59,360
+معناته أنتوا طابق اللي هو الستة و أنتوا طابق
+
+19
+00:01:59,360 --> 00:02:05,200
+التمانية نضله عشرة هذا
+
+20
+00:02:05,200 --> 00:02:10,000
+اللي حكيناه المرة الماضيةعن الـ Even Perfect
+
+21
+00:02:10,000 --> 00:02:15,560
+Numbers اليوم هنكمل الحديث عن المفسيين بـ Numbers
+
+22
+00:02:15,560 --> 00:02:23,700
+وانا اللي هو هنعرج على اللي هو الـ Odd Perfect
+
+23
+00:02:23,700 --> 00:02:30,180
+Numberإذا كانت موجودة، فهي موجودة بالشكل اللي
+
+24
+00:02:30,180 --> 00:02:32,980
+سنحكي عنه الشكل اللي سنشوفه ان شاء الله ندى
+
+25
+00:02:32,980 --> 00:02:38,400
+لنرسيني برايمز هنحكي عن اللي هو اللوعية الجديدة من
+
+26
+00:02:38,400 --> 00:02:45,310
+الأرقام اللي هي اسمها نرسيني numberبنقول ان الرقم
+
+27
+00:02:45,310 --> 00:02:48,930
+اللي على الصورة اللي هي اتنين اص ام ماقص واحد
+
+28
+00:02:48,930 --> 00:02:53,750
+بنسميها ده ايش ماله مرسين number مرسين number على
+
+29
+00:02:53,750 --> 00:02:59,910
+اسم حالة اسمه مرسين الان ام واحد ام واحد بيساوي
+
+30
+00:02:59,910 --> 00:03:06,730
+اتنين اص واحد ماقص واحد ويساوي واحد ام اتنين2 أُس
+
+31
+00:03:06,730 --> 00:03:12,850
+2 ناقص 1 يساوي 3 أن 3 بيساوي 2 أُس 3 ناقص 1 يساوي
+
+32
+00:03:12,850 --> 00:03:21,790
+7 أن 4 بيساوي 2 أُس 4 ناقص 1 يساوي دبياش 15 وهكذا
+
+33
+00:03:22,510 --> 00:03:26,810
+واضح أنه في الـ Mercian numbers اللي هي Primes
+
+34
+00:03:26,810 --> 00:03:32,990
+وفيه composite معايا؟ إذا الأن لو كان هذا الـ
+
+35
+00:03:32,990 --> 00:03:36,430
+Mercian number is a prime بنسميه Mercian prime
+
+36
+00:03:36,430 --> 00:03:40,910
+بسمي أشماله Mercian prime إذا الـ N integer MN
+
+37
+00:03:40,910 --> 00:03:44,750
+بساوة 2 وساعة نقص 1 is called Mercian number if
+
+38
+00:03:44,750 --> 00:03:49,150
+this MN is a prime then it is called أشماله
+
+39
+00:03:49,150 --> 00:03:56,530
+Mercian primeنأتي الآن ناخد خصائص اللي هو حول
+
+40
+00:03:56,530 --> 00:04:03,290
+المرسين numbers أو المرسين brines خلّينا نشوف
+
+41
+00:04:03,290 --> 00:04:08,890
+الأول نظرية اللي هي theorem 11-3 بتقول مالي
+
+42
+00:04:08,890 --> 00:04:18,090
+theorem 11-3 if b and
+
+43
+00:04:19,570 --> 00:04:29,330
+Q على صورة T بيزايد واحد R برايمز ثم نفترض ان P وQ
+
+44
+00:04:29,330 --> 00:04:36,330
+بيساوي 2M او 2B زايد واحد R برايمز number او R
+
+45
+00:04:36,330 --> 00:04:41,350
+برايمز number ثم ثم
+
+46
+00:04:41,350 --> 00:04:58,390
+هيكون Q بتجسم ال MB or لـ Q تجسم M بي زائد اتنين
+
+47
+00:04:58,390 --> 00:05:12,650
+but not both أبروف كمان مرة كمان مرة إذا كانت بي
+
+48
+00:05:13,520 --> 00:05:19,300
+الـ Q بيساوي 2B زائد 1 برايمز، ماشي؟ إذا، هيكون
+
+49
+00:05:19,300 --> 00:05:24,700
+عند الـ Q بتكسب الـ MB قريب الـ Q بتكسب مين؟ الـ
+
+50
+00:05:24,700 --> 00:05:29,380
+MB زائد 2، but not both يعني مستحيل تكسب التنين مع
+
+51
+00:05:29,380 --> 00:05:36,680
+بعض، يعني بس هتكسب exactly one of them الـ
+
+52
+00:05:36,680 --> 00:05:46,430
+Q أسوأ تتنين بيزايد واحد، بيز برايمB is prime لأن
+
+53
+00:05:46,430 --> 00:05:53,690
+المقطع عنده اش انه B and Q are primes و الـ Q على
+
+54
+00:05:53,690 --> 00:06:05,510
+سورة 2 بيزايد واحد واضح؟ طيب نجي للبرهان بروف عندي
+
+55
+00:06:05,510 --> 00:06:12,850
+واضح ان الـ Q لا تقسم بين التنين
+
+56
+00:06:14,820 --> 00:06:18,220
+أو الـ Greatest Common Divisor بين الـ Q والتمناش
+
+57
+00:06:18,220 --> 00:06:27,220
+بيساوي واحد إذا أكيد by Fermat theorem اتنين الـ Q
+
+58
+00:06:27,220 --> 00:06:36,560
+ناقص واحد مظبوط؟ تطابق الواحد مدله مين؟ مدله الـ Q
+
+59
+00:06:36,560 --> 00:06:45,710
+واضح أه؟هذه by Fermat's theorem 2Sq-1 تطابق الواحد
+
+60
+00:06:45,710 --> 00:06:58,650
+modulo Q لاحظ عندي الـ Q-1 عبارة عن عدد زودي وكأنه
+
+61
+00:06:58,650 --> 00:07:07,510
+بيقدر يقول إن 2Sq-1 على 2 لكل تربيع ماقص واحد
+
+62
+00:07:07,510 --> 00:07:14,740
+تطابقالـ 0 مدلوا مين؟ مدلوا Q نجرت العدين هذه
+
+63
+00:07:14,740 --> 00:07:20,400
+وكتبت 2Q 2 على صورة Q مانس واحد على اتنين تربيع هل
+
+64
+00:07:20,400 --> 00:07:25,340
+هذه انتجار؟ اه انتجار لأن Q ناقص واحد بساوي 2B
+
+65
+00:07:25,340 --> 00:07:30,820
+يعني Q ناقص واحد على اتنين عبارة عن عدد واضح؟
+
+66
+00:07:30,820 --> 00:07:42,000
+ويساوي هذا بساوي 2 أس بي تربيع ناقص واحدلأن عندي
+
+67
+00:07:42,000 --> 00:07:49,060
+الـ Q بساوة 2B زائد 1 يعني Q ناقص 1 على 2 مش
+
+68
+00:07:49,060 --> 00:07:57,880
+متساوم بساوة B واضح؟ طيب الان هذا فرق بين مربعين
+
+69
+00:07:57,880 --> 00:08:04,360
+بقدر أحلله هو عبارة عن 2 أس B ناقص 1 في 2 أس B
+
+70
+00:08:04,360 --> 00:08:09,760
+زائد 1 وهذا مين هو؟
+
+71
+00:08:15,940 --> 00:08:26,640
+وهذا أدارة عامية NB زائد 2 إذن سعر عندي اللي هو NB
+
+72
+00:08:26,640 --> 00:08:32,600
+في NB زائد 2 بقادر الصفر المدنو من كله مدنو Q إيش
+
+73
+00:08:32,600 --> 00:08:37,460
+معناته هذا؟ معناته إنه سعر عندي Q تقسم الـ NB في
+
+74
+00:08:37,460 --> 00:08:43,570
+الـ NB زائد 2ماذا يعني هذا؟ لدي الـ Q زبرايا مادام
+
+75
+00:08:43,570 --> 00:08:49,430
+الـ Q زبرايا إذن إذا الـ Q تجسم الـ NB أو الـ Q
+
+76
+00:08:49,430 --> 00:08:54,850
+تجسم الـ NB زاد اتنين اللي نريد أن نثبت هو but not
+
+77
+00:08:54,850 --> 00:09:01,590
+both but not both سببه not يعني سببه إن الـ Q تجسم
+
+78
+00:09:01,590 --> 00:09:08,700
+هذا و هذا مع بعضمفترض أن الـ Q تجسم الـ NB and الـ
+
+79
+00:09:08,700 --> 00:09:13,460
+Q تجسم الـ NB زاد 2 إذاً هتجسم أي لينة combination
+
+80
+00:09:13,460 --> 00:09:19,040
+بينهم إذاً أكيد هتصير then الـ Q هتجسم الـ NB زاد
+
+81
+00:09:19,040 --> 00:09:25,720
+2 ماقص الـ NB اللي هو كل جدّش هذا اتنين صارت الـ Q
+
+82
+00:09:25,720 --> 00:09:29,820
+تجسم اتنين وهذا Contradiction لأن الـ Q أشمالها is
+
+83
+00:09:29,820 --> 00:09:38,370
+an odd primeTherefore الـ Q تجسم أن بي or Q تجسم
+
+84
+00:09:38,370 --> 00:09:45,070
+أن بي زائد اتنين but not both but not both اطلع
+
+85
+00:09:45,070 --> 00:09:55,990
+على فوق نيجي للنظرية 11-4 11-4 تقول ما يليه
+
+86
+00:09:55,990 --> 00:10:00,450
+theorem 11-4
+
+87
+00:10:01,950 --> 00:10:08,390
+عندي الـ Q عبارة عن odd prime if الـ Q بتساوي 2
+
+88
+00:10:08,390 --> 00:10:14,630
+and زي 1 then الـ
+
+89
+00:10:14,630 --> 00:10:22,330
+Q بتساوي 2 and زي 1 مجرد odd prime عبارة عن if الـ
+
+90
+00:10:22,330 --> 00:10:31,110
+Q بتساوي 2 and زي 1 is prime then الـ Qبتبسم N N
+
+91
+00:10:31,110 --> 00:10:42,710
+في حال provided that الـ B على صورة 8K زائد 1 يعني
+
+92
+00:10:42,710 --> 00:10:48,430
+B تطابق الواحد الـ Q تطابق الواحد modulo تمانية أو
+
+93
+00:10:48,430 --> 00:10:56,760
+الـ Q تطابق السبعة modulo أيش تمانية اتنينالـ Q
+
+94
+00:10:56,760 --> 00:11:04,120
+بتجسم الـ N N زي 2 في حال كانت الـ Q بالطابق
+
+95
+00:11:04,120 --> 00:11:12,520
+التلاتة Modulo 8 أو الـ Q بالطابق الخمسة Modulo 8
+
+96
+00:11:12,520 --> 00:11:19,590
+ماشي الحال تمام مرةإذا كان الـ Q عبارة عن إبراهيم
+
+97
+00:11:19,590 --> 00:11:24,910
+الـ Q هذا مدام إبراهيم قد إبراهيم إذا هو على صورة
+
+98
+00:11:24,910 --> 00:11:30,570
+أحد الصور الأربعة التالية يا تمانية كزايد واحد يا
+
+99
+00:11:30,570 --> 00:11:35,130
+تمانية كزايد تلاتة يا تمانية كزايد خمسة يا تمانية
+
+100
+00:11:35,130 --> 00:11:40,380
+كزايد سبعةماشي الحال عندى إذا كان كيوب تكسب الام
+
+101
+00:11:40,380 --> 00:11:45,960
+ان هذا بيحدث متى بس للأرقام اللى بتكون بكيوب
+
+102
+00:11:45,960 --> 00:11:51,480
+الطابق الواحد أو كيوب الطابق مين السبعة الان وإذا
+
+103
+00:11:51,480 --> 00:11:54,320
+كانت الأرقام ع صورة كيوب تكسب ثلاثة أو كيوب تكسب
+
+104
+00:11:54,320 --> 00:11:59,960
+خمسة هذا هيكون يشمال وكيوب تكسب نين الام زائد واحد
+
+105
+00:11:59,960 --> 00:12:06,470
+زائد اتنينالأن المظلة بتطلب اللي هو شبتر تسعة عشان
+
+106
+00:12:06,470 --> 00:12:09,430
+هيك احنا مااخدنا الشبتر تسعة أو مش هناخد شبتر تسعة
+
+107
+00:12:09,430 --> 00:12:14,170
+فالبرنامج مش مطلوب نيفي للـ Corollary اللي بقتها
+
+108
+00:12:14,170 --> 00:12:23,590
+الـ Corollary بتقول ما يلي FB and Q على صورة 2B زي
+
+109
+00:12:23,590 --> 00:12:28,250
+1 are both brands يعني الباق لأن الـ B هذه برضه
+
+110
+00:12:28,250 --> 00:12:34,850
+أشمالها برايهناك Q مجرد عصورة 2N زي 1 هنا الـ B is
+
+111
+00:12:34,850 --> 00:12:40,070
+prime ومع تيني الـ B أشملها بالتالتة مدلوا مين؟
+
+112
+00:12:40,070 --> 00:12:47,090
+مدلوا أربعة الـ Corollary الـ Corollary بتقول مالي
+
+113
+00:12:47,090 --> 00:12:57,130
+if B وQ بساوة 2B زي 1 are odd grams هاي واحد اتنين
+
+114
+00:12:57,130 --> 00:13:04,000
+قال لك إنهB تطابق التلاتة modulo أربعة يعني الـ B
+
+115
+00:13:04,000 --> 00:13:09,280
+على صورة أربعة K زائد تلاتة B تطابق التلاتة modulo
+
+116
+00:13:09,280 --> 00:13:12,360
+أربعة يعني الـ B أشمالها على صورة أربعة K زائد
+
+117
+00:13:12,360 --> 00:13:20,520
+تلاتة then هذا بأكد لك إن الـ Q هتجسم مين الـ MB
+
+118
+00:13:20,520 --> 00:13:27,980
+الـ Q هتجسم الـ MB البروف صغير البروف مباشر البروف
+
+119
+00:13:29,590 --> 00:13:34,430
+إن الـ B تُطابق التلاتة مدونه مين؟ مدونه أربعة
+
+120
+00:13:34,430 --> 00:13:39,970
+يعني الـ B هتساوي أربعة K زائد تلاتة for some K
+
+121
+00:13:39,970 --> 00:13:46,690
+element in Z معايا منه إيش هتطلع الـ Q؟ then الـ Q
+
+122
+00:13:46,690 --> 00:13:54,590
+هتساوي اتنين في أربعة K زائد تلاتة زائد واحد
+
+123
+00:13:54,590 --> 00:14:01,920
+ويساويتمنية K زائد سبعة ما هو معناته هذا؟ معناته
+
+124
+00:14:01,920 --> 00:14:09,040
+أنه تقع عندك Q تطابق السبعة موديلو تمانية إذا
+
+125
+00:14:09,040 --> 00:14:16,220
+الحسب اللي هو واحد إذا عندي hence الـQ هتجسم من
+
+126
+00:14:16,220 --> 00:14:26,060
+الـM أنا اللي في هذا الحال اللي هي B Q بتجسم الـMB
+
+127
+00:14:30,290 --> 00:14:39,630
+أي سؤال نجي لنظرية 11-5 نظرية 11-5 برهانة بيتمد
+
+128
+00:14:39,630 --> 00:14:44,690
+على chapter 8 هناخد
+
+129
+00:14:44,690 --> 00:14:49,750
+chapter 8 أحنا ان شاء الله بس هأحكي معلمتين في
+
+130
+00:14:49,750 --> 00:14:54,110
+chapter 8 على أساس الاستخدام من الآن في إثبات
+
+131
+00:14:54,110 --> 00:14:58,690
+النظرية خلينا نشوف أيش المعلومتين وبناء عليهم اللي
+
+132
+00:14:58,690 --> 00:15:12,760
+هوانبهر النظرية الـ
+
+133
+00:15:12,760 --> 00:15:22,900
+Definition موجود في Chapter 8 الـ Definition K
+
+134
+00:15:22,900 --> 00:15:36,940
+is called the orderof two modulo Q in
+
+135
+00:15:36,940 --> 00:15:46,360
+the case that واحد اللي هو اتنين to the K تطابق
+
+136
+00:15:46,360 --> 00:15:55,500
+الواحد modulo Q اتنين K is the smallest
+
+137
+00:15:58,530 --> 00:16:05,850
+such that it means to the end طبق الواحد modulo q
+
+138
+00:16:05,850 --> 00:16:12,350
+او modulo b زي ما بدكم اذا الان ال definition هذا
+
+139
+00:16:12,350 --> 00:16:18,770
+بدنا نعرف شو معنات k اي عبارة عن ال order لتو
+
+140
+00:16:18,770 --> 00:16:22,850
+modulo mean modulo q هذا ال definition من شرط
+
+141
+00:16:22,850 --> 00:16:28,400
+التمانية نحتاجينه عشان نبره النظريةالآن K is
+
+142
+00:16:28,400 --> 00:16:32,940
+called the order of two modulo Q في حال ما يليه Q
+
+143
+00:16:32,940 --> 00:16:39,770
+طبعا اللي هنستخدمها عنا هنا عبارة عن إبراهيم2 to
+
+144
+00:16:39,770 --> 00:16:44,670
+the K تطابق الواحد modulo Q هاي أول شرط الشرط
+
+145
+00:16:44,670 --> 00:16:49,810
+الثاني أنه لو كان عند أي 2 أُس M تطابق الواحد
+
+146
+00:16:49,810 --> 00:16:55,070
+modulo Q هتكون ال K أشمالها أصغر أو تساومين M يعني
+
+147
+00:16:55,070 --> 00:16:59,470
+ال K شرطين عليها أن 2 to the K تطابق الواحد شرط
+
+148
+00:16:59,470 --> 00:17:03,670
+الثاني K is the smallest such M بحيث أن 2 to the M
+
+149
+00:17:03,670 --> 00:17:10,100
+تطابق الواحد modulo Q في نظريةبرضه هستخدمها
+
+150
+00:17:10,100 --> 00:17:14,220
+theorem 8-1 هنجيها بالتفصيل لما ناخد شرطر 8
+
+151
+00:17:14,220 --> 00:17:27,320
+theorem 8-1 بتقول if K is the order of two modulo
+
+152
+00:17:27,320 --> 00:17:39,000
+Q and اتنين to the B مثلا تطابق الواحد modulo Qثم
+
+153
+00:17:39,000 --> 00:17:46,020
+الـ K تكسب ميان قلبي هذا ما علمتناه دولة بديها من
+
+154
+00:17:46,020 --> 00:17:49,800
+chapter تمانية عينية بستخدمها في برهان النظرية
+
+155
+00:17:49,800 --> 00:17:59,610
+كمان مرة if K is the order of twoModulo Q وكان
+
+156
+00:17:59,610 --> 00:18:04,090
+عندى 2 to the B تطابق الواحد Modulo Q هتكون هذه
+
+157
+00:18:04,090 --> 00:18:07,550
+الـ K طبعا هي smallest مش عدد smallest النظرية
+
+158
+00:18:07,550 --> 00:18:13,750
+بتقولك لأ هتكون الـ K بتقسم الـ B K عامل من عوامل
+
+159
+00:18:13,750 --> 00:18:22,170
+الـ B طيب نجي لنظريتنا اللى في شبترنا في شبتر 11
+
+160
+00:18:22,170 --> 00:18:31,060
+النظرية بتقول ماليفيه نمرة أحداشر وخمسة بتقول if B
+
+161
+00:18:31,060 --> 00:18:47,840
+if B is an odd prime then then any divisor
+
+162
+00:18:47,840 --> 00:18:50,960
+of M is
+
+163
+00:18:55,160 --> 00:19:03,520
+of the form of the
+
+164
+00:19:03,520 --> 00:19:07,960
+form اتنين كب زائد واحد
+
+165
+00:19:21,100 --> 00:19:29,340
+ان اي برايم دفعزر مب فان
+
+166
+00:19:29,340 --> 00:19:30,120
+اي برايم
+
+167
+00:19:36,590 --> 00:19:42,570
+of m,b is of the form 2a,b,z,1 إيش الـ m,b يا
+
+168
+00:19:42,570 --> 00:19:46,810
+جماعة؟ موضوعنا للذين متأخرين هو عبارة عن مرسيل
+
+169
+00:19:46,810 --> 00:19:51,270
+number المرسيل number، العدد العصور تتنين، m ناقص
+
+170
+00:19:51,270 --> 00:19:56,830
+واحد، بنسميه m,m، بنسميه مرسيل numberلو هذا الـ MN
+
+171
+00:19:56,830 --> 00:20:01,550
+طلع برايم لو هذا طلع برايم بنسميه مرسين إبراهيم
+
+172
+00:20:01,550 --> 00:20:05,310
+ماشي الحال و بدنا ناخد خواصه الأن أخدنا خواص واين
+
+173
+00:20:05,310 --> 00:20:11,650
+بنكمل على الخواص الأخرى الآن المظلية اللي عندنا
+
+174
+00:20:11,650 --> 00:20:16,210
+بتقول إن إذا كانت B is an odd prime then any prime
+
+175
+00:20:16,210 --> 00:20:24,610
+divisor of MB is of the form 2KB زائد 1 معايا؟ طيب
+
+176
+00:20:25,630 --> 00:20:33,050
+الآن بدنا نرهم بدي أخد الـ Q الآن بقول let Q be
+
+177
+00:20:33,050 --> 00:20:39,450
+any prime divisor لمين؟ لـ NB الـ Q بتكسب مين؟ الـ
+
+178
+00:20:39,450 --> 00:20:47,310
+NB الان مدام الـ Q بتكسب الـ NB then الـ NB تطابق
+
+179
+00:20:47,310 --> 00:20:53,030
+السفر modulo مين؟ modulo Qالـ Q بتكسب من الـ NB
+
+180
+00:20:53,030 --> 00:20:55,550
+إذا الـ NB تطابق اللي هو الـ Zero modulo N modulo
+
+181
+00:20:55,550 --> 00:21:01,410
+Q الـ NB إيش اسمها؟ اتنين أس بي ناقص واحد هي
+
+182
+00:21:01,410 --> 00:21:05,850
+بتعريف المرسيين number اتنين أس بي ناقص واحد إيش
+
+183
+00:21:05,850 --> 00:21:12,190
+معناته هذا الكلام؟ معناته أنه then اتنين أس بي
+
+184
+00:21:12,190 --> 00:21:20,230
+تطابق الواحد modulo N اكيو ميحك؟ طيب اللي هبقى
+
+185
+00:21:20,230 --> 00:21:21,070
+أقولك مت
+
+186
+00:21:41,940 --> 00:21:43,340
+كيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكيكي
+
+187
+00:21:44,000 --> 00:21:49,080
+الآن عندي 2 أُس بي تطابق الواحد بدون الـQ إذا من
+
+188
+00:21:49,080 --> 00:21:53,680
+النتيجة اللي جابني بشوية مدامة الـK of order 2
+
+189
+00:21:53,680 --> 00:21:57,520
+بدون الـQ و2 أُس بي تطابق الواحد بدون الـQ إذا
+
+190
+00:21:57,520 --> 00:22:05,760
+الـK هتكسب من هذا الـB إذا then الـK تبتسم من الـB
+
+191
+00:22:05,760 --> 00:22:13,840
+مدام الـK هذه بقى theorem 8.1الآن الـ B زبران والـ
+
+192
+00:22:13,840 --> 00:22:18,140
+K بتجسيم الـ B إذا الـ K يا بتساوي واحد يا B إذا
+
+193
+00:22:18,140 --> 00:22:22,580
+الـ K عندي يا بتساوي واحد يا الـ K بتساوي بيه
+
+194
+00:22:22,580 --> 00:22:29,200
+بقولك K بتساوي واحد مستحيل ليش؟ لإن إيش معناة الـ
+
+195
+00:22:29,200 --> 00:22:33,100
+K هي الأرض الاتنين modulo Q؟ معناته إن اتنين ..
+
+196
+00:22:33,100 --> 00:22:36,600
+إيش معناته هذه؟ معناته إن اتنين أس K أو بتعطي
+
+197
+00:22:36,600 --> 00:22:45,020
+تطابق الواحد moduloين Qمعنى هذا أن
+
+198
+00:22:45,020 --> 00:22:49,800
+كيوب تكسب نينوس كيه ماينوس؟ لو كانت كيوب واحد
+
+199
+00:22:49,800 --> 00:22:54,240
+بيصيب كيوب تكسب مين واحد؟ يعني معناته كيوب تساوي
+
+200
+00:22:54,240 --> 00:22:59,690
+واحد كون كيوب زبرايهإذا الـ K أشمالها قطعا لا
+
+201
+00:22:59,690 --> 00:23:04,950
+تساوي الواحد إذا we must have K إش بتساوي بساوي B
+
+202
+00:23:04,950 --> 00:23:10,610
+إذا أخل في الذاكرة إن الـ K إن إش بتساوي بتساوي
+
+203
+00:23:10,610 --> 00:23:15,230
+الـ B الآن
+
+204
+00:23:15,230 --> 00:23:21,730
+ال clue ال clue is N of the primeيعني لا الاتنين
+
+205
+00:23:21,730 --> 00:23:26,130
+بتقسم بـQ ولا الـQ بيقسم اتنين يعني العام المشترك
+
+206
+00:23:26,130 --> 00:23:30,230
+اللي على بين الـQ والـ8 مش بيسافر يعني by Fermat's
+
+207
+00:23:30,230 --> 00:23:35,710
+theorem بيصير اتنين Q minus واحد تطابق الواحد
+
+208
+00:23:35,710 --> 00:23:43,590
+modulo Q كم مرة؟ طيب صلوا على النبي عليه الصلاة
+
+209
+00:23:43,590 --> 00:23:52,670
+والسلام الان بالبونإنه الـ 2 و الـ Q العامل
+
+210
+00:23:52,670 --> 00:23:57,990
+المشترك الأعلى بين الواحد لأن Q is odd if I divide
+
+211
+00:23:57,990 --> 00:24:02,870
+by Fermat's theorem 2 to the Q minus .. و Q برقام
+
+212
+00:24:02,870 --> 00:24:06,630
+طبعا .. 2 to the Q .. و 2 كمان برقام بالمرة 2 to
+
+213
+00:24:06,630 --> 00:24:10,830
+the Q minus 1 تطابق الواحد بدون مين؟ by Fermat's
+
+214
+00:24:10,830 --> 00:24:16,130
+theorem طيب، احنا بنقول الـ K هي مين؟الـ order لـ
+
+215
+00:24:16,130 --> 00:24:20,790
+2 modulo Q معناته بنطبق تمانية واحد كمان مرة لإن
+
+216
+00:24:20,790 --> 00:24:25,090
+ساعة عندي 2 نص Q مانس واحد تطابق واحد modulo Q إذا
+
+217
+00:24:25,090 --> 00:24:33,450
+.. إذا أكيد .. إذا K تجسمين Q مانس واحد واضح أه؟
+
+218
+00:24:33,450 --> 00:24:36,650
+كامل هي أصلا .. احنا لازم نهلش فوق اللي عملنا كمية
+
+219
+00:24:36,650 --> 00:24:43,730
+مين الـ B معناته أنه hence الـ B بيجسم الـ Q مانس
+
+220
+00:24:43,730 --> 00:24:53,400
+واحدمعايا؟ إذا صار عندك الـ Q Q minus واحد بساوي T
+
+221
+00:24:53,400 --> 00:25:01,760
+في B for some T element in Z إيش معناته هذا؟ هذا
+
+222
+00:25:01,760 --> 00:25:10,900
+بيعطيني إن الـ Q بتساوي T في B زايد واحد معايا؟
+
+223
+00:25:10,900 --> 00:25:12,320
+طيب
+
+224
+00:25:16,380 --> 00:25:25,460
+عندي الـ B أد براين صح ولا لأ؟ و هذا الـ T في B
+
+225
+00:25:25,460 --> 00:25:33,520
+زاد مين؟ زاد واحد الـ Q زاد أد براين الآن الـ T لو
+
+226
+00:25:33,520 --> 00:25:38,420
+كانت أد بيصير هذا على هذا أد فأد بيطلع إياش زاد
+
+227
+00:25:38,420 --> 00:25:42,760
+واحد بيطلع even contradiction إذا الـ T لازم تطلع
+
+228
+00:25:42,760 --> 00:25:48,810
+إياش evenأد في أد أد زائد أد بيطلع even
+
+229
+00:25:48,810 --> 00:25:54,450
+contradiction إذا الـ T must be even الآن إذا T
+
+230
+00:25:54,450 --> 00:26:01,910
+بتساوي 2M for some M يعني صارت الـ Q لازم تطلع
+
+231
+00:26:01,910 --> 00:26:09,590
+صورتها 2M B زائد 1for some m element in z وهي
+
+232
+00:26:09,590 --> 00:26:12,810
+الصورة المطلوبة اتنين ك بي زائد واحد طبعا ال K هذه
+
+233
+00:26:12,810 --> 00:26:16,710
+مش هي ال K اللي انا فايد معاها اه انها دي for some
+
+234
+00:26:16,710 --> 00:26:23,310
+k element in z اذا اللي اثبتناه انه لو كانت B of
+
+235
+00:26:23,310 --> 00:26:27,310
+the prime اذا any prime divisor of m B is of the
+
+236
+00:26:27,310 --> 00:26:33,690
+form اتنين ك بي زائد واحد اي
+
+237
+00:26:33,690 --> 00:26:38,770
+سؤالاللي بعده يلّا اطلعنا على اللي بعدها بخليها في
+
+238
+00:26:38,770 --> 00:26:44,450
+الأخر على سريع قبل ما نحكي عن نظرية الـ 11.6 نيجي
+
+239
+00:26:44,450 --> 00:26:53,130
+على 11.7 11.7 مش هنبرهنها 11.7 إذا بتتذكر المرة
+
+240
+00:26:53,130 --> 00:26:58,690
+الماضية المرة الماضية حكينا عن مين عن perfect
+
+241
+00:26:58,690 --> 00:27:03,010
+numbers في الواقع اللي حكينا عنه عن ال even
+
+242
+00:27:03,010 --> 00:27:07,620
+perfect numbersمعايا الـ even perfect numbers
+
+243
+00:27:07,620 --> 00:27:12,640
+واخرنا أنثى لأو concrete examples ستة وتمانية
+
+244
+00:27:12,640 --> 00:27:17,850
+عشرين وفي أرقام أخرى ميديودة في الكتابوقلنا
+
+245
+00:27:17,850 --> 00:27:23,890
+الأرقام الـ Perfect Numbers عزيزة إنها كل فترة
+
+246
+00:27:23,890 --> 00:27:28,290
+بيظهر اللي هو يعني كل زيادة خانة بيظهر وأحيانا
+
+247
+00:27:28,290 --> 00:27:33,650
+خانة بتزيد لكن مابيظهرش فيها في كل اللي هو يعني
+
+248
+00:27:33,650 --> 00:27:36,570
+الأرقام اللي بالأربع خنات أو الخمس خنات ممكن
+
+249
+00:27:36,570 --> 00:27:41,860
+مايدهرش ممكن يظهر كل بعدينما حكيناش عن الـ odd
+
+250
+00:27:41,860 --> 00:27:46,240
+number الـ odd perfect number ما حكيناش فش
+
+251
+00:27:46,240 --> 00:27:50,220
+concrete example لحد تلان ان وحد يقولنا هذا هو odd
+
+252
+00:27:50,220 --> 00:27:55,120
+number وهو الـ perfect number ما حدش لحد تلان
+
+253
+00:27:55,120 --> 00:28:01,380
+أعطاهلكن الآن هذه النظرية بتقولك ان لو في .. لو في
+
+254
+00:28:01,380 --> 00:28:05,900
+odd perfect number هيكون صورته على الصورة التالية
+
+255
+00:28:05,900 --> 00:28:10,460
+بس هي اللي بتحكي النظرية .. اه؟ الان بتقول if N is
+
+256
+00:28:10,460 --> 00:28:14,140
+an odd perfect number if N is an odd perfect
+
+257
+00:28:14,140 --> 00:28:19,740
+number then this N must be of the formبـ1K1 يعني
+
+258
+00:28:19,740 --> 00:28:25,880
+ما تفكروش تدوروا في الـOdd Perfect Numbers في غير
+
+259
+00:28:25,880 --> 00:28:29,020
+هذه العائلة يعني اللي بده يفكر يروح يدور على
+
+260
+00:28:29,020 --> 00:28:31,800
+الـOdd Perfect Number اللي هو إذا بده يلاقي
+
+261
+00:28:31,800 --> 00:28:36,370
+بناديهان براطن مش هيلاقيهلأن if n is an odd
+
+262
+00:28:36,370 --> 00:28:40,110
+perfect number then n can be written على صورة بي
+
+263
+00:28:40,110 --> 00:28:45,070
+واحد أُس كي واحد بي بنيين أُس اتنين جي اتنين لعين
+
+264
+00:28:45,070 --> 00:28:51,590
+بي ار أُس اتنين جي ار واضح ان هدولةكل واحد فيه
+
+265
+00:28:51,590 --> 00:28:59,170
+مربع كامل يعني مرفوع لاتنين Alpha او اتنين J او
+
+266
+00:28:59,170 --> 00:29:02,910
+اتنين اللي بدكيه هذول بي واحد بي اتنين بي ار ار
+
+267
+00:29:02,910 --> 00:29:07,620
+Distant Primes معايا يا شباب؟اللي يعمل مش هاد
+
+268
+00:29:07,620 --> 00:29:13,120
+ويحدّبك أكثر بيقولّك الرقم الأول فيه، هذا الـB1
+
+269
+00:29:13,120 --> 00:29:19,920
+هتلاقي اللي هو على صورة 4K زائد 1 الـB1 على صورة
+
+270
+00:29:19,920 --> 00:29:24,720
+مين؟ 4K زائد 1، هتفاجأ نقض يعني مش هيكون even، مش
+
+271
+00:29:24,720 --> 00:29:30,120
+هيبقى احد even على صورة مين؟ 4K زائد 1 والأس تبعه
+
+272
+00:29:30,120 --> 00:29:35,990
+برضه على صورة 4M زائد 1باضح؟ إذا بيقولك إذا كانت n
+
+273
+00:29:35,990 --> 00:29:42,070
+is an odd perfect number then it must has the form
+
+274
+00:29:42,070 --> 00:29:46,070
+n بيسوء بي واحد كواحد بي اتنين جتنين و بي اتنين
+
+275
+00:29:46,070 --> 00:29:48,930
+جتنين و بي اتنين جتنين و بي اتنين جتنين و بي اتنين
+
+276
+00:29:48,930 --> 00:29:50,690
+جتنين و بي اتنين جتنين و بي اتنين جتنين و بي اتنين
+
+277
+00:29:50,690 --> 00:29:50,690
+جتنين و بي اتنين جتنين و بي اتنين جتنين و بي اتنين
+
+278
+00:29:50,690 --> 00:29:50,690
+جتنين و بي اتنين جتنين و بي اتنين جتنين و بي اتنين
+
+279
+00:29:50,690 --> 00:29:58,530
+جتنين و بي اتنين جتنين و بي اتنين جتنين و بي اتنين
+
+280
+00:29:58,530 --> 00:30:07,270
+جتنواللي هي الـ أس تبعه برضه على صورة أربع M تساوي
+
+281
+00:30:07,270 --> 00:30:13,230
+الواحد أي شوية انزل لتحت بقولك اللي هو الـ
+
+282
+00:30:13,230 --> 00:30:18,730
+Corollary اللي هي بتقولك if M is an odd perfect
+
+283
+00:30:18,730 --> 00:30:25,470
+number then M has the form M بتساوي بيقص K في مين
+
+284
+00:30:25,470 --> 00:30:33,630
+في M تربيع where Bis an odd prime وB مش من عامل
+
+285
+00:30:33,630 --> 00:30:37,670
+أمتر بيعي يعني بقى ان الـ B اشمع من مصحوبة كل الـ
+
+286
+00:30:37,670 --> 00:30:43,430
+value برا وعلى صورة B كفي المربع كامل حيث الـ B
+
+287
+00:30:43,430 --> 00:30:48,730
+عبارة على صورة 4K زيادة واحد والـ K على صورة 8 4K
+
+288
+00:30:48,730 --> 00:30:52,600
+زيادة واحدةهذا اللي بتعرفوه عن الـOdd Prime. أو
+
+289
+00:30:52,600 --> 00:30:55,960
+Odd Perfect Number. عموماً في كلام كتير في الكتاب
+
+290
+00:30:55,960 --> 00:31:00,880
+حول التاريخ الـMerced Number وتاريخ الـPerfect
+
+291
+00:31:00,880 --> 00:31:05,100
+Numbers وحتى صار حديث عن بعض اللي هي مسائل مش
+
+292
+00:31:05,100 --> 00:31:08,460
+محلولة و Open Problems وآخري أنا منصح بقراءة
+
+293
+00:31:08,460 --> 00:31:15,820
+الكتاب في هذا يعني جيدا بتعطيك صورة اللي هي يعني
+
+294
+00:31:15,820 --> 00:31:20,410
+خلفية منيحة عن اللي هو الموضوع.نجي الاخر نظرية
+
+295
+00:31:20,410 --> 00:31:31,350
+عندنا رجعلي ال 11 6 فيون 11 6 if
+
+296
+00:31:31,350 --> 00:31:41,490
+B is an odd prime
+
+297
+00:31:41,490 --> 00:31:45,110
+then
+
+298
+00:31:45,110 --> 00:31:47,390
+اني
+
+299
+00:31:51,400 --> 00:32:05,020
+prime divisor Q of MB is
+
+300
+00:32:05,020 --> 00:32:13,160
+of the form Q
+
+301
+00:32:13,160 --> 00:32:17,900
+بالطابق الواحد زي ذا ناقص واحد modulo
+
+302
+00:32:37,210 --> 00:32:47,530
+800 حضارة يعني الحضارة الأشياء وسيطة فيها لكم نشوف
+
+303
+00:32:47,530 --> 00:32:54,940
+أشياء نظرية بتقولFB is an odd prime then any prime
+
+304
+00:32:54,940 --> 00:33:02,620
+divisor Q of M B is of the form Q تطابق الواحد او
+
+305
+00:33:02,620 --> 00:33:06,660
+ناقص واحد مضله تمانية يعني يعني الـ Q يان الطابق
+
+306
+00:33:06,660 --> 00:33:11,380
+الواحد او الطابق السبعة يعني فالاخر الـ Q هتكون
+
+307
+00:33:11,380 --> 00:33:15,320
+على سورة تمانية K او ايش او سبعة K
+
+308
+00:33:22,200 --> 00:33:34,260
+طبعا ال .. ال .. ال odd prime ال odd prime او .. و
+
+309
+00:33:34,260 --> 00:33:43,240
+ال .. و ال prime divisor ال q لل mb ال q هذه اكيد
+
+310
+00:33:43,240 --> 00:33:49,960
+صورتهامدام تبرايم قد برايم الـ Q هتكون على صورة يا
+
+311
+00:33:49,960 --> 00:33:54,620
+تمانية K زائد واحد يا تمانية K زائد تلاتة يا
+
+312
+00:33:54,620 --> 00:33:58,940
+تمانية K زائد خمسة يا تمانية K زائد إيش زائد سبعة
+
+313
+00:33:58,940 --> 00:34:08,000
+ماشي الحل الآن تمانية K زائد تلاتة و تمانية K زائد
+
+314
+00:34:08,000 --> 00:34:15,370
+خمسة بأهلنه حسب النظرية اللي فاتت بأهلنهإنه يقسم
+
+315
+00:34:15,370 --> 00:34:18,810
+الـ
+
+316
+00:34:18,810 --> 00:34:28,290
+NB زائد 2 إذا
+
+317
+00:34:28,290 --> 00:34:36,130
+هدولة مش هيكون الورداتلأن ما دام الـ Q قسم الـ NP
+
+318
+00:34:36,130 --> 00:34:40,790
+أكيد مش هيجسم الـ NP زاد اتنين اتفجنا عليه انه
+
+319
+00:34:40,790 --> 00:34:46,130
+قلنا الـ Q هتجسم هذه او هذه اذا نضل اللي هو ان الـ
+
+320
+00:34:46,130 --> 00:34:53,590
+Q تجسم اللي هو الـ Q على صورة واحد او ايه او سالب
+
+321
+00:34:53,590 --> 00:35:00,750
+واحد نشوف كيفإن الـ Q تكسب الـ NP ستجعل الـ Q
+
+322
+00:35:00,750 --> 00:35:07,730
+بالطابق الذئب أو ناقص واحد اللي هو المدل و تمانية
+
+323
+00:35:07,730 --> 00:35:14,330
+نجي الأمر هنا ال proof نفترض
+
+324
+00:35:14,330 --> 00:35:24,510
+الآن suppose that Q is an odd primeاللي هو الـ
+
+325
+00:35:24,510 --> 00:35:29,250
+device mean الـ NB هيكون على صورة الـ Q يعيش 2N
+
+326
+00:35:29,250 --> 00:35:43,010
+زائد 1 is a prime divisor of mean of NB فرضنا إيش
+
+327
+00:35:43,010 --> 00:35:50,860
+إحنا أنه الـ Qبتبسم صورته على 2N زائد 1 وهو الـ
+
+328
+00:35:50,860 --> 00:35:58,040
+Grand Divisor لمن؟ للـ N بيه شوف الـ N خدها
+
+329
+00:35:58,040 --> 00:36:05,680
+الأدالة اللي بديها let A بساوي 2 أُس B زائد 1 على
+
+330
+00:36:05,680 --> 00:36:10,760
+2 ربيع
+
+331
+00:36:10,760 --> 00:36:13,640
+للـ A بصير الـ A تربيع
+
+332
+00:36:16,250 --> 00:36:22,990
+الـ letter دي بيساوي اتنين أُس بي زائد واحد معايا
+
+333
+00:36:22,990 --> 00:36:30,530
+اترحلي من هنا إلى اتنين و من هنا مين اتنين واضح
+
+334
+00:36:30,530 --> 00:36:38,190
+اه؟ الان هذه بتساوي اتنين
+
+335
+00:36:38,190 --> 00:36:51,280
+خُد عامل مشترك بيصير2B-1 ويساومين
+
+336
+00:36:51,280 --> 00:37:02,240
+هي 2NB نفترض أن الـ Q بتكسب مين الـ NB إذا صارت
+
+337
+00:37:02,240 --> 00:37:10,720
+هذه أشمالها مطابق السفر Modulo مين Modulo Q من أين
+
+338
+00:37:10,720 --> 00:37:18,500
+جبتها؟اللي هو الـ Q بتكسب مين الـ N بيه إيش معناته
+
+339
+00:37:18,500 --> 00:37:26,400
+هذا؟ معناته أن A تربية تطابق 2 مضله مين؟ مضله Q صح
+
+340
+00:37:26,400 --> 00:37:34,300
+ولا لأ؟ الآن ارفعلي الجهتين للـ أُس N هذا الـ N
+
+341
+00:37:34,300 --> 00:37:47,280
+بصير A أُس 2N تطابق 2 أُس Nمدله مين؟ مدله Q واضح
+
+342
+00:37:47,280 --> 00:37:57,360
+أه؟ أي سؤال؟ طيب الآن اتنين أسن اتنين
+
+343
+00:37:57,360 --> 00:38:05,800
+ان عبارة عن الـ Q نقص واحد واضح أه؟ اتنين أن هي
+
+344
+00:38:05,800 --> 00:38:13,520
+عبارة عن الـ Q إذا اللي هذي بتصير عبارة عنA SQ-1
+
+345
+00:38:13,520 --> 00:38:22,360
+وده
+
+346
+00:38:22,360 --> 00:38:32,640
+صار عندي الـ A واضحة صار عندي الـ A SQ-1 تطابق 2N
+
+347
+00:38:32,640 --> 00:38:40,820
+Modulo EQ الآن
+
+348
+00:38:42,930 --> 00:38:47,830
+أيش العلاقة بين الـ A و بين الـ Q؟ الـ A عبارة عن
+
+349
+00:38:47,830 --> 00:38:54,670
+power of two يعني اتنين، أربعة، تمانية، ستة عشر،
+
+350
+00:38:54,670 --> 00:38:58,910
+الاخرين إذاً أكيد العامل المشترك اللي على بين الـ
+
+351
+00:38:58,910 --> 00:39:03,690
+A و بين الـ Q أيش مساعد؟ واحد إذاً بإمكانك تطبيق
+
+352
+00:39:03,690 --> 00:39:08,010
+مين في الـ Math's theorem يعني اتنين يعني ايه؟ to
+
+353
+00:39:08,010 --> 00:39:15,820
+the Q minus واحد تطابقالواحد modulo a cube by
+
+354
+00:39:15,820 --> 00:39:22,880
+Fermat's theorem من التنتين مع بعض بس يعني عندي
+
+355
+00:39:22,880 --> 00:39:29,100
+اتنين أس أن تطابق الواحد modulo معناته ان الـQ ايش
+
+356
+00:39:29,100 --> 00:39:38,580
+بتيب سن اتنين أس أن ماقص واحد طيبالـ Q بتكسب 2 أُس
+
+357
+00:39:38,580 --> 00:39:45,420
+N ناقص 1 يعني الـ Q بتكسب 2 الـ M N الـ Q بتكسب 2
+
+358
+00:39:45,420 --> 00:39:58,060
+الـ M N إذا الـ Q هتكون صورتها يا إما 1 يا إما 7
+
+359
+00:39:58,060 --> 00:40:05,700
+Modulo 8 Modulo 8
+
+360
+00:40:06,930 --> 00:40:12,490
+وانتوا بتقولوا ليش و الله يعطيكوا العافية مرة
+
+361
+00:40:12,490 --> 00:40:13,650
+أجابة نكمل ان شاء الله
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/SQIrcReoLXE_postprocess.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/SQIrcReoLXE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..43e4ad178ee2032b6fe8d88381868cc56030a8b8
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/SQIrcReoLXE_postprocess.srt
@@ -0,0 +1,1560 @@
+1
+00:00:20,280 --> 00:00:26,420
+بسم الله الرحمن الرحيم المحاضرة رقم 17 نظرية
+
+2
+00:00:26,420 --> 00:00:33,020
+الاعداد لطلبة قسم رياضيات بالجامعة الإسلامية كليتي
+
+3
+00:00:33,020 --> 00:00:38,020
+العلوم والتربية استكمالاً
+
+4
+00:00:38,020 --> 00:00:43,660
+للمحاضرة السابقة شبطة 5 Fermat's theorem بدأنا
+
+5
+00:00:43,660 --> 00:00:49,160
+نحكي عن Fermat's little theoremواليوم بدنا نكمل
+
+6
+00:00:49,160 --> 00:00:54,740
+الحديث عن Fermat's little theorem ونبدأ
+
+7
+00:00:54,740 --> 00:01:00,860
+الحديث أيضًا عن Wilson's theorem عنوانين مهمات من
+
+8
+00:01:00,860 --> 00:01:05,940
+عنوين نظرية الأعداد حكينا المرة الماضية على
+
+9
+00:01:05,940 --> 00:01:11,580
+Fermat's little theorem قلنا لو كانت عندي if B is
+
+10
+00:01:11,580 --> 00:01:21,390
+prime is a prime numberوكان عندى and B لتقسم الـ A
+
+11
+00:01:21,390 --> 00:01:28,450
+then الـ A to the B تطابق الواحد B minus واحد
+
+12
+00:01:28,450 --> 00:01:38,690
+تطابق الواحد modulo B واخدنا
+
+13
+00:01:38,690 --> 00:01:42,490
+Corollary لها هذا اللي هي Fermat's theorem او
+
+14
+00:01:42,490 --> 00:01:48,100
+little theoremوالـ Correlator اللي أخدناها المرة
+
+15
+00:01:48,100 --> 00:01:55,220
+الماضية if B is a prime بغض النظر إيش هو then
+
+16
+00:01:55,220 --> 00:02:03,700
+دائماً A to the B تطابق الـ A modulo B اليوم
+
+17
+00:02:03,700 --> 00:02:08,800
+بالنسبة لـ Fermat's theorem هناخد اللي هو دل عندنا
+
+18
+00:02:08,800 --> 00:02:15,560
+ملاحظتين الأولى عبارة عن لمّةهنذكرها ونبرهنها
+
+19
+00:02:15,560 --> 00:02:20,840
+والملاحظة الأخرى هنثبت أن الـ Converse of Fermat's
+
+20
+00:02:20,840 --> 00:02:25,700
+theorem need not to be true in general نبدأ الآن
+
+21
+00:02:25,700 --> 00:02:31,780
+في اللممة اللي هنستخدمها لإثبات أنه الـ Deep
+
+22
+00:02:31,780 --> 00:02:36,080
+counter example يدل على أن Fermat's little theorem
+
+23
+00:02:36,080 --> 00:02:39,460
+الـ Converse لها need not to be true in general
+
+24
+00:02:39,460 --> 00:02:50,990
+اللممة بتقول ما يليB and Q are distinct abrams
+
+25
+00:02:50,990 --> 00:03:04,290
+وكان عندي A to the B تطابق الـ A modulo Q and A to
+
+26
+00:03:04,290 --> 00:03:12,410
+the Q تطابق الـ A modulo B then النتيجة النهائيةإن
+
+27
+00:03:12,410 --> 00:03:20,750
+الـ A to the B فى Q تطابق الـ A modulo B فى Q
+
+28
+00:03:20,750 --> 00:03:27,150
+برهان، a proof لحظة
+
+29
+00:03:27,150 --> 00:03:31,530
+مالية الـ
+
+30
+00:03:31,530 --> 00:03:35,970
+corollary اللى عندى بتقولى إنه كانت B is a prime
+
+31
+00:03:35,970 --> 00:03:40,940
+هو A and a numberبكون الـ A to the B تطابق الـ A
+
+32
+00:03:40,940 --> 00:03:45,540
+modulo B يعني خلّينا نحكي برمز آخر عشان نعرف نطبق
+
+33
+00:03:45,540 --> 00:03:48,080
+خان ما تصيرش فيه خلق بين الـ A اللي هان والـ A
+
+34
+00:03:48,080 --> 00:03:54,580
+اللي هان عند الـ X to the B تطابق الـ X modulo مين
+
+35
+00:03:54,580 --> 00:03:58,680
+modulo B هذا اللي هي الـ Corollary اللي فوق بدي
+
+36
+00:03:58,680 --> 00:04:03,160
+استخدمها الآن بدي استخدم X في هذه الحالة اللي هي
+
+37
+00:04:03,160 --> 00:04:10,650
+عبارة عن A to the B فبصير عند الآن Ato the B الكل
+
+38
+00:04:10,650 --> 00:04:13,650
+الان الـ prime اللي بتاخده مش الـ prime B اللي هنا
+
+39
+00:04:13,650 --> 00:04:18,450
+بتاخده Q بيصير A to the B هو العدد X to the prime
+
+40
+00:04:18,450 --> 00:04:25,230
+Q يطابق العدد X هذا اللي هو A to the B مدنومياً
+
+41
+00:04:25,230 --> 00:04:28,850
+الـ prime اللي رفعته اللي في هذه الحالة الشمالها
+
+42
+00:04:28,850 --> 00:04:34,490
+الـ Q ماشي الحال هذا ضينياً by الكورولار اللي فوق
+
+43
+00:04:34,490 --> 00:04:42,050
+but butعندي الـ a to the b معطينيها تطابق الـ a
+
+44
+00:04:42,050 --> 00:04:48,150
+modulo mean q هذه الان together التنتين مع بعض
+
+45
+00:04:48,150 --> 00:04:55,450
+بخاصية التعدي بيصير عندي a to the b q تطابق ال a
+
+46
+00:04:55,450 --> 00:05:01,010
+modulo mean q اذا then بخاصية التعدي a to the b في
+
+47
+00:05:01,010 --> 00:05:09,730
+q تطابق ال a modulo qوهذا ايش بيعني هذا بيعني انه
+
+48
+00:05:09,730 --> 00:05:18,270
+انه ال Q بتجسم A to the B في Q ناقص ايش ال A،
+
+49
+00:05:18,270 --> 00:05:24,250
+مظبوط؟ هذا ايش بتعني انه ال Q بتجسم ال A to the B
+
+50
+00:05:24,250 --> 00:05:30,350
+في Q ناقص ايش ال A Similarly وفعلا Similarly اللي
+
+51
+00:05:30,350 --> 00:05:33,350
+طبقته على A to the B بيبقى طبقه على مين؟ على A to
+
+52
+00:05:33,350 --> 00:05:38,100
+the Q بس بالنسبة ل Bالآن من الـ Corollary هذه برضه
+
+53
+00:05:38,100 --> 00:05:44,200
+شيء من X حُك مكانها إيه شمالها A to the Q to the
+
+54
+00:05:44,200 --> 00:05:48,220
+mean to the B تطابق الـ X اللي هي من الـ X اللي
+
+55
+00:05:48,220 --> 00:05:55,300
+أخدتها ASQ مدلوا الـ mean مدلوا الـ B إذاً By ال
+
+56
+00:05:55,300 --> 00:05:58,640
+Corollary اللي حكينا عنها المرة الماضية But بنفس
+
+57
+00:05:58,640 --> 00:05:59,480
+الأسلوب
+
+58
+00:06:25,960 --> 00:06:27,360
+AQAB�
+
+59
+00:06:27,620 --> 00:06:32,600
+بقى بي تقسم هذا المقدار و كيو تقسم هذا المقدار لكن
+
+60
+00:06:32,600 --> 00:06:37,020
+كيو عبارة عن إبراهيم كتلة واحدة مختلفة عن بي
+
+61
+00:06:37,020 --> 00:06:41,580
+لإبراهيم الكتلة الواحدة إذا كيو جزء من هذه و بي
+
+62
+00:06:41,580 --> 00:06:48,860
+جزء من هذه إذا أكيد بي في كيو أشمالهب في q يطابق
+
+63
+00:06:48,860 --> 00:06:54,100
+ال a to the b في q ناقص a لإن ال b و ال q are
+
+64
+00:06:54,100 --> 00:07:01,040
+distinct abrahams إذا صار عندي that is ال هو a to
+
+65
+00:07:01,040 --> 00:07:10,280
+the b في q تطابق ال a modulo b في q وهو المقلوب أي
+
+66
+00:07:10,280 --> 00:07:16,820
+سؤاللأن الـ remark الأخيرة في هذا الـ section الـ
+
+67
+00:07:16,820 --> 00:07:24,700
+remark منقول the converse of
+
+68
+00:07:24,700 --> 00:07:35,140
+Fermat's little theorem need not be a true أو is
+
+69
+00:07:35,140 --> 00:07:46,300
+not a true in generalماشي الحال is not true in
+
+70
+00:07:46,300 --> 00:07:51,960
+general is not true in general ماشي الحال الآن
+
+71
+00:07:51,960 --> 00:07:55,420
+عشان النظرية تكون ال conference تكون عليه صحيح
+
+72
+00:07:55,420 --> 00:08:01,220
+لازم يكون صحيح دائما لو جبنا بس counter example
+
+73
+00:08:01,220 --> 00:08:06,340
+واحد انه بيخلل النظرية معناته النظرية is not true
+
+74
+00:08:06,340 --> 00:08:12,860
+عشان هيك بنقولاللي هو if a to the b minus 1 تطابق
+
+75
+00:08:12,860 --> 00:08:17,580
+الواحد مضله b then b لا تقسم ال a and b is a prime
+
+76
+00:08:17,580 --> 00:08:23,280
+هذا need not to be true in general او is not a
+
+77
+00:08:23,280 --> 00:08:28,120
+true theorem is not true as a theorem ماذا بقولنا
+
+78
+00:08:28,120 --> 00:08:32,260
+is not true as a theorem اذا we have a
+
+79
+00:08:32,260 --> 00:08:38,020
+counterexample that make the theorem failواضح أه
+
+80
+00:08:38,020 --> 00:08:43,160
+نيجي الأن نشوف how that makes the theorem fail
+
+81
+00:08:43,160 --> 00:08:49,360
+الأن نيجي ناخد إيش اللي هي ال conversة والاشي ال
+
+82
+00:08:49,360 --> 00:08:55,440
+conversة إيش ال conversة بالنظرية if a to the b
+
+83
+00:08:55,440 --> 00:09:03,900
+minus واحد تطابق الواحد modulo b then اللي هو b is
+
+84
+00:09:03,900 --> 00:09:13,360
+primeوالـ B لا تقسم الـ A. الآن، لكي أثبت أن هذه
+
+85
+00:09:13,360 --> 00:09:19,660
+النظرية ليست صحيحة أو ليست نظرية أو ليست نظرية أو
+
+86
+00:09:19,660 --> 00:09:20,320
+ليست نظرية أو ليست نظرية أو ليست نظرية أو ليست
+
+87
+00:09:20,320 --> 00:09:20,340
+نظرية أو ليست نظرية أو ليست نظرية أو ليست نظرية أو
+
+88
+00:09:20,340 --> 00:09:20,520
+ليست نظرية أو ليست نظرية أو ليست نظرية أو ليست
+
+89
+00:09:20,520 --> 00:09:20,780
+نظرية أو ليست نظرية أو ليست نظرية أو ليست نظرية أو
+
+90
+00:09:20,780 --> 00:09:25,160
+ليست نظرية أو ليست نظرية أو ليست نظرية أو ليست
+
+91
+00:09:25,160 --> 00:09:25,800
+نظرية
+
+92
+00:09:38,610 --> 00:09:46,210
+الـ B-1 يُطابق الواحد مُدُلُ B والـ B مش برايم هذا
+
+93
+00:09:46,210 --> 00:09:50,170
+يتحقق لكن الـ B أشمالها is not a prime خلّيني نشوف
+
+94
+00:09:50,170 --> 00:09:53,690
+هستخدم اللمّة طبعاً في الإثبات شوف عندي
+
+95
+00:10:10,410 --> 00:10:16,490
+example we show
+
+96
+00:10:16,490 --> 00:10:24,910
+that اتنين تتلاتمية و اربعين تطابق الواحد modulo
+
+97
+00:10:24,910 --> 00:10:29,210
+تلاتة اربعة واحد but
+
+98
+00:10:30,670 --> 00:10:41,710
+it is clear that 341 بساوي 31 في 11 is composite
+
+99
+00:10:41,710 --> 00:10:44,750
+إذن الـ Converse أشمالها لو أتبعتنا هذا الـ
+
+100
+00:10:44,750 --> 00:10:51,210
+Converse معناته أشمالها is not true شوفوا صلى الله
+
+101
+00:10:51,210 --> 00:10:55,910
+عليه الصلاة والسلام الآن عندي اللي هي 31 وعندي 112
+
+102
+00:10:55,910 --> 00:11:10,380
+اللي بيوصلكم إياهبدا أثبت لكم أن 2 أس 31 تطابق 2
+
+103
+00:11:10,380 --> 00:11:14,180
+مدلو الـ 11 هذا اللي بدا أثبته للوصول للنظرية
+
+104
+00:11:14,180 --> 00:11:24,720
+للمثال و بدا أثبتلك 2 أس 11 تطابق 2 مدلو الـ 31
+
+105
+00:11:24,720 --> 00:11:31,970
+ماشي الحال إذا أثبتت هيكإذا أثبتت هذا الكلام ..
+
+106
+00:11:31,970 --> 00:11:37,750
+إذا أثبتت هذا بيصير عندي إيش حسب النظرية؟ بيصير
+
+107
+00:11:37,750 --> 00:11:50,590
+عندي 2 أصف B في Q اللي هو 31 في 11 أطابق 2 modulo
+
+108
+00:11:50,590 --> 00:11:59,260
+من 3 أربعة واحدة من 11 في 31الآن لو أثبتت هذا و
+
+109
+00:11:59,260 --> 00:12:03,760
+أثبتت هذا إذا بقى اللي لمّا اللي فوق هذه صحيحة طيب
+
+110
+00:12:03,760 --> 00:12:07,560
+هذه صحيحة إيش معناة هذا صار؟ صار معناة هذا اللي هو
+
+111
+00:12:07,560 --> 00:12:12,180
+ده تلاتمية و واحد و أربعين مظبوط الان الاتنين و
+
+112
+00:12:12,180 --> 00:12:14,880
+التلاتمية و واحد و أربعين relatively prime إذا
+
+113
+00:12:14,880 --> 00:12:18,520
+بقدر أكسب الجهتين على مين؟ على اتنين و بحصل على
+
+114
+00:12:18,520 --> 00:12:22,780
+اتنين أس تلاتمية و أربعين تطابق الواحد مدون و جداش
+
+115
+00:12:22,780 --> 00:12:28,420
+تلاتة أربعة واحدبكون حصلت على مثالي إذا إيش اللي
+
+116
+00:12:28,420 --> 00:12:33,860
+ضال علي أثبت بس بدأ أثبت 2 اص 31 طبق 2 ودول 11 و2
+
+117
+00:12:33,860 --> 00:12:39,000
+اص 11 طبق 2 ودول ومين 31 سهل ان شاء الله شوفوا كيف
+
+118
+00:12:39,000 --> 00:12:48,600
+الآن عندي هذا prime وهذا 2 لا تقسم ل 11 إذا حسب
+
+119
+00:12:48,600 --> 00:12:53,240
+النظرية اللي أخدناها ال affirmation theorem بكون 2
+
+120
+00:12:53,240 --> 00:13:01,630
+اص 10تطابق الواحد مدله كم؟ من أين هذا؟ By Fermat's
+
+121
+00:13:01,630 --> 00:13:05,270
+little theorem اتنين أس بي مايلوس واحد تطابق
+
+122
+00:13:05,270 --> 00:13:12,780
+الواحد مدله مين؟ مدله ماعنى محمودالان ارفع الجهة
+
+123
+00:13:12,780 --> 00:13:16,900
+تانى مين بدي اقصها اللى 31 ارفع اللى اللى هو ايش
+
+124
+00:13:16,900 --> 00:13:21,260
+اش ثلاثة فبصير عندى هذه اقص ثلاثة وهذه اقص ثلاثة
+
+125
+00:13:21,260 --> 00:13:26,580
+اللى واحد وضرب الجهة تانى في ايش فبصير اتنين معايا
+
+126
+00:13:26,580 --> 00:13:30,320
+يا شباب اتنين plus واحد و تلاتين تطابق اتنين
+
+127
+00:13:30,320 --> 00:13:36,660
+modulo 11 وبهك انا كنت انهيت اللى هى اثبات الاولى
+
+128
+00:13:36,660 --> 00:13:39,440
+اتنين plus واحد و تلاتين تطابق اتنين modulo 11 نجي
+
+129
+00:13:39,440 --> 00:13:44,440
+للتانيةالتانية الـ 11 طبعاً أشماله بعيد كثير عن
+
+130
+00:13:44,440 --> 00:13:47,820
+الـ 31 فبنفعش أستخدم ال firm as little theorem
+
+131
+00:13:47,820 --> 00:13:51,500
+لأنه بتعطيك 2 نقص 30 تطابق ال 1 مدرومين مدروا 31
+
+132
+00:13:51,500 --> 00:13:57,560
+فالآن بدنا نعمل الحسبة و الحسبة بتغلبش مين المرفق
+
+133
+00:13:57,560 --> 00:14:04,500
+ال 2 القوات اللي هي أشدريت من ال 31؟ ال 2 نقص 5 ال
+
+134
+00:14:04,500 --> 00:14:10,880
+2 نقص 5 32 فالآن ال 2 نقص 5التي هي الـ 32 أكيد ايش
+
+135
+00:14:10,880 --> 00:14:17,260
+بتساوي بالنسبة للـ 31؟ 1 modulo ارفع
+
+136
+00:14:17,260 --> 00:14:20,280
+التانية الأعلى اللي هو عياش 2 هذه حسابات طبعا
+
+137
+00:14:20,280 --> 00:14:26,550
+بيصير 2 أس عشرةتطابق الواحد مدله واحد و تلاتين
+
+138
+00:14:26,550 --> 00:14:29,590
+اضرب الجهتين في ايش في اتنين فبتصير اتنين اصحى
+
+139
+00:14:29,590 --> 00:14:34,610
+احداش تطابق اتنين مدله واحد و تلاتين هي عندي هذه و
+
+140
+00:14:34,610 --> 00:14:37,690
+هي عندي هذه اذا حصلت على التنتين هذوله اذا صار
+
+141
+00:14:37,690 --> 00:14:41,070
+عندي هذوله صحيحه و هذه صحيحه اذا صار عندي the
+
+142
+00:14:41,070 --> 00:14:44,390
+converse of Fermat's theorem need not to be true
+
+143
+00:14:44,390 --> 00:14:51,130
+in general اي سؤال مجلب على
+
+144
+00:14:54,830 --> 00:14:58,970
+اللي هو الجزء الثاني من المحاضرة اللي هو Wilson's
+
+145
+00:14:58,970 --> 00:15:04,090
+theorem بقى فوق يا أبو سيم شوية Wilson's theorem
+
+146
+00:15:04,090 --> 00:15:09,790
+الان Wilson's theorem برضه عنوان أو إعلان مهم
+
+147
+00:15:09,790 --> 00:15:19,470
+عندنا في نظرية الإعداد Wilson's
+
+148
+00:15:19,470 --> 00:15:24,230
+theorem إيش بتقول؟و برضه هنشوف ان الـ converse
+
+149
+00:15:24,230 --> 00:15:30,170
+إلها true ولا is not true سلام على النبي عليه
+
+150
+00:15:30,170 --> 00:15:33,810
+الصلاة والسلام سلام على السيد محمد الآن ويلسونز
+
+151
+00:15:33,810 --> 00:15:37,230
+theorem ويلسونز
+
+152
+00:15:37,230 --> 00:15:45,610
+theorem ويلسونز theorem بتقول كمالي if B is prime
+
+153
+00:15:45,610 --> 00:15:48,790
+then
+
+154
+00:15:51,310 --> 00:16:11,970
+اللي هو B-1! تطابق ناقص واحد مودولو B أبروف الـ
+
+155
+00:16:11,970 --> 00:16:18,770
+Winsor's theorem بتقول if B is a primethen B-1!
+
+156
+00:16:19,230 --> 00:16:27,950
+تطابق نقص واحد مدلبي في جسر للبرهان الجسر هذا هو
+
+157
+00:16:27,950 --> 00:16:35,250
+الست التالية S بتساوي واحد و اتنين و تلاتة لما اصل
+
+158
+00:16:35,250 --> 00:16:40,190
+عند ال B-1 اول ملاحظة احنا عارفين ان هذا عبارة عن
+
+159
+00:16:40,190 --> 00:16:44,350
+complete residue system بس خاص اسمين الصفر يعني
+
+160
+00:16:44,350 --> 00:16:51,920
+الآن اللي هو الصفروالمضاعفات الـ B مش ممثلة هان
+
+161
+00:16:51,920 --> 00:16:56,640
+يعني لإنه مين اللي بتقن الـ B هان الـ 0 والـ B و2B
+
+162
+00:16:56,640 --> 00:17:00,900
+و3B و4B و-B و-2B و-3B إذا كل هذا ال branch غير
+
+163
+00:17:00,900 --> 00:17:05,540
+ممثل في اللي عندي اللي هو الـ 6 هذا يعني هذا
+
+164
+00:17:05,540 --> 00:17:10,200
+complete residue system بس خاصة من اللي هو السفر
+
+165
+00:17:11,750 --> 00:17:14,570
+هذه ملاحظة على الجهة اللي هنقش علاقة هذه في
+
+166
+00:17:14,570 --> 00:17:19,590
+موضوعنا في B-1 factorial اللي بيدثبتلك إياه اللي
+
+167
+00:17:19,590 --> 00:17:27,830
+بيدثبتلك أروح أثباته بدي أقولك إن الواحد والتنين
+
+168
+00:17:27,830 --> 00:17:38,710
+تلاتة B-2 في B-1 هذه إيش بتمثلنا الـB-1 factorial
+
+169
+00:17:38,710 --> 00:17:44,460
+اللي بيدثبتلك إياهبتثبت لك إنه هذولة طبعاً اللي هي
+
+170
+00:17:44,460 --> 00:17:49,800
+من اتنين لعند الـ B minus اتنين بيثبت لك إنه كل
+
+171
+00:17:49,800 --> 00:17:53,640
+واحد في .. في .. في الواحد .. كل واحد هنا في
+
+172
+00:17:53,640 --> 00:18:01,000
+الواحد مختلف عنه جواته لو ضربنا فيه هيطلع يطابق
+
+173
+00:18:01,000 --> 00:18:07,010
+الواحد مدلبييعني بمعنى آخر صار إن كل هذه اللي حاصل
+
+174
+00:18:07,010 --> 00:18:08,150
+ضربه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+175
+00:18:08,150 --> 00:18:09,370
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+176
+00:18:09,370 --> 00:18:12,250
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+177
+00:18:12,250 --> 00:18:12,310
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+178
+00:18:12,310 --> 00:18:12,530
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+179
+00:18:12,530 --> 00:18:18,370
+إيه إيه إيه إيه إيه إيه
+
+180
+00:18:18,370 --> 00:18:23,530
+إيه
+
+181
+00:18:23,530 --> 00:18:29,810
+إيه
+
+182
+00:18:29,810 --> 00:18:40,450
+إالتفاصيل هتمر عبر أمرين هتبتلك أن الـ A الان
+
+183
+00:18:40,450 --> 00:18:45,650
+تفاصيل البرهان برضه فيه لها sketch هتبتلك شغلتين
+
+184
+00:18:45,650 --> 00:18:50,350
+بالنسبة للـ S ركز معايا هتبتلك أن الـ A لكل A في
+
+185
+00:18:50,350 --> 00:18:55,730
+الـ S بلاقي A' في الـ S بحيث أن A في A' تطابق
+
+186
+00:18:55,730 --> 00:19:02,990
+الواحد مدنومين مدنومين هذه أول حاجة اتنينهأثبت لك
+
+187
+00:19:02,990 --> 00:19:10,290
+إن الـ A هذه هتساوي الـ A' if and only if اللي هو
+
+188
+00:19:10,290 --> 00:19:15,570
+الـ A بتساوي واحد or الـ A بتساوي ايش بي ماينس
+
+189
+00:19:15,570 --> 00:19:16,050
+واحد
+
+190
+00:19:18,840 --> 00:19:26,500
+تعني إن الـ 1 و الـ B-1 خلّين على جهة و اتطلعلي
+
+191
+00:19:26,500 --> 00:19:30,320
+على هذولة هذولة بناءً على هذا الحديث وبناءً على
+
+192
+00:19:30,320 --> 00:19:35,280
+هذا الحديث هيثير إن كل واحد في إيه الواحد هو مختلف
+
+193
+00:19:35,280 --> 00:19:39,400
+عنه لإن هذولة متساويات بس في حالة مين الـ 1 و الـ
+
+194
+00:19:39,400 --> 00:19:45,180
+B-1 كل واحد غير الواحد و غير الـ B-1 من هذولة
+
+195
+00:19:45,180 --> 00:19:51,390
+هتلاقي في element جوالو ضربت فيه هيطابق للواحد
+
+196
+00:19:51,390 --> 00:19:55,970
+مدله B معناته ان حاصل ضرب هذين كلهم بطابق الواحد
+
+197
+00:19:55,970 --> 00:19:59,650
+وفي عند الواحد مضروب فيهم وفي عند ال B ماينس واحد
+
+198
+00:19:59,650 --> 00:20:02,990
+مضروب فيهم يعني هذا كله هيطابق ال B ماينس واحد
+
+199
+00:20:02,990 --> 00:20:06,950
+وهذا هيطابق الناقص واحد مدله B واضح يا محمد اه؟
+
+200
+00:20:06,950 --> 00:20:09,510
+طيب نيجي الآن للتفاصيل
+
+201
+00:20:17,630 --> 00:20:20,870
+الشيء الأسف عندي 1 و 2 و 3 أو B- 1 consider this
+
+202
+00:20:20,870 --> 00:20:30,710
+set لو جيت أخدت أي A في الاس أكيد
+
+203
+00:20:30,710 --> 00:20:36,770
+مدام أخدت ال A في الاس صارت ال A 1 2 3 أو B- 1 إذن
+
+204
+00:20:36,770 --> 00:20:40,110
+أكيد ال greatest common divisor بين ال A و ال
+
+205
+00:20:40,110 --> 00:20:46,350
+prime B إيش هيساويماش؟ لأن بي براين كتلة واحدة و
+
+206
+00:20:46,350 --> 00:20:52,630
+أصغر من الـ B يعني مش سهل يكون لا اتنين ولا واحد
+
+207
+00:20:52,630 --> 00:20:55,610
+ولا اتنين ولا تلاتة ولا بي ماينوس إذا الـ greatest
+
+208
+00:20:55,610 --> 00:20:58,410
+common divisor بين الـ A و الـ B إيش هيساوي؟
+
+209
+00:20:58,410 --> 00:21:03,830
+هيساوي واحد، هذا أول حاجة بناء على هيك أكيد أكيد
+
+210
+00:21:03,830 --> 00:21:10,890
+ذم المتطابقة الـ X تطابق الواحد modulo B has a
+
+211
+00:21:10,890 --> 00:21:17,470
+unique solutionالنظرية أن لو كانت العاملة مشتركة
+
+212
+00:21:17,470 --> 00:21:21,510
+على بين الـA والـB بيساوي واحد معناته الـX وطابق
+
+213
+00:21:21,510 --> 00:21:25,850
+الواحد مضلوا بيه أشمالها has a unique solution if
+
+214
+00:21:25,850 --> 00:21:32,710
+and then there exists T element in Z such that T
+
+215
+00:21:32,710 --> 00:21:39,510
+أو A في T يطابق الواحد مضلوا مين يا جماعة؟ مضلوا
+
+216
+00:21:39,510 --> 00:21:47,150
+بيه وهذا is unique مضلوا بيهطيب، ركز في اللي بحكيه
+
+217
+00:21:47,150 --> 00:21:53,610
+الـ P هذا unique ودون الـ B الـ P هذا مستحيل يكون
+
+218
+00:21:53,610 --> 00:22:00,190
+السفر أو ما يطابق السفر، ليش؟ لأن لو كان السفر،
+
+219
+00:22:00,190 --> 00:22:03,330
+معناته الـ B بدا تكسب الواحد contradiction لأن الـ
+
+220
+00:22:03,330 --> 00:22:08,970
+B is prime ولو كانت من المضعفة اللي هو بطابق السفر
+
+221
+00:22:08,970 --> 00:22:15,550
+برضه هيصير اللي هو ده سفر يطابق الواحدإذن يستحيل
+
+222
+00:22:15,550 --> 00:22:20,230
+يكون الـ T إيش ماله الصفر أو ما يطابقه إذا الـ T
+
+223
+00:22:20,230 --> 00:22:24,470
+مدام مش صفر إذا أكيد هيجيله واحد هانا إيش ماله
+
+224
+00:22:24,470 --> 00:22:29,020
+بطابقهما دام الـ T مش هو السفر ولا من المضاعفات
+
+225
+00:22:29,020 --> 00:22:33,560
+الـ B إذن أكيد هنلاجيلنا 1 في الـ S element في الـ
+
+226
+00:22:33,560 --> 00:22:37,960
+S يطابق من الـ T بمعنى آخر there exists A prime
+
+227
+00:22:37,960 --> 00:22:44,100
+element in S such that ان A في الـ A prime هتطابق
+
+228
+00:22:44,100 --> 00:22:54,680
+الواحد modulo من modulo B إذن صار الآن عندي
+
+229
+00:22:56,610 --> 00:23:00,050
+كل element في الـ S بالنظيره element في الـ S
+
+230
+00:23:00,050 --> 00:23:06,970
+يطابقه مدلبي الآن الخوف عشان أعرف أحسب بدي أشوف
+
+231
+00:23:06,970 --> 00:23:14,030
+مين اللي من ال elements هدولة الـ A هو الـ A' وإن
+
+232
+00:23:14,030 --> 00:23:19,690
+في حد إنه مش الـ A' ولا لأأيش اللي هيوصلني لهذه
+
+233
+00:23:19,690 --> 00:23:25,530
+النتيجة أنه الآن a بتساوي a prime if and only if a
+
+234
+00:23:25,530 --> 00:23:31,150
+بتساوي واحد or a بتساوي b minus واحد هذا الآن
+
+235
+00:23:31,150 --> 00:23:38,410
+الإدعاء بدي أثبته ماشي الحال عشان أثبته بدي أقول
+
+236
+00:23:38,410 --> 00:23:45,590
+أخده الطرف الأول بدي أقول suppose that ال a بتساوي
+
+237
+00:23:45,590 --> 00:23:52,380
+a primeما دام الـ A بتساوي البرامج A' إذا حيصير
+
+238
+00:23:52,380 --> 00:23:56,080
+حاصل ضرب ينقش معانا واحد يعني بمعنى آخر هيكي يحصل
+
+239
+00:23:56,080 --> 00:24:02,580
+عندي A تربيع تطابق الواحد مضله مين؟ مضله B، مظبوط؟
+
+240
+00:24:02,580 --> 00:24:05,540
+لأن الـ A هو الـ A'
+
+241
+00:24:08,480 --> 00:24:11,920
+الـ A اللي في الـ S الـ A اللي في الـ S ماشي
+
+242
+00:24:11,920 --> 00:24:15,200
+الحالة A تربيع تطابق الواحد مضلوا مين؟ مضلوا B
+
+243
+00:24:15,200 --> 00:24:20,480
+وإيش هذا معنى؟ then B تجسم الـ A تربيع ماقص واحد
+
+244
+00:24:20,480 --> 00:24:25,900
+الـ A تربيع ماقص واحد هذه مين؟ هي A ماقص واحد في A
+
+245
+00:24:25,900 --> 00:24:30,840
+زايد واحد الان B prime يعني يا بي بيجسم الأول يا
+
+246
+00:24:30,840 --> 00:24:37,850
+بيجسم إيش التاني إذا thenB بكسيم الـ A-1 أو B
+
+247
+00:24:37,850 --> 00:24:46,330
+بكسيم 2 الـ A زائد 1إذا B تكسب الـ A-1 معناته الـ
+
+248
+00:24:46,330 --> 00:24:51,690
+A تطابق الواحد مضله مين؟ مضله B وإذا الـ A الـ B
+
+249
+00:24:51,690 --> 00:24:56,250
+تكسب الـ A زاد واحد معناته أن الـ A تطابق السالب
+
+250
+00:24:56,250 --> 00:25:01,450
+واحد مضله مين؟ مضله B تنسوش يا جماعة أن الـ A
+
+251
+00:25:01,450 --> 00:25:05,830
+تبعتي هذه من وين جيبها أنا؟ من الـ S مين اللي في
+
+252
+00:25:05,830 --> 00:25:11,600
+الـ S اللي بتطابق الواحد؟ طبعاً مين؟ الواحدمظبوط؟
+
+253
+00:25:11,600 --> 00:25:15,380
+إذاً الـ A هذه بما إنه A في الـ S and A تطابق
+
+254
+00:25:15,380 --> 00:25:24,340
+الواحد إذاً الـ A لازم تساوي الواحد or الآن
+
+255
+00:25:24,340 --> 00:25:29,440
+A في الـ S والـ A بتطابق مين؟ سالب واحد مين إنهان
+
+256
+00:25:29,440 --> 00:25:34,200
+اللي بتطابق سالب واحد؟ B minus واحد إذاً صار عندي
+
+257
+00:25:34,200 --> 00:25:40,040
+A بتساوي B minus واحد إذاً اللي أثبته أثبتت إنه لو
+
+258
+00:25:40,770 --> 00:25:45,910
+اللي هي A بتساوي الـ A' هيعطيلي الـ A بتساوي واحد
+
+259
+00:25:45,910 --> 00:25:48,610
+أو الـ A بتساوي B- واحد الآن إيش بده أعمل
+
+260
+00:25:48,610 --> 00:25:54,790
+Conversely بده أثبت الـ Converse الآن Conversely
+
+261
+00:25:54,790 --> 00:26:00,890
+بده أمسح هذا بعد أذنكم Conversely
+
+262
+00:26:00,890 --> 00:26:04,650
+Conversely
+
+263
+00:26:04,650 --> 00:26:15,120
+let A بتساوي واحدR A بيتساوي ايش؟ B-1 وبدي اتبعك
+
+264
+00:26:15,120 --> 00:26:19,100
+ان في حالة A بيتساوي 1 الـ A هتساوي A' والـ A
+
+265
+00:26:19,100 --> 00:26:24,440
+بتساوي B-1 برضه الـ A هتساوي A' لان بما ان A
+
+266
+00:26:24,440 --> 00:26:29,120
+بيتساوي 1 اذا من هذه اللي اثبتناها اذا حيصير عندي
+
+267
+00:26:29,120 --> 00:26:33,400
+A' تطابق الواحد عوضت يا شباب
+
+268
+00:26:36,180 --> 00:26:39,880
+الـ A' أصلا من الـ S زي اللي حكينا قبله شوية إذا
+
+269
+00:26:39,880 --> 00:26:45,940
+الـ A' إيش هتساوي؟ then الـ A' بتساوي 1 يعني A
+
+270
+00:26:45,940 --> 00:26:50,800
+بتساوي 1 و A' بتساوي 1 إيش معناته؟ then A بتساوي
+
+271
+00:26:50,800 --> 00:26:54,940
+A' in this case في ال case التاني إيه بتساوي إيش؟
+
+272
+00:26:54,940 --> 00:27:03,790
+B-1 بصير عنديب-1 في الـ A' تطابق الواحد modulo
+
+273
+00:27:03,790 --> 00:27:09,290
+مين؟ modulo B لكن أنا بعرف الـ B-1 إيش هي السلب
+
+274
+00:27:09,290 --> 00:27:13,930
+واحد ده سهل على حالي الـ B-1 مين هي؟ modulo B
+
+275
+00:27:13,930 --> 00:27:17,830
+فاهمين عليها عشان أحللوا التطابقة أو التطابقة إذا
+
+276
+00:27:17,830 --> 00:27:22,330
+عندي هذا تطابق ناقص واحد modulo B إذا صار عندي
+
+277
+00:27:22,330 --> 00:27:29,520
+then اللي هو ناقص A' يطابق الواحد modulo Bومنها
+
+278
+00:27:29,520 --> 00:27:33,580
+إيش مدام أناقص A بضرب الجهد إتنين في مين؟ في سالب
+
+279
+00:27:33,580 --> 00:27:38,780
+فبصير A' تطابق مين؟ سالب واحد والسالب واحد بطابق
+
+280
+00:27:38,780 --> 00:27:48,740
+مين هنا؟ B-1 لأنه الـA' جواته بيساوي B-1 A بيساوي
+
+281
+00:27:48,740 --> 00:27:54,920
+B-1 وA' بيساوي B-1 إذن برضه الـA بيساوي إيش؟ A'
+
+282
+00:27:55,080 --> 00:28:03,020
+إذن الآنبكون ايش اللي عملته اثبتت الأمرين الأمر
+
+283
+00:28:03,020 --> 00:28:07,400
+الأول ان a a prime تطابق الواحد مدل بيه و ال a
+
+284
+00:28:07,400 --> 00:28:10,380
+بيساوي a prime اف اندول اف a بيساوي واحد او بي
+
+285
+00:28:10,380 --> 00:28:19,780
+ماينس واحد و من ثم بكون a g تضمنت ان العناصر اللي
+
+286
+00:28:19,780 --> 00:28:25,950
+هي من اتنين لعند ال b ماينس اتنينهذه العناصر تحدث
+
+287
+00:28:25,950 --> 00:28:34,050
+أزواجا يعني بمعنى آخر حاصل ضرب كل هذولة 2 في 3 لما
+
+288
+00:28:34,050 --> 00:28:40,590
+أصل لـ B-2 تفادنا أنه حسب الاتنتين هذولة أنه لكل
+
+289
+00:28:40,590 --> 00:28:45,770
+واحد هنا في واحد جوا مختلف عنه حاصل ضرب إياشوا إذا
+
+290
+00:28:45,770 --> 00:28:52,840
+هذولة بطابق الواحد مضلهبالضبط أضرب الطرفين في مين؟
+
+291
+00:28:52,840 --> 00:29:00,560
+في B-1 أضرب الطرفين في B-1 فهذا بيصير B-1 هذا مين
+
+292
+00:29:00,560 --> 00:29:08,040
+هو؟ عبارة عن B-1 فكتوريال والـ B-1 أيش بالطبق؟
+
+293
+00:29:08,040 --> 00:29:14,730
+سالب واحد موضوله Bوكون هيك احنا أثبتنا ويلسون's
+
+294
+00:29:14,730 --> 00:29:18,810
+theorem اللي دي الآن اللي هو the converse of
+
+295
+00:29:18,810 --> 00:29:26,510
+Wilson's theorem is true أثبتنا احنا قولنا
+
+296
+00:29:26,510 --> 00:29:30,470
+Fermat's theorem little theorem أثبتناها ومن ثم
+
+297
+00:29:30,470 --> 00:29:35,870
+روحنا و أثبتنا أنه the converse of Fermat's little
+
+298
+00:29:35,870 --> 00:29:39,390
+theorem need not to be true بينما الآن ويلسون's
+
+299
+00:29:39,390 --> 00:29:46,840
+theorem صحيحةوعكسها أيضًا أيش صحيح طيب نشوف الآن
+
+300
+00:29:46,840 --> 00:29:56,500
+كده بدنا نثبت the converse of Wilson's theorem the
+
+301
+00:29:56,500 --> 00:29:56,600
+converse
+
+302
+00:30:16,140 --> 00:30:24,040
+of wilson's theorem
+
+303
+00:30:24,040 --> 00:30:34,400
+الـ converse منها تنجلون إيا f b-1 factorial أو زي
+
+304
+00:30:34,400 --> 00:30:40,090
+ما هو كاتبهان ناقص واحد فكتوريال تطابق ناقص واحد
+
+305
+00:30:40,090 --> 00:30:53,590
+modulo n then n is prime proof من
+
+306
+00:30:53,590 --> 00:30:57,990
+الهنشرة البسيطة الـ Converse of Wilson's theorem
+
+307
+00:30:57,990 --> 00:31:02,050
+if n ناقص واحد فكتوريال تطابق ناقص واحد modulo n
+
+308
+00:31:02,050 --> 00:31:10,660
+then n is prime أيش بيبقى بيقولبدي اقول let N ناقص
+
+309
+00:31:10,660 --> 00:31:18,420
+واحد factorial تطابق ناقص واحد modulo N الان بدي
+
+310
+00:31:18,420 --> 00:31:23,520
+افرضلك ان N is not a prime و اسألك contradiction
+
+311
+00:31:23,520 --> 00:31:37,010
+suppose suppose that N is not a primeماذا يعني انه
+
+312
+00:31:37,010 --> 00:31:43,330
+ليس الـPrime؟ يعني انه مرتبط. لذلك بالتأكيد يوجد
+
+313
+00:31:43,330 --> 00:31:47,730
+دي بتقسم الان يعني يوجد دي اشماله بيقسم الان ومش
+
+314
+00:31:47,730 --> 00:31:51,990
+هيك كمان و الدي هذا اكبر من واحد و اصغر من مين من
+
+315
+00:31:51,990 --> 00:31:54,530
+انا عشان يكون مرتبط عشان يصير ان حاصل ضرب ايش
+
+316
+00:31:54,530 --> 00:32:00,530
+عددين ولا واحد منه واحد ولا واحد منه ان معايا؟ طيب
+
+317
+00:32:00,530 --> 00:32:03,690
+الان
+
+318
+00:32:03,690 --> 00:32:11,050
+الدي اللي عندي هذهيا تنين يا تلاتة لما أصل عند مين
+
+319
+00:32:11,050 --> 00:32:17,070
+الناقص واحد إذا أكيد ال D هذه بتنتمي التنين
+
+320
+00:32:17,070 --> 00:32:21,810
+للتلاتة اللي عند ال D ناقص واحد أسف ال N ناقص واحد
+
+321
+00:32:21,810 --> 00:32:29,010
+صح ولا لا أكيد إذا أكيد بناء على هذا الحديث then
+
+322
+00:32:29,010 --> 00:32:38,050
+ال D بتجسم 2 في 3 في N ناقص واحدالواحد منهم مظبوط
+
+323
+00:32:38,050 --> 00:32:47,150
+ولا لا اذا الان ال D بتجسم من الناقص واحد
+
+324
+00:32:47,150 --> 00:32:58,030
+factorial اي
+
+325
+00:32:58,030 --> 00:33:00,990
+سؤال طيب
+
+326
+00:33:01,750 --> 00:33:05,830
+خلّي هذه في الذاكرة إذا صار عندي D بيقسم N ناقص
+
+327
+00:33:05,830 --> 00:33:12,550
+واحد factorial ودحت الصورة بتصور الان من هذه من
+
+328
+00:33:12,550 --> 00:33:24,410
+هذه عندي N by star given عندي ال N هتقسم N ناقص
+
+329
+00:33:24,410 --> 00:33:31,480
+واحد factorial زاداش واحد صح ولا لأ؟الـ N والـ D
+
+330
+00:33:31,480 --> 00:33:39,340
+بتجسم مين؟ But D بتجسم الـ N ثم التنتين مع بعض الـ
+
+331
+00:33:39,340 --> 00:33:46,940
+D تجسم N نقص واحد فيكتوريال زائد واحد إذا صار عندي
+
+332
+00:33:46,940 --> 00:33:51,760
+أيضا الـ D تجسم الـ N نقص واحد فيكتوريال زائد واحد
+
+333
+00:33:51,760 --> 00:33:55,380
+together الـ D بتجسم أي linear combination بينين؟
+
+334
+00:33:55,380 --> 00:34:01,710
+الـ D بتجسم هذه و الـ D بتجسم هذه إذا henceدى
+
+335
+00:34:01,710 --> 00:34:08,070
+بتجسم اناقص واحد factorial زي واحد ناقص دى اناقص
+
+336
+00:34:08,070 --> 00:34:15,790
+واحد factorial يعني هذا معناته ان دى تجسم الواحد
+
+337
+00:34:15,790 --> 00:34:21,370
+contradiction لان دى بتجسم الواحد معناته ايه اش دى
+
+338
+00:34:21,370 --> 00:34:28,200
+واحد اه و دى strictly اكبر من مين من واحدTherefore
+
+339
+00:34:28,200 --> 00:34:32,480
+Therefore Therefore اللي هو our assumption أن N is
+
+340
+00:34:32,480 --> 00:34:36,180
+not prime is not true يعني بمعنى أخر هذا بطابق هذا
+
+341
+00:34:36,180 --> 00:34:46,940
+يؤدي إلى أن N is prime فضلا فرضنا
+
+342
+00:34:46,940 --> 00:34:50,380
+أن نحن إشمالها مش prime مادام مش prime إذا
+
+343
+00:34:50,380 --> 00:34:53,340
+composite مظبوط إيش معنات composite يعني أن N
+
+344
+00:34:53,340 --> 00:34:59,350
+بتساوي D في D صح؟و B في B أكيد الـ B مش واحد و الـ
+
+345
+00:34:59,350 --> 00:35:04,290
+D أشمالها مش واحد و لا بتبصي و بترجع براي ماشي ايش
+
+346
+00:35:04,290 --> 00:35:07,250
+معناته الـ B مش واحد و الـ D مش واحد معناته الـ B
+
+347
+00:35:07,250 --> 00:35:11,530
+و الـ D تمتين أكبر من واحد إذا أكيد تمتين أكبر من
+
+348
+00:35:11,530 --> 00:35:17,570
+مين أصغر من مين مش بتبوتش إذا فاهم واضح إذا صار
+
+349
+00:35:17,570 --> 00:35:25,710
+عند الـ D بين الواحد و بين الانبعاد أي سؤالأي
+
+350
+00:35:25,710 --> 00:35:31,410
+استفسار الآن احنا نهينا اللي هو Fermat's theorem
+
+351
+00:35:31,410 --> 00:35:36,970
+ونهينا اللي هي Wilson's theorem وان شاء الله المرة
+
+352
+00:35:36,970 --> 00:35:43,810
+القادمة هنحكي عن اللي هو طبعا اتحدثنا احنا عن مين
+
+353
+00:35:43,810 --> 00:35:50,110
+عن ال linear congruences لأن
+
+354
+00:35:50,110 --> 00:35:56,450
+بعد ما أخدنا Wilson's theorem يمكننا الحديثعن الـ
+
+355
+00:35:56,450 --> 00:36:03,090
+quadratic congruences ونعمل الـ congruences يكون
+
+356
+00:36:03,090 --> 00:36:08,330
+فيها إيه نبحث في ال solutions اللي لها ال theorem
+
+357
+00:36:08,330 --> 00:36:19,080
+الأولى التي تتعلق بالـ quadratic congruencesالتي
+
+358
+00:36:19,080 --> 00:36:22,820
+على الشكل اللي أمامنا وهي اللي بنبحث فيها The
+
+359
+00:36:22,820 --> 00:36:25,660
+quadrant of congrance is x terbia زاد واحد وطابق
+
+360
+00:36:25,660 --> 00:36:30,700
+ال zero modulo b has a solution if and only if b
+
+361
+00:36:30,700 --> 00:36:35,580
+تطابق الواحد modulo أربعة where b is an odd number
+
+362
+00:36:35,580 --> 00:36:43,310
+إيش النظرية بتقول كمان مانوة؟اللي هنحكي فيها في
+
+363
+00:36:43,310 --> 00:36:45,510
+الـ Quadrate of congruences لأن موضوع الـ Quadrate
+
+364
+00:36:45,510 --> 00:36:51,350
+of congruences موضوع كبير هناخد الجزئية التطبيقية
+
+365
+00:36:51,350 --> 00:36:55,910
+على Wilson's theorem على اللي أخدناها النظرية
+
+366
+00:36:55,910 --> 00:37:02,330
+بتقول إن الـ Quadrate of congruences X تربية زائد
+
+367
+00:37:02,330 --> 00:37:08,980
+واحد وطابق Zero Modulo BHas a solution has a
+
+368
+00:37:08,980 --> 00:37:13,440
+solution is solvable or has a solution has a
+
+369
+00:37:13,440 --> 00:37:20,400
+solution if and only if إيش اللي هو كيف شكل اللي
+
+370
+00:37:20,400 --> 00:37:24,480
+هي ال بي اللي اللي اللي بتخلي هذا إيه solution أن
+
+371
+00:37:24,480 --> 00:37:31,880
+بي تطابق الواحد modulo مين modulo أربعة و ال بي
+
+372
+00:37:31,880 --> 00:37:39,600
+إشماله is an odd إبرانيعني الآن لو كان عندي اللي
+
+373
+00:37:39,600 --> 00:37:45,120
+هي P بتساوي تلاتة P بتساوي تلاتة فاكدوا معايا لو P
+
+374
+00:37:45,120 --> 00:37:50,580
+بتساوي تلاتة التلاتة طبعا لا تطابق الواحد، مظبوط؟
+
+375
+00:37:50,580 --> 00:37:56,220
+إذن الآن ال X تربيع زائد واحد تطابق ال zero modulo
+
+376
+00:37:56,220 --> 00:38:01,500
+تلاتة إيش مالها؟ has no solutions
+
+377
+00:38:04,050 --> 00:38:09,730
+ماشي الان لو أخدنا P بتساوي خمسة بتقوليلنا هذا X
+
+378
+00:38:09,730 --> 00:38:17,030
+تربيع زاد واحد تطابق ال zero مدله خمسة has a
+
+379
+00:38:17,030 --> 00:38:25,260
+solution no solutionالآن خُد الـ B .. الـ B عبارة
+
+380
+00:38:25,260 --> 00:38:31,680
+عن إيش؟ عن سبعة .. سبعة أوضًا لا تطابق الواحد مدل
+
+381
+00:38:31,680 --> 00:38:34,880
+أربعة يعني هذه برضه X تربيع زي الواحد تطابق الـ
+
+382
+00:38:34,880 --> 00:38:38,760
+Zero مدل هذا كبرضه إشمالة has no solution إذن
+
+383
+00:38:38,760 --> 00:38:45,750
+المظنية هذه بس بتبحثفي الـ X تربية أو بتجاوبنا على
+
+384
+00:38:45,750 --> 00:38:51,650
+الـ X تربية تطابق ناقص واحد Modulo اللي هو بيه فيه
+
+385
+00:38:51,650 --> 00:38:58,930
+لا solution أو مافيش إلها لل odd مين لل odd
+
+386
+00:38:58,930 --> 00:39:04,050
+إبراهيمز المرة الجاية ان شاء الله بنبث النظرية و
+
+387
+00:39:04,050 --> 00:39:08,290
+بناخد المثال اللي عليها أو المرة اللي جاية أو اللي
+
+388
+00:39:08,290 --> 00:39:12,730
+بعد لأن المرة الجاية احنا هنعمل discussionهنعمل
+
+389
+00:39:12,730 --> 00:39:15,130
+discussion في أربعة ان شاء الله هنكمل chapter
+
+390
+00:39:15,130 --> 00:39:15,590
+أربعة
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/SQIrcReoLXE_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/SQIrcReoLXE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f406ab96e69aaec2251a3287ba34b336f7689bef
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/SQIrcReoLXE_raw.json
@@ -0,0 +1 @@
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modulo mean q اذا then بخاصية التعدي a to the b في q تطابق ال a modulo q", "tokens": [3615, 1863, 16254, 2423, 39184, 257, 281, 264, 272, 20449, 9566, 9957, 1829, 11296, 6055, 9566, 16758, 4587, 2423, 39184, 257, 1072, 13455, 914, 9505, 29538, 2423, 7649, 1214, 16712, 29399, 9957, 20449, 45030, 11242, 4724, 9778, 33546, 10632, 16712, 22488, 1829, 4724, 1829, 9381, 13546, 18871, 16254, 257, 281, 264, 272, 9505, 6055, 9566, 16758, 4587, 2423, 257, 1072, 13455, 914, 9505, 1975, 15730, 550, 4724, 9778, 33546, 10632, 16712, 22488, 1829, 257, 281, 264, 272, 8978, 9505, 6055, 9566, 16758, 4587, 2423, 257, 1072, 13455, 9505], "avg_logprob": -0.21962780764933382, "compression_ratio": 1.9423076923076923, "no_speech_prob": 0.0, "words": [{"start": 278.03, "end": 278.67, "word": "عندي", "probability": 0.7589518229166666}, {"start": 278.67, "end": 279.45, "word": " الـ", "probability": 0.851318359375}, {"start": 279.45, "end": 279.63, "word": " a", "probability": 0.2900390625}, {"start": 279.63, 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"text": "اللي هو الجزء الثاني من المحاضرة اللي هو Wilson's theorem بقى فوق يا أبو سيم شوية Wilson's theorem الان Wilson's theorem برضه عنوان أو إعلان مهم عندنا في نظرية الإعداد Wilson's theorem إيش بتقول؟", "tokens": [6027, 20292, 31439, 25724, 11622, 38207, 6024, 104, 7649, 1829, 9154, 9673, 5016, 46958, 25720, 13672, 1829, 31439, 15388, 311, 20904, 4724, 4587, 7578, 6156, 30543, 35186, 5551, 3555, 2407, 8608, 32640, 13412, 2407, 10632, 15388, 311, 20904, 2423, 7649, 15388, 311, 20904, 4724, 43042, 3224, 18871, 2407, 7649, 34051, 11933, 30241, 7649, 3714, 16095, 43242, 8315, 8978, 8717, 19913, 2288, 10632, 33688, 22488, 18513, 15388, 311, 20904, 11933, 1829, 8592, 39894, 39648, 22807], "avg_logprob": -0.24020833810170492, "compression_ratio": 1.6779661016949152, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 894.83, "end": 895.09, "word": "اللي", "probability": 0.41082763671875}, {"start": 895.09, "end": 895.19, "word": " هو", "probability": 0.982421875}, {"start": 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38688, 16472, 2423, 39184, 416, 4308, 11933, 1211, 11296, 2074, 49429, 307, 406, 2074, 8608, 37440, 15844, 28239, 21292, 47356, 31767, 15040, 3660, 16070, 3794, 37440, 8608, 37440, 15844, 21136, 25708, 3714, 35571, 3215, 6024, 48506, 4032, 26895, 3794, 11536, 11622, 20904, 4032, 26895, 3794, 11536, 11622, 20904, 4032, 26895, 3794, 11536, 11622, 20904, 39894, 39648, 9122, 2304, 6027, 1829, 498, 363, 307, 5835, 550], "avg_logprob": -0.35916095563810163, "compression_ratio": 1.7052023121387283, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 922.39, "end": 922.61, "word": "و", "probability": 0.496337890625}, {"start": 922.61, "end": 922.93, "word": " برضه", "probability": 0.698486328125}, {"start": 922.93, "end": 923.47, "word": " هنشوف", "probability": 0.86572265625}, {"start": 923.47, "end": 923.65, "word": " ان", "probability": 0.6103515625}, {"start": 923.65, "end": 923.83, "word": " الـ", "probability": 0.5234375}, {"start": 923.83, "end": 924.23, "word": " converse", "probability": 0.74658203125}, {"start": 924.23, "end": 924.51, "word": " إلها", "probability": 0.523193359375}, {"start": 924.51, "end": 924.85, "word": " true", "probability": 0.88720703125}, {"start": 924.85, "end": 925.65, "word": " ولا", "probability": 0.74072265625}, {"start": 925.65, "end": 926.83, "word": " is", "probability": 0.68994140625}, {"start": 926.83, "end": 927.17, "word": " not", "probability": 0.96142578125}, {"start": 927.17, "end": 927.75, "word": " true", "probability": 0.9853515625}, {"start": 927.75, "end": 929.63, "word": " سلام", "probability": 0.4364013671875}, {"start": 929.63, "end": 929.77, "word": " على", "probability": 0.416259765625}, {"start": 929.77, "end": 929.95, "word": " النبي", "probability": 0.9521484375}, {"start": 929.95, "end": 930.17, "word": " عليه", "probability": 0.433349609375}, {"start": 930.17, "end": 930.51, "word": " الصلاة", "probability": 0.9705403645833334}, {"start": 930.51, "end": 930.93, "word": " والسلام", "probability": 0.9348958333333334}, {"start": 930.93, "end": 931.45, "word": " سلام", "probability": 0.6220703125}, {"start": 931.45, "end": 931.53, "word": " على", "probability": 0.61669921875}, {"start": 931.53, "end": 931.67, "word": " السيد", "probability": 0.746826171875}, {"start": 931.67, "end": 931.99, "word": " محمد", "probability": 0.9347330729166666}, {"start": 931.99, "end": 933.05, "word": " الآن", "probability": 0.52911376953125}, {"start": 933.05, "end": 933.81, "word": " ويلسونز", "probability": 0.64791259765625}, {"start": 933.81, "end": 934.17, "word": " theorem", "probability": 0.25927734375}, {"start": 934.17, "end": 937.23, "word": " ويلسونز", "probability": 0.8953125}, {"start": 937.23, "end": 938.75, "word": " theorem", "probability": 0.92626953125}, {"start": 938.75, "end": 940.03, "word": " ويلسونز", "probability": 0.861767578125}, {"start": 940.03, "end": 940.31, "word": " theorem", "probability": 0.92626953125}, {"start": 940.31, "end": 940.67, "word": " بتقول", "probability": 0.978515625}, {"start": 940.67, "end": 941.33, "word": " كمالي", "probability": 0.97412109375}, {"start": 941.33, "end": 942.13, "word": " if", "probability": 0.77392578125}, {"start": 942.13, "end": 944.01, "word": " B", "probability": 0.5615234375}, {"start": 944.01, "end": 945.03, "word": " is", "probability": 0.916015625}, {"start": 945.03, "end": 945.61, "word": " prime", "probability": 0.7275390625}, {"start": 945.61, "end": 948.79, "word": " then", "probability": 0.8310546875}], "temperature": 1.0}, {"id": 35, "seek": 97671, "start": 951.31, "end": 976.71, "text": "اللي هو B-1! تطابق ناقص واحد مودولو B أبروف الـ Winsor's theorem بتقول if B is a prime", "tokens": [6027, 20292, 31439, 363, 12, 16, 0, 6055, 9566, 16758, 4587, 8717, 995, 4587, 9381, 36764, 24401, 3714, 23328, 12610, 2407, 363, 5551, 26890, 38688, 2423, 39184, 343, 1292, 284, 311, 20904, 39894, 39648, 498, 363, 307, 257, 5835], "avg_logprob": -0.473046887665987, "compression_ratio": 1.024793388429752, "no_speech_prob": 0.0, "words": [{"start": 951.31, "end": 951.65, "word": "اللي", "probability": 0.4984130859375}, {"start": 951.65, "end": 951.87, "word": " هو", "probability": 0.9599609375}, {"start": 951.87, "end": 952.25, "word": " B", "probability": 0.11865234375}, {"start": 952.25, "end": 953.59, "word": "-1!", "probability": 0.5692138671875}, {"start": 954.59, "end": 955.89, "word": " تطابق", "probability": 0.8746337890625}, {"start": 955.89, "end": 956.57, "word": " ناقص", "probability": 0.64556884765625}, {"start": 956.57, "end": 957.19, "word": " واحد", "probability": 0.755126953125}, {"start": 957.19, "end": 958.93, "word": " مودولو", "probability": 0.70782470703125}, {"start": 958.93, "end": 959.83, "word": " B", "probability": 0.77099609375}, {"start": 959.83, "end": 962.09, "word": " أبروف", "probability": 0.5650227864583334}, {"start": 962.09, "end": 971.97, "word": " الـ", "probability": 0.3546142578125}, {"start": 971.97, "end": 973.39, "word": " Winsor's", 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"word": " تطابق", "probability": 0.83154296875}, {"start": 979.75, "end": 980.13, "word": " نقص", "probability": 0.6861165364583334}, {"start": 980.13, "end": 980.69, "word": " واحد", "probability": 0.7314453125}, {"start": 980.69, "end": 981.99, "word": " مدلبي", "probability": 0.7108154296875}, {"start": 981.99, "end": 984.57, "word": " في", "probability": 0.74609375}, {"start": 984.57, "end": 985.09, "word": " جسر", "probability": 0.94580078125}, {"start": 985.09, "end": 985.85, "word": " للبرهان", "probability": 0.949951171875}, {"start": 985.85, "end": 987.43, "word": " الجسر", "probability": 0.9375}, {"start": 987.43, "end": 987.73, "word": " هذا", "probability": 0.9150390625}, {"start": 987.73, "end": 987.95, "word": " هو", "probability": 0.89404296875}, {"start": 987.95, "end": 988.33, "word": " الست", "probability": 0.661376953125}, {"start": 988.33, "end": 988.97, "word": " التالية", "probability": 0.982421875}, {"start": 988.97, "end": 990.13, "word": " S", "probability": 0.408935546875}, {"start": 990.13, "end": 991.35, "word": " بتساوي", "probability": 0.733154296875}, {"start": 991.35, "end": 992.29, "word": " واحد", "probability": 0.8349609375}, {"start": 992.29, "end": 992.85, "word": " و", "probability": 0.89892578125}, {"start": 992.85, "end": 993.27, "word": " اتنين", "probability": 0.79736328125}, {"start": 993.27, "end": 993.69, "word": " و", "probability": 0.79248046875}, {"start": 993.69, "end": 994.29, "word": " تلاتة", "probability": 0.899658203125}, {"start": 994.29, "end": 994.95, "word": " لما", "probability": 0.9248046875}, {"start": 994.95, "end": 995.25, "word": " اصل", "probability": 0.695068359375}, {"start": 995.25, "end": 995.55, "word": " عند", "probability": 0.38525390625}, {"start": 995.55, "end": 995.73, "word": " ال", "probability": 0.6904296875}, {"start": 995.73, "end": 995.97, "word": " B", "probability": 0.52978515625}, {"start": 995.97, "end": 997.17, "word": "-1", "probability": 0.35003662109375}, {"start": 997.17, "end": 998.23, "word": " اول", "probability": 0.864990234375}, {"start": 998.23, "end": 998.75, "word": " ملاحظة", "probability": 0.95087890625}, {"start": 998.75, "end": 998.91, "word": " احنا", "probability": 0.8997395833333334}, {"start": 998.91, "end": 999.27, "word": " عارفين", "probability": 0.974609375}, {"start": 999.27, "end": 999.43, "word": " ان", "probability": 0.86083984375}, {"start": 999.43, "end": 999.71, "word": " هذا", "probability": 0.80029296875}, {"start": 999.71, "end": 1000.03, "word": " عبارة", "probability": 0.993896484375}, {"start": 1000.03, "end": 1000.19, "word": " عن", "probability": 0.9921875}, {"start": 1000.19, "end": 1000.53, "word": " complete", "probability": 0.634765625}, {"start": 1000.53, "end": 1000.99, "word": " residue", "probability": 0.52587890625}, {"start": 1000.99, "end": 1001.41, "word": " system", "probability": 0.94970703125}, {"start": 1001.41, "end": 1001.67, "word": " بس", "probability": 0.9453125}, {"start": 1001.67, "end": 1001.95, "word": " خاص", "probability": 0.807861328125}, {"start": 1001.95, "end": 1002.55, "word": " اسمين", "probability": 0.6947428385416666}, {"start": 1002.55, "end": 1003.59, "word": " الصفر", "probability": 0.8658854166666666}, {"start": 1003.59, "end": 1004.35, "word": " يعني", "probability": 0.947265625}, {"start": 1004.35, "end": 1004.75, "word": " الآن", "probability": 0.707763671875}, {"start": 1004.75, "end": 1005.27, "word": " اللي", "probability": 0.93896484375}, {"start": 1005.27, "end": 1005.61, "word": " هو", "probability": 0.994140625}, {"start": 1005.61, "end": 1006.81, "word": " الصفر", "probability": 0.9431966145833334}], "temperature": 1.0}, {"id": 37, "seek": 103020, "start": 1007.94, "end": 1030.2, "text": "والمضاعفات الـ B مش ممثلة هان يعني لإنه مين اللي بتقن الـ B هان الـ 0 والـ B و2B و3B و4B و-B و-2B و-3B إذا كل هذا ال branch غير ممثل في اللي عندي اللي هو الـ 6 هذا يعني هذا complete residue system بس خاصة من اللي هو السفر", "tokens": [2407, 45340, 11242, 45761, 5172, 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"probability": 0.7765299479166666}], "temperature": 1.0}, {"id": 75, "seek": 203968, "start": 2010.32, "end": 2039.68, "text": "الـ N والـ D بتجسم مين؟ But D بتجسم الـ N ثم التنتين مع بعض الـ D تجسم N نقص واحد فيكتوريال زائد واحد إذا صار عندي أيضا الـ D تجسم الـ N نقص واحد فيكتوريال زائد واحد together الـ D بتجسم أي linear combination بينين؟ الـ D بتجسم هذه و الـ D بتجسم هذه إذا hence", "tokens": [6027, 39184, 426, 16070, 39184, 413, 39894, 7435, 38251, 3714, 9957, 22807, 583, 413, 39894, 7435, 38251, 2423, 39184, 426, 38637, 2304, 16712, 29399, 9957, 20449, 45030, 11242, 2423, 39184, 413, 6055, 7435, 38251, 426, 8717, 4587, 9381, 36764, 24401, 8978, 4117, 2655, 13063, 1829, 6027, 30767, 16373, 3215, 36764, 24401, 11933, 15730, 20328, 9640, 18871, 16254, 36632, 11242, 995, 2423, 39184, 413, 6055, 7435, 38251, 2423, 39184, 426, 8717, 4587, 9381, 36764, 24401, 8978, 4117, 2655, 13063, 1829, 6027, 30767, 16373, 3215, 36764, 24401, 1214, 2423, 39184, 413, 39894, 7435, 38251, 36632, 8213, 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"word": " كبير", "probability": 0.99462890625}, {"start": 2207.25, "end": 2208.51, "word": " هناخد", "probability": 0.7958984375}, {"start": 2208.51, "end": 2209.33, "word": " الجزئية", "probability": 0.9498291015625}, {"start": 2209.33, "end": 2211.35, "word": " التطبيقية", "probability": 0.9794921875}, {"start": 2211.35, "end": 2212.49, "word": " على", "probability": 0.84912109375}, {"start": 2212.49, "end": 2213.53, "word": " Wilson's", "probability": 0.51348876953125}, {"start": 2213.53, "end": 2213.93, "word": " theorem", "probability": 0.8056640625}, {"start": 2213.93, "end": 2214.15, "word": " على", "probability": 0.1812744140625}, {"start": 2214.15, "end": 2214.25, "word": " اللي", "probability": 0.968505859375}, {"start": 2214.25, "end": 2215.29, "word": " أخدناها", "probability": 0.8052734375}, {"start": 2215.29, "end": 2215.91, "word": " النظرية", "probability": 0.951171875}, {"start": 2215.91, "end": 2216.31, "word": " بتقول", "probability": 0.95068359375}, {"start": 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0.6318359375}, {"start": 2225.15, "end": 2225.47, "word": " B", "probability": 0.869140625}], "temperature": 1.0}, {"id": 83, "seek": 225523, "start": 2226.64, "end": 2255.24, "text": "Has a solution has a solution is solvable or has a solution has a solution if and only if إيش اللي هو كيف شكل اللي هي ال بي اللي اللي اللي بتخلي هذا إيه solution أن بي تطابق الواحد modulo مين modulo أربعة و ال بي إشماله is an odd إبران", "tokens": [39, 296, 257, 3827, 575, 257, 3827, 307, 1404, 17915, 420, 575, 257, 3827, 575, 257, 3827, 498, 293, 787, 498, 11933, 1829, 8592, 13672, 1829, 31439, 9122, 33911, 13412, 28820, 13672, 1829, 39896, 2423, 4724, 1829, 13672, 1829, 13672, 1829, 13672, 1829, 39894, 9778, 20292, 23758, 11933, 1829, 3224, 3827, 14739, 4724, 1829, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 1072, 13455, 3714, 9957, 1072, 13455, 5551, 25513, 27884, 4032, 2423, 4724, 1829, 11933, 8592, 2304, 6027, 3224, 307, 364, 7401, 11933, 26890, 7649], "avg_logprob": -0.32558140539845754, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/T1Jiw040RUs.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/T1Jiw040RUs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9d4f6572cadf4146ecd306c965dab8879ea8e0ad
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/T1Jiw040RUs.srt
@@ -0,0 +1,3975 @@
+1
+00:00:21,040 --> 00:00:25,800
+بسم الله الرحمن الرحيم محاضرة رقم ستة وثلاثين
+
+2
+00:00:25,800 --> 00:00:30,840
+مساق نظرية الأعداد طلاب قسم الرياضيات بالجامعة
+
+3
+00:00:30,840 --> 00:00:36,500
+الإسلامية قسم الرياضيات بالجامعة الإسلامية كليتي
+
+4
+00:00:36,500 --> 00:00:42,620
+العلوم والتربية المحاضرة اليوم رقم ستة وثلاثين
+
+5
+00:00:42,620 --> 00:00:52,200
+اليوم سيكون عندنا مراجعة أو discussion أو بالأحرى 
+
+6
+00:00:52,200 --> 00:01:01,640
+مناقشة لـ Section 7-2 و7-3 للأسئلة المطلوبة في هذا
+
+7
+00:01:01,640 --> 00:01:05,480
+الشابتر خلّيني 
+
+8
+00:01:05,480 --> 00:01:11,130
+أن أراجع في البداية بعض المفاهيم التي أذكركم فيها في
+
+9
+00:01:11,130 --> 00:01:15,750
+سبعة اثنين الـ phi function في فانكشن اللي هي five and 
+
+10
+00:01:15,750 --> 00:01:21,270
+هي عبارة عن the number of positive integers not 
+
+11
+00:01:21,270 --> 00:01:25,610
+exceeding n and that are relatively prime with n
+
+12
+00:01:25,610 --> 00:01:29,290
+أخذنا
+
+13
+00:01:29,290 --> 00:01:34,090
+الذي هو ملاحظة أن five and بتساوي n ناقص واحد if
+
+14
+00:01:34,090 --> 00:01:42,200
+and only if n  و الـ Z' من ثم قلنا لو كانت n' بيكون 
+
+15
+00:01:42,200 --> 00:01:51,140
+Phi of n أُس k بتساوي الذي هو الـ n أُس k في واحد
+
+16
+00:01:51,140 --> 00:01:57,260
+ناقص واحد على n أو بيساوي الـ n أُس k ناقص n أُس k
+
+17
+00:01:57,260 --> 00:02:04,940
+minus واحد وهذا هو النظرية الأولى بعد ذلك أخذنا أن 
+
+18
+00:02:04,940 --> 00:02:08,960
+الـ Phi is multiplicative function والآن in
+
+19
+00:02:08,960 --> 00:02:17,520
+general لو كانت n عندي التي هي عبارة عن كتبناها
+
+20
+00:02:17,520 --> 00:02:21,680
+في الـ canonical form n أكبر من واحد كونها كصورة p1
+
+21
+00:02:21,680 --> 00:02:30,230
+α1 التي عند pr αr بيكون عندي Phi of n بساوي الذي هو
+
+22
+00:02:30,230 --> 00:02:37,510
+n نفسها في واحد ناقص واحد على p واحد لما أصل لعند
+
+23
+00:02:37,510 --> 00:02:43,990
+واحد ناقص واحد على pr أو بتعبير آخر بساوي الذي هو
+
+24
+00:02:43,990 --> 00:02:50,910
+p أس k ناقص p أس k minus واحد p واحد p واحد لما
+
+25
+00:02:50,910 --> 00:03:05,860
+أصل لعند pr prk-1 هذه هي النظرية حكينا عنها الآن على
+
+26
+00:03:05,860 --> 00:03:11,960
+ال ...
+
+27
+00:03:11,960 --> 00:03:19,000
+أيوه أيوه توكل على الله كبر وأخذنا مثال على إيجاد الـ
+
+28
+00:03:19,000 --> 00:03:26,390
+Phi للـ 360 وبعدين وصلنا لنظرية أن لو كانت n أكبر
+
+29
+00:03:26,390 --> 00:03:34,670
+من 2 يكون عندي الـ Phi of n دائماً is an even
+
+30
+00:03:34,670 --> 00:03:41,150
+integer هذا الذي حكيناه في سبعة اثنين الآن نشوف 
+
+31
+00:03:41,150 --> 00:03:46,630
+الأسئلة المطلوبة في سبعة اثنين مفتوح الـ folder هاي
+
+32
+00:03:46,630 --> 00:03:52,790
+بتاعت الآن سؤال من واحد إلى ثلاثة لعب تأثير حسابية بسيطة
+
+33
+00:03:52,790 --> 00:03:59,450
+وسهلة فما داعي أن نحسبها زيها كثيراً لأن خلينا 
+
+34
+00:03:59,450 --> 00:04:04,950
+نبدأ في سؤال أربعة الجزء الأول السؤال الرابع مكون 
+
+35
+00:04:04,950 --> 00:04:09,490
+من عدد أجزاء الجزء الأول برضه جزء سهل الذي هو
+
+36
+00:04:09,490 --> 00:04:14,930
+establish each of the following assertions الأول 
+
+37
+00:04:14,930 --> 00:04:28,550
+if n is odd then فاي of اثنين n بيساوي فاي of n
+
+38
+00:04:28,550 --> 00:04:37,170
+وهذه سهلة سهلة كثيراً a proof مدام n is odd إذا
+
+39
+00:04:37,170 --> 00:04:40,050
+أنصار الـ greatest common divisor بين الاثنين والـ n
+
+40
+00:04:40,050 --> 00:04:46,480
+ماذا يساوي يساوي واحد ومن ثم الـ Phi of اثنين n
+
+41
+00:04:46,480 --> 00:04:51,140
+مدام أن Phi is multiplicative فهي تساوي Phi of اثنين
+
+42
+00:04:51,140 --> 00:04:56,040
+في Phi of n Phi of اثنين هي عبارة عن واحد في Phi
+
+43
+00:04:56,040 --> 00:05:06,320
+of n وهي تساوي Phi of n نجي لسؤال b سؤال b if n is
+
+44
+00:05:06,320 --> 00:05:21,330
+even then Phi of اثنين n بساوي اثنين five of n الآن
+
+45
+00:05:21,330 --> 00:05:25,870
+الأسئلة من هذا النوع أسهل التي تكتبها في الصورة 
+
+46
+00:05:25,870 --> 00:05:31,810
+العامة لها التي هو العدد n طبعاً في حالة الـ n
+
+47
+00:05:31,810 --> 00:05:35,870
+بتساوي واحد it is a trivial case لو بيصير five of
+
+48
+00:05:35,870 --> 00:05:41,160
+اثنين بساوي الذي هو ال ... ال ... ال ... ال ... ال
+
+49
+00:05:41,160 --> 00:05:41,520
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+50
+00:05:41,520 --> 00:05:41,560
+ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال
+
+51
+00:05:41,560 --> 00:05:41,740
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+52
+00:05:41,740 --> 00:05:42,020
+ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال
+
+53
+00:05:42,020 --> 00:05:42,080
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+54
+00:05:42,080 --> 00:05:43,220
+ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال
+
+55
+00:05:43,220 --> 00:05:43,340
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+56
+00:05:43,340 --> 00:05:49,840
+ال ... ال ... ال ... ال ... ال ... ال ...
+
+57
+00:05:49,840 --> 00:05:51,980
+ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال
+
+58
+00:05:51,980 --> 00:05:52,020
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+59
+00:05:52,020 --> 00:05:53,460
+ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال
+
+60
+00:05:53,460 --> 00:05:54,220
+... ال ... ال ... ال ... ال ... ال ... ال ... ال ... ال ...
+
+61
+00:05:54,220 --> 00:06:00,520
+ال ... ال ... ال ... ال ... ال ... ال ... ال ...is even
+
+62
+00:06:00,520 --> 00:06:04,240
+يعني n أكبر من واحد يعني نستطيع أن نكتبها على صورة
+
+63
+00:06:04,240 --> 00:06:09,180
+prime factorization n بتساوي اثنين أس ألف واحد
+
+64
+00:06:09,180 --> 00:06:15,250
+لأنه جاي إنها even في q واحد أو خلّيني أسميها
+
+65
+00:06:15,250 --> 00:06:20,730
+alpha ألف واحد لعند qr alpha r هذه التي هي صورة
+
+66
+00:06:20,730 --> 00:06:25,030
+الـ Canonical Form لمن؟ للـ n لما تكون n is even و
+
+67
+00:06:25,030 --> 00:06:33,210
+الـ q1 لعند الـ qr q1 لعند الـ qr are distinct odd
+
+68
+00:06:33,210 --> 00:06:40,860
+primes واضح أهو؟ بسحبت كل اثنينات وحطيتها على صورة 2
+
+69
+00:06:40,860 --> 00:06:46,760
+أُس ألفة الآن الحسابات تصير سهلة فاي of اثنين n 
+
+70
+00:06:46,760 --> 00:07:01,040
+بساوي الذي هو فاي of اثنين أس ألفة زائد واحد q
+
+71
+00:07:01,040 --> 00:07:12,120
+واحد ألف واحد لعند q r ألف r ماذا أهو ويساوي احسبها 
+
+72
+00:07:12,120 --> 00:07:18,360
+الآن التي هو نفس العدد هذا الذي هو عبارة عن اثنين
+
+73
+00:07:18,360 --> 00:07:25,800
+بس alpha زائد واحد في q واحد alpha واحد لعندي qr
+
+74
+00:07:25,800 --> 00:07:33,720
+alpha r مضروب في واحد ناقص نصف هي الـ primes التي
+
+75
+00:07:33,720 --> 00:07:38,730
+عندي من الصيغة العامة التي عندي الآن في واحد ناقص
+
+76
+00:07:38,730 --> 00:07:42,250
+عوامله الأولية واحد ناقص واحد على العامل الأول الأول
+
+77
+00:07:42,250 --> 00:07:46,870
+لما أصل عند واحد ناقص آخر عامل واحد على آخر عامل 
+
+78
+00:07:46,870 --> 00:07:53,450
+آخر في أين؟ واحد ناقص واحد على q واحد لعند مثل 
+
+79
+00:07:53,450 --> 00:08:01,710
+واحد ناقص واحد على qr واضح أهو؟ الآن هذا عبارة عن
+
+80
+00:08:01,710 --> 00:08:07,400
+ماذا؟ شو يساوي اثنين في المتبقي المتبقي في الواقع
+
+81
+00:08:07,400 --> 00:08:15,300
+الذي هو من هو n صحيح أم لا المتبقي هنا n هاي
+
+82
+00:08:15,300 --> 00:08:22,940
+n في من هذا مظبوط مضروب في واحد ناقص نصف لما اصلنا
+
+83
+00:08:22,940 --> 00:08:27,560
+عند واحد ناقص واحد على qr هذا في الواقع كله على 
+
+84
+00:08:27,560 --> 00:08:33,640
+بعضه هو عبارة عن Phi of n إذا أصبح 2 في من في Phi 
+
+85
+00:08:33,640 --> 00:08:43,440
+of n بيجي للسؤال الذي بعده السؤال c Phi of 3n 
+
+86
+00:08:50,030 --> 00:08:57,710
+في الظاهرة دولة ذكرتوها عشان هنبني عليها شغل التي
+
+87
+00:08:57,710 --> 00:09:07,570
+سيكون عليها الأسئلة
+
+88
+00:09:07,570 --> 00:09:17,770
+تقريباً في السؤال الرابع الفروع المتشابهة five of 
+
+89
+00:09:17,770 --> 00:09:24,030
+ثلاثة n بساوي ثلاثة five and if and only if الثلاثة
+
+90
+00:09:24,030 --> 00:09:29,770
+تقسم من الـ n الـ n
+
+91
+00:09:29,770 --> 00:09:35,370
+a proof suppose
+
+92
+00:09:35,370 --> 00:09:38,430
+that
+
+93
+00:09:38,430 --> 00:09:44,160
+الثلاثة تقسم من n يعني الثلاثة عامل من عوامل 
+
+94
+00:09:44,160 --> 00:09:48,280
+الـ n مدام الثلاثة عامل من عوامل الـ n إذا أكيد 
+
+95
+00:09:48,280 --> 00:09:51,780
+الـ n أكبر من واحد إذا by unique factorization
+
+96
+00:09:51,780 --> 00:10:01,340
+theorem then n can be written as الذي هو ثلاثة
+
+97
+00:10:01,340 --> 00:10:08,900
+to أكيد في ثلاثة to the alpha واحد معي يا جماعة أهو
+
+98
+00:10:08,900 --> 00:10:14,070
+الـ n تساوي ثلاثة ل alpha واحد في p1 أو خلّيني أسميها
+
+99
+00:10:14,070 --> 00:10:22,310
+alpha ألف واحد لعند pr أس alpha r و p1 و pr are
+
+100
+00:10:22,310 --> 00:10:28,250
+distinct primes غير الثلاثة طبعاً الـ n احسبلي Phi
+
+101
+00:10:28,250 --> 00:10:36,490
+of ثلاثة n then Phi of ثلاثة n زي السؤال الذي
+
+102
+00:10:36,490 --> 00:10:40,730
+جاء له بالظبط يعني لن يختلف بساوي الذي قبل شوية
+
+103
+00:10:40,730 --> 00:10:47,030
+حليناه الذي هو ثلاثة أس alpha واحد أو alpha زائد واحد 
+
+104
+00:10:47,030 --> 00:10:55,530
+في p واحد alpha واحد لعند p r alpha r فايله هذا هو
+
+105
+00:10:55,530 --> 00:11:00,630
+عبارة عن العدد مضروب في من في واحد ناقص ثلث في
+
+106
+00:11:00,630 --> 00:11:05,010
+واحد ناقص واحد على p واحد لما أصل لعند واحد ناقص
+
+107
+00:11:05,010 --> 00:11:06,670
+واحد على p r
+
+108
+00:11:10,320 --> 00:11:17,360
+معي أهو الآن نأخذ الثلاثة براها من برا المقدار
+
+109
+00:11:17,360 --> 00:11:21,920
+يصبح ثلاثة مضروبة في المقدار الذي يظل الذي هو
+
+110
+00:11:21,920 --> 00:11:28,660
+من هذا n معي في واحد ناقص ثلث في واحد ناقص واحد 
+
+111
+00:11:28,660 --> 00:11:33,300
+على p واحد لما اصل لواحد ناقص واحد على p r هذا 
+
+112
+00:11:33,300 --> 00:11:39,240
+كله الذي هو عبارة عن من Phi of n
+
+113
+00:11:44,590 --> 00:11:49,690
+الآن conversely ... conversely
+
+114
+00:11:49,690 --> 00:11:57,630
+... conversely ... suppose that
+
+115
+00:11:57,630 --> 00:12:00,990
+... لنفترض أن هذا بيساوي هذا ونصل إلى ثلاثة تكسب
+
+116
+00:12:00,990 --> 00:12:05,880
+من؟ أنا ... بتأخذ الـ contraposition له يعني بدي 
+
+117
+00:12:05,880 --> 00:12:11,840
+أفترض أن الثلاثة لا تقسم من n وأثبت لك أن five
+
+118
+00:12:11,840 --> 00:12:17,660
+ثلاثة n أشمالها لا تساوي الثلاثة five of n معي
+
+119
+00:12:17,660 --> 00:12:27,220
+طيب عند الثلاثة لا تقسم n إذا أكيد n ماذا
+
+120
+00:12:27,220 --> 00:12:33,690
+ستكون صورتها بساوي p1 alpha واحد عند p r alpha
+
+121
+00:12:33,690 --> 00:12:36,750
+r حيث والـ p1 والـ p2 والـ p r distinct
+
+122
+00:12:36,750 --> 00:12:41,970
+primes different from three ولا واحد منهم بيساوي
+
+123
+00:12:41,970 --> 00:12:51,670
+ماذا يساوي ثلاثة احسبلي الآن في of ثلاثة n في of
+
+124
+00:12:51,670 --> 00:12:56,310
+ثلاثة n ماذا سيساوي الذي هو في ثلاثة في هذا المقدار
+
+125
+00:12:56,310 --> 00:13:03,580
+معي إذا يصبح ثلاثة n نفسها مضروب في من؟ في واحد
+
+126
+00:13:03,580 --> 00:13:10,400
+ناقص ثلث في واحد ناقص واحد على p واحد لما اصل في
+
+127
+00:13:10,400 --> 00:13:18,040
+واحد ناقص واحد على p r ويساوي ثلاثة في واحد ناقص 
+
+128
+00:13:18,040 --> 00:13:24,240
+ثلث جداش ثلثين في ثلاثة تلاقي اثنين في من؟ في
+
+129
+00:13:24,240 --> 00:13:29,910
+n في واحد ناقص واحد على p واحد لما اصل في واحد
+
+130
+00:13:29,910 --> 00:13:35,890
+ناقص واحد على p r وهذا بيساوي اثنين في من في
+
+131
+00:13:35,890 --> 00:13:41,070
+five n أكيد لا يساوي ثلاثة في من في five n
+
+132
+00:13:41,070 --> 00:13:44,250
+لأنه لا يحيل التي هي ال five n تساوي صفر
+
+133
+00:13:54,700 --> 00:13:58,580
+طبعاً أكيد الذي هو في حالة ... طبعاً هذا ... الحالة
+
+134
+00:13:58,580 --> 00:14:01,960
+التي n تساوي واحد is a trivial case لأنه عندي
+
+135
+00:14:01,960 --> 00:14:05,660
+في حالة التي n تساوي واحد five ثلاثة التي هي
+
+136
+00:14:05,660 --> 00:14:12,760
+لا تساوي ثلاثة في five of واحد طيب نجي للسؤال 
+
+137
+00:14:12,760 --> 00:14:16,860
+الذي بعده السؤال الذي بعده الذي علاقة فيه أو الذي 
+
+138
+00:14:16,860 --> 00:14:25,100
+هو فرع d فرع d ماذا يقول يقول five of ثلاثة n بيساوي
+
+139
+00:14:25,100 --> 00:14:31,660
+اثنين five n if and only if الثلاثة لا تقسم من 
+
+140
+00:14:31,660 --> 00:14:35,820
+الـ n الـ reason الأول لما أثبتنا أنه لما ثلاثة لا 
+
+141
+00:14:35,820 --> 00:14:39,660
+تقسم الـ N كده  أيش طلعت عندي five تلاتة N اتنين
+
+142
+00:14:39,660 --> 00:14:43,940
+five N الـ N conversely لأن نفترض five تلاتة N
+
+143
+00:14:43,940 --> 00:14:48,120
+أشمالها بتساوي اتنين five N proof
+
+144
+00:14:51,390 --> 00:14:54,910
+الجزء الأولاني زي ما قلنا تلاتة لتقسم الـ N يؤدي
+
+145
+00:14:54,910 --> 00:14:57,610
+إلى five of تلاتة N بساوة اتنين five of N اثبتناه
+
+146
+00:14:57,610 --> 00:15:04,890
+في الجزء B أو C لأن conversely بندن افترض أن فاي 
+
+147
+00:15:04,890 --> 00:15:08,790
+suppose that
+
+148
+00:15:08,790 --> 00:15:17,690
+five of تلاتة N بساوة اتنين five أيش of N معايا؟
+
+149
+00:15:18,070 --> 00:15:21,310
+إذا مادام فاي of تلاتة N بتساوي فاي of اتنين N
+
+150
+00:15:21,310 --> 00:15:29,190
+then فاي of تلاتة N لا تساوي تلاتة
+
+151
+00:15:29,190 --> 00:15:34,770
+فاي of أيش of N ما ده اللي بيعطينيها five تلاتة N
+
+152
+00:15:34,770 --> 00:15:38,630
+أيش بيساوي اتنين five of N إذا أكيد الـ five تلاتة
+
+153
+00:15:38,630 --> 00:15:45,310
+N لساويش تلاتة في five of N فبما أن مثبت فور أنه 
+
+154
+00:15:45,310 --> 00:15:47,850
+five تلاتة N بيساوي تلاتة five of N إذا انتقلت
+
+155
+00:15:47,850 --> 00:15:53,370
+تلاتة لتقسم مين الـ N مظبوط مدام هذه لا تساوي إذا
+
+156
+00:15:53,370 --> 00:16:02,370
+أكيد التلاتة أشمالها لتقسم الـ N تلاتة لتقسم الـ N by
+
+157
+00:16:02,370 --> 00:16:15,370
+problem 4C أي سؤال نيجي للسؤال اللي بعده السؤال E
+
+158
+00:16:15,370 --> 00:16:23,430
+سؤال E five N بيساوي N على 2 if and only if N
+
+159
+00:16:23,430 --> 00:16:28,850
+بتساوي كده نيجي للجزء الأخير من السؤال الرابع
+
+160
+00:16:36,870 --> 00:16:45,350
+هذا الجزء بيقول لي E Phi of N بيساوي N على 2 if
+
+161
+00:16:45,350 --> 00:16:53,930
+and only if N بتساوي 2 أس K for some K أكبر أو
+
+162
+00:16:53,930 --> 00:17:01,210
+يساوي 1 Proof في
+
+163
+00:17:01,210 --> 00:17:06,030
+الجزء الأولاني جزء حسابات سهل الجزء الأولاني
+
+164
+00:17:08,540 --> 00:17:17,560
+if N بيتساوى 2 أُس K وK أكبر سوى 1 then 5N بتساوي
+
+165
+00:17:17,560 --> 00:17:22,640
+حسب القانون اللي أخذناه عبارة عن 2 5N اللي هي 5 2
+
+166
+00:17:22,640 --> 00:17:28,700
+أُس K اللي هو عبارة عن 2 أُس K في 1 ماقص نص صح ولا
+
+167
+00:17:28,700 --> 00:17:39,220
+لا هو يساوي 2K-1 ويساوي اللي هو نفس الـ N 2K على 2
+
+168
+00:17:39,220 --> 00:17:47,120
+على 2 ماضح طيب
+
+169
+00:17:47,120 --> 00:17:58,960
+conversely suppose that suppose that 5N بيساوي N
+
+170
+00:17:58,960 --> 00:18:07,460
+على 2 على 2 ما دا انفرضنا أن 5N بتساوي N على 2 و5N
+
+171
+00:18:07,460 --> 00:18:11,800
+احنا عارفينها أنها عبارة عن Integer اذا N على 2
+
+172
+00:18:11,800 --> 00:18:17,700
+Integer اذا معناته الـ N ايه شمالها is even كما
+
+173
+00:18:17,700 --> 00:18:22,680
+أمرنا 5N عبارة عن Integer واحنا فرضين الـ N الفرضية
+
+174
+00:18:22,680 --> 00:18:27,330
+المعطنية 5N بتساوي N على 2 بعدين أنا على اتنين is
+
+175
+00:18:27,330 --> 00:18:31,370
+integer اذا الـ N أيش مالها عبارة عن even number
+
+176
+00:18:31,370 --> 00:18:35,790
+مدام even number اذا بقدر أكتبها على صورة اتنين أُس K
+
+177
+00:18:35,790 --> 00:18:47,230
+في N for some odd number N والـ K أكبر أو يساوي
+
+178
+00:18:47,230 --> 00:18:57,600
+أيش واحد واضح نيجي الآن بدنا من الفرضية هذه نصل لأن
+
+179
+00:18:57,600 --> 00:19:02,600
+الـ N هذه لا زم تساوي تساوي واحد معناته صارت الـ N
+
+180
+00:19:02,600 --> 00:19:08,200
+ايه شمالها صورتها عبارة عن اتنين أُس K نحسب بحساب
+
+181
+00:19:08,200 --> 00:19:13,160
+الـ N معطيني five N بساوي N على مين على اتنين إذا
+
+182
+00:19:13,160 --> 00:19:18,660
+صار عندي then N على اتنين اللي عبارة عن اتنين أُس
+
+183
+00:19:18,660 --> 00:19:23,700
+K في N يعني عبارة عن 2 أُس K ناقص واحد في N
+
+184
+00:19:24,680 --> 00:19:30,480
+مظبوط؟ اللي هي N على 2 بتساوي Phi of N هذا المقطع
+
+185
+00:19:30,480 --> 00:19:35,940
+قاعد أنا بعوض في المعادلة المقطع بساوي Phi of N
+
+186
+00:19:35,940 --> 00:19:43,160
+مين Phi of N؟ Phi 2 أُس K في مين؟ في N الـ N is odd
+
+187
+00:19:43,160 --> 00:19:48,100
+قول إذا الـ N والـ 2 أُس K are relatively prime إذا
+
+188
+00:19:48,100 --> 00:19:53,740
+قول Phi multiplicative إذا هيتساوي Phi of 2 أُس K في
+
+189
+00:19:53,740 --> 00:19:59,740
+فاي of N فاي of 2 أُس K ما احنا حسبناها أيش
+
+190
+00:19:59,740 --> 00:20:07,480
+بتساوي 2 أُس K minus واحد في فاي of N اللي هي
+
+191
+00:20:07,480 --> 00:20:13,720
+2 أُس K على 2 الآن اختصروا أن عندي هذا
+
+192
+00:20:13,720 --> 00:20:18,760
+المقدار بساوي هذا المقدار معايا
+
+193
+00:20:22,250 --> 00:20:27,990
+الآن أنت عندي صار عندي الـ N الـ N hence الـ five N
+
+194
+00:20:27,990 --> 00:20:34,250
+تساوي مين تساوي الـ N تساوي
+
+195
+00:20:34,250 --> 00:20:37,990
+الـ N وهذا مستحيل إلا لما تكون الـ N أيش وده تساوي
+
+196
+00:20:37,990 --> 00:20:42,890
+بتساوي واحد لأن عدد الأعداد relatively prime لأكبر
+
+197
+00:20:42,890 --> 00:20:48,310
+من صفر وأصغر من N أكيد أجل من N إلا في حالة مين
+
+198
+00:20:48,310 --> 00:20:56,930
+الواحد إذا hence and so منه مباشرة and بتساوي واحد
+
+199
+00:20:56,930 --> 00:21:05,070
+therefore بيصير عندي الـ N تبعتي هتساوي 2
+
+200
+00:21:05,070 --> 00:21:10,770
+أُس K حين أو حين ما تكون five N بتساوي N على
+
+201
+00:21:10,770 --> 00:21:18,770
+اتنين وخلصنا السؤال الرابع كبر الآن السؤال اللي
+
+202
+00:21:18,770 --> 00:21:20,950
+بعده السؤال الخامس
+
+203
+00:21:23,700 --> 00:21:28,660
+نشوف أيش بيقول السؤال الخامس ونشوف كيف نبرهن اللي
+
+204
+00:21:28,660 --> 00:21:40,620
+بيطلبه السؤال اللي 
+
+205
+00:21:40,620 --> 00:21:42,980
+بيقول السؤال معاني السؤال الخامس
+
+206
+00:21:45,580 --> 00:21:51,280
+اللي بيطلبوا مني بيقولي prove that five N على
+
+207
+00:21:51,280 --> 00:21:54,920
+اتنين four N بتساوي اتنين في كده يعني ما عطيك
+
+208
+00:21:54,920 --> 00:22:04,360
+بيقولك بصيغة أخرى let N بتساوي اتنين في 2
+
+209
+00:22:04,360 --> 00:22:14,320
+بيناقص واحد وما عطيك بي و 2 بي ناقص واحد are
+
+210
+00:22:14,320 --> 00:22:22,980
+both odd prime و الـ بي و 2 بي ناقص واحد odd
+
+211
+00:22:22,980 --> 00:22:33,440
+primes بقول لك prove that prove that
+
+212
+00:22:33,440 --> 00:22:46,700
+Phi of N بساوي five of N زائد 2 معايا يا شباب
+
+213
+00:22:46,700 --> 00:22:52,760
+اه لأن بقولي اذا كانت N بتساوي 2 في 2
+
+214
+00:22:52,760 --> 00:22:58,880
+بيناقص واحد حيث الـ B والـ 2 بيناقص واحد are قد
+
+215
+00:22:58,880 --> 00:23:03,140
+برايمز بقولي اثبتلي أن الـ five of N هي نفسها
+
+216
+00:23:03,140 --> 00:23:07,460
+هتطلع منين five of N زائد 2 الـ proof
+
+217
+00:23:10,610 --> 00:23:18,750
+Proof Phi of N بساوي Phi of 2 في 2B ناقص واحد
+
+218
+00:23:18,750 --> 00:23:22,230
+الـ 2 و 2 بي minus واحد are relatively prime
+
+219
+00:23:22,230 --> 00:23:29,150
+إذن بساوي Phi of 2 في Phi of 2 بي ناقص واحد ويساوي
+
+220
+00:23:29,150 --> 00:23:33,350
+Phi of 2 هي عبارة عن واحد اللي هو 2 ناقص واحد واحد
+
+221
+00:23:34,800 --> 00:23:40,920
+فاي of 2 بي ناقص واحد أيش بيكون 2 بي ناقص
+
+222
+00:23:40,920 --> 00:23:44,120
+واحد is a prime فايلة الابراهيم أيش بيساوي
+
+223
+00:23:44,120 --> 00:23:49,440
+الابراهيم ناقص واحد إذا بيساوي 2 بي ناقص واحد
+
+224
+00:23:49,440 --> 00:23:55,020
+ناقص واحد اه هذا فاي of 2 بي ناقص واحد since
+
+225
+00:23:55,020 --> 00:24:00,040
+2 بي ناقص واحد is a prime
+
+226
+00:24:03,740 --> 00:24:15,580
+و يساوي 2 بي ناقص 2 و يساوي 2
+
+227
+00:24:15,580 --> 00:24:21,780
+بي ناقص 2 و يساوي 2 بي ناقص 2 و يساوي
+
+228
+00:24:21,780 --> 00:24:25,040
+2
+
+229
+00:24:25,040 --> 00:24:27,140
+بي ناقص 2 و يساوي 2 بي ناقص 2 و يساوي
+
+230
+00:24:27,140 --> 00:24:31,420
+2 بي ناقص 2 و يساوي 2 بي ناقص 2 و
+
+231
+00:24:31,420 --> 00:24:32,480
+يساوي 2 بي ناقص 2 و يساوي 2 بي ناقص
+
+232
+00:24:32,480 --> 00:24:32,640
+2 و يساوي 2 بي ناقص 2 و يساوي 2 بي
+
+233
+00:24:32,640 --> 00:24:34,960
+ناقص 2 و يساوي 2 بي ناقص 2 بي نقص واحد
+
+234
+00:24:34,960 --> 00:24:41,800
+زائد أيش؟ زائد 2 معايا ياخد الـ 2 عامل مشترك
+
+235
+00:24:41,800 --> 00:24:47,320
+ويساوي Phi of 2 في 2 بي نقص واحد زائد 1
+
+236
+00:24:47,320 --> 00:24:57,580
+مظبوط؟ ويساوي Phi of 4 في Phi of بي لأن أيش
+
+237
+00:24:57,580 --> 00:25:02,640
+هتطلع هذه عبارة عن Phi of 4 بي
+
+238
+00:25:05,610 --> 00:25:09,310
+مظبوط الـ 4 أو الـ بي relative الـ برايم ما عرفين ليش
+
+239
+00:25:09,310 --> 00:25:17,550
+نعم و يساوي five 4 أيش بيساوي 2 تربيع يعني
+
+240
+00:25:17,550 --> 00:25:25,070
+2 في 2 في five بي قداش بيناقص و يساوي
+
+241
+00:25:25,070 --> 00:25:30,730
+2 بيناقص 2 from 1
+
+242
+00:25:30,730 --> 00:25:43,880
+and 2 نحصل على الـ Phi of N زائد 2 في هذه
+
+243
+00:25:43,880 --> 00:25:49,520
+الحالة في القـرن بتساوي 2 في 2 بي ناقص واحد
+
+244
+00:25:51,380 --> 00:25:55,100
+نيجي للسؤال اللي بعده بقول show that there are
+
+245
+00:25:55,100 --> 00:25:58,040
+infinitely many integers N for which five of N
+
+246
+00:25:58,040 --> 00:26:04,520
+is a perfect square is a perfect square نشوف كيف
+
+247
+00:26:04,520 --> 00:26:16,080
+نفكر في السؤال و نحل السؤال سويا سؤال
+
+248
+00:26:16,080 --> 00:26:19,520
+ستة show that
+
+249
+00:26:22,110 --> 00:26:32,650
+So that there are infinitely many
+
+250
+00:26:32,650 --> 00:26:41,770
+integers N for
+
+251
+00:26:41,770 --> 00:26:47,590
+which 5N
+
+252
+00:26:47,590 --> 00:26:50,110
+is a perfect
+
+253
+00:26:53,560 --> 00:27:03,600
+S² Proof خلّينا على جهة احنا قلنا لو كان N أكبر من
+
+254
+00:27:03,600 --> 00:27:08,040
+واحد بيساوي بي واحد ألف واحد خلّينا إلى أخرى
+
+255
+00:27:08,040 --> 00:27:12,920
+خلّينا نأخذ بي واحد أيش سالفته واحد لو جينا أخذنا
+
+256
+00:27:12,920 --> 00:27:20,620
+five N أو خلّيني نقول بي سالفته five N أيش هيساوي
+
+257
+00:27:22,390 --> 00:27:28,230
+هيساوي بي سالفته في 1 ناقص بي أو بتعبير آخر بي
+
+258
+00:27:28,230 --> 00:27:34,050
+أس ألفة ناقص 1 أنا بدي أيش علاقته باللي بحكيه
+
+259
+00:27:34,050 --> 00:27:37,530
+هنا هو بقولي اثبتلي أنه في عدد لا نهائي من الـ
+
+260
+00:27:37,530 --> 00:27:41,650
+integers N اللي بيطلع لي الـ five one أيش ماله إذا
+
+261
+00:27:41,650 --> 00:27:45,490
+perfect square أيش معنى perfect square يعني يطلع لي
+
+262
+00:27:45,490 --> 00:27:52,710
+هذا المقدار عبارة عن المضاعفات مين الـ 2 ماشي يعني
+
+263
+00:27:52,710 --> 00:27:58,230
+هيكون على صورة 2 2 2 2 2 2
+
+264
+00:27:58,230 --> 00:28:01,630
+2 2 2 2 2 2 2 2
+
+265
+00:28:01,630 --> 00:28:05,690
+2 2 2 2 2 2 2 2
+
+266
+00:28:05,690 --> 00:28:10,970
+2 2 2 2 2 2 2 2
+
+267
+00:28:10,970 --> 00:28:11,190
+2 2 2 2 2 2 2 2
+
+268
+00:28:11,190 --> 00:28:11,630
+2 2 2 2 2 2 2 2
+
+269
+00:28:11,630 --> 00:28:14,750
+2 2 2 2 2 2 
+
+270
+00:28:17,240 --> 00:28:25,200
+كـ Be any positive integer
+
+271
+00:28:25,200 --> 00:28:28,220
+and
+
+272
+00:28:28,220 --> 00:28:33,780
+consider بيقص
+
+273
+00:28:33,780 --> 00:28:42,660
+Alpha أو كسم منها بيقص 2 كزائد 1 then
+
+274
+00:28:45,990 --> 00:28:53,450
+of بي قصت 2 ك زائد 1 بساوي بي قصت 2 ك
+
+275
+00:28:53,450 --> 00:28:58,570
+which is
+
+276
+00:28:58,570 --> 00:29:05,670
+a perfect square but
+
+277
+00:29:05,670 --> 00:29:19,960
+we have infinite number of such be to the K زائد
+
+278
+00:29:19,960 --> 00:29:31,900
+واحد where the number of primes be or حتى the
+
+279
+00:29:31,900 --> 00:29:43,420
+number of exponents K is infinite therefore
+
+280
+00:29:43,420 --> 00:29:45,580
+we have infinite number 
+
+281
+00:29:54,230 --> 00:30:05,370
+أي سؤال؟ نجي للسؤال الثامن، السؤال 
+
+282
+00:30:05,370 --> 00:30:12,650
+الثامن اللي بقول معاني approve 
+
+283
+00:30:12,650 --> 00:30:13,190
+that
+
+284
+00:30:22,720 --> 00:30:31,020
+إذا إنتجار N لديه 
+
+285
+00:30:31,020 --> 00:30:36,880
+قدرات 
+
+286
+00:30:36,880 --> 00:30:40,640
+مختلفة أو أعضاء 
+
+287
+00:30:40,640 --> 00:30:43,220
+أعضاء ثم 
+
+288
+00:30:50,390 --> 00:31:02,730
+two to the R بتسميه الـ 5N proof معايا
+
+289
+00:31:02,730 --> 00:31:12,370
+يا شباب الآن عندي a proof that if N has R distinct
+
+290
+00:31:12,370 --> 00:31:19,320
+prime factors ضمن اثنين أثار بتسميه الـ 5Nand
+
+291
+00:31:19,320 --> 00:31:30,960
+since n has a distinct prime
+
+292
+00:31:30,960 --> 00:31:34,000
+factors
+
+293
+00:31:34,000 --> 00:31:35,720
+than
+
+294
+00:31:47,750 --> 00:31:53,410
+Then N can be written as عند الـ N إيه شمالها؟ في 
+
+295
+00:31:53,410 --> 00:31:58,510
+داخلها عوامل R من الـ Distinct Odd Primes يعني 
+
+296
+00:31:58,510 --> 00:32:01,850
+فيها بي واحد و بي اتنين لعند بي R من الـ Odd
+
+297
+00:32:01,850 --> 00:32:06,570
+Primes من عوامل مين؟ الـ N إذا الـ N أكيد إيه
+
+298
+00:32:06,570 --> 00:32:13,630
+شمالها؟ هيكون بي واحد أس ألف واحد لعند بي R 
+
+299
+00:32:13,630 --> 00:32:18,490
+أس ألف Rبصبح؟ عشان  ان بي واحد و بيتنين و بي ار
+
+300
+00:32:18,490 --> 00:32:22,990
+كل ان أشمالهم من عوامل الان لكن بخلي العمل ان
+
+301
+00:32:22,990 --> 00:32:27,690
+يكون في عند اتنين اثمين اث الف والالفة في هذه
+
+302
+00:32:27,690 --> 00:32:32,030
+الحالة أكبر أو ساوي سفر على اعتبار ان ممكن ماتكونش 
+
+303
+00:32:32,030 --> 00:32:36,150
+فيه اتنينات فحطينا الف بالساوية سفر والالفة واحد
+
+304
+00:32:36,990 --> 00:32:41,470
+لعند الـ α R أكبر strictly من الـ million من سفر 
+
+305
+00:32:41,470 --> 00:32:46,110
+لأن الموجودات في الـ million في الـ N يعني بمعنى
+
+306
+00:32:46,110 --> 00:32:50,570
+أخر أكبر أو ساوي واحد هذولة الألفات اللي فوق واضح
+
+307
+00:32:50,570 --> 00:32:56,690
+أن جهازة الـ N اللي هو وصف ليهاواصف لي أن N لها Un
+
+308
+00:32:56,690 --> 00:32:59,990
+-distinct prime factors يقول لي اثبت انه اتنين اص
+
+309
+00:32:59,990 --> 00:33:04,270
+ار اشمالها بتقسم من الـPhi of N إذا المرحلة الأولى
+
+310
+00:33:04,270 --> 00:33:11,130
+المهمة ان توصف الـN اللي معطيكي إياها اذا then Phi
+
+311
+00:33:11,130 --> 00:33:21,330
+of N بتساوي اللي هو الـN نفسها اللي هي اتنين اص
+
+312
+00:33:21,330 --> 00:33:29,090
+الفابواحد ألف واحد لعن بي ار الف ار في واحد ناقص 
+
+313
+00:33:29,090 --> 00:33:40,170
+نص في واحد ناقص واحد طبعا هذا في حالة اللي هي مين
+
+314
+00:33:40,170 --> 00:33:44,490
+الفا بتسويش سفر لكن في حالة الألف بتسوي سفر بيصير
+
+315
+00:33:44,490 --> 00:33:49,230
+هذا كله مش موجود ماشي الحال واضح عليا ايش بحكيه لو
+
+316
+00:33:49,230 --> 00:33:53,330
+Alpha بتسوي أكبر من سفر هي كما نكتب بتساوي سفر هذا
+
+317
+00:33:53,330 --> 00:33:56,910
+ماتكونش مدود الواحد ناقص نص ولا اتنين أس Alpha
+
+318
+00:33:56,910 --> 00:34:04,090
+واضح اه ويساوي في اللي هو واحد ناقص واحد على بي
+
+319
+00:34:04,090 --> 00:34:10,310
+واحد لما أصل عند واحد ناقص واحد على بي ار ويساوي
+
+320
+00:34:10,310 --> 00:34:21,030
+اتنين أس Alphaنقص واحد هنا في معايا في اللي بضل
+
+321
+00:34:21,030 --> 00:34:26,290
+هذا بضل هذا لما نضربه في هذا بصير بي واحد أس الف
+
+322
+00:34:26,290 --> 00:34:34,570
+واحد ناقص واحد اه فاهمين
+
+323
+00:34:34,570 --> 00:34:40,690
+اهلما أصل عند الأخر PR ألف R ناقص واحد مضروب في
+
+324
+00:34:40,690 --> 00:34:44,610
+مين؟ في اللي دال يعني اللي هو واحد ناقص P واحد او
+
+325
+00:34:44,610 --> 00:34:54,310
+P واحد ناقص واحد فيه لما أصل الأخر واحد PR ناقص
+
+326
+00:34:54,310 --> 00:34:58,690
+واحد ايش اللي عملته؟ عارفين ايش اللي عملته؟ اللي
+
+327
+00:34:58,690 --> 00:35:03,370
+أخدناه الآن وحّكت المقامات هذه صارت P واحد P واحد
+
+328
+00:35:03,370 --> 00:35:08,430
+ناقص واحدوالتانيات بنفس الأسلوب إذا اختصرت هذه مع
+
+329
+00:35:08,430 --> 00:35:11,810
+اللي هنا صارت بي واحد أسالفة واحد ناقص واحد لما
+
+330
+00:35:11,810 --> 00:35:17,030
+صار لعين بي ار اف ار ناقص مين ناقص واحد هذولا كلهم
+
+331
+00:35:17,030 --> 00:35:20,570
+قد برايمز ال بي واحد والبتنين وال بي ار إذا هذولا 
+
+332
+00:35:20,570 --> 00:35:25,150
+كلهم ياشمالهم even ومضربات في حال إن أكم مرة ار من
+
+333
+00:35:25,150 --> 00:35:29,130
+المرات إذا كل واحدة فيها اتنين اتنين اتنين ار من
+
+334
+00:35:29,130 --> 00:35:38,670
+مين من المرات but بي واحدبي ماقص واحد is even for
+
+335
+00:35:38,670 --> 00:35:43,310
+every I الـ I بين الواحد و بين مين الـ R hence
+
+336
+00:35:43,310 --> 00:35:51,730
+اللي هو اتنين اكمرة الـ I مكررة واحدة اتنتين R من
+
+337
+00:35:51,730 --> 00:36:01,950
+الـ R مرات اتنين اقصر تجسمين الف I of L اللي
+
+338
+00:36:01,950 --> 00:36:08,940
+بعدالسؤال الثالث هو اذا
+
+339
+00:36:08,940 --> 00:36:18,160
+كل جزء من هذا البرامج الذي يقسم N يقسم أيضًا M فإن 
+
+340
+00:36:18,160 --> 00:36:23,480
+5N في N بيساوي N في 5 of M في الواضح أن 5N تربية
+
+341
+00:36:23,480 --> 00:36:27,560
+بيساوى N في 5 of N لكل N element in Z positive
+
+342
+00:36:27,560 --> 00:36:29,640
+سنشوف ما يقول السؤال الثالث
+
+343
+00:36:33,230 --> 00:36:37,250
+زي ما قلنا اول اشي بدك هو بناء على الوصف اللي 
+
+344
+00:36:37,250 --> 00:36:43,250
+ماعطيكيا بدك تحدد كيف شكل الان او كيف شكل الام او
+
+345
+00:36:43,250 --> 00:36:47,030
+كيف شكل الان والام حسب السؤال اللي بيعطيكيا
+
+346
+00:36:47,030 --> 00:36:51,970
+وبيوصفلك فيه اللي هو الان او الام اللي بدك تشتغل
+
+347
+00:36:51,970 --> 00:37:00,970
+فيها السؤال عشرة بقول لي عندي if every 
+
+348
+00:37:02,420 --> 00:37:06,480
+Ibrahim divides
+
+349
+00:37:06,480 --> 00:37:13,540
+N also divides
+
+350
+00:37:13,540 --> 00:37:19,400
+M prove
+
+351
+00:37:19,400 --> 00:37:23,760
+that
+
+352
+00:37:23,760 --> 00:37:35,360
+Phi of N في M يساوي N في Phi of M in particular in
+
+353
+00:37:35,360 --> 00:37:48,320
+particular فاي of أن تربيع بتساوي أن فاي of أن لكل
+
+354
+00:37:48,320 --> 00:37:56,660
+أن element in set positive اللي
+
+355
+00:37:56,660 --> 00:38:01,960
+معطينيها اللي بيوصفليها بيقوللي أي ابراهيم بيقسم
+
+356
+00:38:01,960 --> 00:38:08,220
+الان هتلاقيه اشماله automatically بيقسم مين بيقسم الام
+
+357
+00:38:08,220 --> 00:38:18,080
+ماشي معايا الوصف كالتالي الوصف بس كالتالي بيقوللي
+
+358
+00:38:18,080 --> 00:38:24,290
+في عندك ال و ام عبارة عن أعداد أي قارع يقسم الـ N 
+
+359
+00:38:24,290 --> 00:38:29,090
+هتلاقيه بيقسم مين الـ N هذا اللي معطيكي يه بس ومنه
+
+360
+00:38:29,090 --> 00:38:33,810
+طلب لك أنه Phi of N في M مش بيساوي N في Phi of M 
+
+361
+00:38:33,810 --> 00:38:38,860
+بقولك بعدين كحلقة خاصة اللي بعدها ده نشوف الآن نشوف
+
+362
+00:38:38,860 --> 00:38:44,860
+هذه الأوصاف كيف بدنا من خلالها نحدد شكل الان وشكل
+
+363
+00:38:44,860 --> 00:38:50,120
+الام الان في حالة الام بتساوي واحد في حالة الام
+
+364
+00:38:50,120 --> 00:38:54,020
+بتساوي واحد case trivial case five of em هيساوي
+
+365
+00:38:54,020 --> 00:38:55,820
+five of em five of em هيساوي five of em five of em
+
+366
+00:38:55,820 --> 00:39:00,340
+five of em five of em five of em five of em five 
+
+367
+00:39:00,340 --> 00:39:05,040
+of em five of em five of em five of em five of em
+
+368
+00:39:05,040 --> 00:39:05,120
+five of em five of em five of em five of em five
+
+369
+00:39:05,120 --> 00:39:09,950
+five of em five of em five ofأكبر من واحد ذنب أن 
+
+370
+00:39:09,950 --> 00:39:15,990
+كان بيرتن على صورة بواحد ألف واحد لعين بار ألف 
+
+371
+00:39:15,990 --> 00:39:22,980
+اياش ألف ارالـ N بتحدد الـ M الـ N بتحددها من خلال
+
+372
+00:39:22,980 --> 00:39:28,840
+ما هو مُعطَى من علاقة بين الـ N وبين الـ M هذه 
+
+373
+00:39:28,840 --> 00:39:33,140
+حددتها على أساس أنها N أكبر من 1 than by unique
+
+374
+00:39:33,140 --> 00:39:36,780
+factorization theorem اللي هو N can be written as
+
+375
+00:39:36,780 --> 00:39:40,580
+a product of the primes والـ B1 والـ B2 اللي عند
+
+376
+00:39:40,580 --> 00:39:44,670
+الـ B هم إشمالين distinct primes بقول لك الـ N اللي 
+
+377
+00:39:44,670 --> 00:39:49,210
+بيجسم N لازم يجسم مين M معناته الـ B1 والـ B2 اللي 
+
+378
+00:39:49,210 --> 00:39:53,810
+عند الـ VR اللي بيجسم الـ N هدول لازم يجسم مين Can
+
+379
+00:39:53,810 --> 00:40:01,730
+be written على صورة B1 ماشي الحال سميها Beta 1
+
+380
+00:40:01,730 --> 00:40:10,370
+Beta 2 ع 2 Beta 1 بار بيتامين ار و ال بي واحد و ال
+
+381
+00:40:10,370 --> 00:40:15,530
+بي ار اللي هو مش شرط يساوي ان هذوله العلاقة انه
+
+382
+00:40:15,530 --> 00:40:18,570
+مادام موجود ال بي واحد و ال بي ار هنا لازم يكون
+
+383
+00:40:18,570 --> 00:40:25,330
+الموجودات في مين في الام والان ال Q واحد ال Q واحد 
+
+384
+00:40:25,330 --> 00:40:31,410
+أُس مثلا ار واحد لعند Q أس ار أس او خلينا نسميها 
+
+385
+00:40:31,410 --> 00:40:37,760
+جاما واحد لعند جاما أنا أقول اتفضل All of betas
+
+386
+00:40:37,760 --> 00:40:42,400
+that are greater than or equal to alphas لأ لأ 
+
+387
+00:40:42,400 --> 00:40:46,040
+مالوش علاقة ممكن تسويها جدها او تسويها او ازرار 
+
+388
+00:40:46,040 --> 00:40:52,560
+منها اللي جاي ال .. لأ العلاقة موجودة العلاقة ايش 
+
+389
+00:40:52,560 --> 00:40:57,480
+بتقول every prime divides N ال prime اللي بيقسم N
+
+390
+00:40:57,480 --> 00:41:02,660
+بيقسم مين بيقسم M ال P واحد ألف واحد مش prime 
+
+391
+00:41:03,820 --> 00:41:09,340
+الـPrime Mean هو الـP1 إذا بدو يكون الأسس هذه في
+
+392
+00:41:09,340 --> 00:41:15,460
+ذاتة في N والـP1 عند PR أسس M ولا علاقة بين الأسس
+
+393
+00:41:15,460 --> 00:41:21,760
+المهم أن يكون عند P1 عند PR strictly أكبر من 0
+
+394
+00:41:21,760 --> 00:41:27,440
+عشان نضمن وجود الـP زدولة و N في الـN واضح؟ ماشي 
+
+395
+00:41:27,440 --> 00:41:31,770
+الحلنأتي الآن بعد ما حددنا اللي هي الـ M والـ N 
+
+396
+00:41:31,770 --> 00:41:40,490
+بيصير الأمر سهل الآن شوف الآن احسب then Phi of M 
+
+397
+00:41:40,490 --> 00:41:52,330
+في N بيساوي الـ M في N نفسها معايا يا شباب في واحد 
+
+398
+00:41:52,330 --> 00:41:57,590
+ناقص واحد على بي واحد فاهمين
+
+399
+00:41:59,200 --> 00:42:06,980
+في لما أصل 1 ناقص 1 على PR في 1 ناقص 1 على Q1 لما 
+
+400
+00:42:06,980 --> 00:42:12,240
+أصل عند 1 ناقص 1 على QS لأن العوامل اللى فى الـ N 
+
+401
+00:42:12,240 --> 00:42:22,280
+N هي عبارة عن P1 PR P1 Q1 لاندنين لعند QS واضح هذا 
+
+402
+00:42:22,280 --> 00:42:24,860
+اللى هى الـ N في M ويساوي 
+
+403
+00:42:29,000 --> 00:42:35,000
+اطلعلي الـ N لحالها واطلعلي
+
+404
+00:42:35,000 --> 00:42:44,120
+لهذه هذه مين هي؟ five of N صحيح
+
+405
+00:42:44,120 --> 00:42:54,540
+five of N وهم المفضل واضح
+
+406
+00:42:55,660 --> 00:43:02,380
+لحد الآن واضح طبعا الـ 5NM واضح كيف أوجدتها الـ N 
+
+407
+00:43:02,380 --> 00:43:06,780
+في الـ M في النهاية هيكون B1 Beta 1 زي Delta 1 
+
+408
+00:43:06,780 --> 00:43:13,880
+Beta R زي Delta R في Q1 Gamma 1 and Gamma S الـ 5N 
+
+409
+00:43:13,880 --> 00:43:18,440
+في M هي الـ N في M في اللي هو واحد ناقص اللي هي 
+
+410
+00:43:18,440 --> 00:43:23,000
+مين اللي هو واحد على ال prime factors ل الـ N في M
+
+411
+00:43:24,230 --> 00:43:28,530
+فاضح أه؟ لأن in particular اللي بتكون إياها five
+
+412
+00:43:28,530 --> 00:43:34,270
+of n تربيع بيساوي مين؟ n في five of n عند بدم الأم 
+
+413
+00:43:34,270 --> 00:43:38,550
+إيش في n؟ يعني الـN بتساوي ن و أكيد كل واحد بيكسب
+
+414
+00:43:38,550 --> 00:43:43,450
+الـN بيكسب مين؟ الـN التالية، وظهور؟ إذا فعلا هي 
+
+415
+00:43:43,450 --> 00:43:48,750
+حالة خاصة من الـFour فطبقتها فبصير five of n تربيع 
+
+416
+00:43:48,750 --> 00:43:53,950
+اللي هي عبارة عن five of n في الـM اللي هي الـNY 
+
+417
+00:43:53,950 --> 00:43:58,270
+ساوي الـ N بتطلع برّه في Phi of N من الـ N اللي هي 
+
+418
+00:43:58,270 --> 00:44:04,910
+و بيصير عندي Phi of N تربيع بيساوي N في Phi of N أي 
+
+419
+00:44:04,910 --> 00:44:13,750
+سؤال اللي بعده بيجي لسؤال 11 سؤال 11 يلا 11 ايه 11
+
+420
+00:44:13,750 --> 00:44:20,130
+A التصوير هذا هيبقى للطول يعني مش عارف اللي
+
+421
+00:44:20,130 --> 00:44:29,180
+بيصوروا أن  أنه في رمضان إذا كان 5N بيقسم الـ N
+
+422
+00:44:29,180 --> 00:44:36,520
+ناقص واحد يثبت أن
+
+423
+00:44:36,520 --> 00:44:41,360
+N
+
+424
+00:44:41,360 --> 00:44:45,140
+هو 
+
+425
+00:44:45,140 --> 00:44:52,060
+مجموعة ثلاثة 
+
+426
+00:44:52,060 --> 00:44:53,020
+انتاج
+
+427
+00:45:05,590 --> 00:45:12,150
+نعم بدنا اللي هو نفترض
+
+428
+00:45:12,150 --> 00:45:20,730
+أن five N يشملها بتجسم N ناقص واحد و بدنا نثبت
+
+429
+00:45:20,730 --> 00:45:27,230
+منها أن N is a square free integer بدنا نفترض 
+
+430
+00:45:27,230 --> 00:45:36,510
+العكس، نفترض أن N is not square free ونفترض أن الـ
+
+431
+00:45:36,510 --> 00:45:53,710
+5N التي تكسب مين N ناقص واحد فبنشوف 
+
+432
+00:45:53,710 --> 00:45:55,190
+كيف نصل لcontradiction
+
+433
+00:46:01,470 --> 00:46:12,190
+اعتبار أن الـ N ليس 
+
+434
+00:46:12,190 --> 00:46:28,510
+كتابة لكل جمهور، ثم الـ N يمكن أن يكون كتابة ك
+
+435
+00:46:29,050 --> 00:46:34,950
+أن يعني في على الأقل ايه شماله في واحد من الأسس
+
+436
+00:46:34,950 --> 00:46:41,090
+اثنين أو أكثر، يعني في في داخله ايه شماله مربع كامل 
+
+437
+00:46:41,090 --> 00:46:46,050
+يعني في في داخل الان مربع كامل، واضح square of three
+
+438
+00:46:46,050 --> 00:46:50,110
+معناته أنه مافيش ولا مربع كامل في داخل اللي هو 
+
+439
+00:46:50,110 --> 00:46:53,850
+الان، يعني معناته أن can be written as بي واحد بي 
+
+440
+00:46:53,850 --> 00:46:59,910
+اثنين بي تلاتة بي ار إلى لعين بي ار ولا واحد من
+
+441
+00:46:59,910 --> 00:47:04,430
+هدولة متكرر، يعني كلهم distinct primes هذا معناه
+
+442
+00:47:04,430 --> 00:47:08,390
+square of three، فاهمين مش بحكي الان is not square
+
+443
+00:47:08,390 --> 00:47:11,970
+free، معناته أنه ال can be written as بي واحد كي 
+
+444
+00:47:11,970 --> 00:47:18,450
+واحد بي ار بي اتنين كي اتنين لعين بي ار كي اش ار
+
+445
+00:47:18,450 --> 00:47:23,370
+وفي واحد على الأقل من الأسس هذولة على الأقل كي 
+
+446
+00:47:23,370 --> 00:47:29,030
+واحد مثلا أكبر أو يساوي اثنين معايا؟
+
+447
+00:47:40,480 --> 00:47:47,820
+في داخله مربع كامل من الـprimes يعني في واحد من 
+
+448
+00:47:47,820 --> 00:47:53,010
+الـprimes الأس تبعه اثنين أو اكثر، ماشي الحال square
+
+449
+00:47:53,010 --> 00:47:57,010
+of three شو معناته أن أن بتساوي بي واحد بي اتنين 
+
+450
+00:47:57,010 --> 00:48:01,690
+بي تلاتة لعين بي ار وكل ال distinct brines هذا
+
+451
+00:48:01,690 --> 00:48:05,310
+square of three الان is not square of three في
+
+452
+00:48:05,310 --> 00:48:10,810
+واحد على أقل من ال brines اللي عندي قصه أكبر أو
+
+453
+00:48:10,810 --> 00:48:15,750
+يساوي اثنين ماشي الحال والتانية مافيش مشكلة عندي
+
+454
+00:48:15,750 --> 00:48:19,550
+الآن زي ما قلنا suppose that أن is not a square of 
+
+455
+00:48:19,550 --> 00:48:24,770
+three integer، إذا الـ N can be written as P1 K1 P2
+
+456
+00:48:24,770 --> 00:48:30,490
+K2 لعين PR KR و K1 أكبر أو يساوي مين اثنين ال N مش
+
+457
+00:48:30,490 --> 00:48:34,340
+شرط أن تكون مكتوبة في ال canonical form، الان مش
+
+458
+00:48:34,340 --> 00:48:38,320
+شرط يكون P1 P2 P3 تصعدي لأ لأ لأ ماكننا الشيء بس
+
+459
+00:48:38,320 --> 00:48:43,620
+فرضنا أن P1 K1 حيث ال K1 أكبر أو يساوي مين أكبر أو
+
+460
+00:48:43,620 --> 00:48:50,200
+يساوي اثنين طيب الان بدنا اللي هو نشوف كيف يكون فيه
+
+461
+00:48:50,200 --> 00:48:56,700
+تناقض عند ال 5N ايش هتكسم ال 5N اول شي بنكتبها 5N 
+
+462
+00:48:56,700 --> 00:49:00,340
+هتكسم ال N نقص واحد و يساوي خليني احسبها جبالي
+
+463
+00:49:01,070 --> 00:49:08,590
+معايش يا بابا فايفان بتساوي بي واحد ال a نفسها بي 
+
+464
+00:49:08,590 --> 00:49:15,450
+واحد كي واحد لعند ال بي ار كي ار في واحد ناقص واحد 
+
+465
+00:49:15,450 --> 00:49:22,110
+على بي واحد لعند واحد ناقص واحد على بي ار مظبوط؟
+
+466
+00:49:22,110 --> 00:49:29,740
+واضح اه؟وإذا بدك حتى لو ما حسبتش يمكن كمان أسهل 
+
+467
+00:49:29,740 --> 00:49:33,840
+لنا لو ما حسبناش هيك بدل ما نقعد نحسب مرتين لو 
+
+468
+00:49:33,840 --> 00:49:40,240
+كتبت في of بي واحد يمكن أسهل لنا هيك في of بي واحد 
+
+469
+00:49:40,240 --> 00:49:45,640
+كواحد في في of التانيات بي اتنين كتنين لعند ال بي 
+
+470
+00:49:45,640 --> 00:49:53,680
+ار كار معايا؟و يساوي بي 
+
+471
+00:49:53,680 --> 00:50:05,880
+واحد أس كواحد ناقص واحد في بي واحد ناقص واحد في في
+
+472
+00:50:05,880 --> 00:50:15,790
+بي واحد كتنين لعند بي ار كي ارهذه ايش تقبل هي بي 
+
+473
+00:50:15,790 --> 00:50:21,410
+واحد كواحد في واحد ناقص واحد على بي واحد مظبوط على 
+
+474
+00:50:21,410 --> 00:50:27,670
+بي واحد نصير بي واحد ناقص هذا بي واحد معايا 
+
+475
+00:50:27,670 --> 00:50:37,150
+عملناها مش مشكلة الان هذا الان الان كواحد ناقص 
+
+476
+00:50:37,150 --> 00:50:43,320
+واحد يا واحد يا اكترلأن الـ K واحد أكبر يساوي من 
+
+477
+00:50:43,320 --> 00:50:49,580
+اثنين إذا K واحد نقص واحد أكبر أو يساوي واحد إذا 
+
+478
+00:50:49,580 --> 00:51:00,560
+هذا معناته أنه ضمن ال B واحد بيكسب من فاي بي 
+
+479
+00:51:00,560 --> 00:51:05,000
+واحد بيكسب من فاي of N مظبوط ال B واحد بيكسب من
+
+480
+00:51:05,000 --> 00:51:06,880
+فاي of N
+
+481
+00:51:14,240 --> 00:51:18,260
+فاي اف ان بيساوي بي واحد في هذا المقدار هذا 
+
+482
+00:51:18,260 --> 00:51:25,040
+المقدار ايش ماله انتجر مظبوط إذا ال بي واحد تكسب 
+
+483
+00:51:25,040 --> 00:51:28,500
+مين الفاي اف ان ليش حسبت الفاي اف ان إذا ال بي
+
+484
+00:51:28,500 --> 00:51:33,840
+واحد تكسب فاي اف ان ومعطيك اللي هو ال بي واحد 
+
+485
+00:51:33,840 --> 00:51:42,010
+الفاي اف ان بتكسب مين but فاي اف ان بتكسب مين، صح 
+
+486
+00:51:42,010 --> 00:51:52,230
+ولا لأ؟ واضح together then الـ B1 بتكسب الـ N ناقص
+
+487
+00:51:52,230 --> 00:52:02,590
+واحد but من عندي من الأصل أنا N تبعتي الـ B1 من 
+
+488
+00:52:02,590 --> 00:52:08,630
+مين جاي؟ بتكسب الـ N مظبوط ولا لأ الـ B1 معامل من 
+
+489
+00:52:08,630 --> 00:52:15,170
+أولا من من الـ N الـ N بتنتقل مع بعض hence اللي هو 
+
+490
+00:52:15,170 --> 00:52:26,250
+B1 بتجسم N ناقص N ناقص 1 that is B1 بتجسم الواحد
+
+491
+00:52:26,250 --> 00:52:32,250
+contradiction therefore
+
+492
+00:52:33,950 --> 00:52:51,450
+No such exponent K can be more than or equal to 
+
+493
+00:52:51,450 --> 00:53:04,120
+Therefore M على صورة B1 بتنين لعند بي ار و بي واحد 
+
+494
+00:53:04,120 --> 00:53:10,800
+لعند بي ار are distinct primes
+
+495
+00:53:12,290 --> 00:53:15,730
+إذا الآن الفرضية الأولى إن فرضنا واحد من هذول الـ 
+
+496
+00:53:15,730 --> 00:53:21,630
+exponents على أقل أكبر وسوء 2 غير واردة إذا مدامة
+
+497
+00:53:21,630 --> 00:53:27,390
+الـ 5N بتجسب الـ N نقص 1 لازم تكون الـ N بتسوأ بي 
+
+498
+00:53:27,390 --> 00:53:30,650
+واحد بي اتنين عن بي ار where ال بي واحد و ال بي
+
+499
+00:53:30,650 --> 00:53:33,870
+اتنين و ال بي ار distinct primes يعني الـ N is 
+
+500
+00:53:33,870 --> 00:53:38,350
+square free دي جينا السؤال اللي بعده
+
+501
+00:53:42,260 --> 00:53:46,280
+be sure that if n is equal to 2 to the k or 2 to
+
+502
+00:53:46,280 --> 00:53:47,340
+the k times 3 times 3 times 3 times 3 times 3
+
+503
+00:53:47,340 --> 00:53:47,940
+times 3 times 3 times 3 times 3 times 3 times 3
+
+504
+00:53:47,940 --> 00:53:48,900
+times 3 times 3 times 3 times 3 times 3 times 3
+
+505
+00:53:48,900 --> 00:53:51,140
+times 3 times 3 times 3 times 3 times 3 times 3
+
+506
+00:53:51,140 --> 00:53:51,520
+times 3 times 3 times 3 times 3 times 3 times 3
+
+507
+00:53:51,520 --> 00:53:52,340
+times 3 times 3 times 3 times 3 times 3 times 3
+
+508
+00:53:52,340 --> 00:53:53,700
+times 3 times 3 times 3 times 3 times 3 times 3
+
+509
+00:53:53,700 --> 00:53:53,720
+times 3 times 3 times 3 times 3 times 3 times 3
+
+510
+00:53:53,720 --> 00:53:54,000
+times 3 times 3 times 3 times 3 times 3 times 3
+
+511
+00:53:54,000 --> 00:53:54,240
+times 3 times 3 times 3 times 3 times 3 times 3
+
+512
+00:53:54,240 --> 00:53:54,580
+times 3 times 3 times 3 times 3 times 3 times 3
+
+513
+00:53:54,580 --> 00:53:54,840
+times 3 times 3 times 3 times 3 times 3 times 3
+
+514
+00:53:54,840 --> 00:53:55,920
+times 3 times 3 times 3 times 3 times 3 times 3
+
+515
+00:54:12,110 --> 00:54:21,790
+الـ 3 أقص جي و الـ K و الـ J أكبر و يسوى واحد الـ
+
+516
+00:54:21,790 --> 00:54:29,170
+N ثم الـ Phi of N divides من الـ N Phi of N
+
+517
+00:54:29,170 --> 00:54:38,790
+divides الـ N Phi of N divides الـ N نحسب الـ N
+
+518
+00:54:38,790 --> 00:54:47,050
+Phi of 25 of n في حالة الأولى 2k بيسوي 2 أُس k 
+
+519
+00:54:47,050 --> 00:54:54,350
+minus واحد واضحة
+
+520
+00:54:54,350 --> 00:55:02,410
+هذا ما حسبناها وأكيد بتجسمين 2 أُس k نيجيرا اللي 
+
+521
+00:55:02,410 --> 00:55:08,310
+بعيدها 5 of 2 أُس k في 3 أُس j الأولى trivial
+
+522
+00:55:09,200 --> 00:55:11,660
+حسبناها كتير التانية تانية تانية تانية تانية تانية
+
+523
+00:55:11,660 --> 00:55:12,220
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+524
+00:55:12,220 --> 00:55:12,800
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+525
+00:55:12,800 --> 00:55:17,600
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+526
+00:55:17,600 --> 00:55:23,640
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+527
+00:55:23,640 --> 00:55:25,460
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+528
+00:55:25,460 --> 00:55:26,400
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+529
+00:55:26,400 --> 00:55:28,460
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+530
+00:55:28,460 --> 00:55:36,580
+تانية تانية
+
+531
+00:55:36,580 --> 00:55:44,900
+تنص في تلتين اللي هو تلت مع بعض فبصير اثنين اص كي
+
+532
+00:55:44,900 --> 00:55:51,820
+في تلت اص جي ناقص واحد واضح أن هذا بيجسم يعني
+
+533
+00:55:51,820 --> 00:55:59,560
+اثنين اص كي five undivided mean one سواء في الحالة
+
+534
+00:55:59,560 --> 00:56:01,400
+هذه أو في الحالة هذه
+
+535
+00:56:15,640 --> 00:56:20,120
+فاي اف اثنين اث كيه ايش بيساوي اثنين اث كيه في 
+
+536
+00:56:20,120 --> 00:56:35,080
+واحد ناقص نص اه واحد ناقص نص ايش بيساوي نص نيجي
+
+537
+00:56:35,080 --> 00:56:41,780
+للسؤال اللي بعده السؤال تلاتاش، assume that D بتجسم 
+
+538
+00:56:41,780 --> 00:56:48,580
+N prove that Phi of D بتجسم mean Phi of N يعني 
+
+539
+00:56:48,580 --> 00:56:52,940
+بيقولك إذا كانت ال D من قواصم ال N هتكون Phi من
+
+540
+00:56:52,940 --> 00:56:54,880
+قواصم Phi الثاني 
+
+541
+00:57:07,530 --> 00:57:10,710
+طيب يا جماعة نشوف كيف نصيح ال .. ال .. ال .. ال D
+
+542
+00:57:10,710 --> 00:57:14,870
+و ال .. و ال N تبعتها و بعدها بيصير الأمور سهلة D
+
+543
+00:57:14,870 --> 00:57:21,650
+implies N بتعطيني Phi of D بتجسم Phi of N لأن ال
+
+544
+00:57:21,650 --> 00:57:31,950
+proof if D بتساوي واحد then it is trivial that Phi
+
+545
+00:57:31,950 --> 00:57:37,510
+of واحد بتجسم Phi of N أين كانت ال N، 5 واحد بيسوي
+
+546
+00:57:37,510 --> 00:57:44,390
+واحد معايا يا شباب الان suppose that if D أكبر من
+
+547
+00:57:44,390 --> 00:57:51,310
+واحد then D can be written as بي واحد ألف واحد
+
+548
+00:57:51,310 --> 00:57:56,270
+لعين بي ار ألف اياش ار حيث بي واحد و بي اتنين و بي 
+
+549
+00:57:56,270 --> 00:58:01,250
+ا الا او بي ار اما لهم distinct primes هو معطيلي
+
+550
+00:58:01,250 --> 00:58:09,330
+أن دي بتجسمين ان but دي بتبسم الـ N إذا أكيد الـ N 
+
+551
+00:58:09,330 --> 00:58:14,650
+هتكون على صورة بي واحد Alpha واحد زائد اللى هو 
+
+552
+00:58:14,650 --> 00:58:23,270
+مثلا Beta واحد لعندي PR Alpha R زائد Beta R و Q
+
+553
+00:58:23,270 --> 00:58:29,830
+واحد Gamma واحد لعندي QS Gamma Iاش S واضح
+
+554
+00:58:32,290 --> 00:58:37,650
+مدام دي من عوامل الـ N إذا هتكون اللي هو ال
+
+555
+00:58:37,650 --> 00:58:42,870
+factorization للـ N لبرايمز اللي فيها ابقصهم دير 
+
+556
+00:58:42,870 --> 00:58:47,930
+بالك أعلى من مين من اللي برايمز أو تساوي اللي هو 
+
+557
+00:58:47,930 --> 00:58:52,400
+اللي برايمز اللي موجودة ابقصهم، بس كان هناك 
+
+558
+00:58:52,400 --> 00:58:57,180
+الـprimes هدول يعني كان جاي لي انه انا الـprime
+
+559
+00:58:57,180 --> 00:59:03,160
+بيقسم هذه بيقسم هذه الان هذا كله بيقسم هذا مدام دي 
+
+560
+00:59:03,160 --> 00:59:08,280
+كلها بتقسم الان إذا لازم دي كلها تظهر في وين؟ في
+
+561
+00:59:08,280 --> 00:59:15,860
+داخل .. اه طبعا في داخل مين؟ الآن واضح؟ طيب نيجي
+
+562
+00:59:15,860 --> 00:59:22,620
+الآن نثبت five دي بيقسم مين؟ five أنا هأحسب 5N 5N ايش
+
+563
+00:59:22,620 --> 00:59:29,240
+بيساوي اللي هو N نفسها اه اللي هي بي واحد Alpha
+
+564
+00:59:29,240 --> 00:59:37,200
+واحد زائد Beta واحد لعند PR Alpha R زائد Beta R في
+
+565
+00:59:37,200 --> 00:59:44,620
+Q واحد Gamma واحد لعندي QS Gamma S صحيح في مين؟
+
+566
+00:59:54,140 --> 01:00:03,220
+أو كما كتبنا سابقا على صورة مين إذا نقص واحد نقص
+
+567
+01:00:03,220 --> 01:00:06,500
+واحد نقص واحد نقص واحد في اللي هو الباقي
+
+568
+01:00:10,910 --> 01:00:16,430
+اه أعيدها ولا كيف اللي هي عبارة عن ناقص واحد ناقص
+
+569
+01:00:16,430 --> 01:00:22,950
+واحد ناقص واحد ناقص واحد في بي واحد ناقص واحد لما
+
+570
+01:00:22,950 --> 01:00:28,650
+أصل ل بي ار ناقص واحد في الباقيات و لو ما عملناها زي
+
+571
+01:00:28,650 --> 01:00:32,790
+جابل زي جابل بشوية خليتها بفايهة هذه ما فيش مشكلة
+
+572
+01:00:32,790 --> 01:00:37,260
+برضه عشان ما أغلبش حالة في الحسابات مرتين يعني لو
+
+573
+01:00:37,260 --> 01:00:42,760
+الآن بس اشتغلت على هدول و قلت five هذه عشان ما أغلبش
+
+574
+01:00:42,760 --> 01:00:46,860
+حالة في الحسابات برضه بنفع أعملها لكم بيها
+
+575
+01:00:46,860 --> 01:00:57,180
+التانية برضه في Q1-1 لعندك U S ناقص اللي هو واحد
+
+576
+01:01:02,720 --> 01:01:08,980
+5n مظبوط هاي اللي هي ال primes ناقص واحد ال primes 
+
+577
+01:01:08,980 --> 01:01:13,360
+ناقص واحد في بي واحد ناقص واحد في بي ار ناقص واحد
+
+578
+01:01:13,360 --> 01:01:20,440
+لما أصل لكي و أس ناقص ايش واحد واضح
+
+579
+01:01:20,440 --> 01:01:24,660
+احنا
+
+580
+01:01:24,660 --> 01:01:31,540
+لما قلنا five of بي واحد ألف واحد يابني تبها الـ B
+
+581
+01:01:31,540 --> 01:01:35,560
+أُس ألف هي بنكتبها على صورة B ألفة في واحد ناقص
+
+582
+01:01:35,560 --> 01:01:40,500
+واحد على B أو على صورة B أُس ألفة ناقص واحد في B
+
+583
+01:01:40,500 --> 01:01:44,860
+ناقص واحد هذه اللي كتبتها على صورة B ناقص واحد
+
+584
+01:01:44,860 --> 01:01:58,800
+واضح؟ ماشي الحل و يساوي بدي أطلع اللي الآن 5D منها
+
+585
+01:01:59,700 --> 01:02:08,300
+بصير بي واحد أُس بيتا واحد لعند بي ار أُس بيتا ار في
+
+586
+01:02:08,300 --> 01:02:14,460
+q واحد جامع واحد ناقص واحد لعند q اس جامع اس ناقص
+
+587
+01:02:14,460 --> 01:02:23,340
+واحد كل هذا مضروب في q واحد ناقص واحد لعند q اس
+
+588
+01:02:23,340 --> 01:02:29,180
+ناقص واحد هذا مع بعض أخدت هذولة
+
+589
+01:02:31,600 --> 01:02:37,400
+مع الهانة مع الهانة بس خليت الألف واحد بتاع
+
+590
+01:02:37,400 --> 01:02:42,760
+واحد بس فصلها لحظها في اللي هو بي واحد ألف واحد
+
+591
+01:02:42,760 --> 01:02:51,240
+ناقص واحد لعندي ال بي ار الف ار ناقص واحد في ال بي
+
+592
+01:02:51,240 --> 01:02:58,360
+واحد ناقص واحد لعندي ال بي ار ناقص واحد هذا كله من
+
+593
+01:02:58,360 --> 01:03:07,260
+هال لهان اللي هو في of D إذا صار five and بيساوي عدد
+
+594
+01:03:07,260 --> 01:03:12,380
+في five of D إذا five of D بتكسب مين؟ five and إذا
+
+595
+01:03:12,380 --> 01:03:17,920
+بدك ما تحسبش الحسابات هذه اللي هو بدك تقول أصبح
+
+596
+01:03:17,920 --> 01:03:23,740
+هذه الصورة بتقدر تقول من هنا بطريقة ثانية بحسابات
+
+597
+01:03:23,740 --> 01:03:31,840
+يمكن تكون أسهل تجيه تأخدت اللي هو بواحد five
+
+598
+01:03:33,330 --> 01:03:38,290
+لهذول في فايل هذول ليه؟ لأن هذي و هذي relatively
+
+599
+01:03:38,290 --> 01:03:43,830
+مع بعض فايل هذه مين هي؟ اللي هو عبارة عن بي واحد
+
+600
+01:03:43,830 --> 01:03:49,350
+الف واحد زائد بيتا واحد ناقص واحد لعند بي ار الف
+
+601
+01:03:49,350 --> 01:03:56,570
+ار زائد بيتا ار ناقص واحد في واحد بي واحد ناقص
+
+602
+01:03:56,570 --> 01:04:02,050
+واحد لعند بي ار ناقص واحد هذا كله مع بعض مضروب في
+
+603
+01:04:02,050 --> 01:04:07,590
+مين؟ في file هذه في file واللي بيظل هنا اللي هو
+
+604
+01:04:07,590 --> 01:04:12,430
+بيصير عند بي واحد أُس بيتا واحد لعند بي ار أُس بيتا
+
+605
+01:04:12,430 --> 01:04:17,850
+ار مضروب في file of q واحد جامع واحد لعندي qs
+
+606
+01:04:17,850 --> 01:04:22,910
+جامع s هذا كله عبارة عن integer مضروب في 5D إذا
+
+607
+01:04:22,910 --> 01:04:28,350
+5D بتسميه 5L الحسابات هذه بنفع و الثانية بنفع سبعة
+
+608
+01:04:28,350 --> 01:04:33,250
+اتنين اللي هو آخر سؤال السؤال من 13 يلا اللي بعده
+
+609
+01:04:33,250 --> 01:04:38,330
+طيب نيجي نكمل الآن ال discussion لال سبعة تلاتة
+
+610
+01:04:38,330 --> 01:04:41,090
+نبدأ الآن اللي هو Ehlers theorem
+
+611
+01:04:46,890 --> 01:04:50,010
+خلينا نراجع على السريع المبدأ النظرية اللي موجودة
+
+612
+01:04:50,010 --> 01:04:52,930
+لو كان عندي الآن مشترك الأعلى بين ال a و ال n
+
+613
+01:04:52,930 --> 01:04:56,750
+بيساوي 1 و a1 و a2 عند a5 of n اللي هي positive
+
+614
+01:04:56,750 --> 01:05:00,770
+integers أصغر من n و relatively prime مع ال n إذا
+
+615
+01:05:00,770 --> 01:05:04,750
+ال a في ال a1 ال a في ال a2 عند ال a في ال 5 of n
+
+616
+01:05:05,410 --> 01:05:11,310
+are congruent modulo n to mean to a1, a2, a3, a4,
+
+617
+01:05:11,310 --> 01:05:11,670
+a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15,
+
+618
+01:05:12,790 --> 01:05:17,130
+a16, a17, a18, a19, a20, a21, a22, a23, a22, a23,
+
+619
+01:05:17,130 --> 01:05:18,590
+a22, a22, a22, a22, a22, a22, a22, a22, a22, a22,
+
+620
+01:05:18,590 --> 01:05:18,970
+a22, a22, a22, a22, a22, a22, a22, a22, a22, a22,
+
+621
+01:05:18,970 --> 01:05:19,450
+a22, a22, a22, a22, a22, a22, a22, a22, a22, a22,
+
+622
+01:05:19,450 --> 01:05:19,470
+a22, a22, a22, a22, a22, a22, a22, a22, a22, a22,
+
+623
+01:05:19,470 --> 01:05:26,010
+a22, a22, a22, a22, a22, a22, a22 وشرحناها سابقا
+
+624
+01:05:26,010 --> 01:05:31,090
+اطلع للبعد الآن الارثيوريم
+
+625
+01:05:31,090 --> 01:05:35,810
+المشهورة الارثيوريم الارثيوريم الارثيوريم
+
+626
+01:05:35,810 --> 01:05:38,010
+الارثيوريم الارثيوريم الارثيوريم الارثيوريم
+
+627
+01:05:38,010 --> 01:05:38,070
+الارثيوريم الارثيوريم الارثيوريم الارثيوريم
+
+628
+01:05:38,070 --> 01:05:38,830
+الارثيوريم الارثيوريم الارثيوريم الارثيوريم
+
+629
+01:05:38,830 --> 01:05:39,230
+الارثيوريم الارثيوريم الارثيوريم الارثيوريم
+
+630
+01:05:39,230 --> 01:05:39,590
+الارثيوريم الارثيوريم الارثيوريم الارثيوريم
+
+631
+01:05:39,590 --> 01:05:50,090
+الارثيوريم الارثيوريم الارثيوريم الارثيوريم
+
+632
+01:05:50,090 --> 01:05:55,920
+الارثيوريم في حال أن العامل المشترك الأعلى بين
+
+633
+01:05:55,920 --> 01:05:59,480
+الـ A و الـ N أيش بيساوي؟ بيساوي 1 نيجي للـ
+
+634
+01:05:59,480 --> 01:06:02,740
+Corollary تبعت فيرمات أو .. اللي هي .. اللي ..
+
+635
+01:06:02,740 --> 01:06:07,760
+اللي تبعت .. اللي هي فيرمات فيرمات لأن في حالة الـ B
+
+636
+01:06:07,760 --> 01:06:14,760
+اللي هو A' الـ N' في حالة الـ N' و الـ B لتقسم الـ
+
+637
+01:06:14,760 --> 01:06:19,040
+A بكورين اللي هو الـ a to the b-1 و طبق الواحد
+
+638
+01:06:19,040 --> 01:06:23,460
+مضلومين مضلوا بي اللي هي ايش ده Format's theory
+
+639
+01:06:23,460 --> 01:06:28,760
+اللي هي a to the b-1 و طبق الواحد مضلوا بي حيث ال
+
+640
+01:06:28,760 --> 01:06:32,860
+5b بيساوي بي نقص واحد اللي بعده المثال اللي بعده
+
+641
+01:06:32,860 --> 01:06:38,360
+خلينا نيجي للأسئلة بدنا نحل 1 و 4 و 7 و 12 و 13 بنطلع
+
+642
+01:06:38,360 --> 01:06:42,720
+على الأسئلة الآن بقول use اللي هو Ehlers theorem
+
+643
+01:06:42,720 --> 01:06:48,700
+to establish each of the following الآن السؤال
+
+644
+01:06:48,700 --> 01:06:53,100
+ايه؟ بدنا نحل سؤال واحد نحل ايه؟ و الباقي similarly
+
+645
+01:06:53,100 --> 01:06:59,280
+يعني ممكن اللي هو B مشابه لـ A الـ C شوية بتختلف
+
+646
+01:06:59,280 --> 01:07:04,440
+فهناعطيه الفكرة انتبهوا ايش اللي السؤال بقول بقول
+
+647
+01:07:04,440 --> 01:07:12,040
+لي for any integer a for any a element in z الـ a
+
+648
+01:07:12,040 --> 01:07:22,960
+الـ 37 تطابق الـ a modulo 1729
+
+649
+01:07:22,960 --> 01:07:33,520
+الآن الـ 1729 اللي هو عبارة
+
+650
+01:07:33,520 --> 01:07:39,700
+عن بالضبط سبعة في تلاتاش في تسعة عشر فدلّها مين ال
+
+651
+01:07:39,700 --> 01:07:44,740
+سبعمية و تسعة و عشرين يعني عبارة عن سبعة في تلاتاش
+
+652
+01:07:44,740 --> 01:07:51,400
+في مين في تسعة عشر الآن ندي للسبعة و التلاتاش و
+
+653
+01:07:51,400 --> 01:07:56,760
+التسعة عشر زيها الآن عندي حالتين للـ A هأطلب لك لأي
+
+654
+01:07:56,760 --> 01:08:00,220
+A اللي من تنزد إلا لو تشتغل على الـ A والـ N ايش
+
+655
+01:08:00,220 --> 01:08:07,020
+يكون ال relatively prime الحالة الأولى F الـ
+
+656
+01:08:07,020 --> 01:08:10,020
+greatest common divisor بين الـ A والـ N الـ A
+
+657
+01:08:10,020 --> 01:08:18,150
+و السبعة بيساوي واحد then هذا proof معايا شباب بدأت
+
+658
+01:08:18,150 --> 01:08:22,450
+متركم التطابق هذه أولا بالنسبة للـ 7 ثم بالنسبة
+
+659
+01:08:22,450 --> 01:08:27,790
+للـ 13 ثم بالنسبة للـ 19 و بما أن الـ 7 و 13 و 19
+
+660
+01:08:27,790 --> 01:08:31,830
+Relatively prime inverse إذا على طول المدلو اللي
+
+661
+01:08:31,830 --> 01:08:36,590
+حاصل ضربهم بيكون صحيح برضه إذا إذا الـ greatest
+
+662
+01:08:36,590 --> 01:08:40,070
+common divisor بين الـ A والـ 7 بيساوي واحد فمن خلال
+
+663
+01:08:40,070 --> 01:08:47,830
+الـ Euler's theorem يكون لدي الـ A to the 5 of 7 يطبق
+
+664
+01:08:47,830 --> 01:08:56,470
+الواحد مضلومين السبعة معايا؟ by Ehlers Fein لأن
+
+665
+01:08:56,470 --> 01:08:58,550
+العامل مشترك اللي عارف أن الـ A و السبعة بساوي واحد
+
+666
+01:08:58,550 --> 01:09:03,870
+الـ 5 و السبعة لديه ستة then A أُس 6 تطابق الواحد
+
+667
+01:09:03,870 --> 01:09:10,810
+مضلو سبعة ارفع هذه قماش عندي الأُس 37 الأُس اللي هو
+
+668
+01:09:11,940 --> 01:09:16,540
+الآن ستة في ستة بستة و تلاتين بيصير أُس ستة تطابق
+
+669
+01:09:16,540 --> 01:09:20,340
+من الواحد أُس ستة اللي هو ستة اللي هو واحد اللي هو
+
+670
+01:09:20,340 --> 01:09:21,220
+واحد اللي هو واحد اللي هو واحد اللي هو واحد اللي
+
+671
+01:09:21,220 --> 01:09:21,620
+هو واحد اللي هو واحد اللي هو واحد اللي هو واحد
+
+672
+01:09:21,620 --> 01:09:21,840
+اللي هو واحد اللي هو واحد اللي هو واحد اللي هو
+
+673
+01:09:21,840 --> 01:09:22,680
+واحد اللي هو واحد اللي هو واحد اللي هو واحد اللي
+
+674
+01:09:22,680 --> 01:09:22,760
+هو واحد اللي هو واحد اللي هو واحد اللي هو واحد
+
+675
+01:09:22,760 --> 01:09:24,200
+اللي هو واحد اللي هو واحد اللي هو واحد اللي هو
+
+676
+01:09:24,200 --> 01:09:24,740
+هو واحد اللي هو واحد اللي هو واحد اللي هو واحد
+
+677
+01:09:24,740 --> 01:09:30,360
+اللي هو واحد اللي هو واحد اللي
+
+678
+01:09:30,360 --> 01:09:38,590
+هو واحد اللي هو واحد اللي الآن لو كان العامل
+
+679
+01:09:38,590 --> 01:09:42,170
+المشترك الأعلى بين الـ A و الـ 7 مش .. مش واحد، ايش
+
+680
+01:09:42,170 --> 01:09:45,230
+هيكون؟ سبعة، مش ممكن يغير سبعة، اللي هو السبعة ايش
+
+681
+01:09:45,230 --> 01:09:48,350
+مالها؟ عبارة عن الـ Prime فبيكون الآن الحالة
+
+682
+01:09:48,350 --> 01:09:52,090
+التانية F لـ Greatest Common Divisor بين الـ A
+
+683
+01:09:52,090 --> 01:09:56,950
+و السبعة ايش بيساوي؟ سبعة، مش غير ايه، حالتين اه لأن
+
+684
+01:09:56,950 --> 01:09:59,590
+العامل المشترك الأعلى بين الـ A و السبعة يا سبعة يا
+
+685
+01:09:59,590 --> 01:10:05,960
+واحد إذا كان في حالة بيساوي سبعة، معناته أكيد الـ A
+
+686
+01:10:05,960 --> 01:10:11,620
+في الـ A الـ 36 – 1 اللي هو بيحتوي في داخله السبعة
+
+687
+01:10:11,620 --> 01:10:16,840
+يعني السبعة بتقسم مين هذا المقدار لأن العامل
+
+688
+01:10:16,840 --> 01:10:18,820
+المشترك اللي عارف بين الـ A و السبعة ايش مالها
+
+689
+01:10:18,820 --> 01:10:24,000
+سبعة يعني السبعة بتقسم مين الـ A مدام السبعة بتقسم
+
+690
+01:10:24,000 --> 01:10:27,360
+من الـ A ده السبعة بتقسم من الـ A في الـ A الـ 36
+
+691
+01:10:27,360 --> 01:10:28,020
+– 1
+
+692
+01:10:30,750 --> 01:10:33,930
+العامل المشترك الأعلى بين الـ A و الـ 7 أيش بيساوي؟
+
+693
+01:10:33,930 --> 01:10:37,990
+سبعة إذا السبعة بتكسب مين؟ ليه؟ مدام السبعة بتكسب
+
+694
+01:10:37,990 --> 01:10:42,930
+الـ A إذا بتكسب هذا المقدار و ايش معناته هذا؟ أن
+
+695
+01:10:42,930 --> 01:10:47,770
+السبعة بتكسب الـ A و الـ 37 نقص الـ A ايش معناته هذا؟
+
+696
+01:10:47,770 --> 01:10:54,470
+أن الـ A و الـ 37 تطابق الـ A مضلوا مين؟ مضلوا 7
+
+697
+01:11:02,660 --> 01:11:10,700
+طيب ماشي الحالة من واحد و من اتنين من واحد و من
+
+698
+01:11:10,700 --> 01:11:20,420
+اتنين from واحد and اتنين بكون عندي اللي هو الـ A
+
+699
+01:11:20,420 --> 01:11:25,800
+و السبعة و تلاتين تطابق الـ A modulo سبعة for every
+
+700
+01:11:25,800 --> 01:11:32,690
+A الين تنين انزل Similarly و فعلا Similarly و بنفس
+
+701
+01:11:32,690 --> 01:11:40,390
+الأسلوب بنقدر نثبت أن A 37 تطابق الـ A مدول 13
+
+702
+01:11:40,390 --> 01:11:48,570
+لأن 5×13 هو 65 فبصير 65×3 هو 195 فبنجيب فاهمين لما
+
+703
+01:11:48,570 --> 01:11:53,670
+نقول الـ A و الـ 13 بيساوي واحد إذا A فاقه 13
+
+704
+01:11:53,670 --> 01:11:58,590
+تطابق الواحد مدول 7 فاقه 13 جداش 12 بيصير
+
+705
+01:11:58,590 --> 01:12:03,030
+A أس 12 تطابق الواحد بيصير 12 أس 3
+
+706
+01:12:03,030 --> 01:12:06,890
+تطابق الواحد أس 3 يعني 36 تطابق الواحد
+
+707
+01:12:06,890 --> 01:12:10,530
+نضرب الجهتين في A نحصل على دي نفس الشيء الـ 195
+
+708
+01:12:10,530 --> 01:12:14,010
+عبارة عن جداش جداش فايلها 18 فتمانتاش نضربها
+
+709
+01:12:14,010 --> 01:12:22,760
+إيه؟ في 2 الـ 37
+
+710
+01:12:22,760 --> 01:12:26,120
+تطابق الـ A مدول مدول مدول مدول مدول
+
+711
+01:12:26,120 --> 01:12:26,760
+مدول مدول مدول مدول مدول مدول مدول
+
+712
+01:12:26,760 --> 01:12:28,260
+مدول مدول مدول مدول مدول مدول مدول
+
+713
+01:12:28,260 --> 01:12:31,880
+مدول مدول مدول مدول مدول مدول مدول
+
+714
+01:12:31,880 --> 01:12:38,540
+مدول مدول مدول مدول مدول مدول مدول
+
+715
+01:12:41,220 --> 01:12:46,400
+إذاً A و الـ 37 تطابق الـ A مدول حاصل ضرب إنه
+
+716
+01:12:46,400 --> 01:12:52,820
+7 في 13 في 19 اللي هو جداش اللي هو
+
+717
+01:12:52,820 --> 01:13:03,500
+الرقم اللي معطينيه 1729 أي سؤال؟ طيب نيجي لسؤال C
+
+718
+01:13:03,500 --> 01:13:10,180
+بيه Similarly وفعلاً Similarly نيجي الآن لـ C اللي
+
+719
+01:13:10,180 --> 01:13:10,640
+عندي
+
+720
+01:13:15,020 --> 01:13:21,520
+خلّينا نعطيكم الفكرة والتفاصيل لكم الـ C بيقول
+
+721
+01:13:21,520 --> 01:13:34,380
+for any integer A أثبت إن A أس 33 تطابق الـ A 
+
+722
+01:13:34,380 --> 01:13:46,400
+modulo 4080 الـ 4080 لو حللناها الـ 4080 هتلاقيها
+
+723
+01:13:46,400 --> 01:13:56,520
+عبارة عن 15 في 17 في 16 بنفع تقول اللي
+
+724
+01:13:56,520 --> 01:14:03,340
+هو عندي بدل الـ 15 اللي هو 5 في 3
+
+725
+01:14:03,340 --> 01:14:06,880
+واضحه؟
+
+726
+01:14:06,880 --> 01:14:12,890
+واضح أه؟ الآن بتظل اللي هي مين عنده الإشكالية في
+
+727
+01:14:12,890 --> 01:14:17,430
+مين الـ 16 الباقي كله بنفس الأسلوب اللي جاب
+
+728
+01:14:17,430 --> 01:14:21,350
+الـ 15 زي اللي جاب الـ 15 بالظبط بتحصل على
+
+729
+01:14:21,350 --> 01:14:24,710
+الـ 5 وعلى الـ 3 وعلى الـ 17 لاحظ الـ 5
+
+730
+01:14:24,710 --> 01:14:28,830
+أربعة five خمسة أربعة أربعة من الـ 32
+
+731
+01:14:28,830 --> 01:14:33,110
+أربعة بتقدر ترفحها 4 في 8 بت 32
+
+732
+01:14:33,110 --> 01:14:38,040
+والباقي بتضرب وضرب فاهمين أه؟ ونفس الشيء الـ 3
+
+733
+01:14:38,040 --> 01:14:41,220
+اللي هو five 3 جداش 2 فـ 32 بيصير
+
+734
+01:14:41,220 --> 01:14:44,660
+16 في 2 بـ 32 الـ 17 اش 6
+
+735
+01:14:44,660 --> 01:14:47,760
+عشر 16 في 2 بـ 32 دلوقت عندنا مين
+
+736
+01:14:47,760 --> 01:14:53,460
+اللي هو الـ 16 الآن برضه بيدخلها اللي هو
+
+737
+01:14:53,460 --> 01:15:06,040
+الحالتين for اللي هو for any approved similarly
+
+738
+01:15:08,890 --> 01:15:20,150
+as in A A أس 33 تطابق A مدول 5 A
+
+739
+01:15:20,150 --> 01:15:26,130
+أس 33 تطابق A مدول 3 A أس 33
+
+740
+01:15:26,130 --> 01:15:33,110
+وتلاتين تطابق A مدول 17 هذا كله similarly as
+
+741
+01:15:33,110 --> 01:15:39,380
+in A نيجي الآن ايش بدنا نشتغل هذا على الجهة بالنسبة
+
+742
+01:15:39,380 --> 01:15:45,740
+لمن؟ للـ 16 الآن if هو
+
+743
+01:15:45,740 --> 01:15:54,000
+طبعاً كاتب for any of integer A for any of integer
+
+744
+01:15:54,000 --> 01:15:59,160
+A الآن عندي ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+745
+01:15:59,160 --> 01:15:59,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+746
+01:15:59,520 --> 01:16:00,420
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+747
+01:16:00,420 --> 01:16:00,540
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+748
+01:16:00,540 --> 01:16:01,240
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+749
+01:16:01,240 --> 01:16:01,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+750
+01:16:01,440 --> 01:16:01,940
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+751
+01:16:01,940 --> 01:16:02,460
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+752
+01:16:02,460 --> 01:16:02,580
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+753
+01:16:07,560 --> 01:16:11,040
+أيه؟ الـ greatest common divisor بين الـ A و الـ 16
+
+754
+01:16:11,040 --> 01:16:17,640
+ايش هيساوي؟ 1 لأن الـ 16 بقى عن 2 قوى 4
+
+755
+01:16:17,640 --> 01:16:23,840
+يعني اللي هو مافيش فيها غير 2 يعني هي وال
+
+756
+01:16:23,840 --> 01:16:26,620
+odd integer relatively prime
+
+757
+01:16:29,860 --> 01:16:31,720
+في القرآن يقول الانتجار الـ Great scheme of
+
+758
+01:16:31,720 --> 01:16:35,680
+divisors بين A و 16 بيساوي 1 إذا اللي هي We can
+
+759
+01:16:35,680 --> 01:16:43,940
+apply Ehlers theorem then A to the power of 16
+
+760
+01:16:43,940 --> 01:16:53,400
+تطابق الواحد مدول الـ 16 واضح؟
+
+761
+01:16:53,400 --> 01:16:58,710
+أي سؤال؟ 5 of 16 اللي 2 و 4 اللي 2 و 3 اللي سألت
+
+762
+01:16:58,710 --> 01:17:03,210
+معاها قبل شوية، مظبوط؟ 2 أس 3 اللي هي
+
+763
+01:17:03,210 --> 01:17:10,550
+جداش تطلع 8 معايا then فاي أوف 16 الـ A أس
+
+764
+01:17:10,550 --> 01:17:14,690
+8 تطابق الواحد مدول 16 ظهرت النتيجة الآن
+
+765
+01:17:14,690 --> 01:17:21,150
+الآن 8 بنرفحها للأس 4 وهذه للأس
+
+766
+01:17:21,150 --> 01:17:25,410
+4 فاهمين؟ الآن سارعين دي بنضرب الجهتين في
+
+767
+01:17:25,410 --> 01:17:32,020
+مين؟ فيه فبصير A و الـ 33 تطابق الـ A مدول 16
+
+768
+01:17:32,020 --> 01:17:40,280
+الآن نيجي لـ 1 و 2 و 3 و 4 الـ A الـ 5 و الـ 3
+
+769
+01:17:40,280 --> 01:17:44,500
+والـ 17 والـ 16 relative to prime inverse إذاً
+
+770
+01:17:44,500 --> 01:17:47,880
+اللي هي A الـ 33 تطابق الـ A مدول عصر ضرب اللي
+
+771
+01:17:47,880 --> 01:17:54,640
+هو 4080 ووضحت الصورة نيجي للسؤال اللي بعده السؤال
+
+772
+01:17:54,640 --> 01:17:56,720
+الـ 4 بيقول لك show that إذا كان الـ grace code
+
+773
+01:17:56,720 --> 01:17:59,900
+divisor بين الـ A و الـ N و A-1 و الـ N
+
+774
+01:17:59,900 --> 01:18:06,480
+بيساوي 1 إذا اللي هو استنتج للعلاقة اللي موجودة
+
+775
+01:18:06,480 --> 01:18:13,120
+نقول السؤال كمان مرة ونكتبه ونشوف كيف بدنا نبرهن
+
+776
+01:18:13,120 --> 01:18:21,460
+السؤال السؤال الـ 4 show
+
+777
+01:18:21,460 --> 01:18:23,520
+that
+
+778
+01:18:24,850 --> 01:18:29,190
+if the greatest common divisor بين الـ A و الـ N
+
+779
+01:18:29,190 --> 01:18:33,990
+بيساوي
+
+780
+01:18:33,990 --> 01:18:41,510
+1 then ما يلي صحيح اللي هو 1 + A + A
+
+781
+01:18:41,510 --> 01:18:50,870
+تربيع + A أس 5 N - 1 يطابق صفر مدول N
+
+782
+01:18:50,870 --> 01:19:00,670
+مدول N معايا يا شباب A proof .. A proof since
+
+783
+01:19:00,670 --> 01:19:05,490
+the greatest common divisor بين الـ A و الـ N
+
+784
+01:19:05,490 --> 01:19:13,750
+بيساوي 1 then by Ehlers theorem بدي يكون عندي A
+
+785
+01:19:13,750 --> 01:19:23,110
+to the power of 5 N يطابق الواحد مدول N مظبوط؟ واضح
+
+786
+01:19:23,110 --> 01:19:30,330
+أه؟ لكن لو اجينا but A to the power of 5 N ناقص 1
+
+787
+01:19:30,330 --> 01:19:36,770
+هذه ايش هتساوي بقدر أكتبها على صورة اللي هو اللي
+
+788
+01:19:36,770 --> 01:19:41,910
+موجود عندي بدي أحللها يعني عبارة عن A - 1 في
+
+789
+01:19:41,910 --> 01:19:48,270
+A أس 5 N ناقص 1 زائد و بظل أنزل لما أصل
+
+790
+01:19:48,270 --> 01:19:55,530
+A تربيع + A + 1 لاحظ هذه ستصبح A أس 5 N
+
+791
+01:19:55,530 --> 01:20:03,550
+وهذه ستصبح A أس 5 N ناقص 1 وهذه A تكعيب وهذه
+
+792
+01:20:03,550 --> 01:20:07,790
+A تربيع وهذه A وهذه ناقصها فكل ال terms بيروح مع
+
+793
+01:20:07,790 --> 01:20:12,850
+بعض بيظل بس أول term وآخر term اللي هو A أس 5 N
+
+794
+01:20:12,850 --> 01:20:20,410
+ناقص مين ناقص 1 ماشي الحال طيب هذه الآن من اللي
+
+795
+01:20:20,410 --> 01:20:25,350
+فوق تطابق صفر مدول N إذا هذه ايش هتطابق صفر
+
+796
+01:20:25,350 --> 01:20:34,450
+مدول N إذا from 1 and 2 from 1
+
+797
+01:20:34,450 --> 01:20:40,610
+and 2 بكون عندي A - 1 في A أس 5 N
+
+798
+01:20:40,610 --> 01:20:46,410
+ناقص 1 زائد زائد A تربيع + A + 1 تطابق
+
+799
+01:20:46,410 --> 01:20:52,140
+صفر مدول N لكن العامل المشترك الأعلى بين العدد
+
+800
+01:20:52,140 --> 01:20:57,120
+هذا وبين N ايش بيساوي 1 ماعطيني يعني العامل
+
+801
+01:20:57,120 --> 01:20:59,340
+المشترك الأعلى بين A نقص 1 و N ايش بيساوي
+
+802
+01:20:59,340 --> 01:21:02,300
+1 مدام العامل المشترك الأعلى بين هذا وما ده
+
+803
+01:21:02,300 --> 01:21:09,130
+1 إذا بقدر اختصر وأنا مرتاح إذا بالعامل المشترك
+
+804
+01:21:09,130 --> 01:21:15,430
+اللي أعلى بين الـ A-1 و الـ N بيساوي 1 ثم اللي هو
+
+805
+01:21:15,430 --> 01:21:21,050
+أكيد بـ C بيظل عندي A 5N نقص 1 زائد زائد A تربيع
+
+806
+01:21:21,050 --> 01:21:27,390
+زائد A + 1 تطابق صفر مدول N وهو المطلوب
+
+807
+01:21:39,000 --> 01:21:44,620
+كبّر كبّر سيبه
+
+808
+01:21:44,620 --> 01:21:51,640
+سيبه ماشي الحال هذا الآن سؤال مين سؤال 7 سؤال
+
+809
+01:21:51,640 --> 01:22:00,640
+7 7 3 ما فيش 5 أصلاً 7 4 عالين
+
+810
+01:22:00,640 --> 01:22:07,860
+عالين اه find the unit digits of 3 أس 1000 by
+
+811
+01:22:07,860 --> 01:22:30,560
+means of Ehlers theorem معايا السؤال
+
+812
+01:22:30,560 --> 01:22:33,100
+السابع foreign
+
+813
+01:22:35,880 --> 01:22:46,700
+the unit digit of 3 أس 1000 by means of Ehlers
+
+814
+01:22:46,700 --> 01:22:56,220
+theory معايا الآن بدنا نشوف العدد هذا يطابق ماذا
+
+815
+01:22:56,220 --> 01:23:05,550
+مدول 10 اللي هو خانة الآحاد الآن عندي Solution أو
+
+816
+01:23:05,550 --> 01:23:10,090
+Proof أو اللي بدنا اياها مدام بدنا الـ unit digit
+
+817
+01:23:10,090 --> 01:23:14,330
+معناته بدنا اياها اللي هو مدول 10 على أساس ان هو
+
+818
+01:23:14,330 --> 01:23:19,910
+نعرف المتبقي القسمة على 10 يعني هيكون بدنا ايش
+
+819
+01:23:19,910 --> 01:23:24,910
+خانة الآحاد في 3 أس 1000 إذا الـ modulo اللي بدنا
+
+820
+01:23:24,910 --> 01:23:28,770
+ايه عبارة عن 10 و الـ 3 اللي هي الأساس لـ
+
+821
+01:23:28,770 --> 01:23:31,470
+Greatest Common Divisor بين الـ 3 و الـ 10 بيساوي
+
+822
+01:23:31,470 --> 01:23:39,260
+1 since then اكيد by Ehlers theorem يكون عندي
+
+823
+01:23:39,260 --> 01:23:45,120
+3 و ده power of 10 يطابق الواحد مدول مين مدول
+
+824
+01:23:45,120 --> 01:23:50,120
+10 power of 10 اللي هي عبارة عن قداش 4 مظبوط
+
+825
+01:23:50,120 --> 01:23:53,000
+اللي هي power of 2 و power of 5 اللي مش حافظ power of
+
+826
+01:23:53,000 --> 01:23:57,870
+2 1 و power of 5 4 ماشي الحال فبيصير اللي
+
+827
+01:23:57,870 --> 01:24:02,610
+هو 3 أس 4 أي يطابق الواحد مدول 10
+
+828
+01:24:02,610 --> 01:24:07,550
+الـ 4 تقبل قسمة على 4 إذا بدك تقول أس قداش
+
+829
+01:24:07,550 --> 01:24:12,230
+فـ 25 و هادي أس 25 يعني بمعنى آخر
+
+830
+01:24:12,230 --> 01:24:16,050
+3 أس 1000 يطابق الواحد مدول 10 يعني الـ
+
+831
+01:24:16,050 --> 01:24:20,050
+unit digit قداش بيساوي 1 الـ unit digit is 1
+
+832
+01:24:20,050 --> 01:24:26,630
+اللي بعده السؤال اللي بعده السؤال 8 ايه 8
+
+833
+01:24:26,630 --> 01:24:31,310
+ايه اللي بيقول 8 هي بيقول ده كان العام
+
+834
+01:24:31,310 --> 01:24:35,370
+المشترك الأعلى بين الـ A و الـ N لـ Greatest Common
+
+835
+01:24:35,370 --> 01:24:40,130
+Divisor بين الـ A و الـ N بيساوي 1 show that the
+
+836
+01:24:40,130 --> 01:24:46,830
+linear congruences show that the linear
+
+837
+01:24:46,830 --> 01:24:55,110
+congruences A X و يطابق الـ B مدول N has a solution
+
+838
+01:24:57,310 --> 01:25:04,790
+X تطابق أو has the solution X
+
+839
+01:25:04,790 --> 01:25:12,710
+يطابق الـ B A to the power of 5N ناقص 1 العامل
+
+840
+01:25:12,710 --> 01:25:15,410
+المشترك اللي على بين الـ A و الـ N ايش مقاله بيساوي 1
+
+841
+01:25:15,410 --> 01:25:19,790
+واحد إذا في عندي unique solution لهذه إيش اللي هي
+
+842
+01:25:19,790 --> 01:25:25,390
+التطابق معايا طيب احنا طبعا النظرية العامة أنه
+
+843
+01:25:25,390 --> 01:25:29,070
+العامل المشترك اللي على بين الـA والـN هو D ببسم الـB
+
+844
+01:25:29,070 --> 01:25:31,850
+إذا ان في عندي D mutually in congruent solutions
+
+845
+01:25:31,850 --> 01:25:34,930
+لكن الـA والـN بس واحد كده بتبسم الـB إذا اللي
+
+846
+01:25:34,930 --> 01:25:38,030
+أي B في الدنيا هيكون فيه unique solution بدنا
+
+847
+01:25:38,030 --> 01:25:47,540
+نوجده الآن الـproof بما أنه أو since الـ greatest
+
+848
+01:25:47,540 --> 01:25:51,340
+common divisor بين الـA والـN بيساوي واحد then by
+
+849
+01:25:51,340 --> 01:25:56,120
+Euler's theorem A to the ϕN تطابق الواحد modulo N
+
+850
+01:25:56,120 --> 01:26:02,780
+modulo N صح ولا لأ معايا يا شباب اضرب للجهتين في B
+
+851
+01:26:02,780 --> 01:26:08,900
+فبصير A في B تطابق الـB modulo N
+
+852
+01:26:08,900 --> 01:26:15,620
+هذه هي بالظبط برضه اللي هو A في A أس ϕN ناقص
+
+853
+01:26:15,620 --> 01:26:23,020
+الواحد في B تطابق الـ B مدولو مين؟ مدولو N إذا X
+
+854
+01:26:23,020 --> 01:26:29,620
+بتساوي هذا الكلام hence X تطابق اللي هو A to the
+
+855
+01:26:29,620 --> 01:26:39,550
+ϕN ناقص واحد في B مدولو N is the unique solution
+
+856
+01:26:39,550 --> 01:26:48,910
+solution a هو ال solution الوحيد اللي هو modulo n
+
+857
+01:26:48,910 --> 01:26:55,970
+لما بقول استخدم part a to solve the linear
+
+858
+01:26:55,970 --> 01:27:00,270
+congruences ومعطيك congruences اللي هو الواحدة من
+
+859
+01:27:00,270 --> 01:27:05,330
+هنا اللي هي خلّينا نحل الواحدة غير المحلولة اللي
+
+860
+01:27:05,330 --> 01:27:17,630
+هو 13x تلاتاش اكس تطابق التنين مدلو جداش مدلو أربعين
+
+861
+01:27:17,630 --> 01:27:22,730
+صح هذا
+
+862
+01:27:22,730 --> 01:27:30,390
+بيه بيقول use part a to solve the linear congruence
+
+863
+01:27:30,390 --> 01:27:36,340
+تلاتاش اكس تطابق التنين مدلو مين مدلو أربعين عند الـ
+
+864
+01:27:36,340 --> 01:27:41,040
+A إيش بتساوي؟ الـ A إيش بتساوي حسب اللي ذات؟ اللي
+
+865
+01:27:41,040 --> 01:27:46,900
+هي 13 والـ B إيش بتساوي؟ 2 والـ N إيش بتساوي؟ 40
+
+866
+01:27:46,900 --> 01:27:49,500
+لاحظ العام المشترك اللي على بين الـ 13 والـ 40 إيش
+
+867
+01:27:49,500 --> 01:27:53,700
+بتساوي؟ 1 إذا حسب السؤال في عند unique solution
+
+868
+01:27:53,700 --> 01:27:58,920
+اللي هو مين هو بالظبط؟ اللي هو X ده solution ده
+
+869
+01:27:58,920 --> 01:28:07,090
+unique solution modulo 40 is given by اللي هو X
+
+870
+01:28:07,090 --> 01:28:17,370
+يطابق الـ A جداش الـ A؟ تلتاش أس ϕ of أربعين
+
+871
+01:28:17,370 --> 01:28:23,910
+ناقص الواحد مضروب في مين؟ مضروب في اتنين بيه إيش
+
+872
+01:28:23,910 --> 01:28:32,010
+بتساوي؟ اتنين واضح ها؟ بتوجد الـ ϕ أربعين؟ ها
+
+873
+01:28:32,010 --> 01:28:32,950
+بتعرفوا توجدوها
+
+874
+01:28:56,460 --> 01:28:57,860
+5x8x5x8x5x8x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x5x
+
+875
+01:29:04,000 --> 01:29:13,960
+السؤال التالت هو Verify that the integers from a
+
+876
+01:29:13,960 --> 01:29:21,540
+reduced residue system modulo 9 اطلعنا على الكتابة
+
+877
+01:29:21,540 --> 01:29:27,680
+شوية سؤال 12 Verify
+
+878
+01:29:27,680 --> 01:29:32,230
+that الأعداد اللي عندي هذا واحد اتنين تلاتة أربعة
+
+879
+01:29:32,230 --> 01:29:35,270
+خمسة ستة form a reduced residual system modulo 9
+
+880
+01:29:35,270 --> 01:29:39,190
+modulo 9 بدنا نشوف شو معناه اللي هو ال reduced
+
+881
+01:29:39,190 --> 01:29:43,430
+residual system modulo 9 أو modulo N احنا حكينا عن
+
+882
+01:29:43,430 --> 01:29:46,950
+ال complete residual system modulo N بنقول أنه
+
+883
+01:29:46,950 --> 01:29:53,390
+عندي اللي هو الـ الـ الـ الـ واحد عندي اخذنا مثال و
+
+884
+01:29:53,390 --> 01:29:58,660
+اتنين عندي الـ N ناقص واحد هذه والـ صفر معاهم أو اللي
+
+885
+01:29:58,660 --> 01:30:01,300
+عندك الآن بتعمل ليه Complete Residual System
+
+886
+01:30:01,300 --> 01:30:05,860
+ودلوقتي إذا حققت الشرطين اللي بتذكرها أو أن يكون
+
+887
+01:30:05,860 --> 01:30:11,120
+هؤلاء أولئك عددهم N هذا واحد الثاني أنه يكون أن
+
+888
+01:30:11,120 --> 01:30:17,840
+incongruent لبعض Modulo N أي عدد A1 لعند ال A N
+
+889
+01:30:17,840 --> 01:30:23,200
+بعمل complete system Modulo N إذا كان عددهم N و
+
+890
+01:30:23,200 --> 01:30:28,900
+هؤلاء أشمالهم incongruent أو شرطين تانيات أنه من
+
+891
+01:30:28,900 --> 01:30:36,700
+A1 A2 لعند A N مش عارفين كده عدد نحن ويكون
+
+892
+01:30:36,700 --> 01:30:41,100
+اللي هنا incongruent لبعض وفي نفس الوجهة أي عدد
+
+893
+01:30:41,100 --> 01:30:45,360
+من الـ Z يكون congruent لمين؟ لواحد من هدول إذا هذه
+
+894
+01:30:45,360 --> 01:30:48,840
+مجموعة الأعداد اللي مش عارفين عددها بتحقق الشرطين
+
+895
+01:30:48,840 --> 01:30:51,920
+هذا بقول لأ بنسميهم Complete Residue System Model
+
+896
+01:30:51,920 --> 01:30:55,000
+1 واحنا أسهل Complete Residue System Model 1 اللي
+
+897
+01:30:55,000 --> 01:30:59,130
+بنشتغله من واحد لعند مين؟ لعند N الآن في حاجة اسمها
+
+898
+01:30:59,130 --> 01:31:03,370
+reduced residual system modulo n الـ reduced إيش
+
+899
+01:31:03,370 --> 01:31:10,470
+بتسوي؟ بتيجي للأعداد اللي من واحد لعند N وبتاخد
+
+900
+01:31:10,470 --> 01:31:13,650
+relatively prime .. بتيجي للأعداد .. آسف بتيجي
+
+901
+01:31:13,650 --> 01:31:17,170
+للأعداد اللي في ال complete residual system وبتاخد
+
+902
+01:31:17,170 --> 01:31:21,190
+منه بس اللي relatively prime مع الـ N اللي بيأثر
+
+903
+01:31:21,190 --> 01:31:23,630
+relatively prime مع الـ N هذا اللي بنسميه reduced
+
+904
+01:31:23,630 --> 01:31:27,620
+residual system modulo n أو زي ما هو معرفه في
+
+905
+01:31:27,620 --> 01:31:32,500
+الكتاب في اللي عندها كمالي بنقول أنه إن الأعداد
+
+906
+01:31:32,500 --> 01:31:36,080
+اللي معطية إنها reduced residual modulo n إذا
+
+907
+01:31:36,080 --> 01:31:40,440
+بتحقق شرطين أول شيء عددهم ϕN يعني الـ
+
+908
+01:31:40,440 --> 01:31:45,000
+relatively prime أقل من عند واحد عندنا معايا اتنين
+
+909
+01:31:45,000 --> 01:31:49,680
+يكونوا كلهم incongruent لبعض إذا في عندي شرطين
+
+910
+01:31:49,680 --> 01:31:53,040
+بنقول a set of ϕN of integers that are relatively
+
+911
+01:31:53,040 --> 01:31:57,000
+prime to N and that are incongruent modulo N is
+
+912
+01:31:57,000 --> 01:32:01,660
+called إيش ماله؟ reduced set أو reduced modulo N
+
+913
+01:32:01,660 --> 01:32:05,620
+modulo N أو زي ما بيسميه reduced system modulo N
+
+914
+01:32:05,620 --> 01:32:09,760
+modulo N إذا ال reduced system modulo N بيحقق
+
+915
+01:32:09,760 --> 01:32:16,570
+شرطين إن عددهم هما ϕN اتنين إيه تمنين مع بعض are
+
+916
+01:32:16,570 --> 01:32:21,150
+إيه شمالهم incongruent ويكونوا relatively prime مع
+
+917
+01:32:21,150 --> 01:32:28,650
+مين؟ مع الـ N a
+
+918
+01:32:28,650 --> 01:32:30,690
+set of ϕN of integers that are relatively
+
+919
+01:32:30,690 --> 01:32:36,530
+prime to N and are incongruent نيجي الأن لسؤال
+
+920
+01:32:36,530 --> 01:32:43,510
+خليني أحل واحد منهم شوف كيف عندي اللي هو الأعداد
+
+921
+01:32:45,220 --> 01:32:52,620
+ناقص واحد و تلاتين ناقص ستة عشر ناقص تمانية اللي
+
+922
+01:32:52,620 --> 01:32:59,500
+هو تلات عشر خمسة وعشرين وتمانين هذول اللي بدنا
+
+923
+01:32:59,500 --> 01:33:03,840
+نثبت أنه الـ form produced residual system modulo N
+
+924
+01:33:03,840 --> 01:33:09,840
+معايا الآن إذًا عشان نثبت إنهم reduced residual
+
+925
+01:33:09,840 --> 01:33:14,460
+system مدولو بدنا نثبت إنهم أشمالهم congruent
+
+926
+01:33:14,460 --> 01:33:22,040
+مع بعض أو بدنا نثبت إن عدد هم ϕN عندي أنا مدولو
+
+927
+01:33:22,040 --> 01:33:32,300
+مين جد؟ بده مدولو تسعة بده مدولو تسعة الآن ϕ of
+
+928
+01:33:32,300 --> 01:33:36,140
+تسعة إيش بتساوي؟ تلاتة
+
+929
+01:33:39,460 --> 01:33:48,680
+في اللي هو اتنين فعارفين كيف اه هذه في نسيت في
+
+930
+01:33:48,680 --> 01:33:56,580
+تلاتة تربيع إيش بيساوي؟ تلاتة في تلاتة ناقص واحد أو
+
+931
+01:33:56,580 --> 01:34:02,860
+كيف بنحسبها تلاتة تربيع في واحد ناقص تلت ثاني
+
+932
+01:34:02,860 --> 01:34:08,190
+الواحد إذاً عدد الأعداد إيش بده الدولة ستة واحد اتنين
+
+933
+01:34:08,190 --> 01:34:11,990
+تلاتة أربعة خمسة ستة هي الخطوة الأولى الآن relatively
+
+934
+01:34:11,990 --> 01:34:15,090
+prime مع التسعة أكيد relatively prime مع
+
+935
+01:34:15,090 --> 01:34:17,510
+التسعة التمانين والخمسة وعشرين والتلات عشر
+
+936
+01:34:17,510 --> 01:34:20,090
+والتمانية والستة عشر والواحد والتلاتين أشمالهم
+
+937
+01:34:20,090 --> 01:34:26,850
+relatively prime مع مين؟ مع التسعة الآن الآن كلهم
+
+938
+01:34:26,850 --> 01:34:32,780
+مقارنة لبعض مدولو التسعة الآن كيف نثبت إن
+
+939
+01:34:32,780 --> 01:34:38,500
+الـ incongruent غير متطابق يعني طبعًا إنك تيجي تمسك
+
+940
+01:34:38,500 --> 01:34:42,120
+كل واحد وتشوف مش congruent للتاني يمكن شوية يكون
+
+941
+01:34:42,120 --> 01:34:47,780
+عاش اللي هو متعب شوية لكن في طريقة أسهل إنك بتيجي
+
+942
+01:34:47,780 --> 01:34:55,380
+تمسك كل عدد وبتشوفه متطابق من الواحد والتمنية
+
+943
+01:34:55,380 --> 01:34:59,320
+والأربعة والخمسة والسبعة
+
+944
+01:35:01,300 --> 01:35:05,520
+والتامنية واحد اتنين تلاتة أربعة خمسة ستة اللي من
+
+945
+01:35:05,520 --> 01:35:11,680
+وين جاية هذول اللي جاية من ال complete residue
+
+946
+01:35:11,680 --> 01:35:16,120
+system مدولو وشيل منهم اللي مش relatively prime مع
+
+947
+01:35:16,120 --> 01:35:24,060
+الـ 9 إيش ال complete residue system مدولو تسعة واحد
+
+948
+01:35:24,060 --> 01:35:28,120
+واتنين تلاتة وأربعة وخمسة وستة وسبعة وتمانية
+
+949
+01:35:28,120 --> 01:35:31,360
+وتسعة هذا الـ Complete Residue System مدولو
+
+950
+01:35:31,360 --> 01:35:35,500
+مين؟ مدولو تسعة الآن الـ Relatively Prime من هنا
+
+951
+01:35:35,500 --> 01:35:38,700
+مع التسعة من هنا واحد واثنين وأربعة أو خمسة أو
+
+952
+01:35:38,700 --> 01:35:41,940
+سبعة أو تمانية هذول Incongruent و Relatively
+
+953
+01:35:41,940 --> 01:35:47,180
+Prime وعددهم ϕN إيش عاملين؟ Reduced Residue System
+
+954
+01:35:47,180 --> 01:35:51,160
+يعني كل اتنين من هذول are incongruent مع بعض مدولو
+
+955
+01:35:51,160 --> 01:35:55,690
+سمعروف ماشي اللي هم بتثبت لك إن كل واحد من هدول
+
+956
+01:35:55,690 --> 01:35:59,150
+بيطابق واحد من هدول أو أي واحد من هدول بيطابق واحد
+
+957
+01:35:59,150 --> 01:36:05,290
+من هدول شوف كيف إذا أنا الآن اللي بدنا نثبت ه
+
+958
+01:36:05,290 --> 01:36:12,110
+عندي سالب واحد و تلاتين يطابق module تسعة سالب
+
+959
+01:36:12,110 --> 01:36:17,550
+واحد و تلاتين module تسعة اللي هو خمسة صح؟
+
+960
+01:36:27,480 --> 01:36:36,120
+زيد 36 هنا ماشي الحال؟ طيب السالب 16 اللي هو 2
+
+961
+01:36:36,120 --> 01:36:39,880
+مظبوط؟
+
+962
+01:36:39,880 --> 01:36:48,920
+Modulo 9 التلات عشر السالب تمانية 1 Modulo 9
+
+963
+01:36:48,920 --> 01:37:03,240
+التلات عشر تطابق سالب اللي هو 4 مظبوط؟ معايا الـ 25
+
+964
+01:37:03,240 --> 01:37:15,320
+الواسيل منه 18 بـ 7 فاهمين كيف اه؟ الـ 80 شيل منه
+
+965
+01:37:15,320 --> 01:37:20,460
+كذا؟ شيل
+
+966
+01:37:20,460 --> 01:37:30,680
+منه 72 سالب واحد اللي هو تمانية إذا صار عندي هدول
+
+967
+01:37:30,680 --> 01:37:39,900
+الأعداد كل واحد بيطابق واحد وبس واحد من اللي عندي
+
+968
+01:37:39,900 --> 01:37:45,560
+هنا اه بناء على هذه المعلومات صار إن اللي هو سالب
+
+969
+01:37:45,560 --> 01:37:48,260
+تلت عشر سالب ستة عشر سالب تمانين وتلات عشر وخمسة
+
+970
+01:37:48,260 --> 01:37:52,400
+وعشرين وتمانين أشمالهم are incongruent in pair
+
+971
+01:37:52,400 --> 01:38:03,430
+ماشي لأن since واحد واثنين وأربعة وسبعة وتمانية
+
+972
+01:38:03,430 --> 01:38:19,370
+وخمسة are incongruent in pairs modulo تسعة هذا
+
+973
+01:38:19,370 --> 01:38:26,110
+ساميه star then by star
+
+974
+01:38:27,530 --> 01:38:32,410
+معايا لأن هذول in congruent in pairs عارفين أنه
+
+975
+01:38:32,410 --> 01:38:37,130
+الأعداد اللي هي من واحد لعين تمانية غير متطابقات
+
+976
+01:38:37,130 --> 01:38:42,490
+مدولو تسعة من واحد لعين تسعة غير متطابقات مدولو تسعة
+
+977
+01:38:43,460 --> 01:38:47,940
+الآن إذا هذول الجزء منهم غير متطابقات مدولو 9 هاي
+
+978
+01:38:47,940 --> 01:38:52,500
+واحد وهذول بيطابقن هذول إذا هذول اللي بيطابقنهم
+
+979
+01:38:52,500 --> 01:38:57,880
+أكيد غير متطابقات مدولو 9 then by star اللي هو ناقص
+
+980
+01:38:57,880 --> 01:39:02,620
+واحد وتلاتين وناقص ستاش وناقص تمانية وتلاتاش و
+
+981
+01:39:02,620 --> 01:39:09,420
+خمسة وعشرين وثمانين are incongruent
+
+982
+01:39:09,420 --> 01:39:20,040
+مدل 9 معايا But But
+
+983
+01:39:20,040 --> 01:39:28,300
+اللي هو الأعداد هذه خلّيني أسميها اللي هو A R
+
+984
+01:39:28,300 --> 01:39:31,620
+Relatively
+
+985
+01:39:31,620 --> 01:39:34,720
+Prime
+
+986
+01:39:34,720 --> 01:39:40,320
+Relatively Prime Relatively Prime with مين؟ with 9
+
+987
+01:39:42,050 --> 01:39:50,150
+أه relatively prime of تسعة and the number of
+
+988
+01:39:50,150 --> 01:40:01,030
+elements in A is five تسعة تساوي ستة then اللي هو
+
+989
+01:40:01,030 --> 01:40:09,670
+A is a reduced residue system
+
+990
+01:40:11,160 --> 01:40:16,980
+موضوله تسعة ما هو المطلوب سامحونا لأنه احنا اتأخرنا
+
+991
+01:40:16,980 --> 01:40:26,670
+كتير عليكم ضايل سبعة أربعة وطبعا الـ بي والـ سي
+
+992
+01:40:26,670 --> 01:40:33,650
+مشابه زي اللي جابله الآن سؤال تلتاشر برضه مشابه
+
+993
+01:40:33,650 --> 01:40:39,130
+إذا في نصيب المرة الجاية إن شاء الله بنحله أو
+
+994
+01:40:39,130 --> 01:40:42,750
+بنكمل discussion لسبعة أربعة برك الله فيك 
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/UAsGw2SpSdk_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/UAsGw2SpSdk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..40ea09039d1817393b36b3079988231593720c79
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/UAsGw2SpSdk_raw.json
@@ -0,0 +1 @@
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mod 11شمال العشر العشرة هي أصلا في أصل العدد كتابة العدد مكتوب أصلا عددنا على الصورة العشرية decimal representation فطبيعي أساسه عشرة", "tokens": [2655, 9566, 16758, 4587, 8717, 995, 4587, 9381, 36764, 24401, 1072, 2975, 8592, 2304, 6027, 18863, 46309, 18863, 8592, 25720, 39896, 5551, 9381, 15040, 8978, 5551, 36520, 18863, 3215, 3215, 9122, 2655, 16758, 3660, 18863, 3215, 3215, 3714, 4117, 2655, 37746, 5551, 9381, 15040, 6225, 3215, 3215, 8315, 15844, 31767, 13063, 3660, 18863, 46309, 10632, 26601, 10290, 6156, 9566, 21292, 3615, 1829, 5551, 3794, 32277, 3224, 6225, 8592, 25720], "avg_logprob": -0.2397321371095521, "compression_ratio": 1.559748427672956, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 962.92, "end": 963.78, "word": "تطابق", "probability": 0.68524169921875}, {"start": 963.78, "end": 964.84, "word": " ناقص", "probability": 0.7267913818359375}, {"start": 964.84, "end": 965.46, "word": " واحد", "probability": 0.96484375}, {"start": 965.46, "end": 966.4, 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10 تطابق ال P of ناقص 1 من مين من ال 11 ال P of 10 هي اللي سمناها الان و ال P of ناقص 1 هي اللي سمناها مين ال T similarly زي البرنامج الأولين بالظبط", "tokens": [6027, 7649, 2423, 39184, 12, 16, 31439, 13672, 1829, 5296, 39184, 1500, 4724, 15042, 16472, 2423, 39184, 1266, 6055, 9566, 16758, 4587, 2423, 39184, 12, 16, 9154, 2423, 2975, 550, 538, 20904, 13672, 1829, 12174, 36150, 4724, 8592, 2407, 10632, 430, 295, 1266, 6055, 9566, 16758, 4587, 2423, 430, 295, 8717, 995, 4587, 9381, 502, 9154, 3714, 9957, 9154, 2423, 2975, 2423, 430, 295, 1266, 39896, 13672, 1829, 8608, 2304, 8315, 11296, 2423, 7649, 4032, 2423, 430, 295, 8717, 995, 4587, 9381, 502, 39896, 13672, 1829, 8608, 2304, 8315, 11296, 3714, 9957, 2423, 314, 14138, 30767, 1829, 2423, 26890, 8315, 2304, 7435, 16247, 12610, 9957, 20666, 19913, 3555, 9566], "avg_logprob": -0.27372160147536884, "compression_ratio": 1.9790575916230366, "no_speech_prob": 0.0, "words": [{"start": 981.65, "end": 982.17, "word": "الان", "probability": 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0.8427734375}, {"start": 2024.59, "end": 2025.31, "word": " له،", "probability": 0.5111083984375}, {"start": 2025.31, "end": 2025.61, "word": " de", "probability": 0.8994140625}, {"start": 2025.61, "end": 2026.67, "word": "-incongruent", "probability": 0.97919921875}, {"start": 2026.67, "end": 2027.73, "word": " solutions،", "probability": 0.84130859375}], "temperature": 1.0}, {"id": 81, "seek": 205435, "start": 2027.97, "end": 2054.35, "text": "معايا؟ طيب الان كي بتاخد .. بتاخد اي حالين هنا بتقول let .. اي حالين هنا هكون let X0 زاد Y على D في T1 and .. and X0 زاد N على D في T2 solutions will enough", "tokens": [2304, 3615, 995, 25528, 22807, 23032, 1829, 3555, 2423, 7649, 9122, 1829, 39894, 47283, 3215, 4386, 39894, 47283, 3215, 1975, 1829, 11331, 6027, 9957, 34105, 39894, 39648, 718, 4386, 1975, 1829, 11331, 6027, 9957, 34105, 8032, 30544, 718, 1783, 15, 30767, 18513, 398, 15844, 413, 8978, 314, 16, 293, 4386, 293, 1783, 15, 30767, 18513, 426, 15844, 413, 8978, 314, 17, 6547, 486, 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are congruent وبدأ أسئلة تناقض معناته أنه صار كل ال solutions اللي جوا أشمالهن in congruent إذن فرضت الآن أنه في two", "tokens": [2407, 46958, 5016, 13672, 1829, 4724, 5016, 4117, 1829, 3224, 718, 1783, 406, 293, 9122, 3215, 3224, 312, 732, 6547, 294, 318, 597, 366, 294, 597, 366, 8882, 19226, 4032, 44510, 10721, 5551, 3794, 19986, 37977, 6055, 8315, 4587, 11242, 20449, 8315, 47395, 14739, 3224, 20328, 9640, 28242, 2423, 6547, 13672, 1829, 10874, 14407, 5551, 8592, 2304, 6027, 3224, 1863, 294, 8882, 19226, 11933, 8848, 1863, 6156, 43042, 2655, 6024, 48506, 14739, 3224, 8978, 732], "avg_logprob": -0.3544407749646588, "compression_ratio": 1.435483870967742, "no_speech_prob": 0.0, "words": [{"start": 2082.74, "end": 2083.14, "word": "واضح", "probability": 0.8880208333333334}, {"start": 2083.14, "end": 2083.24, "word": " اللي", "probability": 0.6248779296875}, {"start": 2083.24, "end": 2084.12, "word": " بحكيه", "probability": 0.97080078125}, {"start": 2084.12, "end": 2084.52, "word": " 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بقولنا المغفرة في النظرية اللي بتقول انت بتختصر من هنا تختصر من هنا لازم تختصر من هنا و من هنا تختصر من هنا برضه من الان لذا صار عندي ذنب", "tokens": [6027, 7649, 6225, 8592, 7649, 1975, 46456, 9381, 2288, 9154, 2423, 7649, 15844, 11778, 1829, 11203, 995, 28671, 19446, 11778, 1829, 4724, 39648, 8315, 9673, 17082, 5172, 25720, 8978, 28239, 19913, 2288, 10632, 13672, 1829, 39894, 39648, 16472, 2655, 39894, 46456, 9381, 2288, 9154, 34105, 6055, 46456, 9381, 2288, 9154, 34105, 5296, 31377, 2304, 6055, 46456, 9381, 2288, 9154, 34105, 4032, 9154, 34105, 6055, 46456, 9381, 2288, 9154, 34105, 4724, 43042, 3224, 9154, 2423, 7649, 5296, 15730, 20328, 9640, 18871, 16254, 29910, 1863, 3555], "avg_logprob": -0.2744485280093025, "compression_ratio": 2.26056338028169, "no_speech_prob": 1.4901161193847656e-06, "words": [{"start": 2191.2000000000003, "end": 2191.84, "word": "الان", "probability": 0.5224609375}, {"start": 2191.84, "end": 2192.48, "word": " عشان", "probability": 0.91845703125}, {"start": 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{"start": 2196.9, "end": 2197.0, "word": " اللي", "probability": 0.87890625}, {"start": 2197.0, "end": 2197.38, "word": " بتقول", "probability": 0.974853515625}, {"start": 2197.38, "end": 2197.62, "word": " انت", "probability": 0.7890625}, {"start": 2197.62, "end": 2198.16, "word": " بتختصر", "probability": 0.983642578125}, {"start": 2198.16, "end": 2198.28, "word": " من", "probability": 0.9814453125}, {"start": 2198.28, "end": 2198.4, "word": " هنا", "probability": 0.35693359375}, {"start": 2198.4, "end": 2198.86, "word": " تختصر", "probability": 0.82989501953125}, {"start": 2198.86, "end": 2198.98, "word": " من", "probability": 0.99365234375}, {"start": 2198.98, "end": 2199.22, "word": " هنا", "probability": 0.91748046875}, {"start": 2199.22, "end": 2199.88, "word": " لازم", "probability": 0.9601236979166666}, {"start": 2199.88, "end": 2200.54, "word": " تختصر", "probability": 0.86309814453125}, {"start": 2200.54, "end": 2200.66, "word": " من", "probability": 0.96142578125}, {"start": 2200.66, "end": 2200.88, "word": " هنا", "probability": 0.9453125}, {"start": 2200.88, "end": 2201.0, "word": " و", "probability": 0.59619140625}, {"start": 2201.0, "end": 2201.06, "word": " من", "probability": 0.56494140625}, {"start": 2201.06, "end": 2201.18, "word": " هنا", "probability": 0.96923828125}, {"start": 2201.18, "end": 2201.62, "word": " تختصر", "probability": 0.9267578125}, {"start": 2201.62, "end": 2201.76, "word": " من", "probability": 0.95751953125}, {"start": 2201.76, "end": 2201.92, "word": " هنا", "probability": 0.52880859375}, {"start": 2201.92, "end": 2202.48, "word": " برضه", "probability": 0.7810872395833334}, {"start": 2202.48, "end": 2203.16, "word": " من", "probability": 0.876953125}, {"start": 2203.16, "end": 2203.52, "word": " الان", "probability": 0.91845703125}, {"start": 2203.52, "end": 2203.92, "word": " لذا", "probability": 0.40081787109375}, {"start": 2203.92, "end": 2204.24, "word": " صار", "probability": 0.87060546875}, {"start": 2204.24, "end": 2204.7, "word": " عندي", "probability": 0.847900390625}, {"start": 2204.7, "end": 2205.66, "word": " ذنب", "probability": 0.9318033854166666}], "temperature": 1.0}, {"id": 88, "seek": 222988, "start": 2206.76, "end": 2229.88, "text": "اللي هو اختصر N على D و N على D و من هنا N على D بيصير D بيصير T1 تطابق T2 Modulo D وهذا ايش معنو Contradiction لإنه احنا مفترضين ال T1 و T2 وين موجودات في Zero واحد اتنين عند D ناقص واحد", "tokens": [6027, 20292, 31439, 1975, 46456, 9381, 2288, 426, 15844, 413, 4032, 426, 15844, 413, 4032, 9154, 34105, 426, 15844, 413, 4724, 1829, 9381, 13546, 413, 4724, 1829, 9381, 13546, 314, 16, 6055, 9566, 16758, 4587, 314, 17, 6583, 13455, 413, 37037, 15730, 1975, 1829, 8592, 20449, 1863, 2407, 4839, 6206, 4105, 5296, 28814, 1863, 3224, 1975, 5016, 8315, 3714, 5172, 2655, 43042, 9957, 2423, 314, 16, 4032, 314, 17, 4032, 9957, 3714, 29245, 23328, 9307, 8978, 17182, 36764, 24401, 1975, 2655, 1863, 9957, 43242, 413, 8717, 995, 4587, 9381, 36764, 24401], "avg_logprob": -0.21161684442473494, "compression_ratio": 1.5104166666666667, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2206.76, "end": 2207.08, "word": "اللي", "probability": 0.4801025390625}, {"start": 2207.08, "end": 2207.34, "word": " هو", "probability": 0.97216796875}, {"start": 2207.34, "end": 2207.92, "word": " اختصر", "probability": 0.94921875}, {"start": 2207.92, "end": 2208.1, "word": " N", "probability": 0.447509765625}, {"start": 2208.1, "end": 2208.32, "word": " على", "probability": 0.74609375}, {"start": 2208.32, "end": 2208.48, "word": " D", "probability": 0.9345703125}, {"start": 2208.48, "end": 2208.6, "word": " و", "probability": 0.91064453125}, {"start": 2208.6, "end": 2208.74, "word": " N", "probability": 0.64208984375}, {"start": 2208.74, "end": 2208.94, "word": " على", "probability": 0.91162109375}, {"start": 2208.94, "end": 2209.32, "word": " D", "probability": 0.9814453125}, {"start": 2209.32, "end": 2210.36, "word": " و", "probability": 0.9033203125}, {"start": 2210.36, "end": 2210.52, "word": " من", "probability": 0.72265625}, {"start": 2210.52, "end": 2210.74, "word": " هنا", "probability": 0.66748046875}, {"start": 2210.74, "end": 2211.0, "word": " N", "probability": 0.892578125}, {"start": 2211.0, "end": 2211.24, "word": " على", "probability": 0.8935546875}, {"start": 2211.24, "end": 2211.48, "word": " D", "probability": 0.990234375}, {"start": 2211.48, "end": 2211.86, "word": " بيصير", "probability": 0.76617431640625}, {"start": 2211.86, "end": 2212.12, "word": " D", "probability": 0.9375}, {"start": 2212.12, "end": 2213.08, "word": " بيصير", "probability": 0.8765869140625}, {"start": 2213.08, "end": 2213.88, "word": " T1", "probability": 0.83740234375}, {"start": 2213.88, "end": 2215.0, "word": " تطابق", "probability": 0.8389892578125}, {"start": 2215.0, "end": 2215.76, "word": " T2", "probability": 0.989013671875}, {"start": 2215.76, "end": 2217.16, "word": " Modulo", "probability": 0.694580078125}, {"start": 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0.80224609375}, {"start": 2224.38, "end": 2224.62, "word": " وين", "probability": 0.4444580078125}, {"start": 2224.62, "end": 2225.38, "word": " موجودات", "probability": 0.9578857421875}, {"start": 2225.38, "end": 2226.14, "word": " في", "probability": 0.76953125}, {"start": 2226.14, "end": 2226.44, "word": " Zero", "probability": 0.351318359375}, {"start": 2226.44, "end": 2226.86, "word": " واحد", "probability": 0.863037109375}, {"start": 2226.86, "end": 2227.46, "word": " اتنين", "probability": 0.9334716796875}, {"start": 2227.46, "end": 2227.86, "word": " عند", "probability": 0.7998046875}, {"start": 2227.86, "end": 2228.3, "word": " D", "probability": 0.95458984375}, {"start": 2228.3, "end": 2229.38, "word": " ناقص", "probability": 0.83160400390625}, {"start": 2229.38, "end": 2229.88, "word": " واحد", "probability": 0.986083984375}], "temperature": 1.0}, {"id": 89, "seek": 225873, "start": 2230.52, "end": 2258.74, "text": "وأي عددين هنا أصلا هما أصلا متبقى لقسمة على D والمتبقيين للقسمة إذا كانوا مختلفين على قول إشمالها in congruent فظرية أن العددين يكونوا متطابقين if and only if they have the same divisor the same remainder when they are divided by the modulo ال N المقياس", "tokens": [2407, 10721, 1829, 6225, 3215, 3215, 9957, 34105, 5551, 9381, 15040, 8032, 15042, 5551, 9381, 15040, 44650, 3555, 4587, 7578, 5296, 4587, 38251, 3660, 15844, 413, 16070, 2304, 2655, 3555, 38436, 9957, 24976, 4587, 38251, 3660, 11933, 15730, 25961, 14407, 3714, 46456, 46538, 9957, 15844, 12174, 12610, 11933, 8592, 2304, 6027, 11296, 294, 8882, 19226, 6156, 19913, 2288, 10632, 14739, 18863, 3215, 3215, 9957, 7251, 30544, 14407, 44650, 9566, 16758, 4587, 9957, 498, 293, 787, 498, 436, 362, 264, 912, 25974, 284, 264, 912, 29837, 562, 436, 366, 6666, 538, 264, 1072, 13455, 2423, 426, 9673, 4587, 25528, 3794], "avg_logprob": -0.3109374886751175, "compression_ratio": 1.5905172413793103, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2230.52, "end": 2231.08, "word": "وأي", 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D1 و T1 و T2 متطابقات بينما T1 و T2 في حققتها في حققتها غير متطابقات إذا صار فيها Contradiction Therefore اللي هو ال solutions اللي هنا فيش ولا two solutions congruent لبعض إذا كل ال solutions اللي في us solutions اللي في us are incongruent solutions أي سؤال", "tokens": [33456, 8978, 23758, 21542, 6027, 3660, 11778, 1829, 1975, 15730, 413, 16, 4032, 314, 16, 4032, 314, 17, 44650, 9566, 16758, 4587, 9307, 49374, 15042, 314, 16, 4032, 314, 17, 8978, 11331, 4587, 38149, 11296, 8978, 11331, 4587, 38149, 11296, 32771, 13546, 44650, 9566, 16758, 4587, 9307, 11933, 15730, 20328, 9640, 8978, 11296, 4839, 6206, 4105, 7504, 13672, 1829, 31439, 2423, 6547, 13672, 1829, 34105, 8978, 8592, 49429, 732, 6547, 8882, 19226, 5296, 3555, 3615, 11242, 11933, 15730, 28242, 2423, 6547, 13672, 1829, 8978, 505, 6547, 13672, 1829, 8978, 505, 366, 834, 556, 894, 317, 6547, 36632, 8608, 33604, 6027], "avg_logprob": -0.3066212824075529, "compression_ratio": 1.9099526066350712, "no_speech_prob": 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{"start": 2271.64, "end": 2271.82, "word": " فيها", "probability": 0.705810546875}, {"start": 2271.82, "end": 2272.66, "word": " Contradiction", "probability": 0.7263997395833334}, {"start": 2272.66, "end": 2273.14, "word": " Therefore", "probability": 0.447021484375}, {"start": 2273.14, "end": 2274.16, "word": " اللي", "probability": 0.9423828125}, {"start": 2274.16, "end": 2274.4, "word": " هو", "probability": 0.98388671875}, {"start": 2274.4, "end": 2274.62, "word": " ال", "probability": 0.564453125}, {"start": 2274.62, "end": 2275.32, "word": " solutions", "probability": 0.57958984375}, {"start": 2275.32, "end": 2275.8, "word": " اللي", "probability": 0.970703125}, {"start": 2275.8, "end": 2276.26, "word": " هنا", "probability": 0.94384765625}, {"start": 2276.26, "end": 2277.28, "word": " فيش", "probability": 0.51641845703125}, {"start": 2277.28, "end": 2277.82, "word": " ولا", "probability": 0.96435546875}, {"start": 2277.82, "end": 2278.1, "word": " two", "probability": 0.59814453125}, {"start": 2278.1, "end": 2278.98, "word": " solutions", "probability": 0.9287109375}, {"start": 2278.98, "end": 2279.86, "word": " congruent", "probability": 0.4833984375}, {"start": 2279.86, "end": 2280.32, "word": " لبعض", "probability": 0.9473876953125}, {"start": 2280.32, "end": 2280.58, "word": " إذا", "probability": 0.798828125}, {"start": 2280.58, "end": 2280.88, "word": " كل", "probability": 0.9404296875}, {"start": 2280.88, "end": 2281.02, "word": " ال", "probability": 0.671875}, {"start": 2281.02, "end": 2281.38, "word": " solutions", "probability": 0.7490234375}, {"start": 2281.38, "end": 2281.66, "word": " اللي", "probability": 0.972900390625}, {"start": 2281.66, "end": 2281.82, "word": " في", "probability": 0.96875}, {"start": 2281.82, "end": 2282.08, "word": " us", "probability": 0.3017578125}, {"start": 2282.08, "end": 2282.84, "word": " solutions", "probability": 0.439697265625}, {"start": 2282.84, "end": 2283.14, "word": " اللي", "probability": 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{"start": 2300.43, "end": 2301.57, "word": " بدي", "probability": 0.6038818359375}, {"start": 2301.57, "end": 2301.87, "word": " اقول", "probability": 0.892333984375}, {"start": 2301.87, "end": 2302.67, "word": " لك", "probability": 0.9306640625}, {"start": 2302.67, "end": 2302.67, "word": " let", "probability": 0.49853515625}, {"start": 2302.67, "end": 2304.97, "word": " let", "probability": 0.21337890625}, {"start": 2304.97, "end": 2306.27, "word": " X0", "probability": 0.510986328125}, {"start": 2306.27, "end": 2306.71, "word": " زاد", "probability": 0.23809814453125}, {"start": 2306.71, "end": 2306.97, "word": " M", "probability": 0.677734375}, {"start": 2306.97, "end": 2307.19, "word": " على", "probability": 0.59619140625}, {"start": 2307.19, "end": 2307.55, "word": " D", "probability": 0.93701171875}, {"start": 2307.55, "end": 2308.15, "word": " في", "probability": 0.72607421875}, {"start": 2308.15, "end": 2308.49, "word": " T", "probability": 0.72119140625}, {"start": 2308.49, "end": 2310.65, "word": " بيأمي", "probability": 0.70791015625}, {"start": 2310.65, "end": 2312.71, "word": " solution", "probability": 0.93994140625}, {"start": 2312.71, "end": 2314.53, "word": " of", "probability": 0.95654296875}, {"start": 2314.53, "end": 2314.87, "word": " this", "probability": 0.364990234375}, {"start": 2314.87, "end": 2315.23, "word": " star", "probability": 0.85205078125}], "temperature": 1.0}, {"id": 92, "seek": 234190, "start": 2316.5, "end": 2341.9, "text": "بدي أخد اللي هو هذا أي solution وين لا star و أثبتلك أنه مطابق واحد منها طيب هي الـ T وين موجودة يا عزيزي في Z مدام الـ T في Z إذا by division algorithm بقدر أقسمها على D و يطلع ناتج قسمه متبقى إذا by division algorithm بدي أقسملك الـ T على مين", "tokens": [3555, 16254, 5551, 9778, 3215, 13672, 1829, 31439, 23758, 36632, 3827, 4032, 9957, 20193, 3543, 4032, 5551, 12984, 3555, 2655, 23275, 14739, 3224, 3714, 9566, 16758, 4587, 36764, 24401, 9154, 11296, 23032, 1829, 3555, 39896, 2423, 39184, 314, 4032, 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"probability": 0.96337890625}], "temperature": 1.0}, {"id": 93, "seek": 236942, "start": 2343.13, "end": 2369.43, "text": "بدا أكسب الـ T عادي فالـ T بتساوي Q في D زائد R والـ R أكبر أو أصغر من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من D من", "tokens": [3555, 28259, 5551, 4117, 35457, 2423, 39184, 314, 6225, 995, 16254, 6156, 6027, 39184, 314, 39894, 3794, 995, 45865, 1249, 8978, 413, 30767, 16373, 3215, 497, 16070, 39184, 497, 5551, 4117, 26890, 34051, 5551, 9381, 17082, 2288, 9154, 413, 9154, 413, 9154, 413, 9154, 413, 9154, 413, 9154, 413, 9154, 413, 9154, 413, 9154, 413, 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\ No newline at end of file
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@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4807, "start": 21.13, "end": 48.07, "text": "بسم الله الرحمن الرحيم محاضرة رقم تلاتة و تلاتين مسافة نظرية الأعداد طلاب و طالبات الجامعة الإسلامية قسم أرياضيات كليتي العلوم والتربية موضوعنا اليوم ال primitive roots هنتحدث عن ال primitive roots اللي هو تكملة لتمانية واحد", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 3714, 5016, 46958, 25720, 12602, 4587, 2304, 6055, 1211, 9307, 3660, 4032, 6055, 1211, 9307, 9957, 47524, 31845, 3660, 8717, 19913, 2288, 10632, 16247, 22488, 18513, 23032, 15040, 3555, 4032, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 12174, 38251, 5551, 16572, 46958, 1829, 9307, 9122, 20292, 31371, 18863, 1211, 20498, 16070, 2655, 25513, 10632, 3714, 2407, 11242, 45367, 8315, 45595, 20498, 2423, 28540, 10669, 8032, 29399, 24401, 12984, 18871, 2423, 28540, 10669, 13672, 1829, 31439, 6055, 24793, 37977, 5296, 39237, 7649, 10632, 36764, 24401], "avg_logprob": -0.20344387861538907, 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modulo N هذا يؤدي إلى ان الـ K تقسم من الـ H", "tokens": [6027, 39184, 1668, 24976, 39184, 316, 1072, 13455, 426, 4724, 3794, 995, 45865, 591, 4032, 41361, 18871, 16254, 316, 281, 264, 389, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 1072, 13455, 426, 23758, 7251, 33604, 16254, 30731, 16472, 2423, 39184, 591, 6055, 4587, 38251, 9154, 2423, 39184, 389], "avg_logprob": -0.26610330659516, "compression_ratio": 1.2790697674418605, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 106.58, "end": 106.92, "word": "الـ", "probability": 0.50732421875}, {"start": 106.92, "end": 107.28, "word": " order", "probability": 0.62841796875}, {"start": 107.28, "end": 107.74, "word": " للـ", "probability": 0.6502685546875}, {"start": 107.74, "end": 108.02, "word": " A", "probability": 0.53466796875}, {"start": 108.02, "end": 111.46, "word": " modulo", "probability": 0.48236083984375}, {"start": 111.46, "end": 111.64, "word": " N", "probability": 0.68603515625}, {"start": 111.64, "end": 112.14, 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على ذلك قلنا المرة الماضية أيضا بدأنا في أنه لو", "tokens": [40228, 22653, 2423, 39184, 316, 4032, 2423, 39184, 316, 281, 264, 389, 39896, 8717, 36178, 2423, 39184, 1668, 3714, 11242, 1211, 11536, 11933, 15730, 25961, 18863, 45340, 9673, 8592, 2655, 31747, 16247, 3615, 23942, 49374, 2423, 39184, 389, 4032, 49374, 23758, 2423, 1668, 4724, 3794, 995, 45865, 502, 23758, 11331, 4117, 1829, 8315, 9673, 25720, 9673, 46958, 10632, 4032, 5551, 9778, 3215, 8315, 5551, 2304, 12984, 37977, 15844, 29910, 23275, 12174, 1211, 8315, 9673, 25720, 9673, 46958, 10632, 36632, 11242, 995, 47525, 10721, 8315, 8978, 14739, 3224, 45164], "avg_logprob": -0.2456109510378891, "compression_ratio": 1.7760416666666667, "no_speech_prob": 1.430511474609375e-05, "words": [{"start": 187.56, "end": 188.02, "word": "يعني", "probability": 0.7587890625}, {"start": 188.02, "end": 188.5, "word": " الـ", "probability": 0.76171875}, {"start": 188.5, "end": 188.82, "word": " A", "probability": 0.439208984375}, {"start": 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{"start": 580.87, "end": 581.41, "word": " مدل", "probability": 0.9754231770833334}, {"start": 581.41, "end": 581.89, "word": " وسبعة", "probability": 0.8142903645833334}, {"start": 581.89, "end": 582.49, "word": " بساوي", "probability": 0.82049560546875}, {"start": 582.49, "end": 582.95, "word": " five", "probability": 0.888671875}, {"start": 582.95, "end": 583.17, "word": " of", "probability": 0.9443359375}, {"start": 583.17, "end": 583.67, "word": " سبعة", "probability": 0.96630859375}, {"start": 583.67, "end": 584.31, "word": " اللي", "probability": 0.797607421875}, {"start": 584.31, "end": 584.53, "word": " هي", "probability": 0.91845703125}, {"start": 584.53, "end": 585.57, "word": " الستة", "probability": 0.8434244791666666}, {"start": 585.57, "end": 585.99, "word": " إذا", "probability": 0.893798828125}, {"start": 585.99, "end": 587.57, "word": " تلاتة", "probability": 0.935546875}, {"start": 587.57, "end": 587.95, "word": " is", "probability": 0.91943359375}, {"start": 587.95, 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"end": 602.54, "word": " سؤال", "probability": 0.9895833333333334}, {"start": 602.54, "end": 603.72, "word": " نجي", "probability": 0.7708333333333334}, {"start": 603.72, "end": 604.38, "word": " لمثال", "probability": 0.9024658203125}, {"start": 604.38, "end": 604.92, "word": " آخر", "probability": 0.7900390625}, {"start": 604.92, "end": 606.34, "word": " بتبنيت", "probability": 0.336456298828125}, {"start": 606.34, "end": 606.9, "word": " بتفادل", "probability": 0.7913818359375}, {"start": 606.9, "end": 607.12, "word": " مع", "probability": 0.58740234375}, {"start": 607.12, "end": 607.84, "word": " المثال", "probability": 0.9602864583333334}, {"start": 607.84, "end": 609.16, "word": " أنه", "probability": 0.4862060546875}, {"start": 609.16, "end": 610.32, "word": " ال", "probability": 0.41796875}, {"start": 610.32, "end": 610.7, "word": " name", "probability": 0.5751953125}, {"start": 610.7, "end": 611.12, "word": " is", "probability": 0.95166015625}, {"start": 611.12, "end": 611.44, "word": " not", "probability": 0.95703125}, {"start": 611.44, "end": 611.62, "word": " a", "probability": 0.84326171875}, {"start": 611.62, "end": 612.02, "word": " primitive", "probability": 0.9609375}, {"start": 612.02, "end": 613.26, "word": " root", "probability": 0.9384765625}, {"start": 613.26, "end": 614.36, "word": " لاللي", "probability": 0.5131022135416666}, {"start": 614.36, "end": 614.58, "word": " هي", "probability": 0.837890625}, {"start": 614.58, "end": 615.18, "word": " أفقاً", "probability": 0.604248046875}, {"start": 615.18, "end": 615.44, "word": " ل", "probability": 0.84375}, {"start": 615.44, "end": 616.04, "word": " some", "probability": 0.467041015625}, {"start": 616.04, "end": 616.96, "word": " format", "probability": 0.5458984375}, {"start": 616.96, "end": 617.64, "word": " number", "probability": 0.97412109375}], "temperature": 1.0}, {"id": 26, "seek": 64795, "start": 618.65, "end": 647.95, "text": "الأن بقوللي إذا كان Fn بيساوي 2 to the 2 to the n زيد واحد is a prime number وN أكبر من واحد إذاً هتكون التنين إيه شمالها is not a primitive root of Fn كمان مرة المثال لأن ناخد مثال على أن التنين مشي primitive root لـ Fn بقوللي if example", "tokens": [6027, 33456, 4724, 39648, 20292, 11933, 15730, 25961, 479, 77, 4724, 1829, 3794, 995, 45865, 568, 281, 264, 568, 281, 264, 297, 30767, 1829, 3215, 36764, 24401, 307, 257, 5835, 1230, 4032, 45, 5551, 4117, 26890, 9154, 36764, 24401, 11933, 15730, 14111, 8032, 2655, 30544, 16712, 1863, 9957, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 307, 406, 257, 28540, 5593, 295, 479, 77, 9122, 2304, 7649, 3714, 25720, 9673, 12984, 6027, 5296, 33456, 8717, 47283, 3215, 50113, 6027, 15844, 14739, 16712, 1863, 9957, 37893, 1829, 28540, 5593, 5296, 39184, 479, 77, 4724, 39648, 20292, 498, 1365], "avg_logprob": -0.2849549067389105, "compression_ratio": 1.6111111111111112, "no_speech_prob": 1.430511474609375e-06, "words": [{"start": 618.65, "end": 618.95, "word": "الأن", "probability": 0.61865234375}, {"start": 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"probability": 0.6673990885416666}, {"start": 623.49, "end": 624.01, "word": " واحد", "probability": 0.769287109375}, {"start": 624.01, "end": 625.05, "word": " is", "probability": 0.57373046875}, {"start": 625.05, "end": 625.27, "word": " a", "probability": 0.97119140625}, {"start": 625.27, "end": 625.67, "word": " prime", "probability": 0.94091796875}, {"start": 625.67, "end": 626.35, "word": " number", "probability": 0.98193359375}, {"start": 626.35, "end": 627.05, "word": " وN", "probability": 0.482177734375}, {"start": 627.05, "end": 627.33, "word": " أكبر", "probability": 0.9562174479166666}, {"start": 627.33, "end": 627.47, "word": " من", "probability": 0.88232421875}, {"start": 627.47, "end": 627.89, "word": " واحد", "probability": 0.92822265625}, {"start": 627.89, "end": 628.63, "word": " إذاً", "probability": 0.653076171875}, {"start": 628.63, "end": 628.97, "word": " هتكون", "probability": 0.8463541666666666}, {"start": 628.97, "end": 629.43, "word": " التنين", "probability": 0.7403971354166666}, {"start": 629.43, "end": 629.67, "word": " إيه", "probability": 0.7779947916666666}, {"start": 629.67, "end": 630.17, "word": " شمالها", "probability": 0.7869873046875}, {"start": 630.17, "end": 630.47, "word": " is", "probability": 0.8232421875}, {"start": 630.47, "end": 630.77, "word": " not", "probability": 0.95361328125}, {"start": 630.77, "end": 630.97, "word": " a", "probability": 0.91552734375}, {"start": 630.97, "end": 631.31, "word": " primitive", "probability": 0.92626953125}, {"start": 631.31, "end": 632.03, "word": " root", "probability": 0.947265625}, {"start": 632.03, "end": 633.23, "word": " of", "probability": 0.96826171875}, {"start": 633.23, "end": 634.41, "word": " Fn", "probability": 0.8994140625}, {"start": 634.41, "end": 635.81, "word": " كمان", "probability": 0.9529622395833334}, {"start": 635.81, "end": 636.21, "word": " مرة", "probability": 0.975830078125}, {"start": 636.21, "end": 637.51, "word": " المثال", "probability": 0.9156901041666666}, {"start": 637.51, "end": 638.69, "word": " لأن", "probability": 0.47509765625}, {"start": 638.69, "end": 638.95, "word": " ناخد", "probability": 0.796630859375}, {"start": 638.95, "end": 639.45, "word": " مثال", "probability": 0.98876953125}, {"start": 639.45, "end": 639.85, "word": " على", "probability": 0.91943359375}, {"start": 639.85, "end": 640.89, "word": " أن", "probability": 0.49560546875}, {"start": 640.89, "end": 641.73, "word": " التنين", "probability": 0.84765625}, {"start": 641.73, "end": 642.11, "word": " مشي", "probability": 0.704833984375}, {"start": 642.11, "end": 642.41, "word": " primitive", "probability": 0.80224609375}, {"start": 642.41, "end": 643.23, "word": " root", "probability": 0.9580078125}, {"start": 643.23, "end": 644.67, "word": " لـ", "probability": 0.598388671875}, {"start": 644.67, "end": 645.37, "word": " Fn", "probability": 0.79345703125}, {"start": 645.37, "end": 646.61, "word": " بقوللي", "probability": 0.8084309895833334}, {"start": 646.61, "end": 647.15, "word": " if", "probability": 0.7177734375}, {"start": 647.15, "end": 647.95, "word": " example", "probability": 0.84814453125}], "temperature": 1.0}, {"id": 27, "seek": 67724, "start": 650.42, "end": 677.24, "text": "ف أفقًا بيسوي اتنين to the two to the one زائد واحد وان أكبر من واحد is prime نفترض ان هذا ايش ماله الافقان is a prime number بيقول لي then then عندي اتنين هذه الاتنين الأساس هذا is not", "tokens": [5172, 5551, 5172, 4587, 14111, 995, 4724, 1829, 3794, 45865, 1975, 2655, 1863, 9957, 281, 264, 732, 281, 264, 472, 30767, 16373, 3215, 36764, 24401, 4032, 7649, 5551, 4117, 26890, 9154, 36764, 24401, 307, 5835, 8717, 5172, 2655, 43042, 16472, 23758, 1975, 1829, 8592, 3714, 6027, 3224, 2423, 31845, 4587, 7649, 307, 257, 5835, 1230, 4724, 1829, 39648, 32239, 550, 550, 18871, 16254, 1975, 2655, 1863, 9957, 29538, 2423, 9307, 1863, 9957, 16247, 3794, 32277, 23758, 307, 406], "avg_logprob": -0.34078321351280694, "compression_ratio": 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0.6146240234375}, {"start": 680.0, "end": 683.02, "word": " Root", "probability": 0.8994140625}, {"start": 683.02, "end": 684.46, "word": " of", "probability": 0.54541015625}, {"start": 684.46, "end": 685.42, "word": " FN", "probability": 0.4034423828125}, {"start": 685.42, "end": 686.4, "word": " اقروف", "probability": 0.3280029296875}, {"start": 686.4, "end": 690.56, "word": " الان", "probability": 0.5823974609375}, {"start": 690.56, "end": 691.12, "word": " ايش", "probability": 0.7637532552083334}, {"start": 691.12, "end": 691.88, "word": " معناه", "probability": 0.7530924479166666}, {"start": 691.88, "end": 693.4, "word": " اني", "probability": 0.65966796875}, {"start": 693.4, "end": 694.2, "word": " اثبت", "probability": 0.9783935546875}, {"start": 694.2, "end": 696.32, "word": " ان", "probability": 0.96435546875}, {"start": 696.32, "end": 697.28, "word": " الاتنين", "probability": 0.81982421875}, {"start": 697.28, "end": 698.64, "word": " مش", "probability": 0.9228515625}, {"start": 698.64, "end": 698.84, "word": " ال", "probability": 0.50341796875}, {"start": 698.84, "end": 699.24, "word": " primitive", "probability": 0.7802734375}, {"start": 699.24, "end": 700.1, "word": " root", "probability": 0.91845703125}, {"start": 700.1, "end": 700.82, "word": " لل", "probability": 0.72705078125}, {"start": 700.82, "end": 701.3, "word": " FN", "probability": 0.82275390625}], "temperature": 1.0}, {"id": 29, "seek": 71753, "start": 703.03, "end": 717.53, "text": "عشان أثبت الاتنين مش بيردنا تفروت للأفئن بدي أثبت لك إن ال order للإتنين مضلوا أفئن لا يساوم من five of أفئن لو أثبتنا", "tokens": [3615, 8592, 7649, 5551, 12984, 3555, 2655, 2423, 9307, 1863, 9957, 37893, 4724, 13546, 3215, 8315, 6055, 5172, 32887, 2655, 24976, 10721, 5172, 19986, 1863, 4724, 16254, 5551, 12984, 3555, 2655, 5296, 4117, 36145, 2423, 1668, 24976, 28814, 2655, 1863, 9957, 3714, 11242, 1211, 14407, 5551, 5172, 19986, 1863, 20193, 7251, 3794, 995, 20498, 9154, 1732, 295, 5551, 5172, 19986, 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{"start": 707.41, "end": 707.61, "word": " إن", "probability": 0.327880859375}, {"start": 707.61, "end": 707.81, "word": " ال", "probability": 0.90087890625}, {"start": 707.81, "end": 708.33, "word": " order", "probability": 0.7978515625}, {"start": 708.33, "end": 709.29, "word": " للإتنين", "probability": 0.775244140625}, {"start": 709.29, "end": 709.87, "word": " مضلوا", "probability": 0.581298828125}, {"start": 709.87, "end": 710.61, "word": " أفئن", "probability": 0.9595947265625}, {"start": 710.61, "end": 711.45, "word": " لا", "probability": 0.54638671875}, {"start": 711.45, "end": 712.29, "word": " يساوم", "probability": 0.71038818359375}, {"start": 712.29, "end": 712.69, "word": " من", "probability": 0.40966796875}, {"start": 712.69, "end": 714.41, "word": " five", "probability": 0.19970703125}, {"start": 714.41, "end": 714.99, "word": " of", "probability": 0.77197265625}, {"start": 714.99, "end": 715.55, "word": " أفئن", "probability": 0.95947265625}, {"start": 715.55, "end": 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أفقان هذا العدد اللي هو اتنين قصت اتنين قصة زائد واحد ناقص واحد يعني اتنين قصت اتنين قصة واضح الآن أنا بدي أثبت ان ال order للاتنين مضلوا أفقان أشماله بسويش اتنين قصت اتنين قصة معايا؟", "tokens": [2304, 3215, 10943, 2423, 39184, 5835, 11933, 15730, 6156, 995, 1829, 295, 2423, 39184, 5835, 37893, 3714, 3794, 995, 45865, 4724, 1829, 8717, 995, 4587, 9381, 36764, 24401, 5296, 7649, 20328, 9640, 43242, 7578, 1732, 5551, 5172, 4587, 7649, 23758, 18863, 3215, 3215, 13672, 1829, 31439, 1975, 2655, 1863, 9957, 12174, 9381, 2655, 1975, 2655, 1863, 9957, 12174, 9381, 3660, 30767, 16373, 3215, 36764, 24401, 8717, 995, 4587, 9381, 36764, 24401, 37495, 22653, 1975, 2655, 1863, 9957, 12174, 9381, 2655, 1975, 2655, 1863, 9957, 12174, 9381, 3660, 4032, 46958, 5016, 6024, 48506, 41850, 4724, 16254, 5551, 12984, 3555, 2655, 16472, 2423, 1668, 24976, 9307, 1863, 9957, 3714, 11242, 1211, 14407, 5551, 5172, 4587, 7649, 5551, 8592, 2304, 6027, 3224, 4724, 3794, 45865, 8592, 1975, 2655, 1863, 9957, 12174, 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{"start": 762.93, "end": 763.59, "word": " أشماله", "probability": 0.797705078125}, {"start": 763.59, "end": 764.33, "word": " بسويش", "probability": 0.73455810546875}, {"start": 764.33, "end": 764.95, "word": " اتنين", "probability": 0.9117431640625}, {"start": 764.95, "end": 765.31, "word": " قصت", "probability": 0.8255208333333334}, {"start": 765.31, "end": 765.83, "word": " اتنين", "probability": 0.9635009765625}, {"start": 765.83, "end": 766.75, "word": " قصة", "probability": 0.9669596354166666}, {"start": 766.75, "end": 768.63, "word": " معايا؟", "probability": 0.8673095703125}], "temperature": 1.0}, {"id": 32, "seek": 79963, "start": 772.75, "end": 799.63, "text": "بمعنى إنه بدي أثبتلك إن ال order للتنين modulo of N strictly أصغر من 2 أوس 2 أوس N ليش؟ واحنا بنعرف إنه دايما ال order لل A modulo N", "tokens": [3555, 2304, 3615, 1863, 7578, 36145, 3224, 4724, 16254, 5551, 12984, 3555, 2655, 23275, 36145, 2423, 1668, 24976, 2655, 1863, 9957, 1072, 13455, 295, 426, 20792, 5551, 9381, 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بين ربعين لان هو عبارة عن اتنين قص اتنين قص ان ماقص واحد في اتنين قص اتنين قص ان زائد واحد", "tokens": [3615, 41260, 7578, 45164, 1975, 7435, 1829, 8315, 5296, 10721, 9673, 28543, 9640, 1975, 2655, 1863, 9957, 12174, 9381, 1975, 2655, 1863, 9957, 12174, 9381, 16472, 30767, 16373, 3215, 36764, 24401, 19446, 4587, 9381, 36764, 24401, 4724, 3794, 995, 2407, 7578, 23758, 47525, 7578, 1975, 5016, 1211, 43761, 2423, 7578, 6156, 2288, 4587, 49374, 12602, 3555, 3615, 9957, 2423, 7578, 6156, 2288, 4587, 49374, 12602, 3555, 3615, 9957, 5296, 7649, 31439, 6225, 3555, 9640, 3660, 18871, 1975, 2655, 1863, 9957, 12174, 9381, 1975, 2655, 1863, 9957, 12174, 9381, 16472, 19446, 4587, 9381, 36764, 24401, 8978, 1975, 2655, 1863, 9957, 12174, 9381, 1975, 2655, 1863, 9957, 12174, 9381, 16472, 30767, 16373, 3215, 36764, 24401], "avg_logprob": -0.18791119153039498, "compression_ratio": 2.5174825174825175, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 857.15, "end": 857.91, "word": "عندى", 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{"start": 957.51, "end": 958.69, "word": " modulo", "probability": 0.843505859375}, {"start": 958.69, "end": 960.11, "word": " fn", "probability": 0.92626953125}, {"start": 960.11, "end": 961.41, "word": " معايا", "probability": 0.8683268229166666}, {"start": 961.41, "end": 962.43, "word": " أه؟", "probability": 0.6236165364583334}, {"start": 962.43, "end": 963.31, "word": " الآن", "probability": 0.702880859375}, {"start": 963.31, "end": 963.67, "word": " صار", "probability": 0.817626953125}, {"start": 963.67, "end": 964.21, "word": " أكيد", "probability": 0.9300130208333334}, {"start": 964.21, "end": 964.79, "word": " هذا", "probability": 0.95263671875}, {"start": 964.79, "end": 966.11, "word": " then", "probability": 0.705078125}, {"start": 966.11, "end": 967.61, "word": " اللي", "probability": 0.735595703125}, {"start": 967.61, "end": 967.79, "word": " هو", "probability": 0.97119140625}, {"start": 967.79, "end": 968.37, "word": " اتنين", "probability": 0.8604736328125}, {"start": 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9154, 2423, 9307, 1863, 9957, 47525, 11536, 3714, 9957, 6583, 13455, 5551, 3794, 19986, 1863], "avg_logprob": -0.363797183306712, "compression_ratio": 1.4180327868852458, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 974.06, "end": 974.48, "word": "أو", "probability": 0.790771484375}, {"start": 974.48, "end": 974.72, "word": " اللي", "probability": 0.521148681640625}, {"start": 974.72, "end": 975.22, "word": " عندي", "probability": 0.68408203125}, {"start": 975.22, "end": 979.38, "word": " اتنين", "probability": 0.715576171875}, {"start": 979.38, "end": 980.26, "word": " أسئن", "probability": 0.58642578125}, {"start": 980.26, "end": 980.6, "word": " زائد", "probability": 0.9466145833333334}, {"start": 980.6, "end": 980.98, "word": " واحد", "probability": 0.988037109375}, {"start": 980.98, "end": 981.36, "word": " أكيد", "probability": 0.8124186197916666}, {"start": 981.36, "end": 981.72, "word": " حكمه", "probability": 0.5699869791666666}, {"start": 981.72, "end": 982.1, "word": " أكبر", "probability": 0.9396158854166666}, {"start": 982.1, "end": 982.26, "word": " أو", "probability": 0.84375}, {"start": 982.26, "end": 982.64, "word": " يساوي", "probability": 0.9281005859375}, {"start": 982.64, "end": 983.12, "word": " مين", "probability": 0.69775390625}, {"start": 983.12, "end": 983.88, "word": " ال", "probability": 0.7861328125}, {"start": 983.88, "end": 984.32, "word": " order", "probability": 0.8505859375}, {"start": 984.32, "end": 984.54, "word": " من", "probability": 0.116455078125}, {"start": 984.54, "end": 984.92, "word": " الاتنين", "probability": 0.850341796875}, {"start": 984.92, "end": 985.26, "word": " بدون", "probability": 0.66748046875}, {"start": 985.26, "end": 985.88, "word": " مين", "probability": 0.961669921875}, {"start": 985.88, "end": 988.52, "word": " Modulo", "probability": 0.3492431640625}, {"start": 988.52, "end": 988.98, "word": " أسئن", "probability": 0.845458984375}], "temperature": 1.0}, {"id": 40, "seek": 100552, "start": 993.4, "end": 1005.52, "text": "قلنا إذا حصلنا A to the H تطابق الواحد Modulo N معناه ال order لـ A Modulo H يقسم من H", "tokens": [4587, 1211, 8315, 11933, 15730, 11331, 36520, 8315, 316, 281, 264, 389, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 6583, 13455, 426, 20449, 8315, 3224, 2423, 1668, 5296, 39184, 316, 6583, 13455, 389, 7251, 4587, 38251, 9154, 389], "avg_logprob": -0.38060897435897434, "compression_ratio": 1.117117117117117, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 993.4, "end": 994.0, "word": "قلنا", "probability": 0.5240071614583334}, {"start": 994.0, "end": 994.36, "word": " إذا", "probability": 0.742919921875}, {"start": 994.36, "end": 995.46, "word": " حصلنا", "probability": 0.9005533854166666}, {"start": 995.46, "end": 995.8, "word": " A", "probability": 0.190185546875}, {"start": 995.8, "end": 996.0, "word": " to", "probability": 0.38720703125}, {"start": 996.0, "end": 996.18, "word": " the", "probability": 0.8681640625}, {"start": 996.18, "end": 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"probability": 0.8937174479166666}, {"start": 1002.8, "end": 1004.22, "word": " من", "probability": 0.5478515625}, {"start": 1004.22, "end": 1005.52, "word": " H", "probability": 0.29248046875}], "temperature": 1.0}, {"id": 41, "seek": 103624, "start": 1006.78, "end": 1036.24, "text": "أو بتعبير آخر أو بمعلومة ناخدها من هذه أن ال order لل A modulo N أصغر أو يساوي نين ال H أنا حصلت اتنين to this power يطابق الواحد modulo FN إذن أكيد أكيد أكيد حيكون عند ال order للإتنين modulo FN أصغر أو يساوي اتنين أسن زائد واحد أي سؤال؟", "tokens": [10721, 2407, 39894, 3615, 3555, 13546, 19753, 34740, 34051, 4724, 2304, 30241, 20498, 3660, 8717, 47283, 3215, 11296, 9154, 29538, 14739, 2423, 1668, 24976, 316, 1072, 13455, 426, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 8717, 9957, 2423, 389, 41850, 11331, 36520, 2655, 1975, 2655, 1863, 9957, 281, 341, 1347, 7251, 9566, 16758, 4587, 2423, 14407, 24401, 1072, 13455, 479, 45, 11933, 8848, 1863, 5551, 4117, 25708, 5551, 4117, 25708, 5551, 4117, 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"word": " أو", "probability": 0.955078125}, {"start": 1029.84, "end": 1030.22, "word": " يساوي", "probability": 0.974853515625}, {"start": 1030.22, "end": 1030.66, "word": " اتنين", "probability": 0.9078369140625}, {"start": 1030.66, "end": 1031.26, "word": " أسن", "probability": 0.5533447265625}, {"start": 1031.26, "end": 1032.0, "word": " زائد", "probability": 0.9532877604166666}, {"start": 1032.0, "end": 1033.44, "word": " واحد", "probability": 0.94189453125}, {"start": 1033.44, "end": 1035.56, "word": " أي", "probability": 0.86328125}, {"start": 1035.56, "end": 1036.24, "word": " سؤال؟", "probability": 0.9510498046875}], "temperature": 1.0}, {"id": 42, "seek": 105019, "start": 1036.97, "end": 1050.19, "text": "لأن هذا أكيد أصغر من 2 أُس 2 نُص M لكل M أكبر من مين؟ من واحد أصغر Strictly By induction سهلة", "tokens": [1211, 33456, 23758, 5551, 4117, 25708, 5551, 9381, 17082, 2288, 9154, 568, 5551, 10859, 3794, 568, 8717, 10859, 9381, 376, 5296, 28820, 376, 5551, 4117, 26890, 9154, 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"probability": 0.6201171875}, {"start": 1071.15, "end": 1071.87, "word": " طب", "probability": 0.75244140625}, {"start": 1071.87, "end": 1072.11, "word": " هذا", "probability": 0.73583984375}, {"start": 1072.11, "end": 1072.47, "word": " منهم", "probability": 0.693603515625}, {"start": 1072.47, "end": 1072.73, "word": " هو", "probability": 0.77734375}, {"start": 1072.73, "end": 1073.27, "word": " أصلا", "probability": 0.8614908854166666}, {"start": 1073.27, "end": 1074.01, "word": " هذا", "probability": 0.65380859375}, {"start": 1074.01, "end": 1074.41, "word": " عبارة", "probability": 0.9940185546875}, {"start": 1074.41, "end": 1074.59, "word": " عن", "probability": 0.99658203125}, {"start": 1074.59, "end": 1075.51, "word": " five", "probability": 0.2568359375}, {"start": 1075.51, "end": 1077.01, "word": " of", "probability": 0.89697265625}, {"start": 1077.01, "end": 1077.51, "word": " fn", "probability": 0.3609619140625}], "temperature": 1.0}, {"id": 44, "seek": 110555, "start": 1079.95, "end": 1105.55, "text": "أذن الآن صار عندي ال order للإتنين modulo أفقان strictly أصغر من five of أفقان إذا صار عندي يستحيل أن يكون الاتنين primitive root لمن؟ للأفقان hence اتنين is not a primitive", "tokens": [10721, 8848, 1863, 6024, 48506, 20328, 9640, 18871, 16254, 2423, 1668, 24976, 28814, 2655, 1863, 9957, 1072, 13455, 5551, 5172, 4587, 7649, 20792, 5551, 9381, 17082, 2288, 9154, 1732, 295, 5551, 5172, 4587, 7649, 11933, 15730, 20328, 9640, 18871, 16254, 7251, 14851, 5016, 26895, 14739, 7251, 30544, 2423, 9307, 1863, 9957, 28540, 5593, 5296, 27842, 22807, 24976, 10721, 5172, 4587, 7649, 16678, 1975, 2655, 1863, 9957, 307, 406, 257, 28540], "avg_logprob": -0.3188820540065497, "compression_ratio": 1.5481927710843373, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1079.95, "end": 1080.39, "word": "أذن", "probability": 0.5645345052083334}, {"start": 1080.39, "end": 1080.93, "word": " الآن", "probability": 0.6580810546875}, {"start": 1080.93, "end": 1082.89, 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" أفقان", "probability": 0.99267578125}, {"start": 1089.91, "end": 1090.97, "word": " إذا", "probability": 0.5352783203125}, {"start": 1090.97, "end": 1091.33, "word": " صار", "probability": 0.925537109375}, {"start": 1091.33, "end": 1091.75, "word": " عندي", "probability": 0.89404296875}, {"start": 1091.75, "end": 1093.27, "word": " يستحيل", "probability": 0.9332275390625}, {"start": 1093.27, "end": 1094.23, "word": " أن", "probability": 0.7314453125}, {"start": 1094.23, "end": 1094.83, "word": " يكون", "probability": 0.9638671875}, {"start": 1094.83, "end": 1095.43, "word": " الاتنين", "probability": 0.745941162109375}, {"start": 1095.43, "end": 1095.85, "word": " primitive", "probability": 0.8896484375}, {"start": 1095.85, "end": 1096.25, "word": " root", "probability": 0.966796875}, {"start": 1096.25, "end": 1097.19, "word": " لمن؟", "probability": 0.6228841145833334}, {"start": 1097.19, "end": 1098.81, "word": " للأفقان", "probability": 0.96669921875}, {"start": 1098.81, "end": 1099.45, "word": " hence", "probability": 0.325927734375}, {"start": 1099.45, "end": 1101.65, "word": " اتنين", "probability": 0.8084716796875}, {"start": 1101.65, "end": 1102.33, "word": " is", "probability": 0.869140625}, {"start": 1102.33, "end": 1103.15, "word": " not", "probability": 0.96875}, {"start": 1103.15, "end": 1104.69, "word": " a", "probability": 0.8974609375}, {"start": 1104.69, "end": 1105.55, "word": " primitive", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 45, "seek": 112691, "start": 1116.43, "end": 1126.91, "text": "أي سؤال نجي لنظرية اللي بعدها", "tokens": [10721, 1829, 8608, 33604, 6027, 8717, 7435, 1829, 5296, 1863, 19913, 2288, 10632, 13672, 1829, 39182, 11296], "avg_logprob": -0.5052083366447024, "compression_ratio": 0.9298245614035088, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 1116.4299999999998, "end": 1117.83, "word": "أي", "probability": 0.222076416015625}, {"start": 1117.83, "end": 1119.23, "word": " سؤال", 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0.863037109375}, {"start": 1162.88, "end": 1165.02, "word": " وبالذات", "probability": 0.618408203125}, {"start": 1165.02, "end": 1165.64, "word": " افترض", "probability": 0.95166015625}, {"start": 1165.64, "end": 1166.68, "word": " ان", "probability": 0.64306640625}, {"start": 1166.68, "end": 1166.92, "word": " الـ", "probability": 0.865478515625}, {"start": 1166.92, "end": 1167.44, "word": " A1", "probability": 0.6787109375}, {"start": 1167.44, "end": 1168.06, "word": " و", "probability": 0.791015625}, {"start": 1168.06, "end": 1168.24, "word": " الـ", "probability": 0.705810546875}, {"start": 1168.24, "end": 1168.9, "word": " A2", "probability": 0.924072265625}, {"start": 1168.9, "end": 1169.32, "word": " عند", "probability": 0.75146484375}, {"start": 1169.32, "end": 1169.64, "word": " الـ", "probability": 0.97314453125}, {"start": 1169.64, "end": 1170.8, "word": " A5N", "probability": 0.8748372395833334}], "temperature": 1.0}, {"id": 47, "seek": 119552, "start": 1171.78, "end": 1195.52, "text": "هي عبارة عن كل الـ positive numbers that are relatively prime to N أصغر من N هي عبارة عن بي the positive relatively prime numbers less than N", "tokens": [3224, 1829, 6225, 3555, 9640, 3660, 18871, 28242, 2423, 39184, 3353, 3547, 300, 366, 7226, 5835, 281, 426, 5551, 9381, 17082, 2288, 9154, 426, 39896, 6225, 3555, 9640, 3660, 18871, 4724, 1829, 264, 3353, 7226, 5835, 3547, 1570, 813, 426], "avg_logprob": -0.2785823112580834, "compression_ratio": 1.3650793650793651, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1171.78, "end": 1172.08, "word": "هي", "probability": 0.6600341796875}, {"start": 1172.08, "end": 1172.6, "word": " عبارة", "probability": 0.9935302734375}, {"start": 1172.6, "end": 1172.96, "word": " عن", "probability": 0.99609375}, {"start": 1172.96, "end": 1173.66, "word": " كل", "probability": 0.72509765625}, {"start": 1173.66, "end": 1173.94, "word": " الـ", "probability": 0.78955078125}, {"start": 1173.94, "end": 1174.38, "word": " positive", "probability": 0.53564453125}, {"start": 1174.38, "end": 1175.2, "word": " numbers", "probability": 0.775390625}, {"start": 1175.2, "end": 1175.6, "word": " that", "probability": 0.8115234375}, {"start": 1175.6, "end": 1175.94, "word": " are", "probability": 0.953125}, {"start": 1175.94, "end": 1176.5, "word": " relatively", "probability": 0.8203125}, {"start": 1176.5, "end": 1177.04, "word": " prime", "probability": 0.876953125}, {"start": 1177.04, "end": 1177.32, "word": " to", "probability": 0.583984375}, {"start": 1177.32, "end": 1177.9, "word": " N", "probability": 0.1639404296875}, {"start": 1177.9, "end": 1179.34, "word": " أصغر", "probability": 0.78741455078125}, {"start": 1179.34, "end": 1179.5, "word": " من", "probability": 0.98828125}, {"start": 1179.5, "end": 1179.76, "word": " N", "probability": 0.787109375}, {"start": 1179.76, "end": 1180.78, "word": " هي", "probability": 0.1290283203125}, {"start": 1180.78, "end": 1181.28, "word": " عبارة", "probability": 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a1, a2, a3 الموصولة كانت مين؟ five of n اذا انا اخدت الان صار عندي الان عندي اللي هو a و n عدد ال a عدد بحيث ان العام المشترك كلها بين ال a و ال n مش ميساوي واحد واخدت a واحد و a2 لان دي a five of n عبارة عن relatively prime", "tokens": [9566, 3555, 3615, 995, 14111, 6225, 3215, 3215, 2319, 3714, 1829, 3794, 995, 45865, 1732, 295, 297, 6225, 8592, 7649, 1975, 1829, 3224, 9122, 10943, 1211, 2655, 16472, 2423, 43840, 7251, 33599, 257, 16, 11, 257, 17, 11, 257, 18, 9673, 2407, 9381, 12610, 3660, 25961, 2655, 3714, 9957, 22807, 1732, 295, 297, 1975, 15730, 1975, 8315, 1975, 9778, 3215, 2655, 2423, 7649, 20328, 9640, 18871, 16254, 2423, 7649, 18871, 16254, 13672, 1829, 31439, 257, 4032, 297, 6225, 3215, 3215, 2423, 257, 6225, 3215, 3215, 4724, 5016, 1829, 12984, 16472, 18863, 10943, 9673, 8592, 2655, 31747, 28242, 11296, 49374, 2423, 257, 4032, 2423, 297, 37893, 3714, 1829, 3794, 995, 45865, 36764, 24401, 4032, 47283, 3215, 2655, 257, 36764, 24401, 4032, 257, 17, 5296, 7649, 11778, 1829, 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"probability": 0.81591796875}, {"start": 1922.38, "end": 1922.86, "word": " 5", "probability": 0.9189453125}, {"start": 1922.86, "end": 1923.04, "word": " of", "probability": 0.87890625}, {"start": 1923.04, "end": 1923.42, "word": " 7", "probability": 0.96923828125}, {"start": 1923.42, "end": 1924.18, "word": " صح", "probability": 0.782958984375}, {"start": 1924.18, "end": 1925.14, "word": " و", "probability": 0.62841796875}, {"start": 1925.14, "end": 1925.46, "word": " يساوي", "probability": 0.8499755859375}, {"start": 1925.46, "end": 1925.88, "word": " 5", "probability": 0.82177734375}, {"start": 1925.88, "end": 1926.14, "word": " of", "probability": 0.96337890625}, {"start": 1926.14, "end": 1926.58, "word": " 6", "probability": 0.9873046875}, {"start": 1926.58, "end": 1927.18, "word": " و", "probability": 0.82421875}, {"start": 1927.18, "end": 1927.6, "word": " يساوي", "probability": 0.888671875}, {"start": 1927.6, "end": 1928.08, "word": " كده", "probability": 0.57958984375}, {"start": 1928.08, "end": 1928.46, "word": " ايش", "probability": 0.6456705729166666}, {"start": 1928.46, "end": 1929.98, "word": " اتنين", "probability": 0.7987060546875}, {"start": 1929.98, "end": 1933.16, "word": " الو", "probability": 0.619873046875}, {"start": 1933.16, "end": 1933.58, "word": " عددين", "probability": 0.80291748046875}, {"start": 1933.58, "end": 1934.04, "word": " ايش", "probability": 0.8860677083333334}, {"start": 1934.04, "end": 1936.42, "word": " اتنين", "probability": 0.97412109375}], "temperature": 1.0}, {"id": 77, "seek": 200167, "start": 1981.67, "end": 2001.67, "text": "لو جينا عندنا حسبنا ال primitive roots اللي هي التسعة برضه حالة دي هجداش اتنين لان في", "tokens": [1211, 2407, 10874, 1829, 8315, 43242, 8315, 11331, 35457, 8315, 2423, 28540, 10669, 13672, 1829, 39896, 16712, 3794, 27884, 4724, 43042, 3224, 11331, 6027, 3660, 11778, 1829, 8032, 7435, 3215, 33599, 1975, 2655, 1863, 9957, 5296, 7649, 8978], "avg_logprob": -0.3561698779081687, "compression_ratio": 1.2844036697247707, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 1981.6699999999998, "end": 1983.07, "word": "لو", "probability": 0.766357421875}, {"start": 1983.07, "end": 1983.63, "word": " جينا", "probability": 0.9708658854166666}, {"start": 1983.63, "end": 1986.11, "word": " عندنا", "probability": 0.72607421875}, {"start": 1986.11, "end": 1987.73, "word": " حسبنا", "probability": 0.978515625}, {"start": 1987.73, "end": 1989.93, "word": " ال", "probability": 0.8076171875}, {"start": 1989.93, "end": 1990.31, "word": " primitive", "probability": 0.1453857421875}, {"start": 1990.31, "end": 1990.93, "word": " roots", "probability": 0.82177734375}, {"start": 1990.93, "end": 1995.31, "word": " اللي", "probability": 0.56689453125}, {"start": 1995.31, "end": 1995.83, "word": " هي", "probability": 0.8974609375}, {"start": 1995.83, "end": 1996.57, "word": " التسعة", "probability": 0.9168294270833334}, {"start": 1996.57, "end": 1998.39, "word": " برضه", "probability": 0.9391276041666666}, {"start": 1998.39, "end": 1998.65, "word": " حالة", "probability": 0.538330078125}, {"start": 1998.65, "end": 1998.75, "word": " دي", "probability": 0.798095703125}, {"start": 1998.75, "end": 1999.37, "word": " هجداش", "probability": 0.636016845703125}, {"start": 1999.37, "end": 2000.73, "word": " اتنين", "probability": 0.8671875}, {"start": 2000.73, "end": 2001.49, "word": " لان", "probability": 0.6119384765625}, {"start": 2001.49, "end": 2001.67, "word": " في", "probability": 0.8681640625}], "temperature": 1.0}, {"id": 78, "seek": 202909, "start": 2002.57, "end": 2029.09, "text": "of تسعة ستة five of six اتنين عنا اتنين is a primitive root of تسعة لو بدنا ناجي اللي هو ال primitive root الفاني بنبحث من هذوله من اللي عندنا اللي هذا بنبحث من ال order له ساوي ال order لمين للاتنين", "tokens": [2670, 6055, 3794, 27884, 8608, 2655, 3660, 1732, 295, 2309, 1975, 2655, 1863, 9957, 6225, 8315, 1975, 2655, 1863, 9957, 307, 257, 28540, 5593, 295, 6055, 3794, 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"probability": 0.881103515625}, {"start": 2006.01, "end": 2007.19, "word": " عنا", "probability": 0.505889892578125}, {"start": 2007.19, "end": 2008.21, "word": " اتنين", "probability": 0.95263671875}, {"start": 2008.21, "end": 2008.43, "word": " is", "probability": 0.859375}, {"start": 2008.43, "end": 2008.55, "word": " a", "probability": 0.6650390625}, {"start": 2008.55, "end": 2008.87, "word": " primitive", "probability": 0.96044921875}, {"start": 2008.87, "end": 2009.23, "word": " root", "probability": 0.94384765625}, {"start": 2009.23, "end": 2009.41, "word": " of", "probability": 0.96875}, {"start": 2009.41, "end": 2009.89, "word": " تسعة", "probability": 0.9832356770833334}, {"start": 2009.89, "end": 2011.37, "word": " لو", "probability": 0.90087890625}, {"start": 2011.37, "end": 2011.69, "word": " بدنا", "probability": 0.9765625}, {"start": 2011.69, "end": 2012.19, "word": " ناجي", "probability": 0.76318359375}, {"start": 2012.19, "end": 2012.33, "word": " اللي", "probability": 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0.82373046875}, {"start": 2018.59, "end": 2018.85, "word": " هذا", "probability": 0.189208984375}, {"start": 2018.85, "end": 2021.13, "word": " بنبحث", "probability": 0.9501953125}, {"start": 2021.13, "end": 2023.31, "word": " من", "probability": 0.9794921875}, {"start": 2023.31, "end": 2024.13, "word": " ال", "probability": 0.96826171875}, {"start": 2024.13, "end": 2024.67, "word": " order", "probability": 0.94384765625}, {"start": 2024.67, "end": 2025.35, "word": " له", "probability": 0.59375}, {"start": 2025.35, "end": 2026.53, "word": " ساوي", "probability": 0.7493489583333334}, {"start": 2026.53, "end": 2026.65, "word": " ال", "probability": 0.98974609375}, {"start": 2026.65, "end": 2026.97, "word": " order", "probability": 0.95458984375}, {"start": 2026.97, "end": 2027.59, "word": " لمين", "probability": 0.643310546875}, {"start": 2027.59, "end": 2029.09, "word": " للاتنين", "probability": 0.7747802734375}], "temperature": 1.0}, {"id": 79, "seek": 205859, "start": 2031.65, "end": 2058.59, "text": "الـ order من هذولا ركزوا في الملاحظة ال order من هذولا هو شو معنى primitive root؟ بيكون ال order له modulo التسعة إيش بيساوي؟ five تسعة إيش معناه a primitive root؟ لإن ال order له modulo انده يطلع fiveا لإن أنا عندي فيه primitive root اللي هو مين؟ اتنين", "tokens": [6027, 39184, 1668, 9154, 8032, 8848, 12610, 995, 12602, 4117, 11622, 14407, 8978, 9673, 15040, 5016, 19913, 3660, 2423, 1668, 9154, 8032, 8848, 12610, 995, 31439, 13412, 2407, 20449, 1863, 7578, 28540, 5593, 22807, 4724, 1829, 30544, 2423, 1668, 46740, 1072, 13455, 16712, 3794, 27884, 11933, 1829, 8592, 4724, 1829, 3794, 995, 45865, 22807, 1732, 6055, 3794, 27884, 11933, 1829, 8592, 20449, 8315, 3224, 257, 28540, 5593, 22807, 5296, 28814, 1863, 2423, 1668, 46740, 1072, 13455, 16472, 3215, 3224, 7251, 9566, 1211, 3615, 1732, 995, 5296, 28814, 1863, 41850, 18871, 16254, 8978, 3224, 28540, 5593, 13672, 1829, 31439, 3714, 9957, 22807, 1975, 2655, 1863, 9957], "avg_logprob": -0.32959906278916123, "compression_ratio": 1.899497487437186, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 2031.65, "end": 2031.89, "word": "الـ", "probability": 0.5836181640625}, {"start": 2031.89, "end": 2032.15, "word": " order", "probability": 0.466552734375}, {"start": 2032.15, "end": 2032.33, "word": " من", "probability": 0.98291015625}, {"start": 2032.33, "end": 2033.11, "word": " هذولا", "probability": 0.62481689453125}, {"start": 2033.11, "end": 2034.05, "word": " ركزوا", "probability": 0.76995849609375}, {"start": 2034.05, "end": 2034.09, "word": " في", "probability": 0.80810546875}, {"start": 2034.09, "end": 2034.95, "word": " الملاحظة", "probability": 0.935546875}, {"start": 2034.95, "end": 2036.65, "word": " ال", "probability": 0.890625}, {"start": 2036.65, "end": 2036.99, "word": " order", "probability": 0.86669921875}, {"start": 2036.99, "end": 2037.23, "word": " من", "probability": 0.98974609375}, {"start": 2037.23, "end": 2038.03, "word": " هذولا", "probability": 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"probability": 0.7006022135416666}, {"start": 2043.77, "end": 2045.43, "word": " بيساوي؟", "probability": 0.795654296875}, {"start": 2045.43, "end": 2045.69, "word": " five", "probability": 0.611328125}, {"start": 2045.69, "end": 2046.17, "word": " تسعة", "probability": 0.9166666666666666}, {"start": 2046.17, "end": 2049.09, "word": " إيش", "probability": 0.8994140625}, {"start": 2049.09, "end": 2049.51, "word": " معناه", "probability": 0.7449544270833334}, {"start": 2049.51, "end": 2049.75, "word": " a", "probability": 0.23876953125}, {"start": 2049.75, "end": 2050.07, "word": " primitive", "probability": 0.92822265625}, {"start": 2050.07, "end": 2051.15, "word": " root؟", "probability": 0.86083984375}, {"start": 2051.15, "end": 2051.73, "word": " لإن", "probability": 0.7367350260416666}, {"start": 2051.73, "end": 2051.93, "word": " ال", "probability": 0.98974609375}, {"start": 2051.93, "end": 2052.33, "word": " order", "probability": 0.9619140625}, {"start": 2052.33, "end": 2052.53, "word": " له", "probability": 0.300537109375}, {"start": 2052.53, "end": 2053.07, "word": " modulo", "probability": 0.647216796875}, {"start": 2053.07, "end": 2053.41, "word": " انده", "probability": 0.4241129557291667}, {"start": 2053.41, "end": 2053.77, "word": " يطلع", "probability": 0.906005859375}, {"start": 2053.77, "end": 2054.65, "word": " fiveا", "probability": 0.353271484375}, {"start": 2054.65, "end": 2055.87, "word": " لإن", "probability": 0.6096598307291666}, {"start": 2055.87, "end": 2056.05, "word": " أنا", "probability": 0.81396484375}, {"start": 2056.05, "end": 2056.37, "word": " عندي", "probability": 0.686279296875}, {"start": 2056.37, "end": 2056.65, "word": " فيه", "probability": 0.9013671875}, {"start": 2056.65, "end": 2057.01, "word": " primitive", "probability": 0.96337890625}, {"start": 2057.01, "end": 2057.35, "word": " root", "probability": 0.93603515625}, {"start": 2057.35, "end": 2057.49, "word": " اللي", "probability": 0.81494140625}, {"start": 2057.49, "end": 2057.67, "word": " هو", "probability": 0.8505859375}, {"start": 2057.67, "end": 2058.09, "word": " مين؟", "probability": 0.8502604166666666}, {"start": 2058.09, "end": 2058.59, "word": " اتنين", "probability": 0.9158935546875}], "temperature": 1.0}, {"id": 80, "seek": 208323, "start": 2060.44, "end": 2083.24, "text": "الان ال order اللي هو ال order اللي زيه هنا موجود اللي هو بساوي ال order له five of تسعة اللي هو بساوي مين بساوي ستة بدي أدور على اللي من هنا اللي له نفس ال order", "tokens": [6027, 7649, 2423, 1668, 13672, 1829, 31439, 2423, 1668, 13672, 1829, 30767, 1829, 3224, 34105, 3714, 29245, 23328, 13672, 1829, 31439, 4724, 3794, 995, 45865, 2423, 1668, 46740, 1732, 295, 6055, 3794, 27884, 13672, 1829, 31439, 4724, 3794, 995, 45865, 3714, 9957, 4724, 3794, 995, 45865, 8608, 2655, 3660, 4724, 16254, 5551, 3215, 13063, 15844, 13672, 1829, 9154, 34105, 13672, 1829, 46740, 8717, 36178, 2423, 1668], "avg_logprob": -0.18598413689812618, "compression_ratio": 1.9264705882352942, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 2060.44, "end": 2060.86, "word": "الان", "probability": 0.6356201171875}, {"start": 2060.86, "end": 2061.06, "word": " ال", "probability": 0.61279296875}, {"start": 2061.06, "end": 2061.62, "word": " order", "probability": 0.81396484375}, {"start": 2061.62, "end": 2063.74, "word": " اللي", "probability": 0.710205078125}, {"start": 2063.74, "end": 2063.98, "word": " هو", "probability": 0.93212890625}, {"start": 2063.98, "end": 2064.44, "word": " ال", "probability": 0.86376953125}, {"start": 2064.44, "end": 2065.04, "word": " order", "probability": 0.96923828125}, {"start": 2065.04, "end": 2066.42, "word": " اللي", "probability": 0.93017578125}, {"start": 2066.42, "end": 2067.22, "word": " زيه", "probability": 0.8896484375}, {"start": 2067.22, "end": 2067.54, "word": " هنا", "probability": 0.80615234375}, {"start": 2067.54, "end": 2068.88, "word": " موجود", "probability": 0.9842122395833334}, {"start": 2068.88, "end": 2069.92, 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0.9443359375}, {"start": 2310.9, "end": 2311.12, "word": " B", "probability": 0.85400390625}, {"start": 2311.12, "end": 2311.56, "word": " تجسم", "probability": 0.7941080729166666}, {"start": 2311.56, "end": 2312.98, "word": " A", "probability": 0.60791015625}, {"start": 2312.98, "end": 2313.2, "word": " to", "probability": 0.9423828125}, {"start": 2313.2, "end": 2313.34, "word": " the", "probability": 0.9326171875}, {"start": 2313.34, "end": 2314.08, "word": " 2K", "probability": 0.93359375}, {"start": 2314.08, "end": 2315.3, "word": " نقص", "probability": 0.7220865885416666}, {"start": 2315.3, "end": 2315.78, "word": " واحد", "probability": 0.692138671875}, {"start": 2315.78, "end": 2317.18, "word": " هذه", "probability": 0.5546875}, {"start": 2317.18, "end": 2317.46, "word": " طبعا", "probability": 0.8968505859375}, {"start": 2317.46, "end": 2318.16, "word": " تتحلل", "probability": 0.90859375}], "temperature": 1.0}, {"id": 89, "seek": 234342, "start": 2319.48, "end": 2343.42, "text": "بتجسم الـ a to the k minus واحد في ال a to the k زائد واحد بزبراي اذا نياها تجسم then ب تجسم a to the k minus واحد or ب تجسم a to the k زائد واحد معايا اه الان هذه معناتها then", "tokens": [3555, 2655, 7435, 38251, 2423, 39184, 257, 281, 264, 350, 3175, 36764, 24401, 8978, 2423, 257, 281, 264, 350, 30767, 16373, 3215, 36764, 24401, 4724, 11622, 3555, 23557, 1829, 1975, 15730, 8717, 25528, 11296, 6055, 7435, 38251, 550, 4724, 6055, 7435, 38251, 257, 281, 264, 350, 3175, 36764, 24401, 420, 4724, 6055, 7435, 38251, 257, 281, 264, 350, 30767, 16373, 3215, 36764, 24401, 20449, 995, 25528, 1975, 3224, 2423, 7649, 29538, 20449, 8315, 2655, 11296, 550], "avg_logprob": -0.27455356833222627, "compression_ratio": 1.8776978417266188, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 2319.48, "end": 2320.4, "word": "بتجسم", "probability": 0.57501220703125}, {"start": 2320.4, "end": 2320.64, "word": " الـ", "probability": 0.64599609375}, {"start": 2320.64, "end": 2320.82, "word": " a", "probability": 0.52587890625}, {"start": 2320.82, "end": 2320.92, "word": " to", "probability": 0.310546875}, {"start": 2320.92, "end": 2321.08, "word": " the", "probability": 0.9287109375}, {"start": 2321.08, "end": 2321.22, "word": " k", "probability": 0.83837890625}, {"start": 2321.22, "end": 2321.52, "word": " minus", "probability": 0.578125}, {"start": 2321.52, "end": 2322.16, "word": " واحد", "probability": 0.775390625}, {"start": 2322.16, "end": 2322.88, "word": " في", "probability": 0.69189453125}, {"start": 2322.88, "end": 2323.04, "word": " ال", "probability": 0.69921875}, {"start": 2323.04, "end": 2323.2, "word": " a", "probability": 0.54052734375}, {"start": 2323.2, "end": 2323.3, "word": " to", "probability": 0.98193359375}, {"start": 2323.3, "end": 2323.48, "word": " the", "probability": 0.94189453125}, {"start": 2323.48, "end": 2323.66, "word": " k", "probability": 0.94677734375}, {"start": 2323.66, "end": 2324.34, "word": " زائد", "probability": 0.806640625}, {"start": 2324.34, "end": 2325.2, "word": " واحد", "probability": 0.968017578125}, {"start": 2325.2, "end": 2326.86, "word": " بزبراي", "probability": 0.5833740234375}, {"start": 2326.86, "end": 2327.8, "word": " اذا", "probability": 0.6229248046875}, {"start": 2327.8, "end": 2328.2, "word": " نياها", "probability": 0.509521484375}, {"start": 2328.2, "end": 2328.72, "word": " تجسم", "probability": 0.97265625}, {"start": 2328.72, "end": 2329.76, "word": " then", "probability": 0.525390625}, {"start": 2329.76, "end": 2331.12, "word": " ب", "probability": 0.85693359375}, {"start": 2331.12, "end": 2331.72, "word": " تجسم", "probability": 0.7903645833333334}, {"start": 2331.72, "end": 2331.94, "word": " a", "probability": 0.95068359375}, {"start": 2331.94, "end": 2332.04, "word": " to", "probability": 0.98095703125}, {"start": 2332.04, "end": 2332.2, "word": " the", "probability": 0.9423828125}, {"start": 2332.2, "end": 2332.44, "word": " k", "probability": 0.974609375}, {"start": 2332.44, "end": 2332.82, "word": " minus", "probability": 0.9765625}, {"start": 2332.82, "end": 2333.28, "word": " واحد", "probability": 0.969970703125}, {"start": 2333.28, "end": 2333.62, "word": " or", "probability": 0.59326171875}, {"start": 2333.62, "end": 2334.38, "word": " ب", "probability": 0.9296875}, {"start": 2334.38, "end": 2334.96, "word": " تجسم", "probability": 0.88720703125}, {"start": 2334.96, "end": 2335.18, "word": " a", "probability": 0.9853515625}, {"start": 2335.18, "end": 2335.24, "word": " to", "probability": 0.98828125}, {"start": 2335.24, "end": 2335.42, "word": " the", "probability": 0.9443359375}, {"start": 2335.42, "end": 2335.88, "word": " k", "probability": 0.986328125}, {"start": 2335.88, "end": 2336.78, "word": " زائد", "probability": 0.841796875}, {"start": 2336.78, "end": 2338.28, "word": " واحد", "probability": 0.98779296875}, {"start": 2338.28, "end": 2339.22, "word": " معايا", "probability": 0.9381510416666666}, {"start": 2339.22, "end": 2339.96, "word": " اه", "probability": 0.830322265625}, {"start": 2339.96, "end": 2341.36, "word": " الان", "probability": 0.630126953125}, {"start": 2341.36, "end": 2341.9, "word": " هذه", "probability": 0.80712890625}, {"start": 2341.9, "end": 2342.74, "word": " معناتها", "probability": 0.977783203125}, {"start": 2342.74, "end": 2343.42, "word": " then", "probability": 0.87060546875}], "temperature": 1.0}, {"id": 90, "seek": 236655, "start": 2365.15, "end": 2366.55, "text": "A�", "tokens": [32, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171, 119, 123, 171], "avg_logprob": -0.04076388729943169, "compression_ratio": 13.294117647058824, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 2365.15, "end": 2366.55, "word": "A�", "probability": 0.9706048965454102}], "temperature": 1.0}, {"id": 91, "seek": 239601, "start": 2369.03, "end": 2396.01, "text": "اللي هو a to the k بيبتقسم a to the k زاد واحد فاهمين عليها؟ اه و هذا معناته انه اذا a to the k تطابق نقص واحد modulo b اي سؤال؟ اطلع ارجع للانذاك المهم", "tokens": [6027, 20292, 31439, 257, 281, 264, 350, 4724, 1829, 3555, 2655, 4587, 38251, 257, 281, 264, 350, 30767, 18513, 36764, 24401, 6156, 995, 16095, 9957, 25894, 11296, 22807, 1975, 3224, 4032, 23758, 20449, 8315, 47395, 16472, 3224, 1975, 15730, 257, 281, 264, 350, 6055, 9566, 16758, 4587, 8717, 4587, 9381, 36764, 24401, 1072, 13455, 272, 1975, 1829, 8608, 33604, 6027, 22807, 1975, 9566, 1211, 3615, 1975, 47341, 3615, 24976, 7649, 15730, 4117, 9673, 16095], "avg_logprob": -0.28520833333333334, "compression_ratio": 1.5253164556962024, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 2369.03, "end": 2369.37, "word": "اللي", "probability": 0.6622314453125}, {"start": 2369.37, "end": 2369.65, "word": " هو", "probability": 0.92529296875}, {"start": 2369.65, "end": 2369.97, "word": " a", "probability": 0.50634765625}, {"start": 2369.97, "end": 2370.05, "word": " to", "probability": 0.1695556640625}, {"start": 2370.05, "end": 2370.21, "word": " the", "probability": 0.93017578125}, {"start": 2370.21, "end": 2370.65, "word": " k", "probability": 0.7802734375}, {"start": 2370.65, "end": 2372.35, "word": " بيبتقسم", "probability": 0.8332926432291666}, {"start": 2372.35, "end": 2372.67, "word": " a", "probability": 0.92431640625}, {"start": 2372.67, "end": 2372.75, "word": " to", "probability": 0.96484375}, {"start": 2372.75, "end": 2372.93, "word": " the", "probability": 0.94189453125}, {"start": 2372.93, "end": 2373.33, "word": " k", "probability": 0.95068359375}, {"start": 2373.33, "end": 2373.85, "word": " زاد", "probability": 0.4078369140625}, {"start": 2373.85, "end": 2373.97, "word": " واحد", "probability": 0.9091796875}, {"start": 2373.97, "end": 2374.25, "word": " فاهمين", "probability": 0.782958984375}, {"start": 2374.25, "end": 2375.57, "word": " عليها؟", "probability": 0.7481282552083334}, {"start": 2375.57, "end": 2375.97, "word": " اه", "probability": 0.64697265625}, {"start": 2375.97, "end": 2376.35, "word": " و", "probability": 0.46728515625}, {"start": 2376.35, "end": 2376.59, "word": " هذا", "probability": 0.5751953125}, {"start": 2376.59, "end": 2377.11, "word": " معناته", "probability": 0.9552408854166666}, {"start": 2377.11, "end": 2377.75, "word": " انه", "probability": 0.781982421875}, {"start": 2377.75, "end": 2378.19, "word": " اذا", "probability": 0.784423828125}, {"start": 2378.19, "end": 2378.53, "word": " a", "probability": 0.93505859375}, {"start": 2378.53, "end": 2378.65, "word": " to", "probability": 0.9775390625}, {"start": 2378.65, "end": 2378.81, "word": " the", "probability": 0.93994140625}, {"start": 2378.81, "end": 2379.19, "word": " k", "probability": 0.9794921875}, {"start": 2379.19, "end": 2380.11, "word": " تطابق", "probability": 0.9468994140625}, {"start": 2380.11, "end": 2380.57, "word": " نقص", "probability": 0.83056640625}, {"start": 2380.57, "end": 2381.19, "word": " واحد", "probability": 0.981201171875}, {"start": 2381.19, "end": 2382.51, "word": " modulo", "probability": 0.822509765625}, {"start": 2382.51, "end": 2383.43, "word": " b", "probability": 0.430419921875}, {"start": 2383.43, "end": 2388.87, "word": " اي", "probability": 0.68896484375}, {"start": 2388.87, "end": 2392.45, "word": " سؤال؟", "probability": 0.875244140625}, {"start": 2392.45, "end": 2394.85, "word": " اطلع", "probability": 0.8011474609375}, {"start": 2394.85, "end": 2395.11, "word": " ارجع", "probability": 0.6879069010416666}, {"start": 2395.11, "end": 2395.73, "word": " للانذاك", "probability": 0.58416748046875}, {"start": 2395.73, "end": 2396.01, "word": " المهم", "probability": 0.6181640625}], "temperature": 1.0}, {"id": 92, "seek": 242580, "start": 2399.54, "end": 2425.8, "text": "طيب الان C نقول إذا كان ال A has order N نقص واحد بدول N إذا ال N إيش مالها is prime بعطيني ال order", "tokens": [9566, 1829, 3555, 2423, 7649, 383, 8717, 39648, 11933, 15730, 25961, 2423, 316, 575, 1668, 426, 8717, 4587, 9381, 36764, 24401, 47525, 12610, 426, 11933, 15730, 2423, 426, 11933, 1829, 8592, 3714, 6027, 11296, 307, 5835, 45030, 9566, 1829, 22653, 2423, 1668], "avg_logprob": -0.4037063981211463, "compression_ratio": 1.2377049180327868, "no_speech_prob": 4.291534423828125e-06, "words": [{"start": 2399.54, "end": 2400.02, "word": "طيب", "probability": 0.812744140625}, {"start": 2400.02, "end": 2400.58, "word": " الان", "probability": 0.66259765625}, {"start": 2400.58, "end": 2400.98, "word": " C", "probability": 0.292724609375}, {"start": 2400.98, "end": 2403.12, "word": " نقول", "probability": 0.646484375}, {"start": 2403.12, "end": 2403.5, "word": " إذا", "probability": 0.724609375}, {"start": 2403.5, "end": 2403.88, "word": " كان", "probability": 0.9619140625}, {"start": 2403.88, "end": 2404.3, "word": " ال", "probability": 0.91943359375}, {"start": 2404.3, "end": 2404.7, "word": " A", "probability": 0.767578125}, {"start": 2404.7, "end": 2405.4, "word": " has", "probability": 0.73193359375}, {"start": 2405.4, "end": 2405.72, "word": " order", "probability": 0.93017578125}, {"start": 2405.72, "end": 2405.9, "word": " N", "probability": 0.55810546875}, {"start": 2405.9, "end": 2406.18, "word": " نقص", "probability": 0.6929524739583334}, {"start": 2406.18, "end": 2406.42, "word": " واحد", "probability": 0.935302734375}, {"start": 2406.42, "end": 2406.64, "word": " بدول", "probability": 0.2706298828125}, {"start": 2406.64, "end": 2406.96, "word": " N", "probability": 0.5654296875}, {"start": 2406.96, "end": 2407.78, "word": " إذا", "probability": 0.857666015625}, {"start": 2407.78, "end": 2407.94, "word": " ال", "probability": 0.91796875}, {"start": 2407.94, "end": 2408.12, "word": " N", "probability": 0.9482421875}, {"start": 2408.12, "end": 2408.4, "word": " إيش", "probability": 0.6404622395833334}, {"start": 2408.4, "end": 2409.16, "word": " مالها", "probability": 0.8470052083333334}, {"start": 2409.16, "end": 2410.06, "word": " is", "probability": 0.176513671875}, {"start": 2410.06, "end": 2410.46, "word": " prime", "probability": 0.30908203125}, {"start": 2410.46, "end": 2423.58, "word": " بعطيني", "probability": 0.68194580078125}, {"start": 2423.58, "end": 2425.26, "word": " ال", "probability": 0.95947265625}, {"start": 2425.26, "end": 2425.8, "word": " order", "probability": 0.98046875}], "temperature": 1.0}, {"id": 93, "seek": 245587, "start": 2427.13, "end": 2455.87, "text": "للـ a modulo n بسوء n ناقص واحد ال order لل a modulo n بسوء n ناقص واحد بيقول لي اثبت اثبت n is a is a prime لان عندي proof since ال order لل a modulo n بسوء n ناقص واحد", "tokens": [1211, 1211, 39184, 257, 1072, 13455, 297, 4724, 3794, 2407, 38207, 297, 8717, 995, 4587, 9381, 36764, 24401, 2423, 1668, 24976, 257, 1072, 13455, 297, 4724, 3794, 2407, 38207, 297, 8717, 995, 4587, 9381, 36764, 24401, 4724, 1829, 39648, 32239, 1975, 12984, 3555, 2655, 1975, 12984, 3555, 2655, 297, 307, 257, 307, 257, 5835, 5296, 7649, 18871, 16254, 8177, 1670, 2423, 1668, 24976, 257, 1072, 13455, 297, 4724, 3794, 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"temperature": 1.0}, {"id": 98, "seek": 260062, "start": 2572.58, "end": 2600.62, "text": "أكتر حاجة .. أكتر حاجة اللي بتسأل إيه شمالها N ناقص واحد في حالة الـ Brine و قبل .. أجل التمتين مع بعض together together بتطلع five N سواء ناقص واحد إذن N إيه شماله؟ عارفين هذا ال .. ال Zebra صيمين أه؟", "tokens": [10721, 4117, 2655, 2288, 11331, 26108, 3660, 4386, 5551, 4117, 2655, 2288, 11331, 26108, 3660, 13672, 1829, 39894, 3794, 10721, 1211, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 426, 8717, 995, 4587, 9381, 36764, 24401, 8978, 11331, 6027, 3660, 2423, 39184, 1603, 533, 4032, 12174, 36150, 4386, 5551, 7435, 1211, 16712, 2304, 2655, 9957, 20449, 45030, 11242, 1214, 1214, 39894, 9566, 1211, 3615, 1732, 426, 8608, 2407, 16606, 8717, 995, 4587, 9381, 36764, 24401, 11933, 8848, 1863, 426, 11933, 1829, 3224, 13412, 2304, 6027, 3224, 22807, 6225, 9640, 5172, 9957, 23758, 2423, 4386, 2423, 4853, 6198, 20328, 32640, 9957, 5551, 3224, 22807], "avg_logprob": -0.33161406436012786, 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واحد is a multiple of mean of N شوف كيف الفكرة الفكرة برضه بتسخد مياشي ال order عندي اتنين تدان تطابق الواحد مضله اتنين أسان ناقص واحد مظبوط؟ إذا صار عندي ال N", "tokens": [40, 486, 7081, 300, 286, 295, 1975, 2655, 1863, 9957, 5551, 3794, 7649, 8717, 995, 4587, 9381, 36764, 24401, 307, 257, 3866, 295, 914, 295, 426, 13412, 38688, 9122, 33911, 27188, 4117, 25720, 27188, 4117, 25720, 4724, 43042, 3224, 39894, 3794, 9778, 3215, 3714, 1829, 33599, 1829, 2423, 1668, 18871, 16254, 1975, 2655, 1863, 9957, 6055, 3215, 7649, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 3714, 11242, 43761, 1975, 2655, 1863, 9957, 5551, 3794, 7649, 8717, 995, 4587, 9381, 36764, 24401, 3714, 19913, 3555, 2407, 9566, 22807, 11933, 15730, 20328, 9640, 18871, 16254, 2423, 426], "avg_logprob": -0.2988281116510431, "compression_ratio": 1.6082474226804124, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2631.05, "end": 2631.21, "word": "I", "probability": 0.078857421875}, {"start": 2631.21, "end": 2631.25, 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"word": " of", "probability": 0.97216796875}, {"start": 2640.63, "end": 2641.11, "word": " mean", "probability": 0.6240234375}, {"start": 2641.11, "end": 2642.27, "word": " of", "probability": 0.95703125}, {"start": 2642.27, "end": 2642.53, "word": " N", "probability": 0.5029296875}, {"start": 2642.53, "end": 2643.95, "word": " شوف", "probability": 0.59130859375}, {"start": 2643.95, "end": 2644.15, "word": " كيف", "probability": 0.840576171875}, {"start": 2644.15, "end": 2644.61, "word": " الفكرة", "probability": 0.9773763020833334}, {"start": 2644.61, "end": 2644.97, "word": " الفكرة", "probability": 0.8937174479166666}, {"start": 2644.97, "end": 2645.21, "word": " برضه", "probability": 0.9181315104166666}, {"start": 2645.21, "end": 2645.63, "word": " بتسخد", "probability": 0.43194580078125}, {"start": 2645.63, "end": 2646.05, "word": " مياشي", "probability": 0.781982421875}, {"start": 2646.05, "end": 2646.15, "word": " ال", "probability": 0.92041015625}, {"start": 2646.15, "end": 2646.53, "word": " order", "probability": 0.9287109375}, {"start": 2646.53, "end": 2648.21, "word": " عندي", "probability": 0.79052734375}, {"start": 2648.21, "end": 2649.01, "word": " اتنين", "probability": 0.943115234375}, {"start": 2649.01, "end": 2650.27, "word": " تدان", "probability": 0.47998046875}, {"start": 2650.27, "end": 2650.85, "word": " تطابق", "probability": 0.9495849609375}, {"start": 2650.85, "end": 2651.45, "word": " الواحد", "probability": 0.97900390625}, {"start": 2651.45, "end": 2652.07, "word": " مضله", "probability": 0.7415364583333334}, {"start": 2652.07, "end": 2653.09, "word": " اتنين", "probability": 0.9691162109375}, {"start": 2653.09, "end": 2653.41, "word": " أسان", "probability": 0.9728190104166666}, {"start": 2653.41, "end": 2654.15, "word": " ناقص", "probability": 0.986083984375}, {"start": 2654.15, "end": 2655.95, "word": " واحد", "probability": 0.972900390625}, {"start": 2655.95, "end": 2658.97, "word": " مظبوط؟", "probability": 0.8263346354166666}, {"start": 2658.97, "end": 2659.23, "word": " إذا", "probability": 0.726806640625}, {"start": 2659.23, "end": 2659.59, "word": " صار", "probability": 0.897216796875}, {"start": 2659.59, "end": 2659.95, "word": " عندي", "probability": 0.91259765625}, {"start": 2659.95, "end": 2660.13, "word": " ال", "probability": 0.93603515625}, {"start": 2660.13, "end": 2660.39, "word": " N", "probability": 0.67626953125}], "temperature": 1.0}, {"id": 101, "seek": 269073, "start": 2661.93, "end": 2690.73, "text": "الـ 2 أُس M تطابق الواحد ولو جيت أخدت أي M أصغر من الـ N أي M أصغر من الـ N هتلاقي 2 أُس M لا تطابق الواحد مدله 2 أُس M ناقص واحد ليش لسبب بسيط because انه هيكون عندى الـ 2 أُس M ناقص واحد", "tokens": [6027, 39184, 568, 5551, 10859, 3794, 376, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 4032, 1211, 2407, 10874, 36081, 5551, 9778, 3215, 2655, 36632, 376, 5551, 9381, 17082, 2288, 9154, 2423, 39184, 426, 36632, 376, 5551, 9381, 17082, 2288, 9154, 2423, 39184, 426, 8032, 2655, 15040, 38436, 568, 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"word": " أُس", "probability": 0.8870442708333334}, {"start": 2680.69, "end": 2680.85, "word": " M", "probability": 0.76708984375}, {"start": 2680.85, "end": 2681.19, "word": " ناقص", "probability": 0.8795166015625}, {"start": 2681.19, "end": 2681.65, "word": " واحد", "probability": 0.885009765625}, {"start": 2681.65, "end": 2682.65, "word": " ليش", "probability": 0.6746826171875}, {"start": 2682.65, "end": 2684.09, "word": " لسبب", "probability": 0.89990234375}, {"start": 2684.09, "end": 2684.57, "word": " بسيط", "probability": 0.9976806640625}, {"start": 2684.57, "end": 2685.37, "word": " because", "probability": 0.52294921875}, {"start": 2685.37, "end": 2687.91, "word": " انه", "probability": 0.4862060546875}, {"start": 2687.91, "end": 2688.33, "word": " هيكون", "probability": 0.816650390625}, {"start": 2688.33, "end": 2688.71, "word": " عندى", "probability": 0.666748046875}, {"start": 2688.71, "end": 2688.93, "word": " الـ", "probability": 0.720947265625}, {"start": 2688.93, "end": 2689.15, "word": " 2", "probability": 0.8291015625}, {"start": 2689.15, "end": 2689.59, "word": " أُس", "probability": 0.9567057291666666}, {"start": 2689.59, "end": 2689.75, "word": " M", "probability": 0.98193359375}, {"start": 2689.75, "end": 2690.15, "word": " ناقص", "probability": 0.984130859375}, {"start": 2690.15, "end": 2690.73, "word": " واحد", "probability": 0.95556640625}], "temperature": 1.0}, {"id": 102, "seek": 272026, "start": 2691.78, "end": 2720.26, "text": "أتنين أس أن ناقص واحد يستحيل تجسم اتنين أس أن ناقص واحد فهي نصر فاهمين؟ فده انصار عندي الأن أن is the least positive integer such that two to the n تطابق الواحد modulo منين modulo اتنين أن ناقص واحد يعني ال order للأتنين modulo اتنين أس أن ناقص واحد بساوء أن", "tokens": [10721, 2655, 1863, 9957, 5551, 3794, 14739, 8717, 995, 4587, 9381, 36764, 24401, 7251, 14851, 5016, 26895, 6055, 7435, 38251, 1975, 2655, 1863, 9957, 5551, 3794, 14739, 8717, 995, 4587, 9381, 36764, 24401, 6156, 3224, 1829, 8717, 9381, 2288, 6156, 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"end": 2703.54, "word": " انصار", "probability": 0.7022298177083334}, {"start": 2703.54, "end": 2703.9, "word": " عندي", "probability": 0.744873046875}, {"start": 2703.9, "end": 2704.44, "word": " الأن", "probability": 0.61846923828125}, {"start": 2704.44, "end": 2705.16, "word": " أن", "probability": 0.4599609375}, {"start": 2705.16, "end": 2705.54, "word": " is", "probability": 0.64794921875}, {"start": 2705.54, "end": 2705.8, "word": " the", "probability": 0.921875}, {"start": 2705.8, "end": 2706.4, "word": " least", "probability": 0.966796875}, {"start": 2706.4, "end": 2707.96, "word": " positive", "probability": 0.947265625}, {"start": 2707.96, "end": 2708.54, "word": " integer", "probability": 0.875}, {"start": 2708.54, "end": 2708.9, "word": " such", "probability": 0.9404296875}, {"start": 2708.9, "end": 2709.58, "word": " that", "probability": 0.95849609375}, {"start": 2709.58, "end": 2710.16, "word": " two", "probability": 0.7353515625}, {"start": 2710.16, "end": 2710.34, 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"text": "نشوف إيش علاقته بالموضوع given that A has order 3 modulo B where B zenoth prime show that A زيادة واحد must have order أياش ستة معايا نشوف كيف سؤال خمسة ال order لل A modulo 13 بيساوي ال order modulo B بيساوي تلاتة", "tokens": [1863, 8592, 38688, 11933, 1829, 8592, 11203, 995, 38149, 3224, 20666, 2304, 2407, 11242, 45367, 2212, 300, 316, 575, 1668, 805, 1072, 13455, 363, 689, 363, 710, 5808, 392, 5835, 855, 300, 316, 30767, 1829, 18513, 3660, 36764, 24401, 1633, 362, 1668, 36632, 33599, 8608, 2655, 3660, 20449, 995, 25528, 8717, 8592, 38688, 9122, 33911, 8608, 33604, 6027, 16490, 2304, 3794, 3660, 2423, 1668, 24976, 316, 1072, 13455, 3705, 4724, 1829, 3794, 995, 45865, 2423, 1668, 1072, 13455, 363, 4724, 1829, 3794, 995, 45865, 6055, 1211, 9307, 3660], "avg_logprob": -0.3167134831460674, "compression_ratio": 1.47, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 2772.0, "end": 2772.38, "word": "نشوف", "probability": 0.717529296875}, {"start": 2772.38, "end": 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2911.47, "end": 2911.83, "word": " تربيع", "probability": 0.8212890625}, {"start": 2911.83, "end": 2911.97, "word": " او", "probability": 0.839111328125}, {"start": 2911.97, "end": 2912.13, "word": " a", "probability": 0.9267578125}, {"start": 2912.13, "end": 2912.45, "word": " تربيع", "probability": 0.9144287109375}, {"start": 2912.45, "end": 2912.81, "word": " زياد", "probability": 0.8269856770833334}, {"start": 2912.81, "end": 2913.11, "word": " a", "probability": 0.9033203125}, {"start": 2913.11, "end": 2913.69, "word": " زياد", "probability": 0.9215494791666666}, {"start": 2913.69, "end": 2914.15, "word": " واحد", "probability": 0.97021484375}, {"start": 2914.15, "end": 2916.31, "word": " again", "probability": 0.5986328125}, {"start": 2916.31, "end": 2917.65, "word": " ال", "probability": 0.88134765625}, {"start": 2917.65, "end": 2917.99, "word": " b", "probability": 0.70947265625}, {"start": 2917.99, "end": 2918.55, "word": " تقسم", "probability": 0.767822265625}, {"start": 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معناتها؟ هذه مستحيلة لماذا؟ لأن الـ Order للـ A Modulo بيه تلاتة ماشي يعني يصير عند في واحد جابله .. طبق الواحد و هذا Contradiction لأن الوحيه The least such positive integer فاهمين إيش بحكيه؟ الآن then خليني أفصل اللي قيته طابق الواحد Modulo B و هذا Contradiction", "tokens": [3224, 24192, 19446, 39896, 20449, 8315, 2655, 11296, 22807, 29538, 3714, 14851, 5016, 26895, 3660, 32767, 45636, 995, 22807, 5296, 33456, 2423, 39184, 16321, 24976, 39184, 316, 6583, 13455, 4724, 1829, 3224, 6055, 1211, 9307, 3660, 3714, 33599, 1829, 37495, 22653, 7251, 9381, 13546, 43242, 8978, 36764, 24401, 10874, 16758, 43761, 4386, 23032, 3555, 4587, 2423, 14407, 24401, 4032, 23758, 4839, 6206, 4105, 5296, 33456, 2423, 2407, 5016, 1829, 3224, 440, 1935, 1270, 3353, 24922, 6156, 995, 16095, 9957, 11933, 1829, 8592, 4724, 5016, 4117, 1829, 3224, 22807, 6024, 48506, 550, 16490, 1211, 9957, 1829, 5551, 5172, 36520, 13672, 1829, 12174, 36081, 3224, 23032, 16758, 4587, 2423, 14407, 24401, 6583, 13455, 363, 4032, 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" positive", "probability": 0.93359375}, {"start": 2945.1, "end": 2945.54, "word": " integer", "probability": 0.822265625}, {"start": 2945.54, "end": 2946.7, "word": " فاهمين", "probability": 0.8909912109375}, {"start": 2946.7, "end": 2946.78, "word": " إيش", "probability": 0.6718343098958334}, {"start": 2946.78, "end": 2947.84, "word": " بحكيه؟", "probability": 0.8369954427083334}, {"start": 2947.84, "end": 2948.24, "word": " الآن", "probability": 0.759033203125}, {"start": 2948.24, "end": 2949.06, "word": " then", "probability": 0.2144775390625}, {"start": 2949.06, "end": 2949.38, "word": " خليني", "probability": 0.82177734375}, {"start": 2949.38, "end": 2949.92, "word": " أفصل", "probability": 0.8214518229166666}, {"start": 2949.92, "end": 2950.58, "word": " اللي", "probability": 0.80419921875}, {"start": 2950.58, "end": 2950.84, "word": " قيته", "probability": 0.5165201822916666}, {"start": 2950.84, "end": 2951.18, "word": " طابق", "probability": 0.8463541666666666}, {"start": 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"end": 3243.13, "word": " عبارة", "probability": 0.8856201171875}, {"start": 3243.13, "end": 3243.31, "word": " عن", "probability": 0.99365234375}, {"start": 3243.31, "end": 3243.85, "word": " مين؟", "probability": 0.8709309895833334}], "temperature": 1.0}, {"id": 122, "seek": 326635, "start": 3244.57, "end": 3266.35, "text": "A زي واحد أُس خمسة تطابق اللي هو سالب A وسالب A موضوع لا تطابق مين الواحد وسالب A لا تطابق الواحد Modulo", "tokens": [32, 30767, 1829, 36764, 24401, 5551, 10859, 3794, 16490, 2304, 3794, 3660, 6055, 9566, 16758, 4587, 13672, 1829, 31439, 8608, 6027, 3555, 316, 46952, 6027, 3555, 316, 3714, 2407, 11242, 45367, 20193, 6055, 9566, 16758, 4587, 3714, 9957, 2423, 14407, 24401, 46952, 6027, 3555, 316, 20193, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 6583, 13455], "avg_logprob": -0.3052455373108387, "compression_ratio": 1.6, "no_speech_prob": 9.953975677490234e-06, "words": [{"start": 3244.57, "end": 3245.13, "word": "A", "probability": 0.44970703125}, {"start": 3245.13, "end": 3246.07, "word": " زي", "probability": 0.48095703125}, {"start": 3246.07, "end": 3246.55, "word": " واحد", "probability": 0.6553955078125}, {"start": 3246.55, "end": 3246.81, "word": " أُس", "probability": 0.5941569010416666}, {"start": 3246.81, "end": 3247.87, "word": " خمسة", "probability": 0.96923828125}, {"start": 3247.87, "end": 3249.33, "word": " تطابق", "probability": 0.8599853515625}, {"start": 3249.33, "end": 3250.85, "word": " اللي", "probability": 0.501220703125}, {"start": 3250.85, "end": 3251.07, "word": " هو", "probability": 0.95263671875}, {"start": 3251.07, "end": 3251.85, "word": " سالب", "probability": 0.7867838541666666}, {"start": 3251.85, "end": 3253.59, "word": " A", "probability": 0.7529296875}, {"start": 3253.59, "end": 3256.85, "word": " وسالب", "probability": 0.6513671875}, {"start": 3256.85, "end": 3256.99, "word": " A", "probability": 0.9287109375}, {"start": 3256.99, "end": 3257.25, "word": " موضوع", "probability": 0.594329833984375}, {"start": 3257.25, "end": 3257.47, "word": " لا", "probability": 0.55712890625}, {"start": 3257.47, "end": 3257.85, "word": " تطابق", "probability": 0.9754638671875}, {"start": 3257.85, "end": 3258.29, "word": " مين", "probability": 0.740234375}, {"start": 3258.29, "end": 3259.69, "word": " الواحد", "probability": 0.8951822916666666}, {"start": 3259.69, "end": 3261.03, "word": " وسالب", "probability": 0.9658203125}, {"start": 3261.03, "end": 3261.35, "word": " A", "probability": 0.95263671875}, {"start": 3261.35, "end": 3262.73, "word": " لا", "probability": 0.63134765625}, {"start": 3262.73, "end": 3263.53, "word": " تطابق", "probability": 0.9857177734375}, {"start": 3263.53, "end": 3264.49, "word": " الواحد", "probability": 0.9853515625}, {"start": 3264.49, "end": 3266.35, "word": " Modulo", "probability": 0.57183837890625}], "temperature": 1.0}, {"id": 123, "seek": 330485, "start": 3276.87, "end": 3304.85, "text": "دال إيه؟ الـ6 الآن الـ6 ضرب ليه؟ واحد واتنين حصلنا عليهم from واحد and اتنين معايا يا شباب بيصير ايه؟ زائد واحد والست طابق ايه التكعيب؟ ليه الطابق؟ modulo D", "tokens": [3215, 6027, 11933, 1829, 3224, 22807, 2423, 39184, 21, 6024, 48506, 2423, 39184, 21, 48812, 25513, 32239, 3224, 22807, 36764, 24401, 4032, 9307, 1863, 9957, 11331, 36520, 8315, 25894, 16095, 490, 36764, 24401, 293, 1975, 2655, 1863, 9957, 20449, 995, 25528, 35186, 13412, 3555, 16758, 4724, 1829, 9381, 13546, 1975, 1829, 3224, 22807, 30767, 16373, 3215, 36764, 24401, 16070, 14851, 23032, 16758, 4587, 1975, 1829, 3224, 16712, 4117, 3615, 1829, 3555, 22807, 32239, 3224, 41950, 16758, 4587, 22807, 1072, 13455, 413], "avg_logprob": -0.3018292650216963, "compression_ratio": 1.6280487804878048, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 3276.87, "end": 3277.33, "word": "دال", "probability": 0.343841552734375}, {"start": 3277.33, "end": 3278.05, "word": " إيه؟", "probability": 0.552276611328125}, {"start": 3278.05, "end": 3280.01, "word": " الـ6", "probability": 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"probability": 0.8726806640625}, {"start": 3294.91, "end": 3295.73, "word": " معايا", "probability": 0.92724609375}, {"start": 3295.73, "end": 3295.91, "word": " يا", "probability": 0.93408203125}, {"start": 3295.91, "end": 3296.13, "word": " شباب", "probability": 0.99169921875}, {"start": 3296.13, "end": 3297.11, "word": " بيصير", "probability": 0.676849365234375}, {"start": 3297.11, "end": 3297.33, "word": " ايه؟", "probability": 0.75518798828125}, {"start": 3297.33, "end": 3297.61, "word": " زائد", "probability": 0.8771158854166666}, {"start": 3297.61, "end": 3298.17, "word": " واحد", "probability": 0.979736328125}, {"start": 3298.17, "end": 3299.09, "word": " والست", "probability": 0.5517578125}, {"start": 3299.09, "end": 3299.87, "word": " طابق", "probability": 0.9228515625}, {"start": 3299.87, "end": 3301.05, "word": " ايه", "probability": 0.7216389973958334}, {"start": 3301.05, "end": 3301.63, "word": " التكعيب؟", "probability": 0.8328043619791666}, {"start": 3301.63, "end": 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واحد", "tokens": [1863, 25957, 4724, 5016, 1829, 12984, 21136, 33604, 6027, 8717, 8592, 38688, 21136, 33604, 6027, 32239, 8592, 20666, 2304, 16095, 21136, 33604, 6027, 7081, 300, 498, 363, 293, 1249, 366, 582, 1532, 1649, 363, 293, 1249, 366, 7401, 582, 1532, 4032, 1249, 39894, 4587, 38251, 316, 281, 264, 363, 8717, 995, 4587, 9381, 36764, 24401], "avg_logprob": -0.37946427507059916, "compression_ratio": 1.3478260869565217, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 3336.56, "end": 3336.92, "word": "نعم", "probability": 0.3179931640625}, {"start": 3336.92, "end": 3337.22, "word": " بحيث", "probability": 0.69683837890625}, {"start": 3337.22, "end": 3337.72, "word": " السؤال", "probability": 0.9462890625}, {"start": 3337.72, "end": 3342.8, "word": " نشوف", "probability": 0.7272135416666666}, {"start": 3342.8, "end": 3343.14, "word": " السؤال", "probability": 0.99267578125}, {"start": 3343.14, "end": 3343.3, "word": " ليش", "probability": 0.5814208984375}, {"start": 3343.3, "end": 3343.68, "word": " بالمهم", "probability": 0.546875}, {"start": 3343.68, "end": 3345.48, "word": " السؤال", "probability": 0.9090169270833334}, {"start": 3345.48, "end": 3345.82, "word": " prove", "probability": 0.30712890625}, {"start": 3345.82, "end": 3346.16, "word": " that", "probability": 0.9208984375}, {"start": 3346.16, "end": 3346.42, "word": " if", "probability": 0.91943359375}, {"start": 3346.42, "end": 3346.6, "word": " B", "probability": 0.46484375}, {"start": 3346.6, "end": 3346.9, "word": " and", "probability": 0.869140625}, {"start": 3346.9, "end": 3347.2, "word": " Q", "probability": 0.974609375}, {"start": 3347.2, "end": 3347.4, "word": " are", "probability": 0.94580078125}, {"start": 3347.4, "end": 3348.04, "word": " primes", "probability": 0.795166015625}, {"start": 3348.04, "end": 3349.46, "word": " 8", "probability": 0.1650390625}, {"start": 3349.46, "end": 3352.34, "word": " B", "probability": 0.449462890625}, {"start": 3352.34, "end": 3354.16, "word": " and", "probability": 0.8994140625}, {"start": 3354.16, "end": 3354.68, "word": " Q", "probability": 0.98681640625}, {"start": 3354.68, "end": 3355.78, "word": " are", "probability": 0.94873046875}, {"start": 3355.78, "end": 3356.18, "word": " odd", "probability": 0.335693359375}, {"start": 3356.18, "end": 3356.8, "word": " primes", "probability": 0.869140625}, {"start": 3356.8, "end": 3357.86, "word": " و", "probability": 0.9541015625}, {"start": 3357.86, "end": 3358.12, "word": " Q", "probability": 0.6591796875}, {"start": 3358.12, "end": 3358.78, "word": " بتقسم", "probability": 0.7477213541666666}, {"start": 3358.78, "end": 3361.96, "word": " A", "probability": 0.430908203125}, {"start": 3361.96, "end": 3363.48, "word": " to", "probability": 0.493896484375}, {"start": 3363.48, "end": 3363.6, "word": " the", "probability": 0.46728515625}, {"start": 3363.6, "end": 3363.9, "word": " B", "probability": 0.74169921875}, {"start": 3363.9, "end": 3364.62, "word": " ناقص", 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3366.83, "word": "كيو", "probability": 0.4829305013020833}, {"start": 3366.83, "end": 3367.23, "word": " بتقسم", "probability": 0.5}, {"start": 3367.23, "end": 3367.39, "word": " a", "probability": 0.453369140625}, {"start": 3367.39, "end": 3367.53, "word": " تقسم", "probability": 0.3307291666666667}, {"start": 3367.53, "end": 3367.67, "word": " b", "probability": 0.53857421875}, {"start": 3367.67, "end": 3367.99, "word": " نقص", "probability": 0.7530110677083334}, {"start": 3367.99, "end": 3368.51, "word": " واحد", "probability": 0.9169921875}, {"start": 3368.51, "end": 3369.77, "word": " ثم", "probability": 0.6014404296875}, {"start": 3369.77, "end": 3376.57, "word": " ايضا", "probability": 0.64617919921875}, {"start": 3376.57, "end": 3377.43, "word": " كيو", "probability": 0.8675130208333334}, {"start": 3377.43, "end": 3378.01, "word": " بتقسم", "probability": 0.8849283854166666}, {"start": 3378.01, "end": 3378.27, "word": " a", "probability": 0.9052734375}, {"start": 3378.27, "end": 3378.63, "word": " minus", "probability": 0.40576171875}, {"start": 3378.63, "end": 3379.27, "word": " واحد", "probability": 0.87841796875}, {"start": 3379.27, "end": 3379.91, "word": " او", "probability": 0.7464599609375}, {"start": 3379.91, "end": 3381.07, "word": " كيو", "probability": 0.95703125}, {"start": 3381.07, "end": 3381.49, "word": " بتقسم", "probability": 0.9363606770833334}, {"start": 3381.49, "end": 3382.09, "word": " اتنين", "probability": 0.8939208984375}, {"start": 3382.09, "end": 3383.95, "word": " بتساوي", "probability": 0.8509521484375}, {"start": 3383.95, "end": 3386.01, "word": " اتنين", "probability": 0.9273681640625}, {"start": 3386.01, "end": 3386.51, "word": " كب", "probability": 0.618896484375}, {"start": 3386.51, "end": 3387.67, "word": " زاد", "probability": 0.736328125}, {"start": 3387.67, "end": 3388.01, "word": " واحد", "probability": 0.989013671875}, {"start": 3388.01, "end": 3388.23, "word": " for", "probability": 0.86474609375}, {"start": 3388.23, "end": 3388.73, "word": " some", "probability": 0.9033203125}, {"start": 3388.73, "end": 3390.13, "word": " k", "probability": 0.18798828125}, {"start": 3390.13, "end": 3391.89, "word": " element", "probability": 0.791015625}, {"start": 3391.89, "end": 3392.21, "word": " of", "probability": 0.139892578125}, {"start": 3392.21, "end": 3392.45, "word": " z", "probability": 0.912109375}, {"start": 3392.45, "end": 3393.07, "word": " وقول", "probability": 0.5107421875}, {"start": 3393.07, "end": 3393.19, "word": " لي", "probability": 0.1744384765625}, {"start": 3393.19, "end": 3393.31, "word": " اذا", "probability": 0.850830078125}, {"start": 3393.31, "end": 3393.79, "word": " كانت", "probability": 0.94287109375}, {"start": 3393.79, "end": 3394.03, "word": " b", "probability": 0.560546875}, {"start": 3394.03, "end": 3394.25, "word": " و", "probability": 0.97607421875}, {"start": 3394.25, "end": 3394.59, "word": " q", "probability": 0.7197265625}, {"start": 3394.59, "end": 3395.87, "word": " برامج", "probability": 0.458587646484375}], "temperature": 1.0}, {"id": 127, "seek": 342498, "start": 3396.48, "end": 3424.98, "text": "ميو كيو برايمز وكانت عند الكيو بتقسم a to the b نقص واحد بيقول يا الكيو بتقسم ال a minus واحد او الكيو هتسوقن على صورة اتنين k بيزايد واحد معايا اه الآن ا proof suppose that suppose", "tokens": [2304, 1829, 2407, 9122, 1829, 2407, 4724, 23557, 32640, 11622, 4032, 41361, 2655, 43242, 33251, 1829, 2407, 39894, 4587, 38251, 257, 281, 264, 272, 8717, 4587, 9381, 36764, 24401, 4724, 1829, 39648, 35186, 33251, 1829, 2407, 39894, 4587, 38251, 2423, 257, 3175, 36764, 24401, 1975, 2407, 33251, 1829, 2407, 8032, 2655, 3794, 30543, 1863, 15844, 20328, 13063, 3660, 1975, 2655, 1863, 9957, 350, 4724, 1829, 11622, 995, 25708, 36764, 24401, 20449, 995, 25528, 1975, 3224, 6024, 48506, 1975, 8177, 7297, 300, 7297], "avg_logprob": -0.29631023809134244, "compression_ratio": 1.6457142857142857, "no_speech_prob": 4.410743713378906e-06, "words": [{"start": 3396.48, "end": 3396.86, "word": "ميو", "probability": 0.4573974609375}, {"start": 3396.86, "end": 3397.06, "word": " كيو", "probability": 0.8956705729166666}, {"start": 3397.06, "end": 3397.7, "word": " برايمز", "probability": 0.7259521484375}, {"start": 3397.7, "end": 3398.88, "word": " وكانت", "probability": 0.68359375}, {"start": 3398.88, "end": 3399.1, "word": " عند", "probability": 0.85986328125}, {"start": 3399.1, "end": 3399.58, "word": " الكيو", "probability": 0.6517740885416666}, {"start": 3399.58, "end": 3400.02, "word": " بتقسم", "probability": 0.7210286458333334}, {"start": 3400.02, "end": 3400.22, "word": " a", "probability": 0.701171875}, {"start": 3400.22, "end": 3400.3, "word": " to", "probability": 0.07000732421875}, {"start": 3400.3, "end": 3400.44, "word": " the", "probability": 0.79150390625}, {"start": 3400.44, "end": 3400.62, "word": " b", "probability": 0.68994140625}, {"start": 3400.62, "end": 3401.02, "word": " نقص", "probability": 0.6861165364583334}, {"start": 3401.02, "end": 3401.48, "word": " واحد", "probability": 0.949462890625}, {"start": 3401.48, "end": 3402.5, "word": " بيقول", "probability": 0.730712890625}, {"start": 3402.5, "end": 3402.82, "word": " يا", "probability": 0.498291015625}, {"start": 3402.82, "end": 3403.36, "word": " الكيو", "probability": 0.8987630208333334}, {"start": 3403.36, "end": 3403.76, "word": " بتقسم", "probability": 0.91357421875}, {"start": 3403.76, "end": 3403.92, "word": " ال", "probability": 0.86962890625}, {"start": 3403.92, "end": 3404.02, "word": " a", "probability": 0.86572265625}, {"start": 3404.02, "end": 3404.34, "word": " minus", "probability": 0.459716796875}, {"start": 3404.34, "end": 3404.92, "word": " واحد", "probability": 0.942626953125}, {"start": 3404.92, "end": 3405.56, "word": " او", "probability": 0.837646484375}, {"start": 3405.56, "end": 3405.86, "word": " الكيو", "probability": 0.94677734375}, {"start": 3405.86, "end": 3406.5, "word": " هتسوقن", "probability": 0.77841796875}, {"start": 3406.5, "end": 3406.64, "word": " على", "probability": 0.88720703125}, {"start": 3406.64, "end": 3406.94, "word": " صورة", "probability": 0.9176432291666666}, {"start": 3406.94, "end": 3407.26, "word": " اتنين", "probability": 0.936767578125}, {"start": 3407.26, "end": 3407.68, "word": " k", "probability": 0.3623046875}, {"start": 3407.68, "end": 3409.56, "word": " بيزايد", "probability": 0.785986328125}, {"start": 3409.56, "end": 3410.06, "word": " واحد", "probability": 0.9892578125}, {"start": 3410.06, "end": 3411.74, "word": " معايا", "probability": 0.9431966145833334}, {"start": 3411.74, "end": 3412.42, "word": " اه", "probability": 0.812255859375}, {"start": 3412.42, "end": 3413.32, "word": " الآن", "probability": 0.6014404296875}, {"start": 3413.32, "end": 3413.9, "word": " ا", "probability": 0.7109375}, {"start": 3413.9, "end": 3414.96, "word": " proof", "probability": 0.5458984375}, {"start": 3414.96, "end": 3421.48, "word": " suppose", "probability": 0.884765625}, {"start": 3421.48, "end": 3422.26, "word": " that", "probability": 0.947265625}, {"start": 3422.26, "end": 3424.98, "word": " suppose", "probability": 0.939453125}], "temperature": 1.0}, {"id": 128, "seek": 344766, "start": 3428.34, "end": 3447.66, "text": "الـ Q تقسم A to the B minus واحد ثم A to the B تطابق الواحد مضلومين مضلوا Q صح ولا لأ؟", "tokens": [6027, 39184, 1249, 6055, 4587, 38251, 316, 281, 264, 363, 3175, 36764, 24401, 38637, 2304, 316, 281, 264, 363, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 3714, 11242, 1211, 20498, 9957, 3714, 11242, 1211, 14407, 1249, 20328, 5016, 49429, 5296, 10721, 22807], "avg_logprob": -0.43422965393509977, "compression_ratio": 1.2380952380952381, "no_speech_prob": 1.4603137969970703e-05, "words": [{"start": 3428.3400000000006, "end": 3429.5600000000004, "word": "الـ", "probability": 0.46795654296875}, {"start": 3429.5600000000004, "end": 3430.78, "word": " Q", "probability": 0.53271484375}, {"start": 3430.78, "end": 3431.38, "word": " تقسم", "probability": 0.6170247395833334}, {"start": 3431.38, "end": 3431.62, "word": " A", "probability": 0.52001953125}, {"start": 3431.62, "end": 3431.72, "word": " to", "probability": 0.09735107421875}, {"start": 3431.72, "end": 3431.88, "word": " the", "probability": 0.7724609375}, {"start": 3431.88, "end": 3432.14, "word": " B", "probability": 0.87548828125}, {"start": 3432.14, "end": 3432.76, "word": " minus", "probability": 0.1275634765625}, {"start": 3432.76, "end": 3433.2, "word": " واحد", "probability": 0.68701171875}, {"start": 3433.2, "end": 3434.28, "word": " ثم", "probability": 0.737548828125}, {"start": 3434.28, "end": 3435.68, "word": " A", "probability": 0.93310546875}, {"start": 3435.68, "end": 3435.84, "word": " to", "probability": 0.97314453125}, {"start": 3435.84, "end": 3436.04, "word": " the", "probability": 0.9033203125}, {"start": 3436.04, "end": 3436.42, "word": " B", "probability": 0.9931640625}, {"start": 3436.42, "end": 3437.8, "word": " تطابق", "probability": 0.83837890625}, {"start": 3437.8, "end": 3438.66, "word": " الواحد", "probability": 0.9763997395833334}, {"start": 3438.66, "end": 3441.14, "word": " مضلومين", "probability": 0.5732421875}, {"start": 3441.14, "end": 3442.84, "word": " مضلوا", "probability": 0.6697998046875}, {"start": 3442.84, "end": 3443.04, "word": " Q", "probability": 0.8837890625}, {"start": 3443.04, "end": 3443.7, "word": " صح", "probability": 0.9423828125}, {"start": 3443.7, "end": 3443.86, "word": " ولا", "probability": 0.92578125}, {"start": 3443.86, "end": 3447.66, "word": " لأ؟", "probability": 0.7190755208333334}], "temperature": 1.0}, {"id": 129, "seek": 349062, "start": 3461.16, "end": 3490.62, "text": "أنا مش سامعش قولت أن ال order لل A سواء B مدلو Q لأ ليش ال order then ال order لل A مدلو Q بيبسمي ال B بيبسم ال B اه ماشي الحال", "tokens": [10721, 8315, 37893, 8608, 10943, 3615, 8592, 12174, 12610, 2655, 14739, 2423, 1668, 24976, 316, 8608, 2407, 16606, 363, 3714, 3215, 1211, 2407, 1249, 5296, 10721, 32239, 8592, 2423, 1668, 550, 2423, 1668, 24976, 316, 3714, 3215, 1211, 2407, 1249, 4724, 1829, 3555, 38251, 1829, 2423, 363, 4724, 1829, 3555, 38251, 2423, 363, 1975, 3224, 3714, 33599, 1829, 21542, 6027], "avg_logprob": -0.4569672170232554, "compression_ratio": 1.568, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 3461.16, "end": 3461.34, "word": "أنا", "probability": 0.5050048828125}, {"start": 3461.34, "end": 3461.54, "word": " مش", "probability": 0.80078125}, {"start": 3461.54, "end": 3462.04, "word": " سامعش", "probability": 0.71533203125}, {"start": 3462.04, "end": 3463.1, "word": " قولت", "probability": 0.5846761067708334}, {"start": 3463.1, "end": 3463.22, "word": " أن", "probability": 0.67138671875}, {"start": 3463.22, "end": 3463.32, "word": " ال", "probability": 0.63037109375}, {"start": 3463.32, "end": 3463.56, "word": " order", "probability": 0.84619140625}, {"start": 3463.56, "end": 3463.8, "word": " لل", "probability": 0.65966796875}, {"start": 3463.8, "end": 3463.98, "word": " A", "probability": 0.28173828125}, {"start": 3463.98, "end": 3464.32, "word": " سواء", "probability": 0.3283742268880208}, {"start": 3464.32, "end": 3464.6, "word": " B", "probability": 0.5}, {"start": 3464.6, "end": 3465.32, "word": " مدلو", "probability": 0.48907470703125}, {"start": 3465.32, "end": 3465.44, "word": " Q", "probability": 0.55126953125}, {"start": 3465.44, "end": 3467.34, "word": " لأ", "probability": 0.85107421875}, {"start": 3467.34, "end": 3468.04, "word": " ليش", "probability": 0.803955078125}, {"start": 3468.04, "end": 3470.72, "word": " ال", "probability": 0.263427734375}, {"start": 3470.72, "end": 3474.14, "word": " order", "probability": 0.958984375}, {"start": 3474.14, "end": 3475.86, "word": " then", "probability": 0.56787109375}, {"start": 3475.86, "end": 3477.2, "word": " ال", "probability": 0.91015625}, {"start": 3477.2, "end": 3477.76, "word": " order", "probability": 0.9736328125}, {"start": 3477.76, "end": 3478.32, "word": " لل", "probability": 0.88427734375}, {"start": 3478.32, "end": 3478.78, "word": " A", "probability": 0.94677734375}, {"start": 3478.78, "end": 3480.12, "word": " مدلو", "probability": 0.932861328125}, {"start": 3480.12, "end": 3480.62, "word": " Q", "probability": 0.91015625}, {"start": 3480.62, "end": 3484.02, "word": " بيبسمي", "probability": 0.680712890625}, {"start": 3484.02, "end": 3484.96, "word": " ال", "probability": 0.2261962890625}, {"start": 3484.96, "end": 3485.42, "word": " B", "probability": 0.64404296875}, {"start": 3485.42, "end": 3487.24, "word": " بيبسم", "probability": 0.926025390625}, {"start": 3487.24, "end": 3487.38, "word": " ال", "probability": 0.9462890625}, {"start": 3487.38, "end": 3487.66, "word": " B", "probability": 0.97900390625}, {"start": 3487.66, "end": 3489.52, "word": " اه", "probability": 0.633544921875}, {"start": 3489.52, "end": 3490.24, "word": " ماشي", "probability": 0.6598103841145834}, {"start": 3490.24, "end": 3490.62, "word": " الحال", "probability": 0.9775390625}], "temperature": 1.0}, {"id": 130, "seek": 351445, "start": 3493.89, "end": 3514.45, "text": "ذن بي براين إذا ال order لل A mod Q ياساوي واحد or ال order لل A mod Q أيش بيساوي؟ بيه صح؟ في حالة و هذا يعطيني then", "tokens": [8848, 1863, 4724, 1829, 4724, 23557, 9957, 11933, 15730, 2423, 1668, 24976, 316, 1072, 1249, 7251, 32277, 995, 45865, 36764, 24401, 420, 2423, 1668, 24976, 316, 1072, 1249, 36632, 8592, 4724, 1829, 3794, 995, 45865, 22807, 4724, 1829, 3224, 20328, 5016, 22807, 8978, 11331, 6027, 3660, 4032, 23758, 37495, 9566, 1829, 22653, 550], "avg_logprob": -0.5052083532015482, "compression_ratio": 1.37984496124031, "no_speech_prob": 3.933906555175781e-06, "words": [{"start": 3493.89, "end": 3494.77, "word": "ذن", "probability": 0.43768310546875}, {"start": 3494.77, "end": 3495.65, "word": " بي", "probability": 0.45941162109375}, {"start": 3495.65, "end": 3496.05, "word": " براين", "probability": 0.6267903645833334}, {"start": 3496.05, "end": 3497.53, "word": " إذا", "probability": 0.505126953125}, {"start": 3497.53, "end": 3497.73, "word": " ال", "probability": 0.72314453125}, {"start": 3497.73, "end": 3498.13, "word": " order", "probability": 0.91162109375}, {"start": 3498.13, "end": 3499.51, "word": " لل", "probability": 0.61474609375}, {"start": 3499.51, "end": 3499.73, "word": " A", "probability": 0.287841796875}, {"start": 3499.73, "end": 3499.93, "word": " mod", "probability": 0.57373046875}, {"start": 3499.93, "end": 3500.37, "word": " Q", "probability": 0.2236328125}, {"start": 3500.37, "end": 3501.07, "word": " ياساوي", "probability": 0.38946533203125}, {"start": 3501.07, "end": 3501.61, "word": " واحد", "probability": 0.70947265625}, {"start": 3501.61, "end": 3503.31, "word": " or", "probability": 0.6162109375}, {"start": 3503.31, "end": 3504.19, "word": " ال", "probability": 0.48681640625}, {"start": 3504.19, "end": 3504.53, "word": " order", "probability": 0.9736328125}, {"start": 3504.53, "end": 3504.83, "word": " لل", "probability": 0.857421875}, {"start": 3504.83, "end": 3505.07, "word": " A", "probability": 0.93896484375}, {"start": 3505.07, "end": 3505.33, "word": " mod", "probability": 0.8544921875}, {"start": 3505.33, "end": 3505.69, "word": " Q", "probability": 0.83251953125}, {"start": 3505.69, "end": 3505.85, "word": " أيش", "probability": 0.48223876953125}, {"start": 3505.85, "end": 3507.47, "word": " بيساوي؟", "probability": 0.80322265625}, {"start": 3507.47, "end": 3507.79, "word": " بيه", "probability": 0.642333984375}, {"start": 3507.79, "end": 3509.25, "word": " صح؟", "probability": 0.7095540364583334}, {"start": 3509.25, "end": 3510.15, "word": " في", "probability": 0.78662109375}, {"start": 3510.15, "end": 3511.45, "word": " حالة", "probability": 0.9947916666666666}, {"start": 3511.45, "end": 3513.13, "word": " و", "probability": 0.408935546875}, {"start": 3513.13, "end": 3513.39, "word": " هذا", "probability": 0.6474609375}, {"start": 3513.39, "end": 3514.11, "word": " يعطيني", "probability": 0.781494140625}, {"start": 3514.11, "end": 3514.45, "word": " then", "probability": 0.79833984375}], "temperature": 1.0}, {"id": 131, "seek": 353763, "start": 3515.69, "end": 3537.63, "text": "ما هي معناته أفضل لـ A modulo Q بساوة واحد؟ معناته A تطابق الواحد modulo Q صح؟ معين وهذا يعطينا الـ Q تجسم A minus واحد hence", "tokens": [15042, 39896, 20449, 8315, 47395, 5551, 5172, 11242, 1211, 5296, 39184, 316, 1072, 13455, 1249, 4724, 3794, 995, 2407, 3660, 36764, 24401, 22807, 20449, 8315, 47395, 316, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 1072, 13455, 1249, 20328, 5016, 22807, 20449, 9957, 37037, 15730, 37495, 9566, 1829, 8315, 2423, 39184, 1249, 6055, 7435, 38251, 316, 3175, 36764, 24401, 16678], "avg_logprob": -0.3973958303531011, "compression_ratio": 1.380281690140845, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 3515.69, "end": 3515.91, "word": "ما", "probability": 0.5009765625}, {"start": 3515.91, "end": 3515.93, "word": " هي", "probability": 0.35205078125}, {"start": 3515.93, "end": 3516.25, "word": " معناته", "probability": 0.5858561197916666}, {"start": 3516.25, "end": 3516.67, "word": " أفضل", "probability": 0.778594970703125}, {"start": 3516.67, "end": 3516.85, "word": " لـ", "probability": 0.5340576171875}, {"start": 3516.85, "end": 3517.03, "word": " A", "probability": 0.332275390625}, {"start": 3517.03, "end": 3517.43, "word": " modulo", "probability": 0.45947265625}, {"start": 3517.43, "end": 3517.61, "word": " Q", "probability": 0.68017578125}, {"start": 3517.61, "end": 3517.95, "word": " بساوة", "probability": 0.4925048828125}, {"start": 3517.95, "end": 3518.99, "word": " واحد؟", "probability": 0.7276204427083334}, {"start": 3518.99, "end": 3519.45, "word": " معناته", "probability": 0.8811848958333334}, {"start": 3519.45, "end": 3519.91, "word": " A", "probability": 0.80859375}, {"start": 3519.91, "end": 3521.07, "word": " تطابق", "probability": 0.9453125}, {"start": 3521.07, "end": 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بتعطي هذه صار عندي يا هذه يا هذه لأن a تطابق الواحد من ال q معناته ان ال q تكسب ال a-1 او ال b تكسب ال 5 of q يعني ال b تكسب 100 من q-1 يعني ال q-1", "tokens": [2407, 29538, 39894, 3615, 9566, 1829, 29538, 20328, 9640, 18871, 16254, 35186, 29538, 35186, 29538, 5296, 33456, 257, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 9154, 2423, 9505, 20449, 8315, 47395, 16472, 2423, 9505, 6055, 4117, 35457, 2423, 257, 12, 16, 1975, 2407, 2423, 272, 6055, 4117, 35457, 2423, 1025, 295, 9505, 37495, 22653, 2423, 272, 6055, 4117, 35457, 2319, 9154, 9505, 12, 16, 37495, 22653, 2423, 9505, 12, 16], "avg_logprob": -0.36773768948837066, "compression_ratio": 1.7428571428571429, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 3598.93, "end": 3599.19, "word": "و", "probability": 0.5400390625}, {"start": 3599.19, "end": 3599.43, "word": " هذه", "probability": 0.126220703125}, {"start": 3599.43, "end": 3599.93, "word": " بتعطي", "probability": 0.8331298828125}, {"start": 3599.93, "end": 3600.21, 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"probability": 0.8662109375}, {"start": 3670.93, "end": 3671.21, "word": " minus", "probability": 0.76416015625}, {"start": 3671.21, "end": 3671.89, "word": " واحد", "probability": 0.96240234375}], "temperature": 1.0}, {"id": 137, "seek": 369873, "start": 3672.91, "end": 3698.73, "text": "يوم الـ Q تكسب من A وانس واحد أو الـ Q بساعده اتنين بك زايد واحد for some K element in Z بيناخد لك مثال حالة خاصة بيقولون to show that B is an odd prime او let's show that FB is an odd prime", "tokens": [1829, 20498, 2423, 39184, 1249, 6055, 4117, 35457, 9154, 316, 4032, 7649, 3794, 36764, 24401, 34051, 2423, 39184, 1249, 4724, 3794, 995, 22488, 3224, 1975, 2655, 1863, 9957, 4724, 4117, 30767, 995, 25708, 36764, 24401, 337, 512, 591, 4478, 294, 1176, 4724, 1829, 8315, 9778, 3215, 5296, 4117, 50113, 6027, 11331, 6027, 3660, 16490, 33546, 3660, 4724, 1829, 39648, 11536, 281, 855, 300, 363, 307, 364, 7401, 5835, 1975, 2407, 718, 311, 855, 300, 479, 33, 307, 364, 7401, 5835], "avg_logprob": 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واحد الـ B بيقول let B be an odd prime هذا سؤال B let B be an odd prime معايا يا جماعة", "tokens": [19096, 264, 5835, 25974, 284, 295, 1975, 2655, 1863, 9957, 7251, 9381, 49628, 8717, 4587, 9381, 36764, 24401, 497, 295, 264, 1254, 1975, 2655, 1863, 9957, 591, 33, 30767, 1829, 3215, 36764, 24401, 2423, 39184, 363, 4724, 1829, 39648, 718, 363, 312, 364, 7401, 5835, 23758, 8608, 33604, 6027, 363, 718, 363, 312, 364, 7401, 5835, 20449, 995, 25528, 35186, 10874, 15042, 27884], "avg_logprob": -0.33032226702198386, "compression_ratio": 1.4078947368421053, "no_speech_prob": 1.0132789611816406e-06, "words": [{"start": 3700.53, "end": 3700.89, "word": "then", "probability": 0.311767578125}, {"start": 3700.89, "end": 3701.09, "word": " the", "probability": 0.818359375}, {"start": 3701.09, "end": 3701.41, "word": " prime", "probability": 0.8447265625}, {"start": 3701.41, "end": 3702.33, "word": " divisor", "probability": 0.958984375}, {"start": 3702.33, "end": 3702.89, "word": " of", "probability": 0.931640625}, {"start": 3702.89, "end": 3703.23, "word": " اتنين", "probability": 0.74871826171875}, {"start": 3703.23, "end": 3703.51, "word": " يصبح", "probability": 0.391357421875}, {"start": 3703.51, "end": 3703.83, "word": " نقص", "probability": 0.8787434895833334}, {"start": 3703.83, "end": 3704.19, "word": " واحد", "probability": 0.98876953125}, {"start": 3704.19, "end": 3704.43, "word": " R", "probability": 0.094482421875}, {"start": 3704.43, "end": 3704.55, "word": " of", "probability": 0.87109375}, {"start": 3704.55, "end": 3704.71, "word": " the", "probability": 0.61376953125}, {"start": 3704.71, "end": 3704.93, "word": " form", "probability": 0.70556640625}, {"start": 3704.93, "end": 3705.29, "word": " اتنين", "probability": 0.93310546875}, {"start": 3705.29, "end": 3705.83, "word": " KB", "probability": 0.617919921875}, {"start": 3705.83, "end": 3706.35, "word": " زيد", "probability": 0.625}, {"start": 3706.35, "end": 3706.79, "word": " واحد", "probability": 0.9892578125}, {"start": 3706.79, "end": 3707.83, "word": " الـ", "probability": 0.40869140625}, {"start": 3707.83, "end": 3710.29, "word": " B", "probability": 0.476806640625}, {"start": 3710.29, "end": 3712.29, "word": " بيقول", "probability": 0.7628580729166666}, {"start": 3712.29, "end": 3713.77, "word": " let", "probability": 0.2001953125}, {"start": 3713.77, "end": 3716.71, "word": " B", "probability": 0.833984375}, {"start": 3716.71, "end": 3718.93, "word": " be", "probability": 0.74169921875}, {"start": 3718.93, "end": 3719.89, "word": " an", "probability": 0.9267578125}, {"start": 3719.89, "end": 3720.77, "word": " odd", "probability": 0.96533203125}, {"start": 3720.77, "end": 3722.45, "word": " prime", "probability": 0.9150390625}, {"start": 3722.45, "end": 3723.75, "word": " هذا", "probability": 0.63916015625}, {"start": 3723.75, "end": 3724.29, "word": " سؤال", "probability": 0.9713541666666666}, {"start": 3724.29, "end": 3724.67, "word": " B", "probability": 0.7001953125}, {"start": 3724.67, "end": 3725.53, "word": " let", "probability": 0.8271484375}, {"start": 3725.53, "end": 3726.01, "word": " B", "probability": 0.9599609375}, {"start": 3726.01, "end": 3726.51, "word": " be", "probability": 0.9609375}, {"start": 3726.51, "end": 3726.77, "word": " an", "probability": 0.9677734375}, {"start": 3726.77, "end": 3727.17, "word": " odd", "probability": 0.95556640625}, {"start": 3727.17, "end": 3727.69, "word": " prime", "probability": 0.947265625}, {"start": 3727.69, "end": 3728.41, "word": " معايا", "probability": 0.8619791666666666}, {"start": 3728.41, "end": 3728.61, "word": " يا", "probability": 0.5634765625}, {"start": 3728.61, "end": 3728.85, "word": " جماعة", "probability": 0.9939778645833334}], "temperature": 1.0}, {"id": 139, "seek": 376040, "start": 3730.96, "end": 3760.4, "text": "ثم .. ال .. الـ prime divisor of اتنين to the a .. to the b minus واحد is of the form is of the form اتنين kb", "tokens": [12984, 2304, 4386, 2423, 4386, 2423, 39184, 5835, 25974, 284, 295, 1975, 2655, 1863, 9957, 281, 264, 257, 4386, 281, 264, 272, 3175, 36764, 24401, 307, 295, 264, 1254, 307, 295, 264, 1254, 1975, 2655, 1863, 9957, 350, 65], "avg_logprob": -0.3830078110098839, "compression_ratio": 1.3402061855670102, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3730.96, "end": 3731.52, "word": "ثم", "probability": 0.6798095703125}, {"start": 3731.52, "end": 3731.88, "word": " ..", "probability": 0.12030029296875}, {"start": 3731.88, "end": 3733.2, "word": " ال", "probability": 0.25537109375}, {"start": 3733.2, "end": 3733.2, "word": " ..", "probability": 0.7001953125}, {"start": 3733.2, "end": 3734.58, "word": " الـ", "probability": 0.462158203125}, {"start": 3734.58, "end": 3735.34, "word": " prime", "probability": 0.1500244140625}, {"start": 3735.34, "end": 3738.66, "word": " divisor", "probability": 0.7156982421875}, {"start": 3738.66, "end": 3740.14, "word": " of", "probability": 0.73779296875}, {"start": 3740.14, "end": 3743.2, "word": " اتنين", "probability": 0.714263916015625}, {"start": 3743.2, "end": 3744.4, "word": " to", "probability": 0.51806640625}, {"start": 3744.4, "end": 3744.6, "word": " the", "probability": 0.92431640625}, {"start": 3744.6, "end": 3744.76, "word": " a", "probability": 0.459228515625}, {"start": 3744.76, "end": 3744.92, "word": " ..", "probability": 0.68603515625}, {"start": 3744.92, "end": 3744.96, "word": " to", "probability": 0.97021484375}, {"start": 3744.96, "end": 3745.1, "word": " the", "probability": 0.94287109375}, {"start": 3745.1, "end": 3745.26, "word": " b", "probability": 0.759765625}, {"start": 3745.26, "end": 3745.62, "word": " minus", "probability": 0.51416015625}, {"start": 3745.62, "end": 3746.36, "word": " واحد", "probability": 0.989990234375}, {"start": 3746.36, "end": 3751.24, "word": " is", "probability": 0.75830078125}, {"start": 3751.24, "end": 3751.44, "word": " of", "probability": 0.98388671875}, {"start": 3751.44, "end": 3751.62, "word": " the", "probability": 0.94921875}, {"start": 3751.62, "end": 3752.22, "word": " form", "probability": 0.92919921875}, {"start": 3752.22, "end": 3754.44, "word": " is", "probability": 0.81787109375}, {"start": 3754.44, "end": 3755.16, "word": " of", "probability": 0.98681640625}, {"start": 3755.16, "end": 3756.9, "word": " the", "probability": 0.93994140625}, {"start": 3756.9, "end": 3757.62, "word": " form", "probability": 0.9189453125}, {"start": 3757.62, "end": 3759.6, "word": " اتنين", "probability": 0.9664306640625}, {"start": 3759.6, "end": 3760.4, "word": " kb", "probability": 0.648681640625}], "temperature": 1.0}, {"id": 140, "seek": 379034, "start": 3762.08, "end": 3790.34, "text": "زايد واحد يعني التطبيق المباشر على الـ A let الـ Q أنا براين دفع يزولني من 2 بي ماقص واحد يعني الـ Q الـ Q عشان تكسب 2 بي ماقص واحد إذا من اللي فوق من الـ A then either اللي هو التنين الـ Q على الـ D", "tokens": [11622, 995, 25708, 36764, 24401, 37495, 22653, 16712, 9566, 21292, 4587, 9673, 3555, 33599, 2288, 15844, 2423, 39184, 316, 718, 2423, 39184, 1249, 41850, 4724, 23557, 9957, 11778, 5172, 3615, 7251, 11622, 12610, 22653, 9154, 568, 4724, 1829, 19446, 4587, 9381, 36764, 24401, 37495, 22653, 2423, 39184, 1249, 2423, 39184, 1249, 6225, 8592, 7649, 6055, 4117, 35457, 568, 4724, 1829, 19446, 4587, 9381, 36764, 24401, 11933, 15730, 9154, 13672, 1829, 6156, 30543, 9154, 2423, 39184, 316, 550, 2139, 13672, 1829, 31439, 16712, 1863, 9957, 2423, 39184, 1249, 15844, 2423, 39184, 413], "avg_logprob": -0.4052309743736101, "compression_ratio": 1.8277777777777777, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 3762.08, "end": 3762.5, "word": "زايد", "probability": 0.4752197265625}, {"start": 3762.5, "end": 3762.94, "word": " واحد", "probability": 0.95947265625}, {"start": 3762.94, "end": 3765.1, "word": " يعني", "probability": 0.6490478515625}, {"start": 3765.1, "end": 3766.72, "word": " التطبيق", "probability": 0.8760986328125}, {"start": 3766.72, "end": 3767.18, "word": " المباشر", "probability": 0.841552734375}, {"start": 3767.18, "end": 3767.38, "word": " على", "probability": 0.69921875}, {"start": 3767.38, "end": 3767.74, "word": " الـ", "probability": 0.5213623046875}, {"start": 3767.74, "end": 3767.82, "word": " A", "probability": 0.339111328125}, {"start": 3767.82, "end": 3769.4, "word": " let", "probability": 0.376953125}, {"start": 3769.4, "end": 3770.76, "word": " الـ", "probability": 0.5140380859375}, {"start": 3770.76, "end": 3771.1, "word": " Q", "probability": 0.70849609375}, {"start": 3771.1, "end": 3771.76, "word": " أنا", "probability": 0.130859375}, {"start": 3771.76, "end": 3772.22, "word": " براين", "probability": 0.5096842447916666}, {"start": 3772.22, "end": 3772.5, "word": " دفع", "probability": 0.31683349609375}, {"start": 3772.5, "end": 3772.98, "word": " يزولني", "probability": 0.542724609375}, {"start": 3772.98, "end": 3773.36, "word": " من", "probability": 0.890625}, {"start": 3773.36, "end": 3773.72, "word": " 2", "probability": 0.65673828125}, {"start": 3773.72, "end": 3774.02, "word": " بي", "probability": 0.629150390625}, {"start": 3774.02, "end": 3774.72, "word": " ماقص", "probability": 0.73193359375}, {"start": 3774.72, "end": 3775.8, "word": " واحد", "probability": 0.92822265625}, {"start": 3775.8, "end": 3776.04, "word": " يعني", "probability": 0.922119140625}, {"start": 3776.04, "end": 3776.24, "word": " الـ", "probability": 0.911865234375}, {"start": 3776.24, "end": 3776.4, "word": " Q", "probability": 0.89501953125}, {"start": 3776.4, "end": 3776.66, "word": " الـ", "probability": 0.5447998046875}, {"start": 3776.66, "end": 3776.78, "word": " Q", "probability": 0.8955078125}, {"start": 3776.78, "end": 3776.98, "word": " عشان", "probability": 0.6926676432291666}, {"start": 3776.98, "end": 3777.38, "word": " تكسب", "probability": 0.6957194010416666}, {"start": 3777.38, "end": 3778.88, "word": " 2", "probability": 0.76318359375}, {"start": 3778.88, "end": 3779.28, "word": " بي", "probability": 0.667236328125}, {"start": 3779.28, "end": 3779.66, "word": " ماقص", "probability": 0.8362630208333334}, {"start": 3779.66, "end": 3780.02, "word": " واحد", "probability": 0.963623046875}, {"start": 3780.02, "end": 3780.26, "word": " إذا", "probability": 0.703369140625}, {"start": 3780.26, "end": 3780.5, "word": " من", "probability": 0.943359375}, {"start": 3780.5, "end": 3780.68, "word": " اللي", "probability": 0.798828125}, {"start": 3780.68, "end": 3781.18, "word": " فوق", "probability": 0.98486328125}, {"start": 3781.18, "end": 3782.02, "word": " من", "probability": 0.92578125}, {"start": 3782.02, "end": 3782.24, "word": " الـ", "probability": 0.640869140625}, {"start": 3782.24, "end": 3782.48, "word": " A", "probability": 0.9599609375}, {"start": 3782.48, "end": 3783.2, "word": " then", "probability": 0.64990234375}, {"start": 3783.2, "end": 3785.28, "word": " either", "probability": 0.9189453125}, {"start": 3785.28, "end": 3786.78, "word": " اللي", "probability": 0.967529296875}, {"start": 3786.78, "end": 3786.98, "word": " هو", "probability": 0.9892578125}, {"start": 3786.98, "end": 3788.16, "word": " التنين", "probability": 0.7395833333333334}, {"start": 3788.16, "end": 3789.62, "word": " الـ", "probability": 0.966796875}, {"start": 3789.62, "end": 3789.78, "word": " Q", "probability": 0.85009765625}, {"start": 3789.78, "end": 3790.06, "word": " على", "probability": 0.293212890625}, {"start": 3790.06, "end": 3790.22, "word": " الـ", "probability": 0.7578125}, {"start": 3790.22, "end": 3790.34, "word": " D", "probability": 0.9580078125}], "temperature": 1.0}, {"id": 141, "seek": 381433, "start": 3791.25, "end": 3814.33, "text": "تقسم 2-1 or الـ Q بتساوى 2KB زائد 1 هذي is impossible لأن الـ Q زبراين و هذي واحد لذا الـ Q مش معقول تقسم الواحد لذا بضال عندي Q تساوى 2KB زايد 1 و إلى لقاء آخر", "tokens": [2655, 4587, 38251, 568, 12, 16, 420, 2423, 39184, 1249, 39894, 3794, 995, 2407, 7578, 568, 42, 33, 30767, 16373, 3215, 502, 8032, 8848, 1829, 307, 6243, 5296, 33456, 2423, 39184, 1249, 30767, 26890, 995, 9957, 4032, 8032, 8848, 1829, 36764, 24401, 5296, 15730, 2423, 39184, 1249, 37893, 20449, 39648, 6055, 4587, 38251, 2423, 14407, 24401, 5296, 15730, 4724, 11242, 6027, 18871, 16254, 1249, 6055, 3794, 995, 2407, 7578, 568, 42, 33, 30767, 995, 25708, 502, 4032, 30731, 5296, 4587, 16606, 19753, 34740], "avg_logprob": -0.3954613134264946, "compression_ratio": 1.5029585798816567, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 3791.25, "end": 3791.65, "word": "تقسم", "probability": 0.5638427734375}, {"start": 3791.65, "end": 3791.99, "word": " 2", "probability": 0.61083984375}, {"start": 3791.99, "end": 3792.71, "word": "-1", "probability": 0.6259765625}, {"start": 3792.71, "end": 3793.31, "word": " or", "probability": 0.50390625}, {"start": 3793.31, "end": 3794.27, "word": " الـ", "probability": 0.55126953125}, {"start": 3794.27, "end": 3794.59, "word": " Q", "probability": 0.4970703125}, {"start": 3794.59, "end": 3796.29, "word": " بتساوى", "probability": 0.47598876953125}, {"start": 3796.29, "end": 3797.85, "word": " 2KB", "probability": 0.8079427083333334}, {"start": 3797.85, "end": 3798.65, "word": " زائد", "probability": 0.5128987630208334}, {"start": 3798.65, "end": 3799.61, "word": " 1", "probability": 0.74609375}, {"start": 3799.61, "end": 3800.89, "word": " هذي", "probability": 0.5502522786458334}, {"start": 3800.89, "end": 3801.11, "word": " is", "probability": 0.288818359375}, {"start": 3801.11, "end": 3801.81, "word": " impossible", "probability": 0.70947265625}, {"start": 3801.81, "end": 3803.43, "word": " لأن", "probability": 0.86328125}, {"start": 3803.43, "end": 3803.67, "word": " الـ", "probability": 0.803955078125}, {"start": 3803.67, "end": 3803.83, "word": " Q", "probability": 0.71142578125}, {"start": 3803.83, "end": 3804.59, "word": " زبراين", "probability": 0.503204345703125}, {"start": 3804.59, "end": 3804.89, "word": " و", "probability": 0.7578125}, {"start": 3804.89, "end": 3805.19, "word": " هذي", "probability": 0.5796712239583334}, {"start": 3805.19, "end": 3805.65, "word": " واحد", "probability": 0.78515625}, {"start": 3805.65, "end": 3806.35, "word": " لذا", "probability": 0.669677734375}, {"start": 3806.35, "end": 3806.53, "word": " الـ", "probability": 0.873046875}, {"start": 3806.53, "end": 3806.65, "word": " Q", "probability": 0.8095703125}, {"start": 3806.65, "end": 3807.07, "word": " مش", "probability": 0.978515625}, {"start": 3807.07, "end": 3807.39, "word": " معقول", "probability": 0.76513671875}, {"start": 3807.39, "end": 3807.73, "word": " تقسم", "probability": 0.98291015625}, {"start": 3807.73, "end": 3808.29, "word": " الواحد", "probability": 0.9500325520833334}, {"start": 3808.29, "end": 3808.85, "word": " لذا", "probability": 0.6494140625}, {"start": 3808.85, "end": 3809.19, "word": " بضال", "probability": 0.3722330729166667}, {"start": 3809.19, "end": 3809.45, "word": " عندي", "probability": 0.7890625}, {"start": 3809.45, "end": 3809.65, "word": " Q", "probability": 0.7109375}, {"start": 3809.65, "end": 3809.99, "word": " تساوى", "probability": 0.819580078125}, {"start": 3809.99, "end": 3811.77, "word": " 2KB", "probability": 0.95068359375}, {"start": 3811.77, "end": 3812.07, "word": " زايد", "probability": 0.8084309895833334}, {"start": 3812.07, "end": 3812.33, "word": " 1", "probability": 0.740234375}, {"start": 3812.33, "end": 3813.25, "word": " و", "probability": 0.7880859375}, {"start": 3813.25, "end": 3813.45, "word": " إلى", "probability": 0.55712890625}, {"start": 3813.45, "end": 3813.87, "word": " لقاء", "probability": 0.9166666666666666}, {"start": 3813.87, "end": 3814.33, "word": " آخر", "probability": 0.907470703125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3815.085, "duration_after_vad": 3556.696874999987}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/arGzx_seTzc_postprocess.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/arGzx_seTzc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ae9ccc43dfe56bf2a16fd2a06ae1ccd841c04a02
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/arGzx_seTzc_postprocess.srt
@@ -0,0 +1,1720 @@
+1
+00:00:19,610 --> 00:00:26,430
+بسم الله الرحمن الرحيم المحاضرة رقم 23 مساق نظرية
+
+2
+00:00:26,430 --> 00:00:34,150
+الأعداد طلاب الجامعة الإسلامية قسم الرياضيات كلية
+
+3
+00:00:34,150 --> 00:00:41,490
+التربية وكلية العلوم هنكمل اليوم إن شاء الله في
+
+4
+00:00:41,490 --> 00:00:45,550
+المادة أو في المساق هنبدأ في شبتر سبعة اللي هو
+
+5
+00:00:45,550 --> 00:00:50,150
+Euler's Generalization of Fermat's Theoremهنبدأ في
+
+6
+00:00:50,150 --> 00:00:54,490
+البداية نتعرف على اللي هي number theoretic
+
+7
+00:00:54,490 --> 00:00:58,110
+function جديدة اللي هي بنسميها Euler's phi
+
+8
+00:00:58,110 --> 00:01:03,210
+function هندرس .. هنعرف شو معناه Euler's phi
+
+9
+00:01:03,210 --> 00:01:08,050
+function و هنشوف كيف نوجد ال phi لأي عدد و هناخد
+
+10
+00:01:08,050 --> 00:01:13,510
+بعض الخواص اللي تسهل علينا إيجاد قيمة ال phiأحنا
+
+11
+00:01:13,510 --> 00:01:16,790
+مر علينا الـ number theoretic functions مر عنا
+
+12
+00:01:16,790 --> 00:01:21,270
+اللي هو التاو اللي هي عبارة عن number of divisors
+
+13
+00:01:21,270 --> 00:01:28,030
+والسيجما اللي هي عبارة عن sum of divisors ومر عنا
+
+14
+00:01:28,030 --> 00:01:32,610
+اللي هو product of divisors وكانت هذه من z
+
+15
+00:01:32,610 --> 00:01:38,910
+positive and z positiveومن ثم أخدنا الـ Mu المبيوظ
+
+16
+00:01:38,910 --> 00:01:43,510
+function كانت من Z positive لعند اللي هو ناقص واحد
+
+17
+00:01:43,510 --> 00:01:49,790
+و سفر و واحدالان الان بدنا نحكي عن function جديدة
+
+18
+00:01:49,790 --> 00:01:53,930
+اللي هي ال الارث فانكشن اللي هي اللي هي بنسميها في
+
+19
+00:01:53,930 --> 00:01:59,810
+برضه في هتكون من z positive لعند z positive الان
+
+20
+00:01:59,810 --> 00:02:05,830
+بدنا نعرف ال في of أي عدد اللي هو ان ينتمي إلى z
+
+21
+00:02:05,830 --> 00:02:10,930
+positive يعني في of أي positive integerPhi of N
+
+22
+00:02:10,930 --> 00:02:14,070
+اللي هو برضه اللي هي الـ function Phi عبارة عن
+
+23
+00:02:14,070 --> 00:02:18,410
+عداد زي Tau عداد Tau كانت تتعدى اللي هي number of
+
+24
+00:02:18,410 --> 00:02:23,070
+divisors للعدد هذه بتعدى اللي الأعداد اللي أقل أو
+
+25
+00:02:23,070 --> 00:02:28,650
+يساوي N وتكون relatively براي مع مين؟ مع الـ N اذا
+
+26
+00:02:28,650 --> 00:02:34,150
+Phi of N هي عبارة عن number of positive integers
+
+27
+00:02:34,980 --> 00:02:39,860
+that are relatively prime to n and less than or
+
+28
+00:02:39,860 --> 00:02:46,720
+equal mean equal n الان لو جينا لـ5 of 1 5 of 1
+
+29
+00:02:46,720 --> 00:02:50,000
+ايش الأعداد الـ positive integers الأصغر يساوي
+
+30
+00:02:50,000 --> 00:02:53,580
+واحد و relatively prime مع الواحد بس مين الواحد ده
+
+31
+00:02:53,580 --> 00:02:57,920
+العدد دي ايش هيساوي واحد لو جينا قدّينا 5 of 2
+
+32
+00:02:57,920 --> 00:03:03,500
+برضه نفس الاشي ايش العداد عدد الأعداداللي أصغره
+
+33
+00:03:03,500 --> 00:03:06,240
+يساوي اتنين وrelative الـ prime مع اتنين فش لغير
+
+34
+00:03:06,240 --> 00:03:10,880
+مين الواحد إذاً عدد هنا إيش بيساوي واحد five of
+
+35
+00:03:10,880 --> 00:03:13,740
+تلاتة مين الأعداد اللي relative ال prime مع
+
+36
+00:03:13,740 --> 00:03:18,300
+التلاتة الأصغر يساوي تلاتة الواحد والتنين في غيرين
+
+37
+00:03:18,300 --> 00:03:24,500
+فاهمين؟ بيساوي قداش اتنين عددين اتنين اللي هنوجينا
+
+38
+00:03:24,500 --> 00:03:27,880
+لل five أربعة مين الأعداد اللي relative ال prime
+
+39
+00:03:27,880 --> 00:03:33,710
+اللي أصغر يساوي أربعة واحد وتلاتةإذا إيش بيساوي
+
+40
+00:03:33,710 --> 00:03:41,490
+انت؟ اتنين five of خمسة مين إنه؟ واحد واثنين
+
+41
+00:03:41,490 --> 00:03:47,530
+وتلاتة واربعة كلنا دي relative prime مع مين؟ مع
+
+42
+00:03:47,530 --> 00:03:52,690
+الخمسة وأصغر أو يساوي الخمسة فاهمين؟ أو يساوي
+
+43
+00:03:52,690 --> 00:03:58,570
+أربعة لأن لو جينا لل five of ستة5 of 6 مين الـ
+
+44
+00:03:58,570 --> 00:04:01,930
+Relative Liberal مع الـ 6 الأصغر في 5 و 6 طبعاً
+
+45
+00:04:01,930 --> 00:04:09,110
+واحد اتنين لأ تلاتة لأ أربعة لأ خمسة إذا واحد طبعا
+
+46
+00:04:09,110 --> 00:04:16,850
+الست أكيد لأ إذا اتنين برضه five of سبعة مين
+
+47
+00:04:16,850 --> 00:04:22,390
+الناجداش؟اللي هي الواحد والتنين والتلاتة والاربعة
+
+48
+00:04:22,390 --> 00:04:26,350
+والخمسة والستة إذا مايش بيساوي برضه ستة فأيه في
+
+49
+00:04:26,350 --> 00:04:31,410
+تمانية من الـ negative liberal مع التمانية اللي هو
+
+50
+00:04:31,410 --> 00:04:38,350
+واحد وتلاتة وخمسة وسبعة، مظبوط؟ مايساوي وجديهاش
+
+51
+00:04:38,350 --> 00:04:44,270
+أربعة فأيه في تسعة؟بيصير .. بيصير غلب اه لاحظ انه
+
+52
+00:04:44,270 --> 00:04:47,650
+كل ما كده اللي عدت بيصير يغلب في الحسابات بعد شوية
+
+53
+00:04:47,650 --> 00:04:52,310
+هناخد قوانين اتسهل علينا عملية الحسابات وعملية
+
+54
+00:04:52,310 --> 00:04:57,350
+إيجاب five ان بس قبل ما بروح لاحظ انه ال five واحد
+
+55
+00:04:57,350 --> 00:05:03,040
+و ال five اتنين اللي هو oddبينما five تلاتة أو
+
+56
+00:05:03,040 --> 00:05:05,580
+five أربعة أو five خمسة أو five ستة أو five سبعة
+
+57
+00:05:05,580 --> 00:05:10,660
+أو five تمانية و لو كملت هتلاجيهن دايما even وهذه
+
+58
+00:05:10,660 --> 00:05:15,600
+بعد شوية خاصية هنبرهنها ان five n لكل n أكبر من
+
+59
+00:05:15,600 --> 00:05:19,840
+اتنين هتكون even integer هذه الملاحظة الواحدة
+
+60
+00:05:19,840 --> 00:05:26,500
+الثانية لو اطلعت اتنين prime ايش بيساوي five
+
+61
+00:05:26,500 --> 00:05:32,540
+اتنين؟اللي واحد يعني اتنين ناقص واحد five تلاتة
+
+62
+00:05:32,540 --> 00:05:38,340
+اتنين تلاتة ناقص واحد five خمسةخمسة ناقص واحد،
+
+63
+00:05:38,340 --> 00:05:44,420
+أربعة five سبعة، سبعة ناقص واحد، ستة منطقي، ليش؟
+
+64
+00:05:44,420 --> 00:05:48,820
+لأنه لو جينا ناخد five of B بي براين الأعداد اللي
+
+65
+00:05:48,820 --> 00:05:52,380
+أجيب منه كله ال relative prime معاه لأن بي أصلا
+
+66
+00:05:52,380 --> 00:05:56,300
+كتلة واحدة يعني هيكون الواحد والتنين والتلاتة لعين
+
+67
+00:05:56,300 --> 00:06:00,660
+بي minus واحد كلهم relative prime مع مين؟ مع البي،
+
+68
+00:06:00,660 --> 00:06:08,250
+اذا five of B أش بساوي بي ناقص واحد أي سؤال؟طيب
+
+69
+00:06:08,250 --> 00:06:15,870
+اذا الان بدنا نروح لخاصية ابعد من هيك الان حكينا
+
+70
+00:06:15,870 --> 00:06:20,050
+انه لما يكون بي برايم five بي بيساوي بي ماينس واحد
+
+71
+00:06:20,050 --> 00:06:26,250
+والعكس صحيح يعني لو نجينا عدد five ان له بيساوي ان
+
+72
+00:06:26,250 --> 00:06:31,250
+نغس واحد هيكون الان اشماله z برايم اذا الان
+
+73
+00:06:31,250 --> 00:06:35,970
+الملاحظة التالية اللي بدنا نثبتها بدنا نثبت ما هي
+
+74
+00:06:35,970 --> 00:06:47,140
+ليهfor n أكبر من واحد for n أكبر من واحد five n
+
+75
+00:06:47,140 --> 00:06:56,060
+بيساوي n ماقص واحد if and only if n إيه شمالها is
+
+76
+00:06:56,060 --> 00:07:03,880
+a prime و proof بدنا البرهن الآن
+
+77
+00:07:04,760 --> 00:07:13,920
+بدنا نقول suppose that .. suppose that n is zebra
+
+78
+00:07:15,910 --> 00:07:19,650
+ما دام n زي prime إذا الواحد والاتنين والتلاتة
+
+79
+00:07:19,650 --> 00:07:22,870
+اللي عند ال N ناقص واحد كلهين relative ال prime مع
+
+80
+00:07:22,870 --> 00:07:28,130
+مين؟ مع ال N وعددهين هدولة قداش؟ إذا مباشرة hence
+
+81
+00:07:28,130 --> 00:07:35,390
+ال 5N بساوي N ناقص واحد ال N conversely ..
+
+82
+00:07:35,390 --> 00:07:42,200
+conversely بتثبت أنه لو كان عندي 5of N بساوة N نقص
+
+83
+00:07:42,200 --> 00:07:48,680
+واحد هيعطيني الـ N إيه اشمالها is إبراهيم ركز الآن
+
+84
+00:07:50,290 --> 00:07:54,590
+اللي بيدثبتوا معايا ليه أنه لو كانت 5n بسواء ناقص
+
+85
+00:07:54,590 --> 00:07:58,410
+واحد يعطينا n زبرايم بيدثبتها عن طريق ايه؟
+
+86
+00:07:58,410 --> 00:08:03,810
+بيدثبتلك الـ Contraposition لها انه بيدثبتلك ان لو
+
+87
+00:08:03,810 --> 00:08:09,290
+كان n is not prime بيعطينا الـ 5n أشمالها لا تساوي
+
+88
+00:08:09,290 --> 00:08:13,730
+n ناقص واحد واضح كيف بيدثبتها؟ إذا بيدثبتها بإثبات
+
+89
+00:08:13,730 --> 00:08:22,160
+الـ Contraposition لها أنه بيدثبت أقول سببوزthat N
+
+90
+00:08:22,160 --> 00:08:27,040
+is not prime ايش معناه ان مش prime معناه تكون
+
+91
+00:08:27,040 --> 00:08:33,480
+composite ان هناك D
+
+92
+00:08:33,480 --> 00:08:43,100
+أكبر من واحد وأصغر من N and N بيساوي D في K for
+
+93
+00:08:43,100 --> 00:08:53,820
+some K element and Z مظبوط؟ طيبالـ N الـ D عبارة
+
+94
+00:08:53,820 --> 00:08:59,620
+عن عدد بين الواحد و بين مين الـ N صار العامل
+
+95
+00:08:59,620 --> 00:09:01,840
+المشترك .. و طبعا الـ D أكبر من واحد و أصغر من N
+
+96
+00:09:01,840 --> 00:09:07,360
+صار العامل المشترك الأعلى بين الـ D و بين الـ N هو
+
+97
+00:09:07,360 --> 00:09:13,830
+الـ Dلأن الـ D أشماله بيكسب 100 الـ N يعني صار
+
+98
+00:09:13,830 --> 00:09:18,110
+عندى ال greatest common divisor بين الـ N و الـ D
+
+99
+00:09:18,110 --> 00:09:23,730
+لا يساوي واحد لأنه بيساوي 100 بيساوي الـ D و الـ D
+
+100
+00:09:23,730 --> 00:09:29,770
+أشمالها أكبر من واحد الـ N أنا الـ Phi of N ضمن
+
+101
+00:09:29,770 --> 00:09:34,470
+الـ Phi of N أكيد
+
+102
+00:09:34,470 --> 00:09:43,030
+عندى مدام الـ N أكبر من واحدإذا الـ N مش Relative
+
+103
+00:09:43,030 --> 00:09:45,490
+Library مع حالها لأن الـ Logistic Indivisor بين
+
+104
+00:09:45,490 --> 00:09:48,930
+الـ N و الـ N مش بيساوي N إذا مش Relative Library
+
+105
+00:09:48,930 --> 00:09:53,550
+مع حالها إذا هذا بديش أحسبه فيفهم إيش هي عبارة عن
+
+106
+00:09:53,550 --> 00:09:58,050
+اللي أصغر أو يساوي الـ N و Relative Library مع الـ
+
+107
+00:09:58,050 --> 00:10:04,760
+N إذا الأعداد من عند واحد عند N، Nالان نقسم منين
+
+108
+00:10:04,760 --> 00:10:12,080
+الان صارت اناقص واحد والان نقسم كمان عدد منه هو ال
+
+109
+00:10:12,080 --> 00:10:14,440
+D لأن ال grade is divisible بين الان و ال D ايش
+
+110
+00:10:14,440 --> 00:10:19,340
+بيساوي لا يساوي واحد ال D بين ال واحد و الان اذا
+
+111
+00:10:19,340 --> 00:10:24,260
+صار عندي ال five ان نقسم كمان واحد اذا ال five ان
+
+112
+00:10:24,260 --> 00:10:30,990
+صار اصغر او يساوي منين اناقص اتنين كمان مرةماذا عن
+
+113
+00:10:30,990 --> 00:10:35,850
+الـ N5N؟ هي ببحث عن الأعداد الـ Relatively Prime
+
+114
+00:10:35,850 --> 00:10:39,750
+مع الـ N و أصغر أو نسائر الـ N يعني ببحث في
+
+115
+00:10:39,750 --> 00:10:45,650
+الأعداد من واحد لعند مين لعند N بدي أشوف مين ال
+
+116
+00:10:45,650 --> 00:10:52,370
+Relatively Prime مع ال N و أحسبهاأول حاجة مش هحسب
+
+117
+00:10:52,370 --> 00:10:55,790
+الـ N لإن الـ N مش الـ Relative لـ Brian مع الـ N
+
+118
+00:10:55,790 --> 00:11:00,870
+اتنين مش هحسب مين برضه الـ D لإن الـ D حلقي في
+
+119
+00:11:00,870 --> 00:11:04,550
+الطريق لما أنا أمشي من واحد لعنده إذا هشيل كمان
+
+120
+00:11:04,550 --> 00:11:09,590
+مين الـ D سيرت شاول من هدولة الـ N و الـ D على
+
+121
+00:11:09,590 --> 00:11:13,990
+الأقل إذا صار عندي الـ 5N أقصى حاجة أقصى حاجة
+
+122
+00:11:13,990 --> 00:11:20,360
+هتكون اللي هي أشمالها أصغر من مين من Nأصغر أو سوى
+
+123
+00:11:20,360 --> 00:11:27,760
+مين أن نقص اتنين وهذه ايش سمالها اكيد اكيد five أن
+
+124
+00:11:27,760 --> 00:11:34,280
+اشمالها لات سوى أن نقص واحد اذا انا اوصلت الان ان
+
+125
+00:11:34,280 --> 00:11:38,760
+لو كانت أن مش prime اذا اكيد ال five أن اشمالها
+
+126
+00:11:38,760 --> 00:11:46,490
+لات سوى أن نقص واحد اذا صارت عندي الان5n-1 تؤدي
+
+127
+00:11:46,490 --> 00:11:50,490
+الـ n الـ Zebrame إذا صار في عندي الـ n
+
+128
+00:11:50,490 --> 00:11:56,270
+equivalence ال equivalence بين ال n الـ Zebrame و
+
+129
+00:11:56,270 --> 00:12:04,330
+5n-1 أي سؤال؟ الآن أنا رايح باتجاه أوجد formula
+
+130
+00:12:04,330 --> 00:12:12,150
+للـ 5n عشان أوجد هذه ال formula للـ 5n
+
+131
+00:12:15,560 --> 00:12:21,640
+هيكون عبر الطريق التالي أن الـ N هذه اللي عندي أول
+
+132
+00:12:21,640 --> 00:12:25,580
+إيش حصلت على المعلومة أن الـ Phi of the prime أكيد
+
+133
+00:12:25,580 --> 00:12:33,000
+يشمله بساوي بـ-1 الان بدي عشان أصل للـ Phi of N
+
+134
+00:12:33,000 --> 00:12:38,080
+اللي هو ال formula إلها بدي
+
+135
+00:12:38,080 --> 00:12:47,710
+كخطوة أولى أو deadlockالان هناك نظرية موجودة لك if
+
+136
+00:12:47,710 --> 00:12:58,390
+B is a prime then phi of B أُس K بيوجد قيمتها بعد
+
+137
+00:12:58,390 --> 00:13:03,130
+وجود قيمتهاهتوصل النهاية دي بعد شوية بعد ما أخد
+
+138
+00:13:03,130 --> 00:13:08,450
+خاصية أخرى لإيجاد الـPhi of N بصورة عامة وإيجاد
+
+139
+00:13:08,450 --> 00:13:12,550
+سهل كمان طريقة إيجاد سهلة قبل شوية احنا اتغلبنا
+
+140
+00:13:12,550 --> 00:13:16,410
+لعند التسعة ووقفنا فما بالك لو بدك توجد الـPhi of
+
+141
+00:13:16,410 --> 00:13:20,330
+مليون بدك تقعد تدور من الأعداد اللي اللي تبل برايب
+
+142
+00:13:20,330 --> 00:13:25,290
+مع المليون من واحد لمليون مش عملي فالآن خليني نشوف
+
+143
+00:13:25,290 --> 00:13:31,550
+كيف نصل لإيجاد الـPhi of N in generalالان بقول if
+
+144
+00:13:31,550 --> 00:13:39,210
+P is prime then 5P K بساوي P K ناقص P K minus واحد
+
+145
+00:13:39,210 --> 00:13:44,970
+و هي نفسها P K في واحد ناقص واحد على P الفورمولة
+
+146
+00:13:44,970 --> 00:13:49,170
+هذه بعد شوية لما نحكي عن N in general هتساعدنا
+
+147
+00:13:49,170 --> 00:13:56,210
+كتير في اللي هي تسهيل إيجاب 5N الان اللي بدي أثبته
+
+148
+00:13:56,210 --> 00:14:02,880
+5P K بساويطبعا هذه متساوية هذه عارفين كيف صاحبنا
+
+149
+00:14:02,880 --> 00:14:05,420
+الـ P K عامل مشترك ضالة الواحد ناقص واحد على P
+
+150
+00:14:05,420 --> 00:14:09,540
+نيجي الآن البرنامج شوف كيف المنطق البرمجان علشان
+
+151
+00:14:09,540 --> 00:14:16,760
+ما اعتمد الان انا بدي اوجد الاعداد ال relative ال
+
+152
+00:14:16,760 --> 00:14:23,040
+prime من عند اللي هي الواحد لما اصل لمين للـ P X K
+
+153
+00:14:23,040 --> 00:14:29,070
+الاستراتيجية في الحلقة التاليةالان عدد الاعداد
+
+154
+00:14:29,070 --> 00:14:33,890
+اصلا من واحد عند بي أوس كي جداش هي بي أوس كي بدي
+
+155
+00:14:33,890 --> 00:14:39,770
+اشيل منها اللي مش relative لبراين معنيا مع ال بي
+
+156
+00:14:39,770 --> 00:14:45,900
+أوس كي بضالمياالـ Relative prime إذا صار عندي الآن
+
+157
+00:14:45,900 --> 00:14:51,320
+حصل في النهاية Phi of B أُس K بتساول B أُس K كل
+
+158
+00:14:51,320 --> 00:14:56,240
+الأعداد اللي من واحد لعند B K وبيتشيل منهمين
+
+159
+00:14:56,240 --> 00:15:03,230
+الأعداد اللي مش Relative prime مع B أُس Kهلاجيهم
+
+160
+00:15:03,230 --> 00:15:08,350
+بعد شوية ان بي أس ك ناقص واحد فبتصير في of بي ك
+
+161
+00:15:08,350 --> 00:15:13,170
+ايش بتساوي بي أس ك ناقص بي أس ك ناقص واحد واضح ايش
+
+162
+00:15:13,170 --> 00:15:18,730
+استراتيجية الحل الان في of بي أس ك ايش معناته
+
+163
+00:15:18,730 --> 00:15:23,070
+الاعداد ال relatively prime معنين مع ال بي أس ك
+
+164
+00:15:23,070 --> 00:15:29,290
+اللي اصغر او يساوي بي أس كبدا أوجدها بإن اوجد اللي
+
+165
+00:15:29,290 --> 00:15:33,670
+هو الأعداد اللي مش relative prime مع الـb أسكت
+
+166
+00:15:33,670 --> 00:15:38,290
+وانقسمها من عدد الأعداد الكل عدد الأعداد الكل بيه
+
+167
+00:15:38,290 --> 00:15:42,170
+أسكت ناقص اللي هي اللي بعد داعي إن هي شمالها اللي
+
+168
+00:15:42,170 --> 00:15:46,130
+مش relative prime تطلع اللي هي five of b أسكت اللي
+
+169
+00:15:46,130 --> 00:15:49,870
+هي relative prime مع b أسكت شوفوا في ملاحظة قبل ما
+
+170
+00:15:49,870 --> 00:15:55,260
+نشتغل لو أجيناوبحثنا لـ Greatest Common Divisor
+
+171
+00:15:55,260 --> 00:16:02,400
+بين أي عدد N أصغر أو يساوي بي أس كيه وبين الـ B أس
+
+172
+00:16:02,400 --> 00:16:07,700
+كيه بنلاقي إن العدد هذا بيساوي واحد if and only if
+
+173
+00:16:07,700 --> 00:16:17,980
+الـ B هذا لا يقصر مين إلا أن انتبه لو الـ N اللي
+
+174
+00:16:17,980 --> 00:16:23,530
+هي عوامل العدد بي أس كيه من هي1 الـ B الـ B تربيع
+
+175
+00:16:23,530 --> 00:16:30,570
+لمصير لمن؟ لـ BSK أي واحد عدد في الدنيا بيكون بينه
+
+176
+00:16:30,570 --> 00:16:35,110
+وبين هؤلاء العوامل المشتركة معناته الـ B بيكون ضغط
+
+177
+00:16:35,110 --> 00:16:39,210
+منه غير أنك بيصير العامل المشترك أيش بيساوي؟ واحد
+
+178
+00:16:39,210 --> 00:16:43,890
+إذن العامل المشترك الأعلى بين الـ N والـ BK بيساوي
+
+179
+00:16:43,890 --> 00:16:50,690
+واحد يكافئ أن الـ B مش أياش مش من عوامل الـ Nلأن
+
+180
+00:16:50,690 --> 00:16:55,490
+بكل بساطة لو الـ B بقسم الـ N أكيد هيصير الجاسكم
+
+181
+00:16:55,490 --> 00:16:58,970
+الـ divisor بين الـ N والـ B على كياش ماله مش واحد
+
+182
+00:17:01,270 --> 00:17:05,350
+واضح أه؟ لأن لو كان العامل المشترك الأعلى بين الـ
+
+183
+00:17:05,350 --> 00:17:09,910
+N و الـ B K غير الواحد يا هيكون الـ B يا الـ B
+
+184
+00:17:09,910 --> 00:17:13,970
+تربيع يا لم أصل لـ BK إذا في كل الأحوال هيكون الـ
+
+185
+00:17:13,970 --> 00:17:18,330
+B أشماله بيكسب الـ N إذا الـ N اللي بقوله إنه
+
+186
+00:17:18,330 --> 00:17:21,730
+Greatest Common Divisor بين الـ N و الـ B أس K لا
+
+187
+00:17:21,730 --> 00:17:29,740
+يساوي 1 F N دول في الـ B أشمالها غير فكرة واضح؟إذا
+
+188
+00:17:29,740 --> 00:17:36,260
+من هذا المجدر نستمتج إن الأعداد اللي مش relative
+
+189
+00:17:36,260 --> 00:17:41,220
+لـPrime مع الـPK مين هي اللي بتجسم الـN يعني بمعنى
+
+190
+00:17:41,220 --> 00:17:47,960
+أخر مضاعفات الـP ليه المضاعفات الـP من 1 لعند الـP
+
+191
+00:17:47,960 --> 00:17:57,610
+أُس K؟ الـP ليه الـP؟والتلاتة بيه فاهمين و الأربعة
+
+192
+00:17:57,610 --> 00:18:02,330
+بيه و الخمسة بيه لما حصل الأخر أحد من مبعثات ال
+
+193
+00:18:02,330 --> 00:18:10,470
+بيه مين هو بيوسكي واضح هذولة بس هم مين اللي العامل
+
+194
+00:18:10,470 --> 00:18:16,550
+المشترك الأعلى اللي بين هنا وبين ال بيكي أشماله مش
+
+195
+00:18:16,550 --> 00:18:24,310
+واحد واضح أه؟ بتدعد هنا هذول هذولة هم مين هناهي
+
+196
+00:18:24,310 --> 00:18:30,390
+عندنا بي اتنين بي تلاتة بي أربع بي خمسة بي لعند بي
+
+197
+00:18:30,390 --> 00:18:37,770
+أس كي بي أس كي اللي هو عبارة عن إيش اسمه بي أس كي
+
+198
+00:18:37,770 --> 00:18:45,330
+ماقص واحد في بي يعني الآن لو بد أعد هاي بي هاي
+
+199
+00:18:45,330 --> 00:18:49,270
+اتنين بي هاي تلاتة بي هاي أربع بي هاي خمسة بي هاي
+
+200
+00:18:49,270 --> 00:18:54,840
+ستة بي هاي بي كي ماقص واحد من البيإذاً اكم واحدة
+
+201
+00:18:54,840 --> 00:18:59,500
+هذولة و اكم بيه هذولة او اكم term اللي هو بي الـ
+
+202
+00:18:59,500 --> 00:19:07,260
+square minus واحد إذاً صار عندى الآن هذولة هماللي
+
+203
+00:19:07,260 --> 00:19:12,600
+العامل المشترك الأعلى بينه وبين الـ BK إيش ماله؟
+
+204
+00:19:12,600 --> 00:19:17,140
+مش واحد إذا صارت Phi of BK بتساوي BK العدد الكلي
+
+205
+00:19:17,140 --> 00:19:22,020
+للأعداد من واحد لعند الـ BK ناقص الأعداد اللي مش
+
+206
+00:19:22,020 --> 00:19:25,320
+relative لـ Brian اللي هي BK minus واحد فصارت Phi
+
+207
+00:19:25,320 --> 00:19:31,300
+of BK إيش بتساوي BK ناقص BK minus واحد أي سؤال؟
+
+208
+00:19:31,300 --> 00:19:39,600
+بناء على ذلك بسير عملية الإيجادالآن أسهل لو جبنا
+
+209
+00:19:39,600 --> 00:19:52,260
+نوجد Phi of اللي هو 32 مثلا أو 64 بالطريقة
+
+210
+00:19:52,260 --> 00:19:58,160
+السابقة بتغلب الآن هنا بقولك على طول اللي هو 64
+
+211
+00:19:59,660 --> 00:20:03,020
+أربعة و ستين مضروبة في واحد لأن أربعة و ستين مين
+
+212
+00:20:03,020 --> 00:20:07,940
+هي؟ اتنين أس سبعة اظنين اتنين أس خمس اتنين و
+
+213
+00:20:07,940 --> 00:20:11,920
+تلاتين اتنين أس ستة اربعة أس اتنين أس ستة، مظبوط؟
+
+214
+00:20:11,920 --> 00:20:18,180
+اذا هذه عبارة عن five of اتنين أس ستة يعني اطمأنت
+
+215
+00:20:18,180 --> 00:20:24,240
+انها إيه شمالها؟ power of two بيصير عبارة عن اتنين
+
+216
+00:20:24,240 --> 00:20:27,860
+أس ستة اللي هي اربعة و ستين مضروبة في واحد ماقص
+
+217
+00:20:27,860 --> 00:20:34,170
+واحد على اتنينصح؟ سهل هيك هيك سهل ويساوي عبارة عن
+
+218
+00:20:34,170 --> 00:20:40,490
+اتنين وتلاتين وكذا five of مثلا تلاتة اص مليون
+
+219
+00:20:40,490 --> 00:20:47,350
+ويساوي
+
+220
+00:20:47,350 --> 00:20:57,610
+تلاتة اص مليون في واحد ماقص تلت يعني بيصير تلتين
+
+221
+00:20:57,610 --> 00:20:59,390
+في هذا
+
+222
+00:21:02,390 --> 00:21:11,990
+واضحة؟ أي سؤال؟ عشان نعرف جداش اللي هو الـ Issue
+
+223
+00:21:11,990 --> 00:21:21,010
+النظري مهم ويسهل علينا عملية التقامل مع Issue الـ
+
+224
+00:21:21,010 --> 00:21:25,390
+Issue التطبيقى يعني الآن أخدت هذه اللي هي النظرية
+
+225
+00:21:25,390 --> 00:21:30,680
+وبرهنتهاسهلت عليها عملية الإيجاد لأي عدد كبير في
+
+226
+00:21:30,680 --> 00:21:39,500
+الدنيا من كام دوسان؟ هذا
+
+227
+00:21:39,500 --> 00:21:42,940
+الـ
+
+228
+00:21:42,940 --> 00:21:43,200
+prime
+
+229
+00:21:48,150 --> 00:21:53,010
+طيب نجي الآن في لمّة لمّة هي كأنت عشان النظرية
+
+230
+00:21:53,010 --> 00:21:56,570
+اللي هي لإثبات النظرية بس احنا مش هنتبت النظرية
+
+231
+00:21:56,570 --> 00:22:01,790
+لكن اللمّة عبارة عن exercise بسيط يعني لو ممكن
+
+232
+00:22:01,790 --> 00:22:05,390
+يكون مرض بالهيك خلّينا نبارح انه كأنه exercise
+
+233
+00:22:05,390 --> 00:22:12,650
+يعني هاللمّة لمّة ايش اللمّة بتقول انه اللمّةعندي
+
+234
+00:22:12,650 --> 00:22:15,770
+الـ greatest common divisor بين الـ A و الـ B و
+
+235
+00:22:15,770 --> 00:22:20,730
+الـ C بساوية 1 if and only if الـ greatest common
+
+236
+00:22:20,730 --> 00:22:25,130
+divisor بين الـ A و الـ B بساوية الـ greatest
+
+237
+00:22:25,130 --> 00:22:30,610
+common divisor بين الـ A و الـ C بساوية 1 والـ
+
+238
+00:22:30,610 --> 00:22:38,670
+proof يعني إكسرسيز عادي نعتبره سهل الـ proof بدا
+
+239
+00:22:38,670 --> 00:22:40,470
+أقول سبّوز
+
+240
+00:22:43,780 --> 00:22:47,660
+that الـ greatest common divisor بين الـ A والـ B
+
+241
+00:22:47,660 --> 00:22:55,840
+والـ C بيساوي واحد بيثبت لك أن العامل المشترك
+
+242
+00:22:55,840 --> 00:22:58,260
+الأعلى بين هذه و هذه واحد و بين هذه و هذه واحد
+
+243
+00:22:58,260 --> 00:23:03,400
+بيثبت واحد ده والتاني زيها نقول let ال greatest
+
+244
+00:23:03,400 --> 00:23:09,760
+common divisor بين الـ A والـ C بيساوي D بيثبت لك
+
+245
+00:23:09,760 --> 00:23:14,240
+الـ D أش بتساوي واحدبما أنه الجلسكم هو الـdivisor
+
+246
+00:23:14,240 --> 00:23:21,500
+بين الـA والـC وساوية وD، فD بيقسم الـA وD بيقسم
+
+247
+00:23:21,500 --> 00:23:27,720
+الـC. طيب، مادام الـD بيقسم الـC، إذا أكيد and so
+
+248
+00:23:27,720 --> 00:23:34,860
+D بيقسم الـA وD بيقسم الـB
+
+249
+00:23:34,860 --> 00:23:35,660
+في الـC.
+
+250
+00:23:38,480 --> 00:23:42,840
+أذا مادامي بتقسمها بتقسم هذا و بتقسم هذا إذا بتقسم
+
+251
+00:23:42,840 --> 00:23:47,740
+العامل المشترك اللي علي بينهم إذا hence خدنا هذا
+
+252
+00:23:47,740 --> 00:23:51,680
+برضه D بتقسم ال grades from the divisor بين ال A و
+
+253
+00:23:51,680 --> 00:23:56,260
+ال B و ال C و يساوي إيه إيش؟ واحد ماعطينا إيه
+
+254
+00:23:56,260 --> 00:24:03,440
+واحد؟ إذا D بتقسم الواحد إذا اشملها hence D بتساوي
+
+255
+00:24:03,440 --> 00:24:08,030
+واحد similarlyالـ Greatest Common Divisor بين الـ
+
+256
+00:24:08,030 --> 00:24:14,010
+A و الـ B برضه إيش هيساوي؟ واحد، بنفس الطريقة،
+
+257
+00:24:14,010 --> 00:24:20,670
+واضح؟ الان conversely .. conversely .. conversely
+
+258
+00:24:20,670 --> 00:24:24,930
+suppose
+
+259
+00:24:24,930 --> 00:24:28,410
+that
+
+260
+00:24:28,410 --> 00:24:35,700
+ال Greatest Common Divisorبين الـ A والـ B بيساوي
+
+261
+00:24:35,700 --> 00:24:38,860
+الـ Greatest Common Divisor بين الـ A والـ C
+
+262
+00:24:38,860 --> 00:24:44,200
+بيساوي 1 وبدأ أثبت مين أن العامل المشترك الأعلى
+
+263
+00:24:44,200 --> 00:24:48,980
+بين الـ A والـ B وC أيش بيساوي 1 شوف كيف عامل لما
+
+264
+00:24:48,980 --> 00:24:51,780
+دام العامل المشترك الأعلى بيساوي 1 إذا بقدر ألاقي
+
+265
+00:24:51,780 --> 00:24:58,700
+XY there exists XY element in Z بحيث أن AX زاوية
+
+266
+00:24:58,700 --> 00:25:02,950
+BY بيساوي 1وما دام العام المشترك اللي على بين الـ
+
+267
+00:25:02,950 --> 00:25:06,070
+a و الـ c بساوة واحد and then there exists z و w
+
+268
+00:25:06,070 --> 00:25:13,850
+برضه element in z بحيث اللي هو a z زاد cw بساوة
+
+269
+00:25:13,850 --> 00:25:20,150
+واحد اضرب لها دول فبعض بيصير عندي اذا hence دي ax
+
+270
+00:25:20,150 --> 00:25:29,690
+فيها دي في a z زاد ax في cw زاد هذه فيها دول by a
+
+271
+00:25:29,690 --> 00:25:36,200
+zزائد BYCW كله إيش هيساوي؟ لأن واحد في واحد في
+
+272
+00:25:36,200 --> 00:25:40,400
+واحد خد اللي إن هدول مع بعض خد ال A عملوا اشتراك
+
+273
+00:25:40,400 --> 00:25:51,220
+بيصير A في AXZ زائد XCW زائد BYZ زائد B في C خدها
+
+274
+00:25:51,220 --> 00:25:59,000
+برا مضروبة في YW إيش ميساوي؟ واحدوكأنه سعر هذا كله
+
+275
+00:25:59,000 --> 00:26:04,180
+عبارة عن انتجر اسمه M و هذا انتجر اسمه N فبيصير
+
+276
+00:26:04,180 --> 00:26:11,760
+عند A M زائد B C فن بساوية واحدة إذا العام المشترك
+
+277
+00:26:11,760 --> 00:26:16,720
+اللي على بين ال A و ال B C أشوى ساوية واحدة hence
+
+278
+00:26:16,720 --> 00:26:20,780
+واضح ها hence ال grades from the divisors نظرية
+
+279
+00:26:20,780 --> 00:26:25,600
+سابقة A و B C بساوية واحدة وهو المطلوب
+
+280
+00:26:29,400 --> 00:26:32,640
+العنوان المعلومة اللي هأخدها ناشر برهيلها الـ
+
+281
+00:26:32,640 --> 00:26:36,670
+function فيThe function Phi is a multiplicative
+
+282
+00:26:36,670 --> 00:26:40,910
+function البرمجة ليست صحيحة موجودة في الكتاب يمكن
+
+283
+00:26:40,910 --> 00:26:44,570
+المغضب اغطنا شوية The function Phi اسمها is a
+
+284
+00:26:44,570 --> 00:26:48,450
+multiplicative function Phi is a multiplicative
+
+285
+00:26:48,450 --> 00:26:51,750
+function ايش معناه Phi multiplicative يعني لو كانت
+
+286
+00:26:51,750 --> 00:26:54,250
+الجريس كمين divisor بين الـM والـN بيساوي واحد
+
+287
+00:26:54,250 --> 00:26:58,970
+هيكون Phi of M في N بيساوي Phi of M في Phi of N
+
+288
+00:26:58,970 --> 00:27:05,380
+اطلع لفوق نيدي الـNبدنا نوجد اللي هو الـ 5N in
+
+289
+00:27:05,380 --> 00:27:11,520
+general طبعا أي N التجار أكبر من واحد يا جماعة can
+
+290
+00:27:11,520 --> 00:27:17,640
+be written as economical four يعني product of
+
+291
+00:27:17,640 --> 00:27:27,540
+power over primes مظبوط؟ يعني بمعنى آخر theorem if
+
+292
+00:27:29,140 --> 00:27:37,600
+ن بيتساوي بي واحد كي واحد لعند بي ار كي ار then اه
+
+293
+00:27:37,600 --> 00:27:40,780
+where بي واحد بي اتنين بي ار are distinct primes
+
+294
+00:27:40,780 --> 00:27:46,840
+او n is written as a canonical form then phi of n
+
+295
+00:27:46,840 --> 00:27:55,490
+ايش هتساوي؟أحنا قلنا عنها إيش مالها Multiplicative
+
+296
+00:27:55,490 --> 00:27:58,570
+إذا في الأول في في التاني في في التالت في في الأخر
+
+297
+00:27:58,570 --> 00:28:02,230
+في الأول وجدناه في التاني وجدناه وجدناه هو five
+
+298
+00:28:02,230 --> 00:28:06,790
+bar of brine صح؟ اللي هو عبارة عن الأول بي واحد
+
+299
+00:28:06,790 --> 00:28:14,250
+كواحد ناقص بي واحد كواحد minus واحد لما أصل عند br
+
+300
+00:28:14,250 --> 00:28:24,010
+kr ناقص br kr ناقص واحدو يساوي معايا يا شباب اه و
+
+301
+00:28:24,010 --> 00:28:27,430
+يساوي اللي هو الصورة اللي احنا بدنا نسهّل على
+
+302
+00:28:27,430 --> 00:28:33,650
+حالنا بناخد الـB1 K1 و الـB2 K2 عند الـB R K R كل
+
+303
+00:28:33,650 --> 00:28:39,610
+مع بعض ضرب من مين هيكون الـN إذا هيساوي N في واحد
+
+304
+00:28:39,610 --> 00:28:46,750
+ناقص B واحد على B واحد لما أصل لأخر واحد ناقص واحد
+
+305
+00:28:46,750 --> 00:28:54,360
+على Bإذا العملية صارت سهل عملية الحساب أن 5N
+
+306
+00:28:54,360 --> 00:29:01,340
+بتساوي N في واحد ناقص الو مين او product واحد ناقص
+
+307
+00:29:01,340 --> 00:29:05,920
+بي واحد على بي I I من واحد لعند مين لعند Rيعني بس
+
+308
+00:29:05,920 --> 00:29:10,400
+بتجيب اللي هو الـ prime factorization لها بيصير
+
+309
+00:29:10,400 --> 00:29:13,220
+الـ Phi لها بسوء 1000 في الواحد ناقص واحد على الـ
+
+310
+00:29:13,220 --> 00:29:16,180
+prime الأول في واحد ناقص واحد على الاتاني لما أصل
+
+311
+00:29:16,180 --> 00:29:19,260
+واحد على ناقص واحد على الـ prime الأخر وضربهم في
+
+312
+00:29:19,260 --> 00:29:23,740
+بعض بتطلع الدمين الـ 5000 واضح نيجي للبرهان
+
+313
+00:29:23,740 --> 00:29:27,280
+البرهان زي ما قلت لها بس خلنا نكتبه by اياش by
+
+314
+00:29:27,280 --> 00:29:36,480
+induction by induction on mean on Rby induction on
+
+315
+00:29:36,480 --> 00:29:40,660
+main on R for R بتساوي واحد اللي هي main النظرية
+
+316
+00:29:40,660 --> 00:29:48,040
+اه لأن for R بتساوي واحد N بتساوي بي واحد أس كي
+
+317
+00:29:48,040 --> 00:29:55,180
+واحد then by اللي هو ال theorem اللي قبل بشوية Phi
+
+318
+00:29:55,180 --> 00:29:59,200
+of N اللي هي بتساوي Phi of بي واحد أس كي واحد
+
+319
+00:29:59,200 --> 00:30:04,120
+بساوي بي واحد أس كي واحد ناقص بي واحد أس كي واحد
+
+320
+00:30:04,120 --> 00:30:13,090
+ناقصواحد إذا صارت اللي هي إيه شمالها عندي هذه is
+
+321
+00:30:13,090 --> 00:30:20,430
+true لو سميناها الـ star إذا hence star is true
+
+322
+00:30:20,430 --> 00:30:26,730
+for R بتساوي واحد إلى أن نفترض إنها true for R
+
+323
+00:30:26,730 --> 00:30:31,290
+بتساوي I ونصل إلي إنها true for I زاد واحد إلى أن
+
+324
+00:30:31,290 --> 00:30:33,570
+suppose suppose
+
+325
+00:30:35,340 --> 00:30:43,160
+that star is true for R بتساوي I then مدام true
+
+326
+00:30:43,160 --> 00:30:52,620
+for R بتساوي I إذا صار عندي Phi of P1 K1 لعند PIKI
+
+327
+00:30:52,620 --> 00:31:02,640
+بساوي اللي هو عبارة عن P1 أو ال product ل P A P K
+
+328
+00:31:02,640 --> 00:31:21,510
+P SKS-B S KS-1 S من عند 1 لعند I ثمين الأهمية
+
+329
+00:31:21,510 --> 00:31:25,130
+اللي بتبيتها الأقل جمالها بتساوي I زائد 1 then
+
+330
+00:31:25,130 --> 00:31:36,450
+thenPhi of B1K1 لعند BIKI في BI زائد واحد KI زائد
+
+331
+00:31:36,450 --> 00:31:41,230
+واحد بيساوي هدول distinct برعام كلهم ده اللي
+
+332
+00:31:41,230 --> 00:31:43,030
+جالسكم من ال divisor بيقول الأول و الثاني ايش
+
+333
+00:31:43,030 --> 00:31:46,790
+بيساوي ال Phi multiplicative of Phi الأول في Phi
+
+334
+00:31:46,790 --> 00:31:54,270
+الثاني بيساويو بي واحد كواحد لعند بي اي كي اي في
+
+335
+00:31:54,270 --> 00:32:00,970
+في اثنين او بي اي زائد واحد كي اي زائد واحد و
+
+336
+00:32:00,970 --> 00:32:05,590
+يساوي هذه من الوثوث ال induction هذه اللي هي عبارة
+
+337
+00:32:05,590 --> 00:32:14,260
+عن ال productللـ BS KS ناقص BS KS ناقص واحد S من
+
+338
+00:32:14,260 --> 00:32:19,100
+عند واحد لعند I مضروب نفسه في هذه الـ file اللي
+
+339
+00:32:19,100 --> 00:32:27,340
+عبارة عن BI زائد واحد KI زائد واحد ناقص BI زائد
+
+340
+00:32:27,340 --> 00:32:33,820
+واحد KI زائد واحد ناقص واحد ويساويأبدا عن ال
+
+341
+00:32:33,820 --> 00:32:38,720
+product نفسه من S بتساوي واحد ل I زاد واحد إذا صار
+
+342
+00:32:38,720 --> 00:32:46,160
+true for I زاد واحد hence it is true for any R إذا
+
+343
+00:32:46,160 --> 00:32:51,140
+صار عندي الآن من الآن وطالع الإعلان هذا صحيح Phi
+
+344
+00:32:51,140 --> 00:32:57,600
+of N بتساوي اللي هو المقدار اللي أمامنا أي سؤال؟
+
+345
+00:33:02,320 --> 00:33:06,780
+طيب صلوا عنا بالله الصلاة والسلام ناخد مثال five
+
+346
+00:33:06,780 --> 00:33:12,400
+تلت مية وستين أي مثال الآن أو أي عدد سهل أنه نوجده
+
+347
+00:33:12,400 --> 00:33:17,960
+بس بنسوي انه من فاكفكو إلى الprimes تبعاته بنكتبه
+
+348
+00:33:17,960 --> 00:33:24,610
+على صورة product of bar of primes chemical formولو
+
+349
+00:33:24,610 --> 00:33:27,830
+لم تكتبوا في اللغة الـ Canonical لأنهم كتبوا على
+
+350
+00:33:27,830 --> 00:33:30,790
+صورة Distinct Primes بنفع بس الـ Canonical لغة
+
+351
+00:33:30,790 --> 00:33:36,130
+مشتركة و ألطف وبتساعد في حاجات كتير لأن Phi of 360
+
+352
+00:33:36,130 --> 00:33:42,510
+بساوي Phi of أكم اتنين فيها اتنين اقصى ثلاثة أكم
+
+353
+00:33:42,510 --> 00:33:49,980
+تلاتة فيها تلتينلأنها بـ 9×4 بـ 36 و 5×2 الـ 2 مع
+
+354
+00:33:49,980 --> 00:33:54,640
+الـ 2 الأولانيات بيصير الـ 3 والـ 32 هي الـ 3 والـ
+
+355
+00:33:54,640 --> 00:34:01,720
+5 هي 5 بيساوي عبارة عن N اللي هو 360 بعد ان نحسب
+
+356
+00:34:01,720 --> 00:34:08,780
+كل واحدة لحالها 360 فيه واحد ناقص نص في واحد ناقص
+
+357
+00:34:08,780 --> 00:34:18,290
+تلتفي واحد ماقصهاش خمس بطلع عندك 96 زي ما هو حسبة
+
+358
+00:34:18,290 --> 00:34:26,010
+بسيطة يعني أي سؤال طيب نيجي الآن للمظهرية الأخيرة
+
+359
+00:34:26,010 --> 00:34:32,490
+اللي وعدناكم انه احنا نثبت لكم انه الملاحظة اللي
+
+360
+00:34:32,490 --> 00:34:36,410
+لاحظناها في الأول حسبنا five of واحد واحد five of
+
+361
+00:34:36,410 --> 00:34:41,110
+اتنين واحديعني اقول بعد five of اتنين حسبنا كل
+
+362
+00:34:41,110 --> 00:34:44,850
+اللي حسبناه طلع ايه شماله even five تلاته، five
+
+363
+00:34:44,850 --> 00:34:47,570
+اربعه، five خمسه، five ستة، five كده و هاي five
+
+364
+00:34:47,570 --> 00:34:52,550
+تلاته ستين طلع ايه شماله even هذا مش مصادفة لأي n
+
+365
+00:34:52,550 --> 00:34:58,700
+أكبر من اتنين هتطلع ال five is an even functionis
+
+366
+00:34:58,700 --> 00:35:02,720
+an even .. ال .. ال .. the value of phi is even اه
+
+367
+00:35:02,720 --> 00:35:05,400
+مش even function the value .. the value of phi ايش
+
+368
+00:35:05,400 --> 00:35:11,520
+مالها is even دايما ايش قيمتها عدد زودي واضح اللي
+
+369
+00:35:11,520 --> 00:35:17,860
+بحكيه مش even function عدد زودي قيمة او اللي هو ال
+
+370
+00:35:17,860 --> 00:35:23,840
+image يعني و كأن وين موجود فت name it positive
+
+371
+00:35:26,160 --> 00:35:33,740
+صلى على النبي عليه الصلاة والسلام الآن theorem for
+
+372
+00:35:33,740 --> 00:35:48,080
+N أكبر من 2 Phi of N is an even انتجار proof
+
+373
+00:35:55,240 --> 00:36:01,100
+الـ N بيدثبتلك أن 5N is an even integer بدي أفصل
+
+374
+00:36:01,100 --> 00:36:05,220
+أبدي الـ N الـ N طبعا من وين جاي من Z أو من Z
+
+375
+00:36:05,220 --> 00:36:08,820
+positive بدي أجسم لك Z positive لتسهيل الحسابات
+
+376
+00:36:08,820 --> 00:36:14,620
+كالتالي أي N عدد في الدنيا يا إما هيكون على صورة
+
+377
+00:36:14,620 --> 00:36:20,260
+power of 2 أو مش power of 2 إيش يعني power of 2
+
+378
+00:36:20,260 --> 00:36:27,260
+يعني 2 نقص K بسوالـ K طبعا أكبر أو يساوي 2 لأن
+
+379
+00:36:27,260 --> 00:36:30,660
+احنا مستثنيين منين عندنا في نظريتنا الواحد
+
+380
+00:36:30,660 --> 00:36:35,500
+والاتنين يعني اتنين نقص واحد مستثناء اذا الان عندي
+
+381
+00:36:35,500 --> 00:36:41,780
+caseين ال case الأول case one او عندي two cases ال
+
+382
+00:36:41,780 --> 00:36:46,520
+case الأول case واحد اللي هو N بتساوي two to the K
+
+383
+00:36:46,520 --> 00:36:53,880
+for some K أكبر أو يساوي ايش يا جماعة اتنينالـ
+
+384
+00:36:53,880 --> 00:36:59,580
+case التاني الـ case التاني اللي هو N is not a
+
+385
+00:36:59,580 --> 00:37:06,380
+power of two يعني بمعنى أخر N فيها factor غير
+
+386
+00:37:06,380 --> 00:37:11,380
+التنين ماشي الحال ال factor اللي غير التنين أكيد
+
+387
+00:37:11,380 --> 00:37:18,600
+ماله قد برايم إذا عندي ال N الصورة التانية عبارة
+
+388
+00:37:18,600 --> 00:37:27,680
+عن برايمبرايل odd of k مضروب في مين في some انتجر
+
+389
+00:37:27,680 --> 00:37:32,680
+ام ايش هو مش عارف بلزمنيه بلمنيش الان اي عدد في
+
+390
+00:37:32,680 --> 00:37:37,540
+الدنيا يا هيكون على صورة two of اتنين k او مش على
+
+391
+00:37:37,540 --> 00:37:44,040
+صورة اتنين of k يعني ايش في يعني في كمان عدد odd
+
+392
+00:37:44,040 --> 00:37:50,390
+موجود في داخل مين ام شيلت ال odd برايل بيهمن كل
+
+393
+00:37:50,390 --> 00:37:54,470
+الـ L و حطيته لحاله و كترته بـ B² ده المتبقى ده
+
+394
+00:37:54,470 --> 00:37:57,970
+المتبقى ده بإيش يكون مش عارف ممكن يكون واحد ممكن
+
+395
+00:37:57,970 --> 00:38:01,310
+يكون اتنين ممكن يكون اتنين في خمسة ممكن تكون اتنين
+
+396
+00:38:01,310 --> 00:38:08,270
+في تلاتة بس شمت كل meaning كل الـ B اللي بحكي عنه
+
+397
+00:38:08,270 --> 00:38:14,720
+واضح؟ إذا صار عندى الآنإذا الـ thing هذا اللي هي
+
+398
+00:38:14,720 --> 00:38:19,220
+التجزية اللي ده جيه سهل إحسابات أي سؤال بالنسبة
+
+399
+00:38:19,220 --> 00:38:26,100
+للتجزية طيب نيجي نحسب هذا بيصير 5N بيساوي 5 of 2
+
+400
+00:38:26,100 --> 00:38:34,680
+أس K اللي عبارة عن 2 أس K ناقص 2 أس K minus 1 خد 2
+
+401
+00:38:34,680 --> 00:38:40,740
+أس K minus 1 عامل مشترك بيصير 2اللي هي عبارة عن
+
+402
+00:38:40,740 --> 00:38:50,360
+اتنين نقص واحد صح ولا لأ؟ ايش؟ وهذا ماله الـ K-
+
+403
+00:38:50,360 --> 00:38:55,580
+واحد اتنين او طالع يعني الـ K- واحد بيصير واحد او
+
+404
+00:38:55,580 --> 00:39:00,000
+طالع يعني هذا اتنين او اربع او تمانية او الاخر
+
+405
+00:39:00,000 --> 00:39:07,320
+فاهمين؟ لأن هذا even لأن الـ K أكبر أو يسوى اتنين
+
+406
+00:39:10,300 --> 00:39:16,500
+أي سؤال الـ N التاني فلا مافيش مشكلة Phi of M أيش
+
+407
+00:39:16,500 --> 00:39:21,200
+بيساوي أنا كل من في الـ B اللي في الـ M من الـ B
+
+408
+00:39:21,200 --> 00:39:24,520
+في الـ N إذا صار هذا الـ B أس K و الـ M إيش معناه
+
+409
+00:39:24,520 --> 00:39:28,960
+لإن ال relative لمراهب إذا Phi of M إيش صار Phi of
+
+410
+00:39:28,960 --> 00:39:36,360
+B أس K في Phi of M و يساوي5POSK مين هو عبارة عن
+
+411
+00:39:36,360 --> 00:39:44,640
+POSK ناقص POSK minus واحد مضروب في مين في 5M أي إن
+
+412
+00:39:44,640 --> 00:39:49,540
+كانت قيمته ماليش علاقة فيه ماهيش الحالة الان هذا
+
+413
+00:39:49,540 --> 00:39:56,780
+ايش هو POSK POSK minus واحد هذا قد و هذا قد صح قد
+
+414
+00:39:56,780 --> 00:40:04,540
+ناقص قدeven مش odd odd لاقص odd even بتاكيها بصورة
+
+415
+00:40:04,540 --> 00:40:11,640
+أوضح بي أس كمانس واحد في بي ماقص واحد في five M
+
+416
+00:40:11,640 --> 00:40:17,860
+هذا اللي في النص even لإن بي زاد بي ماينس واحد ايش
+
+417
+00:40:17,860 --> 00:40:24,180
+ماله even even مضروب في أي إشي هيطلع ايه ايش even
+
+418
+00:40:25,170 --> 00:40:30,670
+أذن .. أذن صارت عندي الإعلان الأخير أن فاي of أن
+
+419
+00:40:30,670 --> 00:40:36,750
+is an even integer أذن الواضح أنه احنا امشينا
+
+420
+00:40:36,750 --> 00:40:46,220
+بطريق أنه عشان نجد قيمةالـ Phi of N عشان نودد قيمة
+
+421
+00:40:46,220 --> 00:40:50,620
+الـ Phi of N أول خطوة بسويها بكتب الـ N على صورة
+
+422
+00:40:50,620 --> 00:40:57,380
+الـ canonical form P1K1 لعند PRKR بعد ما اكتبها
+
+423
+00:40:57,380 --> 00:40:59,640
+على صورة ال canonical form اللي احنا كلنا بنعرف
+
+424
+00:40:59,640 --> 00:41:05,680
+نكتبها بيصير عند إيجاد ال Phi of N سهل ويساوي الـ
+
+425
+00:41:05,680 --> 00:41:13,770
+N في 1 ماقص 1 على P1لما أصل عند واحد ناقص واحد على
+
+426
+00:41:13,770 --> 00:41:21,110
+PR و بكون هيك أعرفنا نوجد مين الـPhi of N و درسنا
+
+427
+00:41:21,110 --> 00:41:25,550
+خلاص الـPhi of N اطلع للبعد ده عشان نشوف وين وصلنا
+
+428
+00:41:25,550 --> 00:41:30,470
+المرة الدا ان شاء الله هنحكي على Ehlers theorem
+
+429
+00:41:30,470 --> 00:41:37,050
+اللي هو ال generalization of Fermat's theorem او
+
+430
+00:41:37,050 --> 00:41:40,330
+Fermat's little theorem الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/arGzx_seTzc_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/arGzx_seTzc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ae9ccc43dfe56bf2a16fd2a06ae1ccd841c04a02
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/arGzx_seTzc_raw.srt
@@ -0,0 +1,1720 @@
+1
+00:00:19,610 --> 00:00:26,430
+بسم الله الرحمن الرحيم المحاضرة رقم 23 مساق نظرية
+
+2
+00:00:26,430 --> 00:00:34,150
+الأعداد طلاب الجامعة الإسلامية قسم الرياضيات كلية
+
+3
+00:00:34,150 --> 00:00:41,490
+التربية وكلية العلوم هنكمل اليوم إن شاء الله في
+
+4
+00:00:41,490 --> 00:00:45,550
+المادة أو في المساق هنبدأ في شبتر سبعة اللي هو
+
+5
+00:00:45,550 --> 00:00:50,150
+Euler's Generalization of Fermat's Theoremهنبدأ في
+
+6
+00:00:50,150 --> 00:00:54,490
+البداية نتعرف على اللي هي number theoretic
+
+7
+00:00:54,490 --> 00:00:58,110
+function جديدة اللي هي بنسميها Euler's phi
+
+8
+00:00:58,110 --> 00:01:03,210
+function هندرس .. هنعرف شو معناه Euler's phi
+
+9
+00:01:03,210 --> 00:01:08,050
+function و هنشوف كيف نوجد ال phi لأي عدد و هناخد
+
+10
+00:01:08,050 --> 00:01:13,510
+بعض الخواص اللي تسهل علينا إيجاد قيمة ال phiأحنا
+
+11
+00:01:13,510 --> 00:01:16,790
+مر علينا الـ number theoretic functions مر عنا
+
+12
+00:01:16,790 --> 00:01:21,270
+اللي هو التاو اللي هي عبارة عن number of divisors
+
+13
+00:01:21,270 --> 00:01:28,030
+والسيجما اللي هي عبارة عن sum of divisors ومر عنا
+
+14
+00:01:28,030 --> 00:01:32,610
+اللي هو product of divisors وكانت هذه من z
+
+15
+00:01:32,610 --> 00:01:38,910
+positive and z positiveومن ثم أخدنا الـ Mu المبيوظ
+
+16
+00:01:38,910 --> 00:01:43,510
+function كانت من Z positive لعند اللي هو ناقص واحد
+
+17
+00:01:43,510 --> 00:01:49,790
+و سفر و واحدالان الان بدنا نحكي عن function جديدة
+
+18
+00:01:49,790 --> 00:01:53,930
+اللي هي ال الارث فانكشن اللي هي اللي هي بنسميها في
+
+19
+00:01:53,930 --> 00:01:59,810
+برضه في هتكون من z positive لعند z positive الان
+
+20
+00:01:59,810 --> 00:02:05,830
+بدنا نعرف ال في of أي عدد اللي هو ان ينتمي إلى z
+
+21
+00:02:05,830 --> 00:02:10,930
+positive يعني في of أي positive integerPhi of N
+
+22
+00:02:10,930 --> 00:02:14,070
+اللي هو برضه اللي هي الـ function Phi عبارة عن
+
+23
+00:02:14,070 --> 00:02:18,410
+عداد زي Tau عداد Tau كانت تتعدى اللي هي number of
+
+24
+00:02:18,410 --> 00:02:23,070
+divisors للعدد هذه بتعدى اللي الأعداد اللي أقل أو
+
+25
+00:02:23,070 --> 00:02:28,650
+يساوي N وتكون relatively براي مع مين؟ مع الـ N اذا
+
+26
+00:02:28,650 --> 00:02:34,150
+Phi of N هي عبارة عن number of positive integers
+
+27
+00:02:34,980 --> 00:02:39,860
+that are relatively prime to n and less than or
+
+28
+00:02:39,860 --> 00:02:46,720
+equal mean equal n الان لو جينا لـ5 of 1 5 of 1
+
+29
+00:02:46,720 --> 00:02:50,000
+ايش الأعداد الـ positive integers الأصغر يساوي
+
+30
+00:02:50,000 --> 00:02:53,580
+واحد و relatively prime مع الواحد بس مين الواحد ده
+
+31
+00:02:53,580 --> 00:02:57,920
+العدد دي ايش هيساوي واحد لو جينا قدّينا 5 of 2
+
+32
+00:02:57,920 --> 00:03:03,500
+برضه نفس الاشي ايش العداد عدد الأعداداللي أصغره
+
+33
+00:03:03,500 --> 00:03:06,240
+يساوي اتنين وrelative الـ prime مع اتنين فش لغير
+
+34
+00:03:06,240 --> 00:03:10,880
+مين الواحد إذاً عدد هنا إيش بيساوي واحد five of
+
+35
+00:03:10,880 --> 00:03:13,740
+تلاتة مين الأعداد اللي relative ال prime مع
+
+36
+00:03:13,740 --> 00:03:18,300
+التلاتة الأصغر يساوي تلاتة الواحد والتنين في غيرين
+
+37
+00:03:18,300 --> 00:03:24,500
+فاهمين؟ بيساوي قداش اتنين عددين اتنين اللي هنوجينا
+
+38
+00:03:24,500 --> 00:03:27,880
+لل five أربعة مين الأعداد اللي relative ال prime
+
+39
+00:03:27,880 --> 00:03:33,710
+اللي أصغر يساوي أربعة واحد وتلاتةإذا إيش بيساوي
+
+40
+00:03:33,710 --> 00:03:41,490
+انت؟ اتنين five of خمسة مين إنه؟ واحد واثنين
+
+41
+00:03:41,490 --> 00:03:47,530
+وتلاتة واربعة كلنا دي relative prime مع مين؟ مع
+
+42
+00:03:47,530 --> 00:03:52,690
+الخمسة وأصغر أو يساوي الخمسة فاهمين؟ أو يساوي
+
+43
+00:03:52,690 --> 00:03:58,570
+أربعة لأن لو جينا لل five of ستة5 of 6 مين الـ
+
+44
+00:03:58,570 --> 00:04:01,930
+Relative Liberal مع الـ 6 الأصغر في 5 و 6 طبعاً
+
+45
+00:04:01,930 --> 00:04:09,110
+واحد اتنين لأ تلاتة لأ أربعة لأ خمسة إذا واحد طبعا
+
+46
+00:04:09,110 --> 00:04:16,850
+الست أكيد لأ إذا اتنين برضه five of سبعة مين
+
+47
+00:04:16,850 --> 00:04:22,390
+الناجداش؟اللي هي الواحد والتنين والتلاتة والاربعة
+
+48
+00:04:22,390 --> 00:04:26,350
+والخمسة والستة إذا مايش بيساوي برضه ستة فأيه في
+
+49
+00:04:26,350 --> 00:04:31,410
+تمانية من الـ negative liberal مع التمانية اللي هو
+
+50
+00:04:31,410 --> 00:04:38,350
+واحد وتلاتة وخمسة وسبعة، مظبوط؟ مايساوي وجديهاش
+
+51
+00:04:38,350 --> 00:04:44,270
+أربعة فأيه في تسعة؟بيصير .. بيصير غلب اه لاحظ انه
+
+52
+00:04:44,270 --> 00:04:47,650
+كل ما كده اللي عدت بيصير يغلب في الحسابات بعد شوية
+
+53
+00:04:47,650 --> 00:04:52,310
+هناخد قوانين اتسهل علينا عملية الحسابات وعملية
+
+54
+00:04:52,310 --> 00:04:57,350
+إيجاب five ان بس قبل ما بروح لاحظ انه ال five واحد
+
+55
+00:04:57,350 --> 00:05:03,040
+و ال five اتنين اللي هو oddبينما five تلاتة أو
+
+56
+00:05:03,040 --> 00:05:05,580
+five أربعة أو five خمسة أو five ستة أو five سبعة
+
+57
+00:05:05,580 --> 00:05:10,660
+أو five تمانية و لو كملت هتلاجيهن دايما even وهذه
+
+58
+00:05:10,660 --> 00:05:15,600
+بعد شوية خاصية هنبرهنها ان five n لكل n أكبر من
+
+59
+00:05:15,600 --> 00:05:19,840
+اتنين هتكون even integer هذه الملاحظة الواحدة
+
+60
+00:05:19,840 --> 00:05:26,500
+الثانية لو اطلعت اتنين prime ايش بيساوي five
+
+61
+00:05:26,500 --> 00:05:32,540
+اتنين؟اللي واحد يعني اتنين ناقص واحد five تلاتة
+
+62
+00:05:32,540 --> 00:05:38,340
+اتنين تلاتة ناقص واحد five خمسةخمسة ناقص واحد،
+
+63
+00:05:38,340 --> 00:05:44,420
+أربعة five سبعة، سبعة ناقص واحد، ستة منطقي، ليش؟
+
+64
+00:05:44,420 --> 00:05:48,820
+لأنه لو جينا ناخد five of B بي براين الأعداد اللي
+
+65
+00:05:48,820 --> 00:05:52,380
+أجيب منه كله ال relative prime معاه لأن بي أصلا
+
+66
+00:05:52,380 --> 00:05:56,300
+كتلة واحدة يعني هيكون الواحد والتنين والتلاتة لعين
+
+67
+00:05:56,300 --> 00:06:00,660
+بي minus واحد كلهم relative prime مع مين؟ مع البي،
+
+68
+00:06:00,660 --> 00:06:08,250
+اذا five of B أش بساوي بي ناقص واحد أي سؤال؟طيب
+
+69
+00:06:08,250 --> 00:06:15,870
+اذا الان بدنا نروح لخاصية ابعد من هيك الان حكينا
+
+70
+00:06:15,870 --> 00:06:20,050
+انه لما يكون بي برايم five بي بيساوي بي ماينس واحد
+
+71
+00:06:20,050 --> 00:06:26,250
+والعكس صحيح يعني لو نجينا عدد five ان له بيساوي ان
+
+72
+00:06:26,250 --> 00:06:31,250
+نغس واحد هيكون الان اشماله z برايم اذا الان
+
+73
+00:06:31,250 --> 00:06:35,970
+الملاحظة التالية اللي بدنا نثبتها بدنا نثبت ما هي
+
+74
+00:06:35,970 --> 00:06:47,140
+ليهfor n أكبر من واحد for n أكبر من واحد five n
+
+75
+00:06:47,140 --> 00:06:56,060
+بيساوي n ماقص واحد if and only if n إيه شمالها is
+
+76
+00:06:56,060 --> 00:07:03,880
+a prime و proof بدنا البرهن الآن
+
+77
+00:07:04,760 --> 00:07:13,920
+بدنا نقول suppose that .. suppose that n is zebra
+
+78
+00:07:15,910 --> 00:07:19,650
+ما دام n زي prime إذا الواحد والاتنين والتلاتة
+
+79
+00:07:19,650 --> 00:07:22,870
+اللي عند ال N ناقص واحد كلهين relative ال prime مع
+
+80
+00:07:22,870 --> 00:07:28,130
+مين؟ مع ال N وعددهين هدولة قداش؟ إذا مباشرة hence
+
+81
+00:07:28,130 --> 00:07:35,390
+ال 5N بساوي N ناقص واحد ال N conversely ..
+
+82
+00:07:35,390 --> 00:07:42,200
+conversely بتثبت أنه لو كان عندي 5of N بساوة N نقص
+
+83
+00:07:42,200 --> 00:07:48,680
+واحد هيعطيني الـ N إيه اشمالها is إبراهيم ركز الآن
+
+84
+00:07:50,290 --> 00:07:54,590
+اللي بيدثبتوا معايا ليه أنه لو كانت 5n بسواء ناقص
+
+85
+00:07:54,590 --> 00:07:58,410
+واحد يعطينا n زبرايم بيدثبتها عن طريق ايه؟
+
+86
+00:07:58,410 --> 00:08:03,810
+بيدثبتلك الـ Contraposition لها انه بيدثبتلك ان لو
+
+87
+00:08:03,810 --> 00:08:09,290
+كان n is not prime بيعطينا الـ 5n أشمالها لا تساوي
+
+88
+00:08:09,290 --> 00:08:13,730
+n ناقص واحد واضح كيف بيدثبتها؟ إذا بيدثبتها بإثبات
+
+89
+00:08:13,730 --> 00:08:22,160
+الـ Contraposition لها أنه بيدثبت أقول سببوزthat N
+
+90
+00:08:22,160 --> 00:08:27,040
+is not prime ايش معناه ان مش prime معناه تكون
+
+91
+00:08:27,040 --> 00:08:33,480
+composite ان هناك D
+
+92
+00:08:33,480 --> 00:08:43,100
+أكبر من واحد وأصغر من N and N بيساوي D في K for
+
+93
+00:08:43,100 --> 00:08:53,820
+some K element and Z مظبوط؟ طيبالـ N الـ D عبارة
+
+94
+00:08:53,820 --> 00:08:59,620
+عن عدد بين الواحد و بين مين الـ N صار العامل
+
+95
+00:08:59,620 --> 00:09:01,840
+المشترك .. و طبعا الـ D أكبر من واحد و أصغر من N
+
+96
+00:09:01,840 --> 00:09:07,360
+صار العامل المشترك الأعلى بين الـ D و بين الـ N هو
+
+97
+00:09:07,360 --> 00:09:13,830
+الـ Dلأن الـ D أشماله بيكسب 100 الـ N يعني صار
+
+98
+00:09:13,830 --> 00:09:18,110
+عندى ال greatest common divisor بين الـ N و الـ D
+
+99
+00:09:18,110 --> 00:09:23,730
+لا يساوي واحد لأنه بيساوي 100 بيساوي الـ D و الـ D
+
+100
+00:09:23,730 --> 00:09:29,770
+أشمالها أكبر من واحد الـ N أنا الـ Phi of N ضمن
+
+101
+00:09:29,770 --> 00:09:34,470
+الـ Phi of N أكيد
+
+102
+00:09:34,470 --> 00:09:43,030
+عندى مدام الـ N أكبر من واحدإذا الـ N مش Relative
+
+103
+00:09:43,030 --> 00:09:45,490
+Library مع حالها لأن الـ Logistic Indivisor بين
+
+104
+00:09:45,490 --> 00:09:48,930
+الـ N و الـ N مش بيساوي N إذا مش Relative Library
+
+105
+00:09:48,930 --> 00:09:53,550
+مع حالها إذا هذا بديش أحسبه فيفهم إيش هي عبارة عن
+
+106
+00:09:53,550 --> 00:09:58,050
+اللي أصغر أو يساوي الـ N و Relative Library مع الـ
+
+107
+00:09:58,050 --> 00:10:04,760
+N إذا الأعداد من عند واحد عند N، Nالان نقسم منين
+
+108
+00:10:04,760 --> 00:10:12,080
+الان صارت اناقص واحد والان نقسم كمان عدد منه هو ال
+
+109
+00:10:12,080 --> 00:10:14,440
+D لأن ال grade is divisible بين الان و ال D ايش
+
+110
+00:10:14,440 --> 00:10:19,340
+بيساوي لا يساوي واحد ال D بين ال واحد و الان اذا
+
+111
+00:10:19,340 --> 00:10:24,260
+صار عندي ال five ان نقسم كمان واحد اذا ال five ان
+
+112
+00:10:24,260 --> 00:10:30,990
+صار اصغر او يساوي منين اناقص اتنين كمان مرةماذا عن
+
+113
+00:10:30,990 --> 00:10:35,850
+الـ N5N؟ هي ببحث عن الأعداد الـ Relatively Prime
+
+114
+00:10:35,850 --> 00:10:39,750
+مع الـ N و أصغر أو نسائر الـ N يعني ببحث في
+
+115
+00:10:39,750 --> 00:10:45,650
+الأعداد من واحد لعند مين لعند N بدي أشوف مين ال
+
+116
+00:10:45,650 --> 00:10:52,370
+Relatively Prime مع ال N و أحسبهاأول حاجة مش هحسب
+
+117
+00:10:52,370 --> 00:10:55,790
+الـ N لإن الـ N مش الـ Relative لـ Brian مع الـ N
+
+118
+00:10:55,790 --> 00:11:00,870
+اتنين مش هحسب مين برضه الـ D لإن الـ D حلقي في
+
+119
+00:11:00,870 --> 00:11:04,550
+الطريق لما أنا أمشي من واحد لعنده إذا هشيل كمان
+
+120
+00:11:04,550 --> 00:11:09,590
+مين الـ D سيرت شاول من هدولة الـ N و الـ D على
+
+121
+00:11:09,590 --> 00:11:13,990
+الأقل إذا صار عندي الـ 5N أقصى حاجة أقصى حاجة
+
+122
+00:11:13,990 --> 00:11:20,360
+هتكون اللي هي أشمالها أصغر من مين من Nأصغر أو سوى
+
+123
+00:11:20,360 --> 00:11:27,760
+مين أن نقص اتنين وهذه ايش سمالها اكيد اكيد five أن
+
+124
+00:11:27,760 --> 00:11:34,280
+اشمالها لات سوى أن نقص واحد اذا انا اوصلت الان ان
+
+125
+00:11:34,280 --> 00:11:38,760
+لو كانت أن مش prime اذا اكيد ال five أن اشمالها
+
+126
+00:11:38,760 --> 00:11:46,490
+لات سوى أن نقص واحد اذا صارت عندي الان5n-1 تؤدي
+
+127
+00:11:46,490 --> 00:11:50,490
+الـ n الـ Zebrame إذا صار في عندي الـ n
+
+128
+00:11:50,490 --> 00:11:56,270
+equivalence ال equivalence بين ال n الـ Zebrame و
+
+129
+00:11:56,270 --> 00:12:04,330
+5n-1 أي سؤال؟ الآن أنا رايح باتجاه أوجد formula
+
+130
+00:12:04,330 --> 00:12:12,150
+للـ 5n عشان أوجد هذه ال formula للـ 5n
+
+131
+00:12:15,560 --> 00:12:21,640
+هيكون عبر الطريق التالي أن الـ N هذه اللي عندي أول
+
+132
+00:12:21,640 --> 00:12:25,580
+إيش حصلت على المعلومة أن الـ Phi of the prime أكيد
+
+133
+00:12:25,580 --> 00:12:33,000
+يشمله بساوي بـ-1 الان بدي عشان أصل للـ Phi of N
+
+134
+00:12:33,000 --> 00:12:38,080
+اللي هو ال formula إلها بدي
+
+135
+00:12:38,080 --> 00:12:47,710
+كخطوة أولى أو deadlockالان هناك نظرية موجودة لك if
+
+136
+00:12:47,710 --> 00:12:58,390
+B is a prime then phi of B أُس K بيوجد قيمتها بعد
+
+137
+00:12:58,390 --> 00:13:03,130
+وجود قيمتهاهتوصل النهاية دي بعد شوية بعد ما أخد
+
+138
+00:13:03,130 --> 00:13:08,450
+خاصية أخرى لإيجاد الـPhi of N بصورة عامة وإيجاد
+
+139
+00:13:08,450 --> 00:13:12,550
+سهل كمان طريقة إيجاد سهلة قبل شوية احنا اتغلبنا
+
+140
+00:13:12,550 --> 00:13:16,410
+لعند التسعة ووقفنا فما بالك لو بدك توجد الـPhi of
+
+141
+00:13:16,410 --> 00:13:20,330
+مليون بدك تقعد تدور من الأعداد اللي اللي تبل برايب
+
+142
+00:13:20,330 --> 00:13:25,290
+مع المليون من واحد لمليون مش عملي فالآن خليني نشوف
+
+143
+00:13:25,290 --> 00:13:31,550
+كيف نصل لإيجاد الـPhi of N in generalالان بقول if
+
+144
+00:13:31,550 --> 00:13:39,210
+P is prime then 5P K بساوي P K ناقص P K minus واحد
+
+145
+00:13:39,210 --> 00:13:44,970
+و هي نفسها P K في واحد ناقص واحد على P الفورمولة
+
+146
+00:13:44,970 --> 00:13:49,170
+هذه بعد شوية لما نحكي عن N in general هتساعدنا
+
+147
+00:13:49,170 --> 00:13:56,210
+كتير في اللي هي تسهيل إيجاب 5N الان اللي بدي أثبته
+
+148
+00:13:56,210 --> 00:14:02,880
+5P K بساويطبعا هذه متساوية هذه عارفين كيف صاحبنا
+
+149
+00:14:02,880 --> 00:14:05,420
+الـ P K عامل مشترك ضالة الواحد ناقص واحد على P
+
+150
+00:14:05,420 --> 00:14:09,540
+نيجي الآن البرنامج شوف كيف المنطق البرمجان علشان
+
+151
+00:14:09,540 --> 00:14:16,760
+ما اعتمد الان انا بدي اوجد الاعداد ال relative ال
+
+152
+00:14:16,760 --> 00:14:23,040
+prime من عند اللي هي الواحد لما اصل لمين للـ P X K
+
+153
+00:14:23,040 --> 00:14:29,070
+الاستراتيجية في الحلقة التاليةالان عدد الاعداد
+
+154
+00:14:29,070 --> 00:14:33,890
+اصلا من واحد عند بي أوس كي جداش هي بي أوس كي بدي
+
+155
+00:14:33,890 --> 00:14:39,770
+اشيل منها اللي مش relative لبراين معنيا مع ال بي
+
+156
+00:14:39,770 --> 00:14:45,900
+أوس كي بضالمياالـ Relative prime إذا صار عندي الآن
+
+157
+00:14:45,900 --> 00:14:51,320
+حصل في النهاية Phi of B أُس K بتساول B أُس K كل
+
+158
+00:14:51,320 --> 00:14:56,240
+الأعداد اللي من واحد لعند B K وبيتشيل منهمين
+
+159
+00:14:56,240 --> 00:15:03,230
+الأعداد اللي مش Relative prime مع B أُس Kهلاجيهم
+
+160
+00:15:03,230 --> 00:15:08,350
+بعد شوية ان بي أس ك ناقص واحد فبتصير في of بي ك
+
+161
+00:15:08,350 --> 00:15:13,170
+ايش بتساوي بي أس ك ناقص بي أس ك ناقص واحد واضح ايش
+
+162
+00:15:13,170 --> 00:15:18,730
+استراتيجية الحل الان في of بي أس ك ايش معناته
+
+163
+00:15:18,730 --> 00:15:23,070
+الاعداد ال relatively prime معنين مع ال بي أس ك
+
+164
+00:15:23,070 --> 00:15:29,290
+اللي اصغر او يساوي بي أس كبدا أوجدها بإن اوجد اللي
+
+165
+00:15:29,290 --> 00:15:33,670
+هو الأعداد اللي مش relative prime مع الـb أسكت
+
+166
+00:15:33,670 --> 00:15:38,290
+وانقسمها من عدد الأعداد الكل عدد الأعداد الكل بيه
+
+167
+00:15:38,290 --> 00:15:42,170
+أسكت ناقص اللي هي اللي بعد داعي إن هي شمالها اللي
+
+168
+00:15:42,170 --> 00:15:46,130
+مش relative prime تطلع اللي هي five of b أسكت اللي
+
+169
+00:15:46,130 --> 00:15:49,870
+هي relative prime مع b أسكت شوفوا في ملاحظة قبل ما
+
+170
+00:15:49,870 --> 00:15:55,260
+نشتغل لو أجيناوبحثنا لـ Greatest Common Divisor
+
+171
+00:15:55,260 --> 00:16:02,400
+بين أي عدد N أصغر أو يساوي بي أس كيه وبين الـ B أس
+
+172
+00:16:02,400 --> 00:16:07,700
+كيه بنلاقي إن العدد هذا بيساوي واحد if and only if
+
+173
+00:16:07,700 --> 00:16:17,980
+الـ B هذا لا يقصر مين إلا أن انتبه لو الـ N اللي
+
+174
+00:16:17,980 --> 00:16:23,530
+هي عوامل العدد بي أس كيه من هي1 الـ B الـ B تربيع
+
+175
+00:16:23,530 --> 00:16:30,570
+لمصير لمن؟ لـ BSK أي واحد عدد في الدنيا بيكون بينه
+
+176
+00:16:30,570 --> 00:16:35,110
+وبين هؤلاء العوامل المشتركة معناته الـ B بيكون ضغط
+
+177
+00:16:35,110 --> 00:16:39,210
+منه غير أنك بيصير العامل المشترك أيش بيساوي؟ واحد
+
+178
+00:16:39,210 --> 00:16:43,890
+إذن العامل المشترك الأعلى بين الـ N والـ BK بيساوي
+
+179
+00:16:43,890 --> 00:16:50,690
+واحد يكافئ أن الـ B مش أياش مش من عوامل الـ Nلأن
+
+180
+00:16:50,690 --> 00:16:55,490
+بكل بساطة لو الـ B بقسم الـ N أكيد هيصير الجاسكم
+
+181
+00:16:55,490 --> 00:16:58,970
+الـ divisor بين الـ N والـ B على كياش ماله مش واحد
+
+182
+00:17:01,270 --> 00:17:05,350
+واضح أه؟ لأن لو كان العامل المشترك الأعلى بين الـ
+
+183
+00:17:05,350 --> 00:17:09,910
+N و الـ B K غير الواحد يا هيكون الـ B يا الـ B
+
+184
+00:17:09,910 --> 00:17:13,970
+تربيع يا لم أصل لـ BK إذا في كل الأحوال هيكون الـ
+
+185
+00:17:13,970 --> 00:17:18,330
+B أشماله بيكسب الـ N إذا الـ N اللي بقوله إنه
+
+186
+00:17:18,330 --> 00:17:21,730
+Greatest Common Divisor بين الـ N و الـ B أس K لا
+
+187
+00:17:21,730 --> 00:17:29,740
+يساوي 1 F N دول في الـ B أشمالها غير فكرة واضح؟إذا
+
+188
+00:17:29,740 --> 00:17:36,260
+من هذا المجدر نستمتج إن الأعداد اللي مش relative
+
+189
+00:17:36,260 --> 00:17:41,220
+لـPrime مع الـPK مين هي اللي بتجسم الـN يعني بمعنى
+
+190
+00:17:41,220 --> 00:17:47,960
+أخر مضاعفات الـP ليه المضاعفات الـP من 1 لعند الـP
+
+191
+00:17:47,960 --> 00:17:57,610
+أُس K؟ الـP ليه الـP؟والتلاتة بيه فاهمين و الأربعة
+
+192
+00:17:57,610 --> 00:18:02,330
+بيه و الخمسة بيه لما حصل الأخر أحد من مبعثات ال
+
+193
+00:18:02,330 --> 00:18:10,470
+بيه مين هو بيوسكي واضح هذولة بس هم مين اللي العامل
+
+194
+00:18:10,470 --> 00:18:16,550
+المشترك الأعلى اللي بين هنا وبين ال بيكي أشماله مش
+
+195
+00:18:16,550 --> 00:18:24,310
+واحد واضح أه؟ بتدعد هنا هذول هذولة هم مين هناهي
+
+196
+00:18:24,310 --> 00:18:30,390
+عندنا بي اتنين بي تلاتة بي أربع بي خمسة بي لعند بي
+
+197
+00:18:30,390 --> 00:18:37,770
+أس كي بي أس كي اللي هو عبارة عن إيش اسمه بي أس كي
+
+198
+00:18:37,770 --> 00:18:45,330
+ماقص واحد في بي يعني الآن لو بد أعد هاي بي هاي
+
+199
+00:18:45,330 --> 00:18:49,270
+اتنين بي هاي تلاتة بي هاي أربع بي هاي خمسة بي هاي
+
+200
+00:18:49,270 --> 00:18:54,840
+ستة بي هاي بي كي ماقص واحد من البيإذاً اكم واحدة
+
+201
+00:18:54,840 --> 00:18:59,500
+هذولة و اكم بيه هذولة او اكم term اللي هو بي الـ
+
+202
+00:18:59,500 --> 00:19:07,260
+square minus واحد إذاً صار عندى الآن هذولة هماللي
+
+203
+00:19:07,260 --> 00:19:12,600
+العامل المشترك الأعلى بينه وبين الـ BK إيش ماله؟
+
+204
+00:19:12,600 --> 00:19:17,140
+مش واحد إذا صارت Phi of BK بتساوي BK العدد الكلي
+
+205
+00:19:17,140 --> 00:19:22,020
+للأعداد من واحد لعند الـ BK ناقص الأعداد اللي مش
+
+206
+00:19:22,020 --> 00:19:25,320
+relative لـ Brian اللي هي BK minus واحد فصارت Phi
+
+207
+00:19:25,320 --> 00:19:31,300
+of BK إيش بتساوي BK ناقص BK minus واحد أي سؤال؟
+
+208
+00:19:31,300 --> 00:19:39,600
+بناء على ذلك بسير عملية الإيجادالآن أسهل لو جبنا
+
+209
+00:19:39,600 --> 00:19:52,260
+نوجد Phi of اللي هو 32 مثلا أو 64 بالطريقة
+
+210
+00:19:52,260 --> 00:19:58,160
+السابقة بتغلب الآن هنا بقولك على طول اللي هو 64
+
+211
+00:19:59,660 --> 00:20:03,020
+أربعة و ستين مضروبة في واحد لأن أربعة و ستين مين
+
+212
+00:20:03,020 --> 00:20:07,940
+هي؟ اتنين أس سبعة اظنين اتنين أس خمس اتنين و
+
+213
+00:20:07,940 --> 00:20:11,920
+تلاتين اتنين أس ستة اربعة أس اتنين أس ستة، مظبوط؟
+
+214
+00:20:11,920 --> 00:20:18,180
+اذا هذه عبارة عن five of اتنين أس ستة يعني اطمأنت
+
+215
+00:20:18,180 --> 00:20:24,240
+انها إيه شمالها؟ power of two بيصير عبارة عن اتنين
+
+216
+00:20:24,240 --> 00:20:27,860
+أس ستة اللي هي اربعة و ستين مضروبة في واحد ماقص
+
+217
+00:20:27,860 --> 00:20:34,170
+واحد على اتنينصح؟ سهل هيك هيك سهل ويساوي عبارة عن
+
+218
+00:20:34,170 --> 00:20:40,490
+اتنين وتلاتين وكذا five of مثلا تلاتة اص مليون
+
+219
+00:20:40,490 --> 00:20:47,350
+ويساوي
+
+220
+00:20:47,350 --> 00:20:57,610
+تلاتة اص مليون في واحد ماقص تلت يعني بيصير تلتين
+
+221
+00:20:57,610 --> 00:20:59,390
+في هذا
+
+222
+00:21:02,390 --> 00:21:11,990
+واضحة؟ أي سؤال؟ عشان نعرف جداش اللي هو الـ Issue
+
+223
+00:21:11,990 --> 00:21:21,010
+النظري مهم ويسهل علينا عملية التقامل مع Issue الـ
+
+224
+00:21:21,010 --> 00:21:25,390
+Issue التطبيقى يعني الآن أخدت هذه اللي هي النظرية
+
+225
+00:21:25,390 --> 00:21:30,680
+وبرهنتهاسهلت عليها عملية الإيجاد لأي عدد كبير في
+
+226
+00:21:30,680 --> 00:21:39,500
+الدنيا من كام دوسان؟ هذا
+
+227
+00:21:39,500 --> 00:21:42,940
+الـ
+
+228
+00:21:42,940 --> 00:21:43,200
+prime
+
+229
+00:21:48,150 --> 00:21:53,010
+طيب نجي الآن في لمّة لمّة هي كأنت عشان النظرية
+
+230
+00:21:53,010 --> 00:21:56,570
+اللي هي لإثبات النظرية بس احنا مش هنتبت النظرية
+
+231
+00:21:56,570 --> 00:22:01,790
+لكن اللمّة عبارة عن exercise بسيط يعني لو ممكن
+
+232
+00:22:01,790 --> 00:22:05,390
+يكون مرض بالهيك خلّينا نبارح انه كأنه exercise
+
+233
+00:22:05,390 --> 00:22:12,650
+يعني هاللمّة لمّة ايش اللمّة بتقول انه اللمّةعندي
+
+234
+00:22:12,650 --> 00:22:15,770
+الـ greatest common divisor بين الـ A و الـ B و
+
+235
+00:22:15,770 --> 00:22:20,730
+الـ C بساوية 1 if and only if الـ greatest common
+
+236
+00:22:20,730 --> 00:22:25,130
+divisor بين الـ A و الـ B بساوية الـ greatest
+
+237
+00:22:25,130 --> 00:22:30,610
+common divisor بين الـ A و الـ C بساوية 1 والـ
+
+238
+00:22:30,610 --> 00:22:38,670
+proof يعني إكسرسيز عادي نعتبره سهل الـ proof بدا
+
+239
+00:22:38,670 --> 00:22:40,470
+أقول سبّوز
+
+240
+00:22:43,780 --> 00:22:47,660
+that الـ greatest common divisor بين الـ A والـ B
+
+241
+00:22:47,660 --> 00:22:55,840
+والـ C بيساوي واحد بيثبت لك أن العامل المشترك
+
+242
+00:22:55,840 --> 00:22:58,260
+الأعلى بين هذه و هذه واحد و بين هذه و هذه واحد
+
+243
+00:22:58,260 --> 00:23:03,400
+بيثبت واحد ده والتاني زيها نقول let ال greatest
+
+244
+00:23:03,400 --> 00:23:09,760
+common divisor بين الـ A والـ C بيساوي D بيثبت لك
+
+245
+00:23:09,760 --> 00:23:14,240
+الـ D أش بتساوي واحدبما أنه الجلسكم هو الـdivisor
+
+246
+00:23:14,240 --> 00:23:21,500
+بين الـA والـC وساوية وD، فD بيقسم الـA وD بيقسم
+
+247
+00:23:21,500 --> 00:23:27,720
+الـC. طيب، مادام الـD بيقسم الـC، إذا أكيد and so
+
+248
+00:23:27,720 --> 00:23:34,860
+D بيقسم الـA وD بيقسم الـB
+
+249
+00:23:34,860 --> 00:23:35,660
+في الـC.
+
+250
+00:23:38,480 --> 00:23:42,840
+أذا مادامي بتقسمها بتقسم هذا و بتقسم هذا إذا بتقسم
+
+251
+00:23:42,840 --> 00:23:47,740
+العامل المشترك اللي علي بينهم إذا hence خدنا هذا
+
+252
+00:23:47,740 --> 00:23:51,680
+برضه D بتقسم ال grades from the divisor بين ال A و
+
+253
+00:23:51,680 --> 00:23:56,260
+ال B و ال C و يساوي إيه إيش؟ واحد ماعطينا إيه
+
+254
+00:23:56,260 --> 00:24:03,440
+واحد؟ إذا D بتقسم الواحد إذا اشملها hence D بتساوي
+
+255
+00:24:03,440 --> 00:24:08,030
+واحد similarlyالـ Greatest Common Divisor بين الـ
+
+256
+00:24:08,030 --> 00:24:14,010
+A و الـ B برضه إيش هيساوي؟ واحد، بنفس الطريقة،
+
+257
+00:24:14,010 --> 00:24:20,670
+واضح؟ الان conversely .. conversely .. conversely
+
+258
+00:24:20,670 --> 00:24:24,930
+suppose
+
+259
+00:24:24,930 --> 00:24:28,410
+that
+
+260
+00:24:28,410 --> 00:24:35,700
+ال Greatest Common Divisorبين الـ A والـ B بيساوي
+
+261
+00:24:35,700 --> 00:24:38,860
+الـ Greatest Common Divisor بين الـ A والـ C
+
+262
+00:24:38,860 --> 00:24:44,200
+بيساوي 1 وبدأ أثبت مين أن العامل المشترك الأعلى
+
+263
+00:24:44,200 --> 00:24:48,980
+بين الـ A والـ B وC أيش بيساوي 1 شوف كيف عامل لما
+
+264
+00:24:48,980 --> 00:24:51,780
+دام العامل المشترك الأعلى بيساوي 1 إذا بقدر ألاقي
+
+265
+00:24:51,780 --> 00:24:58,700
+XY there exists XY element in Z بحيث أن AX زاوية
+
+266
+00:24:58,700 --> 00:25:02,950
+BY بيساوي 1وما دام العام المشترك اللي على بين الـ
+
+267
+00:25:02,950 --> 00:25:06,070
+a و الـ c بساوة واحد and then there exists z و w
+
+268
+00:25:06,070 --> 00:25:13,850
+برضه element in z بحيث اللي هو a z زاد cw بساوة
+
+269
+00:25:13,850 --> 00:25:20,150
+واحد اضرب لها دول فبعض بيصير عندي اذا hence دي ax
+
+270
+00:25:20,150 --> 00:25:29,690
+فيها دي في a z زاد ax في cw زاد هذه فيها دول by a
+
+271
+00:25:29,690 --> 00:25:36,200
+zزائد BYCW كله إيش هيساوي؟ لأن واحد في واحد في
+
+272
+00:25:36,200 --> 00:25:40,400
+واحد خد اللي إن هدول مع بعض خد ال A عملوا اشتراك
+
+273
+00:25:40,400 --> 00:25:51,220
+بيصير A في AXZ زائد XCW زائد BYZ زائد B في C خدها
+
+274
+00:25:51,220 --> 00:25:59,000
+برا مضروبة في YW إيش ميساوي؟ واحدوكأنه سعر هذا كله
+
+275
+00:25:59,000 --> 00:26:04,180
+عبارة عن انتجر اسمه M و هذا انتجر اسمه N فبيصير
+
+276
+00:26:04,180 --> 00:26:11,760
+عند A M زائد B C فن بساوية واحدة إذا العام المشترك
+
+277
+00:26:11,760 --> 00:26:16,720
+اللي على بين ال A و ال B C أشوى ساوية واحدة hence
+
+278
+00:26:16,720 --> 00:26:20,780
+واضح ها hence ال grades from the divisors نظرية
+
+279
+00:26:20,780 --> 00:26:25,600
+سابقة A و B C بساوية واحدة وهو المطلوب
+
+280
+00:26:29,400 --> 00:26:32,640
+العنوان المعلومة اللي هأخدها ناشر برهيلها الـ
+
+281
+00:26:32,640 --> 00:26:36,670
+function فيThe function Phi is a multiplicative
+
+282
+00:26:36,670 --> 00:26:40,910
+function البرمجة ليست صحيحة موجودة في الكتاب يمكن
+
+283
+00:26:40,910 --> 00:26:44,570
+المغضب اغطنا شوية The function Phi اسمها is a
+
+284
+00:26:44,570 --> 00:26:48,450
+multiplicative function Phi is a multiplicative
+
+285
+00:26:48,450 --> 00:26:51,750
+function ايش معناه Phi multiplicative يعني لو كانت
+
+286
+00:26:51,750 --> 00:26:54,250
+الجريس كمين divisor بين الـM والـN بيساوي واحد
+
+287
+00:26:54,250 --> 00:26:58,970
+هيكون Phi of M في N بيساوي Phi of M في Phi of N
+
+288
+00:26:58,970 --> 00:27:05,380
+اطلع لفوق نيدي الـNبدنا نوجد اللي هو الـ 5N in
+
+289
+00:27:05,380 --> 00:27:11,520
+general طبعا أي N التجار أكبر من واحد يا جماعة can
+
+290
+00:27:11,520 --> 00:27:17,640
+be written as economical four يعني product of
+
+291
+00:27:17,640 --> 00:27:27,540
+power over primes مظبوط؟ يعني بمعنى آخر theorem if
+
+292
+00:27:29,140 --> 00:27:37,600
+ن بيتساوي بي واحد كي واحد لعند بي ار كي ار then اه
+
+293
+00:27:37,600 --> 00:27:40,780
+where بي واحد بي اتنين بي ار are distinct primes
+
+294
+00:27:40,780 --> 00:27:46,840
+او n is written as a canonical form then phi of n
+
+295
+00:27:46,840 --> 00:27:55,490
+ايش هتساوي؟أحنا قلنا عنها إيش مالها Multiplicative
+
+296
+00:27:55,490 --> 00:27:58,570
+إذا في الأول في في التاني في في التالت في في الأخر
+
+297
+00:27:58,570 --> 00:28:02,230
+في الأول وجدناه في التاني وجدناه وجدناه هو five
+
+298
+00:28:02,230 --> 00:28:06,790
+bar of brine صح؟ اللي هو عبارة عن الأول بي واحد
+
+299
+00:28:06,790 --> 00:28:14,250
+كواحد ناقص بي واحد كواحد minus واحد لما أصل عند br
+
+300
+00:28:14,250 --> 00:28:24,010
+kr ناقص br kr ناقص واحدو يساوي معايا يا شباب اه و
+
+301
+00:28:24,010 --> 00:28:27,430
+يساوي اللي هو الصورة اللي احنا بدنا نسهّل على
+
+302
+00:28:27,430 --> 00:28:33,650
+حالنا بناخد الـB1 K1 و الـB2 K2 عند الـB R K R كل
+
+303
+00:28:33,650 --> 00:28:39,610
+مع بعض ضرب من مين هيكون الـN إذا هيساوي N في واحد
+
+304
+00:28:39,610 --> 00:28:46,750
+ناقص B واحد على B واحد لما أصل لأخر واحد ناقص واحد
+
+305
+00:28:46,750 --> 00:28:54,360
+على Bإذا العملية صارت سهل عملية الحساب أن 5N
+
+306
+00:28:54,360 --> 00:29:01,340
+بتساوي N في واحد ناقص الو مين او product واحد ناقص
+
+307
+00:29:01,340 --> 00:29:05,920
+بي واحد على بي I I من واحد لعند مين لعند Rيعني بس
+
+308
+00:29:05,920 --> 00:29:10,400
+بتجيب اللي هو الـ prime factorization لها بيصير
+
+309
+00:29:10,400 --> 00:29:13,220
+الـ Phi لها بسوء 1000 في الواحد ناقص واحد على الـ
+
+310
+00:29:13,220 --> 00:29:16,180
+prime الأول في واحد ناقص واحد على الاتاني لما أصل
+
+311
+00:29:16,180 --> 00:29:19,260
+واحد على ناقص واحد على الـ prime الأخر وضربهم في
+
+312
+00:29:19,260 --> 00:29:23,740
+بعض بتطلع الدمين الـ 5000 واضح نيجي للبرهان
+
+313
+00:29:23,740 --> 00:29:27,280
+البرهان زي ما قلت لها بس خلنا نكتبه by اياش by
+
+314
+00:29:27,280 --> 00:29:36,480
+induction by induction on mean on Rby induction on
+
+315
+00:29:36,480 --> 00:29:40,660
+main on R for R بتساوي واحد اللي هي main النظرية
+
+316
+00:29:40,660 --> 00:29:48,040
+اه لأن for R بتساوي واحد N بتساوي بي واحد أس كي
+
+317
+00:29:48,040 --> 00:29:55,180
+واحد then by اللي هو ال theorem اللي قبل بشوية Phi
+
+318
+00:29:55,180 --> 00:29:59,200
+of N اللي هي بتساوي Phi of بي واحد أس كي واحد
+
+319
+00:29:59,200 --> 00:30:04,120
+بساوي بي واحد أس كي واحد ناقص بي واحد أس كي واحد
+
+320
+00:30:04,120 --> 00:30:13,090
+ناقصواحد إذا صارت اللي هي إيه شمالها عندي هذه is
+
+321
+00:30:13,090 --> 00:30:20,430
+true لو سميناها الـ star إذا hence star is true
+
+322
+00:30:20,430 --> 00:30:26,730
+for R بتساوي واحد إلى أن نفترض إنها true for R
+
+323
+00:30:26,730 --> 00:30:31,290
+بتساوي I ونصل إلي إنها true for I زاد واحد إلى أن
+
+324
+00:30:31,290 --> 00:30:33,570
+suppose suppose
+
+325
+00:30:35,340 --> 00:30:43,160
+that star is true for R بتساوي I then مدام true
+
+326
+00:30:43,160 --> 00:30:52,620
+for R بتساوي I إذا صار عندي Phi of P1 K1 لعند PIKI
+
+327
+00:30:52,620 --> 00:31:02,640
+بساوي اللي هو عبارة عن P1 أو ال product ل P A P K
+
+328
+00:31:02,640 --> 00:31:21,510
+P SKS-B S KS-1 S من عند 1 لعند I ثمين الأهمية
+
+329
+00:31:21,510 --> 00:31:25,130
+اللي بتبيتها الأقل جمالها بتساوي I زائد 1 then
+
+330
+00:31:25,130 --> 00:31:36,450
+thenPhi of B1K1 لعند BIKI في BI زائد واحد KI زائد
+
+331
+00:31:36,450 --> 00:31:41,230
+واحد بيساوي هدول distinct برعام كلهم ده اللي
+
+332
+00:31:41,230 --> 00:31:43,030
+جالسكم من ال divisor بيقول الأول و الثاني ايش
+
+333
+00:31:43,030 --> 00:31:46,790
+بيساوي ال Phi multiplicative of Phi الأول في Phi
+
+334
+00:31:46,790 --> 00:31:54,270
+الثاني بيساويو بي واحد كواحد لعند بي اي كي اي في
+
+335
+00:31:54,270 --> 00:32:00,970
+في اثنين او بي اي زائد واحد كي اي زائد واحد و
+
+336
+00:32:00,970 --> 00:32:05,590
+يساوي هذه من الوثوث ال induction هذه اللي هي عبارة
+
+337
+00:32:05,590 --> 00:32:14,260
+عن ال productللـ BS KS ناقص BS KS ناقص واحد S من
+
+338
+00:32:14,260 --> 00:32:19,100
+عند واحد لعند I مضروب نفسه في هذه الـ file اللي
+
+339
+00:32:19,100 --> 00:32:27,340
+عبارة عن BI زائد واحد KI زائد واحد ناقص BI زائد
+
+340
+00:32:27,340 --> 00:32:33,820
+واحد KI زائد واحد ناقص واحد ويساويأبدا عن ال
+
+341
+00:32:33,820 --> 00:32:38,720
+product نفسه من S بتساوي واحد ل I زاد واحد إذا صار
+
+342
+00:32:38,720 --> 00:32:46,160
+true for I زاد واحد hence it is true for any R إذا
+
+343
+00:32:46,160 --> 00:32:51,140
+صار عندي الآن من الآن وطالع الإعلان هذا صحيح Phi
+
+344
+00:32:51,140 --> 00:32:57,600
+of N بتساوي اللي هو المقدار اللي أمامنا أي سؤال؟
+
+345
+00:33:02,320 --> 00:33:06,780
+طيب صلوا عنا بالله الصلاة والسلام ناخد مثال five
+
+346
+00:33:06,780 --> 00:33:12,400
+تلت مية وستين أي مثال الآن أو أي عدد سهل أنه نوجده
+
+347
+00:33:12,400 --> 00:33:17,960
+بس بنسوي انه من فاكفكو إلى الprimes تبعاته بنكتبه
+
+348
+00:33:17,960 --> 00:33:24,610
+على صورة product of bar of primes chemical formولو
+
+349
+00:33:24,610 --> 00:33:27,830
+لم تكتبوا في اللغة الـ Canonical لأنهم كتبوا على
+
+350
+00:33:27,830 --> 00:33:30,790
+صورة Distinct Primes بنفع بس الـ Canonical لغة
+
+351
+00:33:30,790 --> 00:33:36,130
+مشتركة و ألطف وبتساعد في حاجات كتير لأن Phi of 360
+
+352
+00:33:36,130 --> 00:33:42,510
+بساوي Phi of أكم اتنين فيها اتنين اقصى ثلاثة أكم
+
+353
+00:33:42,510 --> 00:33:49,980
+تلاتة فيها تلتينلأنها بـ 9×4 بـ 36 و 5×2 الـ 2 مع
+
+354
+00:33:49,980 --> 00:33:54,640
+الـ 2 الأولانيات بيصير الـ 3 والـ 32 هي الـ 3 والـ
+
+355
+00:33:54,640 --> 00:34:01,720
+5 هي 5 بيساوي عبارة عن N اللي هو 360 بعد ان نحسب
+
+356
+00:34:01,720 --> 00:34:08,780
+كل واحدة لحالها 360 فيه واحد ناقص نص في واحد ناقص
+
+357
+00:34:08,780 --> 00:34:18,290
+تلتفي واحد ماقصهاش خمس بطلع عندك 96 زي ما هو حسبة
+
+358
+00:34:18,290 --> 00:34:26,010
+بسيطة يعني أي سؤال طيب نيجي الآن للمظهرية الأخيرة
+
+359
+00:34:26,010 --> 00:34:32,490
+اللي وعدناكم انه احنا نثبت لكم انه الملاحظة اللي
+
+360
+00:34:32,490 --> 00:34:36,410
+لاحظناها في الأول حسبنا five of واحد واحد five of
+
+361
+00:34:36,410 --> 00:34:41,110
+اتنين واحديعني اقول بعد five of اتنين حسبنا كل
+
+362
+00:34:41,110 --> 00:34:44,850
+اللي حسبناه طلع ايه شماله even five تلاته، five
+
+363
+00:34:44,850 --> 00:34:47,570
+اربعه، five خمسه، five ستة، five كده و هاي five
+
+364
+00:34:47,570 --> 00:34:52,550
+تلاته ستين طلع ايه شماله even هذا مش مصادفة لأي n
+
+365
+00:34:52,550 --> 00:34:58,700
+أكبر من اتنين هتطلع ال five is an even functionis
+
+366
+00:34:58,700 --> 00:35:02,720
+an even .. ال .. ال .. the value of phi is even اه
+
+367
+00:35:02,720 --> 00:35:05,400
+مش even function the value .. the value of phi ايش
+
+368
+00:35:05,400 --> 00:35:11,520
+مالها is even دايما ايش قيمتها عدد زودي واضح اللي
+
+369
+00:35:11,520 --> 00:35:17,860
+بحكيه مش even function عدد زودي قيمة او اللي هو ال
+
+370
+00:35:17,860 --> 00:35:23,840
+image يعني و كأن وين موجود فت name it positive
+
+371
+00:35:26,160 --> 00:35:33,740
+صلى على النبي عليه الصلاة والسلام الآن theorem for
+
+372
+00:35:33,740 --> 00:35:48,080
+N أكبر من 2 Phi of N is an even انتجار proof
+
+373
+00:35:55,240 --> 00:36:01,100
+الـ N بيدثبتلك أن 5N is an even integer بدي أفصل
+
+374
+00:36:01,100 --> 00:36:05,220
+أبدي الـ N الـ N طبعا من وين جاي من Z أو من Z
+
+375
+00:36:05,220 --> 00:36:08,820
+positive بدي أجسم لك Z positive لتسهيل الحسابات
+
+376
+00:36:08,820 --> 00:36:14,620
+كالتالي أي N عدد في الدنيا يا إما هيكون على صورة
+
+377
+00:36:14,620 --> 00:36:20,260
+power of 2 أو مش power of 2 إيش يعني power of 2
+
+378
+00:36:20,260 --> 00:36:27,260
+يعني 2 نقص K بسوالـ K طبعا أكبر أو يساوي 2 لأن
+
+379
+00:36:27,260 --> 00:36:30,660
+احنا مستثنيين منين عندنا في نظريتنا الواحد
+
+380
+00:36:30,660 --> 00:36:35,500
+والاتنين يعني اتنين نقص واحد مستثناء اذا الان عندي
+
+381
+00:36:35,500 --> 00:36:41,780
+caseين ال case الأول case one او عندي two cases ال
+
+382
+00:36:41,780 --> 00:36:46,520
+case الأول case واحد اللي هو N بتساوي two to the K
+
+383
+00:36:46,520 --> 00:36:53,880
+for some K أكبر أو يساوي ايش يا جماعة اتنينالـ
+
+384
+00:36:53,880 --> 00:36:59,580
+case التاني الـ case التاني اللي هو N is not a
+
+385
+00:36:59,580 --> 00:37:06,380
+power of two يعني بمعنى أخر N فيها factor غير
+
+386
+00:37:06,380 --> 00:37:11,380
+التنين ماشي الحال ال factor اللي غير التنين أكيد
+
+387
+00:37:11,380 --> 00:37:18,600
+ماله قد برايم إذا عندي ال N الصورة التانية عبارة
+
+388
+00:37:18,600 --> 00:37:27,680
+عن برايمبرايل odd of k مضروب في مين في some انتجر
+
+389
+00:37:27,680 --> 00:37:32,680
+ام ايش هو مش عارف بلزمنيه بلمنيش الان اي عدد في
+
+390
+00:37:32,680 --> 00:37:37,540
+الدنيا يا هيكون على صورة two of اتنين k او مش على
+
+391
+00:37:37,540 --> 00:37:44,040
+صورة اتنين of k يعني ايش في يعني في كمان عدد odd
+
+392
+00:37:44,040 --> 00:37:50,390
+موجود في داخل مين ام شيلت ال odd برايل بيهمن كل
+
+393
+00:37:50,390 --> 00:37:54,470
+الـ L و حطيته لحاله و كترته بـ B² ده المتبقى ده
+
+394
+00:37:54,470 --> 00:37:57,970
+المتبقى ده بإيش يكون مش عارف ممكن يكون واحد ممكن
+
+395
+00:37:57,970 --> 00:38:01,310
+يكون اتنين ممكن يكون اتنين في خمسة ممكن تكون اتنين
+
+396
+00:38:01,310 --> 00:38:08,270
+في تلاتة بس شمت كل meaning كل الـ B اللي بحكي عنه
+
+397
+00:38:08,270 --> 00:38:14,720
+واضح؟ إذا صار عندى الآنإذا الـ thing هذا اللي هي
+
+398
+00:38:14,720 --> 00:38:19,220
+التجزية اللي ده جيه سهل إحسابات أي سؤال بالنسبة
+
+399
+00:38:19,220 --> 00:38:26,100
+للتجزية طيب نيجي نحسب هذا بيصير 5N بيساوي 5 of 2
+
+400
+00:38:26,100 --> 00:38:34,680
+أس K اللي عبارة عن 2 أس K ناقص 2 أس K minus 1 خد 2
+
+401
+00:38:34,680 --> 00:38:40,740
+أس K minus 1 عامل مشترك بيصير 2اللي هي عبارة عن
+
+402
+00:38:40,740 --> 00:38:50,360
+اتنين نقص واحد صح ولا لأ؟ ايش؟ وهذا ماله الـ K-
+
+403
+00:38:50,360 --> 00:38:55,580
+واحد اتنين او طالع يعني الـ K- واحد بيصير واحد او
+
+404
+00:38:55,580 --> 00:39:00,000
+طالع يعني هذا اتنين او اربع او تمانية او الاخر
+
+405
+00:39:00,000 --> 00:39:07,320
+فاهمين؟ لأن هذا even لأن الـ K أكبر أو يسوى اتنين
+
+406
+00:39:10,300 --> 00:39:16,500
+أي سؤال الـ N التاني فلا مافيش مشكلة Phi of M أيش
+
+407
+00:39:16,500 --> 00:39:21,200
+بيساوي أنا كل من في الـ B اللي في الـ M من الـ B
+
+408
+00:39:21,200 --> 00:39:24,520
+في الـ N إذا صار هذا الـ B أس K و الـ M إيش معناه
+
+409
+00:39:24,520 --> 00:39:28,960
+لإن ال relative لمراهب إذا Phi of M إيش صار Phi of
+
+410
+00:39:28,960 --> 00:39:36,360
+B أس K في Phi of M و يساوي5POSK مين هو عبارة عن
+
+411
+00:39:36,360 --> 00:39:44,640
+POSK ناقص POSK minus واحد مضروب في مين في 5M أي إن
+
+412
+00:39:44,640 --> 00:39:49,540
+كانت قيمته ماليش علاقة فيه ماهيش الحالة الان هذا
+
+413
+00:39:49,540 --> 00:39:56,780
+ايش هو POSK POSK minus واحد هذا قد و هذا قد صح قد
+
+414
+00:39:56,780 --> 00:40:04,540
+ناقص قدeven مش odd odd لاقص odd even بتاكيها بصورة
+
+415
+00:40:04,540 --> 00:40:11,640
+أوضح بي أس كمانس واحد في بي ماقص واحد في five M
+
+416
+00:40:11,640 --> 00:40:17,860
+هذا اللي في النص even لإن بي زاد بي ماينس واحد ايش
+
+417
+00:40:17,860 --> 00:40:24,180
+ماله even even مضروب في أي إشي هيطلع ايه ايش even
+
+418
+00:40:25,170 --> 00:40:30,670
+أذن .. أذن صارت عندي الإعلان الأخير أن فاي of أن
+
+419
+00:40:30,670 --> 00:40:36,750
+is an even integer أذن الواضح أنه احنا امشينا
+
+420
+00:40:36,750 --> 00:40:46,220
+بطريق أنه عشان نجد قيمةالـ Phi of N عشان نودد قيمة
+
+421
+00:40:46,220 --> 00:40:50,620
+الـ Phi of N أول خطوة بسويها بكتب الـ N على صورة
+
+422
+00:40:50,620 --> 00:40:57,380
+الـ canonical form P1K1 لعند PRKR بعد ما اكتبها
+
+423
+00:40:57,380 --> 00:40:59,640
+على صورة ال canonical form اللي احنا كلنا بنعرف
+
+424
+00:40:59,640 --> 00:41:05,680
+نكتبها بيصير عند إيجاد ال Phi of N سهل ويساوي الـ
+
+425
+00:41:05,680 --> 00:41:13,770
+N في 1 ماقص 1 على P1لما أصل عند واحد ناقص واحد على
+
+426
+00:41:13,770 --> 00:41:21,110
+PR و بكون هيك أعرفنا نوجد مين الـPhi of N و درسنا
+
+427
+00:41:21,110 --> 00:41:25,550
+خلاص الـPhi of N اطلع للبعد ده عشان نشوف وين وصلنا
+
+428
+00:41:25,550 --> 00:41:30,470
+المرة الدا ان شاء الله هنحكي على Ehlers theorem
+
+429
+00:41:30,470 --> 00:41:37,050
+اللي هو ال generalization of Fermat's theorem او
+
+430
+00:41:37,050 --> 00:41:40,330
+Fermat's little theorem الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/b-NRQp9gqPI_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/b-NRQp9gqPI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c209bc2e56bd64c40e5fcdeca81f78e46012c7d2
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/b-NRQp9gqPI_raw.json
@@ -0,0 +1 @@
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فيها محمد معايا إيجي واحد قاللي أن R .. أن R1 وR2 عند RS قاللي أن هذا عبارة عن Complete Residue System Modulo M", "tokens": [9566, 1829, 3555, 8717, 1829, 7435, 1829, 6024, 48506, 4386, 8717, 1829, 7435, 1829, 6024, 48506, 4386, 8717, 1863, 19913, 2288, 4724, 11622, 995, 2407, 10632, 5551, 34740, 7578, 45164, 11933, 1829, 7435, 1829, 36764, 24401, 4032, 50239, 20292, 14739, 2655, 4724, 4587, 6027, 8978, 11296, 3714, 35571, 3215, 20449, 995, 25528, 11933, 1829, 7435, 1829, 36764, 24401, 50239, 20292, 14739, 497, 4386, 14739, 497, 16, 4032, 49, 17, 43242, 25855, 50239, 20292, 14739, 23758, 6225, 3555, 9640, 3660, 18871, 34687, 5015, 327, 622, 8910, 6583, 13455, 376], "avg_logprob": -0.22208567415730338, "compression_ratio": 1.5945945945945945, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2202.68, "end": 2203.48, "word": "طيب", "probability": 0.8662109375}, {"start": 2203.48, "end": 2204.28, "word": " نيجي", "probability": 0.7806396484375}, {"start": 2204.28, "end": 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هذا الـ Complete الـ R1 و الـ R2 و الـ RS هما عددهم M يعني بدأ أثبت أن الـ S إيش بتساوي؟ بتساوي M الآن خُد اللي هو الـ Complete Residue هذا System وخُد لي أي R", "tokens": [3555, 3215, 10721, 5551, 12984, 3555, 2655, 5296, 24793, 4724, 3215, 10721, 5551, 12984, 3555, 2655, 5296, 24793, 14739, 23758, 2423, 39184, 34687, 2423, 39184, 497, 16, 4032, 2423, 39184, 497, 17, 4032, 2423, 39184, 25855, 8032, 15042, 6225, 3215, 3215, 16095, 376, 37495, 22653, 4724, 3215, 10721, 5551, 12984, 3555, 2655, 14739, 2423, 39184, 318, 11933, 1829, 8592, 39894, 3794, 995, 45865, 22807, 39894, 3794, 995, 45865, 376, 6024, 48506, 16490, 10859, 3215, 13672, 1829, 31439, 2423, 39184, 34687, 5015, 327, 622, 23758, 8910, 4032, 9778, 10859, 3215, 32239, 36632, 497], "avg_logprob": -0.316028223242811, "compression_ratio": 1.719298245614035, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2430.17, "end": 2430.65, "word": "بدأ", "probability": 0.3816731770833333}, {"start": 2430.65, "end": 2431.03, 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0.56890869140625}, {"start": 2658.06, "end": 2658.96, "word": " لو", "probability": 0.74755859375}, {"start": 2658.96, "end": 2660.06, "word": " كان", "probability": 0.9423828125}, {"start": 2660.06, "end": 2660.38, "word": " عند", "probability": 0.6708984375}, {"start": 2660.38, "end": 2660.92, "word": " الآن", "probability": 0.53790283203125}, {"start": 2660.92, "end": 2662.8, "word": " R", "probability": 0.71630859375}, {"start": 2662.8, "end": 2663.42, "word": " واحد", "probability": 0.6612548828125}, {"start": 2663.42, "end": 2663.78, "word": " عند", "probability": 0.86572265625}, {"start": 2663.78, "end": 2664.22, "word": " الـ", "probability": 0.8154296875}, {"start": 2664.22, "end": 2664.72, "word": " RM", "probability": 0.31103515625}, {"start": 2664.72, "end": 2665.5, "word": " يعني", "probability": 0.869384765625}, {"start": 2665.5, "end": 2666.04, "word": " M", "probability": 0.89208984375}, {"start": 2666.04, "end": 2666.42, "word": " من", "probability": 0.99560546875}, {"start": 2666.42, "end": 2667.3, "word": " العناصر", "probability": 0.93017578125}, {"start": 2667.3, "end": 2668.66, "word": " بحكي", "probability": 0.908447265625}, {"start": 2668.66, "end": 2668.84, "word": " M", "probability": 0.9375}, {"start": 2668.84, "end": 2669.0, "word": " من", "probability": 0.99560546875}, {"start": 2669.0, "end": 2669.7, "word": " العناصر", "probability": 0.9822998046875}, {"start": 2669.7, "end": 2670.6, "word": " وكان", "probability": 0.91162109375}, {"start": 2670.6, "end": 2671.0, "word": " في", "probability": 0.92724609375}, {"start": 2671.0, "end": 2671.42, "word": " عندي", "probability": 0.7081298828125}, {"start": 2671.42, "end": 2671.96, "word": " لكل", "probability": 0.979736328125}, {"start": 2671.96, "end": 2672.54, "word": " element", "probability": 0.7451171875}, {"start": 2672.54, "end": 2672.92, "word": " in", "probability": 0.89306640625}, {"start": 2672.92, "end": 2673.22, "word": " Z", "probability": 0.990234375}], "temperature": 1.0}, {"id": 105, "seek": 268957, "start": 2674.21, "end": 2689.57, "text": "بنجيل واحد هنا وحيد بمثله اذا برضه بيعمل complete residue system لإنه هيطلع مباشرة كل هدوء الأشمالين are incongruent", "tokens": [3555, 1863, 7435, 1829, 1211, 36764, 24401, 34105, 4032, 5016, 25708, 4724, 2304, 12984, 43761, 1975, 15730, 4724, 43042, 3224, 4724, 1829, 25957, 1211, 3566, 34799, 1185, 5296, 28814, 1863, 3224, 39896, 9566, 1211, 3615, 3714, 3555, 33599, 25720, 28242, 8032, 3215, 2407, 38207, 16247, 8592, 2304, 6027, 9957, 366, 834, 556, 894, 317], "avg_logprob": -0.3738636439496821, "compression_ratio": 1.217687074829932, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2674.21, "end": 2674.89, "word": "بنجيل", "probability": 0.4445556640625}, {"start": 2674.89, "end": 2675.45, "word": " واحد", "probability": 0.92626953125}, {"start": 2675.45, "end": 2675.97, "word": " هنا", "probability": 0.83056640625}, {"start": 2675.97, "end": 2677.07, "word": " وحيد", "probability": 0.8391927083333334}, {"start": 2677.07, "end": 2677.77, "word": " بمثله", "probability": 0.9560546875}, {"start": 2677.77, "end": 2681.13, "word": " اذا", "probability": 0.200653076171875}, {"start": 2681.13, "end": 2681.49, "word": " برضه", "probability": 0.83349609375}, {"start": 2681.49, "end": 2681.87, "word": " بيعمل", "probability": 0.918212890625}, {"start": 2681.87, "end": 2682.67, "word": " complete", "probability": 0.5771484375}, {"start": 2682.67, "end": 2683.05, "word": " residue", "probability": 0.281982421875}, {"start": 2683.05, "end": 2683.65, "word": " system", "probability": 0.943359375}, {"start": 2683.65, "end": 2684.51, "word": " لإنه", "probability": 0.77716064453125}, {"start": 2684.51, "end": 2685.01, "word": " هيطلع", "probability": 0.8861083984375}, {"start": 2685.01, "end": 2685.57, "word": " مباشرة", "probability": 0.95458984375}, {"start": 2685.57, "end": 2685.81, "word": " كل", "probability": 0.9189453125}, {"start": 2685.81, "end": 2686.07, "word": " هدوء", "probability": 0.47735595703125}, {"start": 2686.07, "end": 2686.93, "word": " الأشمالين", "probability": 0.82080078125}, {"start": 2686.93, "end": 2687.71, "word": " are", "probability": 0.7607421875}, {"start": 2687.71, "end": 2689.57, "word": " incongruent", "probability": 0.887451171875}], "temperature": 1.0}, {"id": 106, "seek": 271552, "start": 2692.08, "end": 2715.52, "text": "إذا ممكن استبدال أي شرط من الشرطين بشرط عدد العناصر يساوي المقياس هكذا خلصنا الـ Basic Properties of congruences والمرة الجاية إن شاء الله بناخد الـ Binary and الـ Decimal Representations الله يعطيكوا العافية", "tokens": [28814, 15730, 3714, 43020, 44713, 44510, 6027, 36632, 13412, 2288, 9566, 9154, 25124, 2288, 9566, 9957, 4724, 8592, 2288, 9566, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 7251, 3794, 995, 45865, 9673, 4587, 25528, 3794, 8032, 4117, 15730, 16490, 1211, 9381, 8315, 2423, 39184, 31598, 27627, 6097, 295, 8882, 84, 2667, 4032, 45340, 25720, 25724, 995, 10632, 36145, 13412, 16606, 21984, 44945, 47283, 3215, 2423, 39184, 363, 4066, 293, 2423, 39184, 12427, 10650, 19945, 763, 21984, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.3095588207244873, "compression_ratio": 1.5, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2692.08, "end": 2692.4, "word": "إذا", "probability": 0.635986328125}, {"start": 2692.4, "end": 2692.8, "word": " ممكن", "probability": 0.7276611328125}, {"start": 2692.8, "end": 2693.52, "word": " استبدال", "probability": 0.9622395833333334}, {"start": 2693.52, "end": 2693.76, "word": " أي", "probability": 0.95263671875}, {"start": 2693.76, "end": 2694.06, "word": " شرط", "probability": 0.9705403645833334}, {"start": 2694.06, "end": 2694.22, "word": " من", "probability": 0.9892578125}, {"start": 2694.22, "end": 2694.92, "word": " الشرطين", "probability": 0.9171142578125}, {"start": 2694.92, "end": 2696.32, "word": " بشرط", "probability": 0.863525390625}, {"start": 2696.32, "end": 2696.82, "word": " عدد", "probability": 0.9845377604166666}, {"start": 2696.82, "end": 2697.56, "word": " العناصر", "probability": 0.8603515625}, {"start": 2697.56, "end": 2698.28, "word": " يساوي", "probability": 0.9564208984375}, {"start": 2698.28, "end": 2701.26, "word": " المقياس", "probability": 0.75592041015625}, {"start": 2701.26, "end": 2702.36, "word": " هكذا", "probability": 0.6660359700520834}, {"start": 2702.36, "end": 2703.38, "word": " خلصنا", "probability": 0.722808837890625}, {"start": 2703.38, "end": 2703.44, "word": " الـ", "probability": 0.41259765625}, {"start": 2703.44, "end": 2703.7, "word": " Basic", "probability": 0.59814453125}, {"start": 2703.7, "end": 2704.5, "word": " Properties", "probability": 0.633544921875}, {"start": 2704.5, "end": 2705.68, "word": " of", "probability": 0.86328125}, {"start": 2705.68, "end": 2706.86, "word": " congruences", "probability": 0.6448567708333334}, {"start": 2706.86, "end": 2707.86, "word": " والمرة", "probability": 0.5975748697916666}, {"start": 2707.86, "end": 2708.2, "word": " الجاية", "probability": 0.7052408854166666}, {"start": 2708.2, "end": 2708.36, "word": " إن", "probability": 0.32861328125}, {"start": 2708.36, "end": 2708.54, "word": " شاء", "probability": 0.9775390625}, {"start": 2708.54, "end": 2708.82, "word": " الله", "probability": 0.95654296875}, {"start": 2708.82, "end": 2709.96, "word": " بناخد", "probability": 0.8629557291666666}, {"start": 2709.96, "end": 2710.18, "word": " الـ", "probability": 0.81005859375}, {"start": 2710.18, "end": 2710.64, "word": " Binary", "probability": 0.6851806640625}, {"start": 2710.64, "end": 2711.78, "word": " and", "probability": 0.67626953125}, {"start": 2711.78, "end": 2712.5, "word": " الـ", "probability": 0.506103515625}, {"start": 2712.5, "end": 2713.28, "word": " Decimal", "probability": 0.79736328125}, {"start": 2713.28, "end": 2714.48, "word": " Representations", "probability": 0.8857421875}, {"start": 2714.48, "end": 2714.94, "word": " الله", "probability": 0.3701171875}, {"start": 2714.94, "end": 2715.24, "word": " يعطيكوا", "probability": 0.81767578125}, {"start": 2715.24, "end": 2715.52, "word": " العافية", "probability": 0.9051106770833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2716.014875, "duration_after_vad": 2617.5206249999883}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/b-NRQp9gqPI_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/b-NRQp9gqPI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..76f83b9929ff9af91b7aff64e7161ce760834290
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/b-NRQp9gqPI_raw.srt
@@ -0,0 +1,1868 @@
+1
+00:00:19,370 --> 00:00:25,430
+بسم الله الرحمن الرحيم المحاضرة رقم 11 في مساق
+
+2
+00:00:25,430 --> 00:00:29,090
+نظرية الأعداد لطلبة قسم الرياضيات في الجامعة
+
+3
+00:00:29,090 --> 00:00:34,700
+الإسلامية كليتي العلوم والتربيةهنكمل الحديث عن
+
+4
+00:00:34,700 --> 00:00:40,280
+شبطر 4 تحت عنوان The Theory of Congruences بدأنا
+
+5
+00:00:40,280 --> 00:00:44,000
+المرة الماضية أو اللي جابلها حكينا عن الـ Basic
+
+6
+00:00:44,000 --> 00:00:48,680
+Properties of Congruences عرفنا شو .. أتذكركم إيش؟
+
+7
+00:00:48,680 --> 00:00:56,270
+عرفنا معنات اللي هو إيهتطابق بي modulo n تعني أن
+
+8
+00:00:56,270 --> 00:01:00,410
+الـ n بتقسم الـ a minus b هذا معناته اللي a تطابق
+
+9
+00:01:00,410 --> 00:01:04,810
+b modulo n وقلنا أن a لا تطابق b modulo n معناته
+
+10
+00:01:04,810 --> 00:01:09,370
+أن الـ n لا تقسم الـ a minus b بعدين أخدنا نظرية
+
+11
+00:01:09,370 --> 00:01:16,620
+مهمة قلنا لو أخدنا أي عددين a و bوكان الهن نفس الـ
+
+12
+00:01:16,620 --> 00:01:21,920
+remainder لما نجسمهم على الـ M أو على الـ N الهن
+
+13
+00:01:21,920 --> 00:01:25,120
+نفس الـ remainder لو جسمناها على الـ M معناته
+
+14
+00:01:25,120 --> 00:01:30,180
+حيصير عند الـ A تطابق بيه مدنومين مودلو Mيعني
+
+15
+00:01:30,180 --> 00:01:35,580
+الأعداد التي لها نفس المتبقي عندما تُقسم على M
+
+16
+00:01:35,580 --> 00:01:42,140
+يتكون هذه الأعداد متطابقة بالنسبة للمقياس M وكذلك
+
+17
+00:01:42,140 --> 00:01:46,620
+العكس الصحيح لو كانت الأعداد A تُطابق B Modulo M
+
+18
+00:01:46,620 --> 00:01:50,600
+معناته إن الـA والـB لو جسمناها هنا على الـM هيطلع
+
+19
+00:01:50,600 --> 00:01:54,600
+من إله النفس الـRemainder هذه اللي هي نظرية أرض
+
+20
+00:01:54,600 --> 00:01:59,670
+واحد وهنحتاجها بعد شوية في اللي هو خواص عديدةالآن
+
+21
+00:01:59,670 --> 00:02:03,730
+في عندى هو نظرية أخرى حكيناها المرة الماضية التي
+
+22
+00:02:03,730 --> 00:02:08,390
+تتحدث عن خواص الـ congruencesو .. او .. او .. اذا
+
+23
+00:02:08,390 --> 00:02:12,590
+بتتذكروا قلنا انه اللي هو ال .. ال .. التطابق او
+
+24
+00:02:12,590 --> 00:02:17,670
+الـ congrance بعمله equivalence relation وخواص
+
+25
+00:02:17,670 --> 00:02:21,150
+اخرى نيجي الآن على ال .. نيجي ل .. اللي اللي بدنا
+
+26
+00:02:21,150 --> 00:02:26,350
+نحكيه اليوم هناخد بعض الأمثلة الآن بعض الأمثلة
+
+27
+00:02:26,350 --> 00:02:30,630
+الآن بدنا نحكي عن اللي هو بعض الأمثلة في عندي
+
+28
+00:02:30,630 --> 00:02:40,170
+مثالين عدديين بنشوف كيف بدنا نوظفما تحدثنا عنه في
+
+29
+00:02:40,170 --> 00:02:46,810
+اللي هو التطابقات والنظريات والخواص لبرهان اللي هي
+
+30
+00:02:46,810 --> 00:02:54,490
+ال examples ال example الأول بدنا نثبت 41 يقسم 2
+
+31
+00:02:54,490 --> 00:03:00,650
+مثلا أُس 2 أو أُس 2000 نقول ناقص 1 بدنا نشوف كيف
+
+32
+00:03:00,650 --> 00:03:11,180
+بدنا نثبت أنه prove thatإن الـ 41 ÷ 2000 – 1 و
+
+33
+00:03:11,180 --> 00:03:17,040
+proof أو solution خلّينا
+
+34
+00:03:17,040 --> 00:03:20,960
+نفكر إيش معناته إيش معناته هذه معناته الواحد
+
+35
+00:03:20,960 --> 00:03:25,820
+مضنوبين مضل واحد واربعين إذاً اتنين أس الفين حطا
+
+36
+00:03:25,820 --> 00:03:31,360
+بكل واحد مضل واربعين عشرين حالة خاصة منها كبرتلك
+
+37
+00:03:31,360 --> 00:03:36,860
+العدد عشان ما تحسبليش بالـ L حاسبةلو حطيت لك 2
+
+38
+00:03:36,860 --> 00:03:40,000
+مليون أو 4 مليون أو 6 مليون طبعاً بيصير أننا
+
+39
+00:03:40,000 --> 00:03:45,580
+نستخدم الأهلة الحاسبة غير ممكن، معايا؟ طيب، الأهلة
+
+40
+00:03:45,580 --> 00:03:48,200
+بدّي .. لسه احنا في بداية الأمر أو في بداية اللي
+
+41
+00:03:48,200 --> 00:03:51,400
+هو التطابقات فبنستخدم المعلومات البدائية اللي
+
+42
+00:03:51,400 --> 00:03:58,060
+عندنا لتسهيل عملية إثبات 41 تقسم 2 أقصى 2000 نقص 1
+
+43
+00:03:58,060 --> 00:04:03,300
+الفكرة من وين تيجي؟الآن بدي أخد 2 أُس something
+
+44
+00:04:03,300 --> 00:04:11,020
+يكون هذا قريب من 41 الآن 2 في المرحلة الحالية 2
+
+45
+00:04:11,020 --> 00:04:21,560
+أُس مثلا 4، 16 2 أُس 5، 32 جربنا على 41 أُس 2، 64،
+
+46
+00:04:21,560 --> 00:04:26,100
+لأ 64 أبعد فبقول 2 أُس 5 و هتخدم 2 أُس 5 كمان
+
+47
+00:04:26,100 --> 00:04:33,850
+تطابققداش مدن مين مدن واحد واربعين اتنين اص خمسة
+
+48
+00:04:33,850 --> 00:04:38,110
+مين هي اتنين و تلاتين اتنين و تلاتين قداش بتفرج عن
+
+49
+00:04:38,110 --> 00:04:42,090
+الواحد واربعين بتسعة اذا انا هتطابق اللي هو سالب
+
+50
+00:04:42,090 --> 00:04:45,910
+تسعة لانه لما اجيب التسعة هان بيصير واحد واربعين
+
+51
+00:04:45,910 --> 00:04:50,930
+فبيصير عندى اتنين اص خمسة تطابق سالب تسعة مدن مين
+
+52
+00:04:51,680 --> 00:04:57,040
+modulo 41 واضح طيب لأن أخدنا المرة الماضية خاصية
+
+53
+00:04:57,040 --> 00:05:04,760
+إن لو A طابقة الـ B modulo M هيكون A أس K تطابق
+
+54
+00:05:04,760 --> 00:05:14,240
+الـ B أس K modulo M لكل K اللي هو أكبر من 0 صح ولا
+
+55
+00:05:14,240 --> 00:05:19,620
+لأ؟ طيب، بدأ أوظف هذه في اللي هو اللي عندي لأن 2
+
+56
+00:05:19,620 --> 00:05:25,270
+نص خمسةخلّيني لو ربعتها بديش أرفعها أو أصلها
+
+57
+00:05:25,270 --> 00:05:28,330
+لـ2000 مباشرة لأن الـ9 أسرار والـ9 بالسيرة بتطير
+
+58
+00:05:28,330 --> 00:05:36,190
+آه فلأ خلّيني أربع هذه وانا عارف أن لما ربعها بصير
+
+59
+00:05:36,190 --> 00:05:44,150
+2 أس 10 تطابق الـ-9 تربيع الـ-9 تربيع اللي هي إيش
+
+60
+00:05:44,150 --> 00:05:49,640
+بتساوي 81 كلهم دلمينمحدود من دول 41 إذا إحنا
+
+61
+00:05:49,640 --> 00:05:55,440
+مقياسنا 41 الـ 81 هذي بتزغرها بجد ما أستطيع عساس
+
+62
+00:05:55,440 --> 00:05:59,640
+ما أرفع حد للقصة و أصل لـ 2000 إنه هذي يكون سهل
+
+63
+00:05:59,640 --> 00:06:06,860
+توصيلها للعدد سهل حسابه واضح اللي بحكيه طيب لأن
+
+64
+00:06:06,860 --> 00:06:13,540
+الـ 41 فيه اتنين 41 الـ 41 الأولى بيبقى لها 40
+
+65
+00:06:13,540 --> 00:06:19,570
+شيرونها كمان 41 بيصير سالب واحدفاهمين إيش معناته
+
+66
+00:06:19,570 --> 00:06:24,690
+أنه .. أنه .. أه فبصير عندي لإنه جاي من وين لإنه
+
+67
+00:06:24,690 --> 00:06:31,070
+الـ 41 ومضاعفاتها تطابق السفر مدلوا مين مدلوا 41
+
+68
+00:06:31,070 --> 00:06:40,130
+دايما مضاعفات الأم تطابق السفر مقياس الأم ماشي ..
+
+69
+00:06:40,130 --> 00:06:44,570
+فعشان هي كباشير جد مابد من العدد من مضاعفات الأم
+
+70
+00:06:44,570 --> 00:06:50,340
+بظل العدد اللي بظل مطابق للعدد الأصليواضح اه فبصير
+
+71
+00:06:50,340 --> 00:06:53,340
+هذا بطابق شيلت منه واحد واربعين بقى الأربعين شيلت
+
+72
+00:06:53,340 --> 00:06:58,040
+منه كمان واحد واربعين بقى المين وهذا هيخدمني مدله
+
+73
+00:06:58,040 --> 00:07:03,460
+مين مدله واحد واربعين وصلت الآن الان اتنين أس عشرة
+
+74
+00:07:03,460 --> 00:07:09,060
+وهذا بده اتنين أس الفين بصله برفعه لمين بصير اتنين
+
+75
+00:07:09,060 --> 00:07:17,360
+أس عشرة أس متين تطابق ناقص واحد أس متين مدله41
+
+76
+00:07:17,360 --> 00:07:23,500
+يعني بمعنى اخر 2 أس الفين تطابق الواحد مدلوا مين
+
+77
+00:07:23,500 --> 00:07:27,980
+مدلوا واحد واربعين يعني الواحد واربعين تقسم اتنين
+
+78
+00:07:27,980 --> 00:07:34,380
+أس الفين ناقص واحد وكذا طبعا احنا لسه خليني اقول
+
+79
+00:07:34,380 --> 00:07:39,930
+في بداية اللي هو ال congruences او التطابقاتبعد
+
+80
+00:07:39,930 --> 00:07:43,950
+شوية هناخد بعض النظريات اللي بتسهل علينا الأسئلة
+
+81
+00:07:43,950 --> 00:07:47,770
+اللي مايعرفش نحلها بالشكل أو بالطريقة اللي حكينا
+
+82
+00:07:47,770 --> 00:07:58,470
+فيها اللي أمامنا طيب نيجي ناخد مثال عددي آخر مثال
+
+83
+00:07:58,470 --> 00:08:03,470
+عددي آخر كله مكتوب كله ملخص المثال بيقول التالي
+
+84
+00:08:03,470 --> 00:08:09,380
+أثبت أنهواحد factorial زائد اتنين factorial زائد
+
+85
+00:08:09,380 --> 00:08:14,600
+ثلاثة factorial زائد أربعة factorial زائد .. زائد
+
+86
+00:08:14,600 --> 00:08:24,420
+ميت مليون واحد اتنين تلاتة أربعة خمسة ستة اللي هو
+
+87
+00:08:24,420 --> 00:08:32,340
+factorial modulo اتن عاش تطابق .. آسف .. تطابق
+
+88
+00:08:33,930 --> 00:08:46,810
+وطابق تسعة مدلوا إيش اتناش معين الآن طبعا عدف لو
+
+89
+00:08:46,810 --> 00:08:52,150
+بدنا نيجي نحسب هدولة و نجمحل لبعض و نشوفهم و ننقص
+
+90
+00:08:52,150 --> 00:08:55,790
+منهم التسعة و نقسمهم على اتناش و نشوف بقسم ولا لأ
+
+91
+00:08:55,790 --> 00:09:03,290
+طبعا هذا الكلام عدف اه فالانبنستخدم خواص الـ
+
+92
+00:09:03,290 --> 00:09:10,750
+Concurrences وعلى رأس هذه الخواص أن مضاعفات 12
+
+93
+00:09:10,750 --> 00:09:20,450
+تطابق الـ 0 مدن 12 مضاعفات 12 تطابق الـ 0 مدن 12
+
+94
+00:09:20,450 --> 00:09:26,450
+ركز معايا بدي أمسك الطرف الأيمن الأيسر عند الطرف
+
+95
+00:09:26,450 --> 00:09:32,500
+الأيسر اللي هو 1factorial زائد اتنين factorial
+
+96
+00:09:32,500 --> 00:09:36,480
+زائد تلاتة factorial زائد أربعة factorial زائد
+
+97
+00:09:36,480 --> 00:09:48,680
+زائد مائة مليون factorial تطابق ماذا تطابق ماذا
+
+98
+00:09:48,680 --> 00:09:56,780
+نيجيالان الواحد بطابق نفسه مدل 12 والاتنين بطابق
+
+99
+00:09:56,780 --> 00:10:01,900
+نفسه مدل 12 والتلاتة بالطابقة اللي هي الستة مدل 12
+
+100
+00:10:01,900 --> 00:10:06,660
+نجل الاربعة الاربعة ايش بتساوي اربعة في تلاتة في
+
+101
+00:10:06,660 --> 00:10:12,870
+اتنينإذاً هي عبارة عن فيها 12 اللي هي 24 يعني من
+
+102
+00:10:12,870 --> 00:10:18,370
+مضاعفات 100 لـ 12 إذا حطها بجميعها الـ 0 الخمسة
+
+103
+00:10:18,370 --> 00:10:22,930
+factorial برضه فيها 12 إذاً من مضاعفات 12 بتطابق
+
+104
+00:10:22,930 --> 00:10:30,670
+الـ 0 وكلهم من مضاعفات 12 إذاً بتظلها للآخر تطابق
+
+105
+00:10:30,670 --> 00:10:35,250
+الـ 0 modulo 12
+
+106
+00:10:37,790 --> 00:10:45,670
+اللي فيها 12 ميم هي من الأربعة وطالع واضح
+
+107
+00:10:45,670 --> 00:10:53,230
+أه؟ إذاً واحد واثنين تلاتة وستة وهكذا
+
+108
+00:10:53,230 --> 00:10:59,270
+طيب أي سؤال؟
+
+109
+00:11:07,510 --> 00:11:15,370
+جمعة تانية؟ واحد
+
+110
+00:11:15,370 --> 00:11:21,350
+زائد اتنين زائد ستة تسعة زائد سفر اللي هو تسعة أنا
+
+111
+00:11:21,350 --> 00:11:25,650
+بشتغل مقياس مين الآن مقياس اتناشر هذا الكلام بطابق
+
+112
+00:11:25,650 --> 00:11:30,990
+التسعة مدل اتناشر اي عدد في الدنيا بطابق نفسك مدله
+
+113
+00:11:30,990 --> 00:11:37,090
+مين مدله الامهذا هو نفس العدد هذا فطبيعي بطابق
+
+114
+00:11:37,090 --> 00:11:41,430
+نفسه لإنه إيش قلنا عنها equivalence relation
+
+115
+00:11:41,430 --> 00:11:48,790
+المتطابقة يعني إيه إيش؟ يعني هذا reflexive طيب
+
+116
+00:11:48,790 --> 00:11:56,030
+نيجي إلى اللي هو نسأل السؤال التالي أو خلّيني أقول
+
+117
+00:11:56,030 --> 00:12:03,240
+هذا الإعلان المهم اللي بعد هيكهيكون بالنسبة لي
+
+118
+00:12:03,240 --> 00:12:09,400
+أداة مهمة جداً في عملية حلول الـcongruences أو
+
+119
+00:12:09,400 --> 00:12:15,160
+التطابقات عندما نبحث عن حلول ويكون عندي مجهيل بس
+
+120
+00:12:15,160 --> 00:12:21,020
+في خلال إيش تطابقة نشوف أشي اللي بحكيه عشان نصل
+
+121
+00:12:21,020 --> 00:12:26,660
+للي بحكيه خمي مثل السؤال التاليأحنا المرة الماضية
+
+122
+00:12:26,660 --> 00:12:35,520
+قلنا لو عندي A تطابق الـ B موضوع N مثلاًأو M قطعاً
+
+123
+00:12:35,520 --> 00:12:43,080
+هذا بيعطيني أن C في A تطابق الـ C في B Modulo مين
+
+124
+00:12:43,080 --> 00:12:48,440
+Modulo M وهذا برهنة برهان بسيط قل هذا شو بتعني؟
+
+125
+00:12:48,440 --> 00:12:53,360
+بتعني M بتكسب من A minus B إذا أكيد هذا بتعطيني
+
+126
+00:12:53,360 --> 00:12:57,240
+أمن اللي هو M بتكسب من C في A minus B يعني هذا
+
+127
+00:12:57,240 --> 00:13:05,880
+معنى أن CA تطابق ال CB Modulo Mالسؤال كالتالي الـ
+
+128
+00:13:05,880 --> 00:13:08,860
+Converse هل صحيح بمعنى والـ Converse هو الأهم
+
+129
+00:13:08,860 --> 00:13:14,250
+بالنسبة لي كمانالأهم فيه اللي هو ال .. ال .. ال ..
+
+130
+00:13:14,250 --> 00:13:17,890
+ال .. إنه .. إنه هحصل من خلاله كيفية ال
+
+131
+00:13:17,890 --> 00:13:24,050
+cancellation بالنسبة للضرب في طرفي المتطابقة لأن
+
+132
+00:13:24,050 --> 00:13:30,730
+لو كان في عندي CA تطابق الـ CB Modulo M أو Modulo
+
+133
+00:13:30,730 --> 00:13:40,130
+N زي ما هو عاملها هل هذا بيعطيني إن الـ Aتطابق الـ
+
+134
+00:13:40,130 --> 00:13:47,090
+B modulo N هذا الكلام in general ليس صحيح وفي عندي
+
+135
+00:13:47,090 --> 00:13:51,550
+عدد لا نهائي من ال counter examples خُد مثال بسيط
+
+136
+00:13:51,550 --> 00:14:01,950
+2×3 تطابق 2×4 modulo 2 صح ولا لأ؟ 2×3 هو 6، 2×4 هو
+
+137
+00:14:01,950 --> 00:14:08,820
+8، 8-6، 6-8، 2 أو نقص 2، 2 بتجسمهاإذن متطابقات لكن
+
+138
+00:14:08,820 --> 00:14:13,840
+قطعاً قطعاً قطعاً بصح الكاش تيجي تقول شيل التنين
+
+139
+00:14:13,840 --> 00:14:18,900
+وشيل التنين بيبقى عند التلاتة مطابق الأربعة مدلو
+
+140
+00:14:18,900 --> 00:14:24,320
+اتنين وهذا الكلام إيش ماله ليس صحيحاً إذن the
+
+141
+00:14:24,320 --> 00:14:30,600
+converse of this اللي هو ال property need not to
+
+142
+00:14:30,600 --> 00:14:37,700
+be true in general إذن طيب كيف بدنا نختصربدي أنا
+
+143
+00:14:37,700 --> 00:14:42,040
+عند C A تطابق C B Modulo N كيف بدي أختصر وما
+
+144
+00:14:42,040 --> 00:14:50,040
+تختلنش المتطابقة ما أكونش أنا أحدثت خطأ الإجابة
+
+145
+00:14:50,040 --> 00:14:59,140
+عبر ما يليه في عندي الخاصية التالية اللي بقولها
+
+146
+00:14:59,140 --> 00:15:04,300
+اللي هي نظريتنا اللي بتقول
+
+147
+00:15:07,390 --> 00:15:19,530
+theorem if C A تطابق الـ C B modulo N then
+
+148
+00:15:19,530 --> 00:15:26,750
+.. بتختصر الآن .. then طيّرت الـ C وطيّرت الـ C
+
+149
+00:15:26,750 --> 00:15:35,850
+بيشيل عند .. بيشيل عند A تطابق الـ B modulo N على
+
+150
+00:15:36,680 --> 00:15:42,020
+الـ greatest common divisor بين الان ومين والـ C
+
+151
+00:15:42,020 --> 00:15:49,220
+إذن هذه إعلان .. هذه إعلان .. هذه إعلان .. إيش
+
+152
+00:15:49,220 --> 00:15:55,440
+الإعلان هذا؟ بقولّي لو كان C إيه تطابق الـ CB
+
+153
+00:15:55,440 --> 00:16:03,370
+modulo N معناتهإذا بدّى أروح نحو الإختصار إن أشيل
+
+154
+00:16:03,370 --> 00:16:07,030
+الـC هنا و أشيل الـC هنا ماشي اتوكل الله شيل الـC
+
+155
+00:16:07,030 --> 00:16:11,130
+من هنا و شيل الـC من هنا حيكون عندك A تطابق بيه بس
+
+156
+00:16:11,130 --> 00:16:16,830
+مدنه مش N الآن مدنه N عالمين على العامل المشترك
+
+157
+00:16:16,830 --> 00:16:21,470
+الأعلى بين اللي بدك تطيره الـC والمقياس اللي هو
+
+158
+00:16:21,470 --> 00:16:27,620
+الـN واضح؟إذا من الآن وطالع لما بدي أجيه أشيل هذه
+
+159
+00:16:27,620 --> 00:16:34,260
+و أشيل هذه بشيلها بس بيصير المقياس Min and N على
+
+160
+00:16:34,260 --> 00:16:39,880
+العامل المشترك الأعلى بين اللي إنت اختصرته أو
+
+161
+00:16:39,880 --> 00:16:45,980
+طيرته والمقياس الأصلي اللي بتحكي عنه واضح؟ هذا
+
+162
+00:16:45,980 --> 00:16:50,840
+بيصير سلوك بعد ذلك شوف الآن برنامج بسيط نيجي لل
+
+163
+00:16:50,840 --> 00:16:58,650
+proofللـ proof كما يلي الان
+
+164
+00:16:58,650 --> 00:17:12,370
+since CA تطابق CB modulo N then أكيد ال N تقسم CA
+
+165
+00:17:12,370 --> 00:17:23,970
+minus mean CB واضحة أو بمعنى آخر that isالـ N
+
+166
+00:17:23,970 --> 00:17:30,550
+بتجسم الـ C في الـ A minus B أخدت الـ C عامل مشترك
+
+167
+00:17:30,550 --> 00:17:41,930
+طيب hence أكيد هيكون الـ N على D بتجسم الـ C على D
+
+168
+00:17:41,930 --> 00:17:48,030
+في الـ A minus B حيث الـ D هي العامل المشترك
+
+169
+00:17:48,030 --> 00:17:56,450
+الأعلى بين الـ N والـ Cأيش اللي سويته؟ الـ N الـ N
+
+170
+00:17:56,450 --> 00:18:00,450
+بتكسب الـ C في هذا، مظبوط ولا لا؟ إذا صار هذا
+
+171
+00:18:00,450 --> 00:18:05,410
+المقدار بسوء N في some عدد يعني صار عند الـ C في
+
+172
+00:18:05,410 --> 00:18:10,890
+الـ A minus B بسوء N في some K الآن سميت الـ D هو
+
+173
+00:18:10,890 --> 00:18:16,100
+العامل المشترك الأعلى بين مين؟ بين N و Cصار اللي
+
+174
+00:18:16,100 --> 00:18:22,980
+هو C على D عدد و N على D برضه عدد فجسمت الجهتين
+
+175
+00:18:22,980 --> 00:18:26,140
+على الـ D وهذا مشروع لأنه طلع عنده أدد هذا و هذا
+
+176
+00:18:26,140 --> 00:18:29,660
+أدد لأن الـ D هو عبارة عن عامل مشترك لأعلى بين N
+
+177
+00:18:29,660 --> 00:18:36,400
+وبين C الآن هذا إيش يعني؟ يعني أن N على D تقسم C
+
+178
+00:18:36,400 --> 00:18:43,310
+على D في A minus B لكن أنا بعرف بطالـ Greatest
+
+179
+00:18:43,310 --> 00:18:48,330
+Common Divisor بين الـ N على D والـ C على D أيش
+
+180
+00:18:48,330 --> 00:18:51,690
+هيساوي؟ لأن العامل المشترك الأعلى بين الـ N و الـ
+
+181
+00:18:51,690 --> 00:18:57,090
+C أيش بيساوي؟ D واضح صار العامل المشترك الأعلى بين
+
+182
+00:18:57,090 --> 00:19:00,870
+الـ N على D و الـ C على D أيش بيساوي؟ و هذا بكسب
+
+183
+00:19:00,870 --> 00:19:06,150
+حصل ضربه، إذا من أين جاي؟ من التاني، إذا hence من
+
+184
+00:19:06,150 --> 00:19:15,620
+هنا و من هنا بيصير عندي henceN على D يقسم الـ A
+
+185
+00:19:15,620 --> 00:19:24,160
+minus B وهذا أيش معناته؟ That is الـ A تطابق الـ B
+
+186
+00:19:24,160 --> 00:19:29,360
+modulo N على D اللي هو مين هو N على الـ greatest
+
+187
+00:19:29,360 --> 00:19:36,640
+common divisor بين الـ N والـ C أي سؤال؟ أي
+
+188
+00:19:36,640 --> 00:19:37,600
+استفسار؟
+
+189
+00:19:42,630 --> 00:19:51,810
+بنأكد على أنه حتى نستطيع أن نختصر عدد مضروب في
+
+190
+00:19:51,810 --> 00:19:58,950
+طرفي المتطابقة أو التطابقة بيصير عندي اللي هو
+
+191
+00:20:00,010 --> 00:20:05,710
+الاختصار جائز ولكن بيصير Modulo أو مقياس المقياس
+
+192
+00:20:05,710 --> 00:20:09,330
+الأصلي الـ N على العامل المشترك الأعلى بين اللي
+
+193
+00:20:09,330 --> 00:20:15,770
+انت اختصرته الـ C و مين و المقياس الأصلي N طيب
+
+194
+00:20:15,770 --> 00:20:20,130
+نيجي لل Corollary الأولى ال Corollary الأولى سهلة
+
+195
+00:20:20,130 --> 00:20:24,510
+بقول لو كان العامل المشترك الأعلى بين ال N و ال C
+
+196
+00:20:24,510 --> 00:20:30,860
+بساوي 1فيش مريح بصير الوضوع مريح بصير .. بنطبق هذه
+
+197
+00:20:30,860 --> 00:20:35,240
+النظرية بنطير الـ C مع الـ C فبصير ايه تطابق الـ B
+
+198
+00:20:35,240 --> 00:20:39,140
+مدنه مين؟ مدنه N على العام المشترك اللي علياش يعني
+
+199
+00:20:39,140 --> 00:20:42,760
+مدنه N هذا حالة خاصة أه هذا حالة خاصة إذا أنت الآن
+
+200
+00:20:42,760 --> 00:20:48,180
+اللي بدك تعرفه وهذا بيجيب كل الحالات أنه أنت لما
+
+201
+00:20:48,180 --> 00:20:54,140
+تختصر تختصر و تختصر بس بتكون مدنه N على العام
+
+202
+00:20:54,140 --> 00:20:57,460
+المشترك اللي عليا بين اللي اختصرتهوبين الانترنت
+
+203
+00:20:57,460 --> 00:21:02,360
+إذا الكورولا بيه automatic C A تطبق C B مدن
+
+204
+00:21:02,360 --> 00:21:05,300
+وانترنت والجريتز كومون دوبازو بين الـ C وانترنت
+
+205
+00:21:05,300 --> 00:21:08,660
+بيساوي واحد يؤدي لـ A تطبق B مدن ومين مدن وانترنت
+
+206
+00:21:08,660 --> 00:21:13,240
+الجزء التاني معلومة سهلة برضه بقول إذا كانت الـ C
+
+207
+00:21:13,240 --> 00:21:17,680
+في A تطبق الـ C في B مدن ومين مدن و B وكانت الـ B
+
+208
+00:21:17,680 --> 00:21:21,580
+مش من عوامل الـ C مدام الـ B مش من عوامل الـ C
+
+209
+00:21:21,580 --> 00:21:25,240
+معناته صار العامل المشارك أعلى لأنه B'صحيح من
+
+210
+00:21:25,240 --> 00:21:29,100
+العامل المشترك اللي على بين الـC والـB واحد لأن
+
+211
+00:21:29,100 --> 00:21:34,100
+الـB أشمالها الـPrime ومش من عامل الـC إذا العامل
+
+212
+00:21:34,100 --> 00:21:37,860
+المشترك اللي على بين الـC والـB واحد إذا على طول
+
+213
+00:21:37,860 --> 00:21:43,440
+تختصر الـC مع الـC تصبح الـA تطابق الـB مضلوا مين؟
+
+214
+00:21:43,440 --> 00:21:51,340
+مضلوا الـB مين
+
+215
+00:21:51,340 --> 00:21:53,580
+هي؟ الـC هي الـB يعني الـC هي الـPrime
+
+216
+00:21:56,210 --> 00:22:03,830
+موديلو C؟ موديلو C؟ نعم موديلو N موديلو
+
+217
+00:22:03,830 --> 00:22:07,310
+يكون N ماشي الحل ومايكونش من .. و العاملة الشيء
+
+218
+00:22:07,310 --> 00:22:10,450
+الأعلى بين ال B و ال N واحد يعني ال B لا تقسم منين
+
+219
+00:22:10,450 --> 00:22:13,810
+ال N نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+220
+00:22:13,810 --> 00:22:13,810
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+221
+00:22:13,810 --> 00:22:14,410
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+222
+00:22:14,410 --> 00:22:14,790
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+223
+00:22:14,790 --> 00:22:14,830
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+224
+00:22:14,830 --> 00:22:15,030
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+225
+00:22:15,030 --> 00:22:15,470
+نعم نعم نعم نعم نعم
+
+226
+00:22:19,650 --> 00:22:25,290
+تطابق الـ Modulo N وكانت الـ B اللي هنا لا تقسم
+
+227
+00:22:25,290 --> 00:22:28,550
+الـ N إذاً يعني صار العام المشترك اللي على بين الـ
+
+228
+00:22:28,550 --> 00:22:31,310
+B و الـ N بساوية واحد معناته صار إيش؟ جائز
+
+229
+00:22:31,310 --> 00:22:34,810
+الإختصار واضح، أه؟ وكتير يعني خلّيني أقول حالات
+
+230
+00:22:34,810 --> 00:22:41,710
+خاصة ممكن الحديث عنها أي سؤال؟ اللي بعد؟ الآن الـ
+
+231
+00:22:41,710 --> 00:22:46,560
+remark، الـ remark سهلةأو .. أو .. يعني ممكن
+
+232
+00:22:46,560 --> 00:22:50,800
+أخذناها بس خلّينا نقول بتعبير آخر لأن التعبير اللي
+
+233
+00:22:50,800 --> 00:22:54,180
+موجودة فيه هو تعبير على صورة اللي هو تطابقات أو
+
+234
+00:22:54,180 --> 00:23:00,580
+concurrences بتقولّي إن لو كان عندك الـAB تطابق
+
+235
+00:23:00,580 --> 00:23:08,380
+السفر modulo مين modulo B إيش معناته؟ معناته إن
+
+236
+00:23:08,380 --> 00:23:13,190
+الـB تقسم الـA في B صح ولا لأ؟ما دام الـ B تقسم
+
+237
+00:23:13,190 --> 00:23:18,310
+الـ A في B معناته B' معناته الـ B يمن الـ A يمن
+
+238
+00:23:18,310 --> 00:23:22,750
+الـ B يعني B ككتلة واحدة تقسم الـ A R B تقسم مين
+
+239
+00:23:22,750 --> 00:23:30,030
+الـ B وهذا إيش بتعني أنه B أنه إيه تطابق الـ Zero
+
+240
+00:23:30,030 --> 00:23:36,910
+modulo B R B تطابق الـ Zero modulo مين modulo B
+
+241
+00:23:37,600 --> 00:23:41,760
+دائما مضاعفات المقياس هي عبارة عن صفر Modulo
+
+242
+00:23:41,760 --> 00:23:48,980
+المقياس أي سؤال؟
+
+243
+00:23:48,980 --> 00:23:53,620
+هذا الخاصية الثاني الخاصية اللي أمامنا تم برهنتها
+
+244
+00:23:53,620 --> 00:23:58,740
+زي ما حكينا نيجي الآن لمفهوم مفهوم من المفاهيم
+
+245
+00:23:58,740 --> 00:24:06,040
+المهمة واللي إنا تطبيقاتها مورد عليه الكتاب مورور
+
+246
+00:24:06,040 --> 00:24:12,300
+الكراملكن خلّيني أنا أركز في الحديث عنه لأنه في حد
+
+247
+00:24:12,300 --> 00:24:21,740
+ذاته مهم وجدّام هيلزمنا في حديث آخر وزي
+
+248
+00:24:21,740 --> 00:24:27,840
+ما احنا بنقول دائما الاسم لما انت بدك تيجي تعرف
+
+249
+00:24:27,840 --> 00:24:35,160
+اشيهتعطل المفهوم اللي عندك اسم يتلاقم مع المفهوم
+
+250
+00:24:35,160 --> 00:24:40,600
+أو يستقر من المفهوم يعني مش معجول بيداروح اعرف
+
+251
+00:24:40,600 --> 00:24:47,340
+اتصالاللي يكون أو الدالة المتصلة اللي يكون فعلا في
+
+252
+00:24:47,340 --> 00:24:52,180
+روح الاتصال في الدالة اللي بحكي فيها يعني بدي أحكي
+
+253
+00:24:52,180 --> 00:24:56,480
+عن اتصال معناته أنه إيهاش أنه فعلا المفهوم يوحي
+
+254
+00:24:56,480 --> 00:25:01,740
+بالاتصال الآن هو بده يعطيني مفهوم جديد اسمه
+
+255
+00:25:01,740 --> 00:25:08,920
+Complete Residue System Modeling انحل لكوا الكلمة
+
+256
+00:25:08,920 --> 00:25:13,820
+ونشوف أيش علاقتها بالمفهوم اللي عندىفي حاجة اسمها
+
+257
+00:25:13,820 --> 00:25:21,740
+بنقول R1 وR2 لعند RN عبارة عن أو RS زي ما هو
+
+258
+00:25:21,740 --> 00:25:30,800
+مسميها بنقول عنها Complete Residue
+
+259
+00:25:30,800 --> 00:25:38,300
+System Modulo N ماشي؟
+
+260
+00:25:39,520 --> 00:25:42,440
+Complete Residue System Module M Module M معناته
+
+261
+00:25:42,440 --> 00:25:45,540
+احنا المقياس اللي بنشتغل عليه إيه إيش؟ اللي هو M
+
+262
+00:25:45,540 --> 00:25:52,120
+Residue بواقي يعني وكأن هذه عبارة عن إيه إيش؟ تمثل
+
+263
+00:25:52,120 --> 00:26:01,580
+البواقي تمثل البواقي الآن Complete يعني تمثيلها
+
+264
+00:26:01,580 --> 00:26:08,260
+هذه لشعبها كامل الشعب اللي بنحكي عنه مين هو؟ الذد
+
+265
+00:26:08,970 --> 00:26:12,450
+الزد عالمنا اللي بنحكي فيه إحنا الـ Integers إذاً
+
+266
+00:26:12,450 --> 00:26:17,770
+وكأنها تمثّل بشكل كامل الـ Integers الـ Land
+
+267
+00:26:17,770 --> 00:26:22,450
+System هي كلها عبارة عن نظام بنسميه نظام البواقي
+
+268
+00:26:22,450 --> 00:26:29,690
+المكتمل مقياس أمن ماشي الحالة طيب قبل مرحلة
+
+269
+00:26:29,690 --> 00:26:36,090
+التعريف بتذكركم في شغلةأحنا by division algorithm
+
+270
+00:26:36,090 --> 00:26:45,790
+لما نيجي نجسم أي عدد N نجسمه على عدد M بنقول أنه
+
+271
+00:26:45,790 --> 00:26:54,470
+لكل N في element Z بنلاقي عنصر وحيد Q و عنصر وحيد
+
+272
+00:26:54,470 --> 00:27:03,500
+Rاللي هو M سوى M في Q زي الـ R حيث الـ R أكبر أو
+
+273
+00:27:03,500 --> 00:27:10,800
+يساوي صفره أصغر من مين من الـ M معايا؟ إذا .. إذا
+
+274
+00:27:10,800 --> 00:27:18,340
+عند الـ R هذا هو يمثل بياق القسمة إذا كل الأعداد
+
+275
+00:27:18,340 --> 00:27:23,080
+اللي في الدنيا الـ Integers هتطلع بياق القسمة اللي
+
+276
+00:27:23,080 --> 00:27:28,440
+لها مين هيالـ 0 أو الـ 1 أو الـ 2 اللي عند مين
+
+277
+00:27:28,440 --> 00:27:37,040
+أماقص 1 وكل عدد له واحد وحيد من هذولة بمثله ماشي
+
+278
+00:27:37,040 --> 00:27:42,380
+الحال؟ وقلنا قبل بشوية في النظرية الأولى اللي حكيت
+
+279
+00:27:42,380 --> 00:27:48,420
+عنها أن الأعداد التي لها نفس الباقي متطابقة مدلوا
+
+280
+00:27:48,420 --> 00:27:52,340
+المقصوم عليه اللي هو الأمن واضح؟
+
+281
+00:27:53,140 --> 00:27:59,020
+الأعداد التي لها نفس الباقي متطابقة modulo M
+
+282
+00:27:59,020 --> 00:28:03,160
+المقسوم عليه يعني لما أقسم الـA على الـM والـB على
+
+283
+00:28:03,160 --> 00:28:07,080
+الـM ولجيله نفس الباقي بيكون عندي الـA تطابق الـB
+
+284
+00:28:07,080 --> 00:28:14,580
+modulo M والعكس صحيح ماشي الحالة بناء عليه عندي
+
+285
+00:28:14,580 --> 00:28:24,440
+الآن أي عدد هنا أنفذتحَلَجِلُ مَن يُمَثْلُ هَانِ
+
+286
+00:28:24,440 --> 00:28:29,020
+حَلَجِلُ
+
+287
+00:28:29,020 --> 00:28:33,260
+مَن يُمَثْلُ هَانِ حَلَجِلُ مَن يُمَثْلُ هَانِ
+
+288
+00:28:33,260 --> 00:28:38,240
+حَلَجِلُ مَن يُمَثْلُ هَانِ حَلَجِلُ مَن يُمَثْلُ
+
+289
+00:28:38,240 --> 00:28:38,240
+هَانِ حَلَجِلُ مَن يُمَثْلُ هَانِ حَلَجِلُ مَن
+
+290
+00:28:38,240 --> 00:28:38,340
+يُمَثْلُ هَانِ حَلَجِلُ مَن يُمَثْلُ هَانِ
+
+291
+00:28:38,340 --> 00:28:40,300
+حَلَجِلُ مَن يُمَثْلُ هَانِ حَلَجِلُ مَن يُمَثْ
+
+292
+00:28:41,160 --> 00:28:46,120
+دائماً العدد ومتبقى القسمة له متطابقين وهنا بتتضح
+
+293
+00:28:46,120 --> 00:28:51,460
+حيها ان جلها دهان M ناقص R بساوية M في مين؟ في few
+
+294
+00:28:51,460 --> 00:28:56,860
+صارت اللي هي M تقسم الـM ناقص R صار الـM تطابق
+
+295
+00:28:56,860 --> 00:29:04,620
+الـR مدله مين؟ مدله الـM واضح إذا صار عندي الآن
+
+296
+00:29:04,620 --> 00:29:11,500
+بناء على الـdivision algorithm كل عدد في الـZهناك
+
+297
+00:29:11,500 --> 00:29:21,860
+من يمثلهان وبشكل وحيد كل واحد العنصر مين وحيد الآن
+
+298
+00:29:21,860 --> 00:29:28,180
+بدنا اشتكرار يعني بدي انا واحد يمثل الطائفة تبعات
+
+299
+00:29:28,180 --> 00:29:33,690
+السفر من هانمن الـ Z والواحد يمثل كل طيفته
+
+300
+00:29:33,690 --> 00:29:38,610
+والاتنين يمثل كل طيفته وماحدش من هدولة يكون متكرر
+
+301
+00:29:38,610 --> 00:29:44,550
+التكرار هنا يعني إيش التطابق يعني ممنوع يكون الإيش
+
+302
+00:29:44,550 --> 00:29:50,050
+مالهن أي عنصرين هدول يكون الإيش مالهن متطابقين
+
+303
+00:29:50,050 --> 00:29:58,180
+وهذا الكلام مضمون هنا ليش؟ لأن لو أخدت A وBفي
+
+304
+00:29:58,180 --> 00:30:02,080
+المجموعة هذه معانا يا محمد اه لو اخدت A و B في هذه
+
+305
+00:30:02,080 --> 00:30:05,420
+المجموعة اه
+
+306
+00:30:07,950 --> 00:30:11,430
+طبعاً الـ A و الـ B في هذه المجموعة و بدأ يخد من A
+
+307
+00:30:11,430 --> 00:30:16,370
+له يساوي B أنا بقولك مش هيكون المتطابقات ليش؟ الآن
+
+308
+00:30:16,370 --> 00:30:20,450
+A بدأت اسمه على مين؟ على الـ M إذا قسمته على الـ M
+
+309
+00:30:20,450 --> 00:30:26,770
+A هيساوي 0 في الـ M لأنه متبقى هو زائد مين الـ A
+
+310
+00:30:26,770 --> 00:30:32,270
+حيث الـ A أكبر أو يساوي 0 وأصغر من مين؟ من M واضح
+
+311
+00:30:32,270 --> 00:30:37,700
+اللي بحكيهSimilarly الـ B برضه هنا إذا لما نقسمها
+
+312
+00:30:37,700 --> 00:30:43,500
+الـ M هيطلع بساوي ناتج القسم صفر في M زائد هو نفسه
+
+313
+00:30:43,500 --> 00:30:48,320
+المتبقى الـ M الـ B أكبر ويساوي صفر وأصغر من مين
+
+314
+00:30:48,320 --> 00:30:54,200
+من M أنا بقول الـ A و الـ B مش متطابقات ليش؟ لأنه
+
+315
+00:30:54,200 --> 00:31:01,460
+يكون المتطابقات إذا بواقف قسم الهم إيش مالهم؟ زي
+
+316
+00:31:01,460 --> 00:31:08,840
+بعضما دام بواق القسمة مش زي بعض التنين أكيد الـA
+
+317
+00:31:08,840 --> 00:31:14,580
+والـB أشمالهم مش congruent لبعض إذا صار هذا
+
+318
+00:31:14,580 --> 00:31:22,980
+الـsystem اللي هو من 0 ل1 لعند M ناقص 1 الـsystem
+
+319
+00:31:22,980 --> 00:31:32,590
+هذا هذا الـsystem هو فعلًا بمثلكل عدد وين موجود في
+
+320
+00:31:32,590 --> 00:31:36,330
+الـ Z يعني لكل واحد في الـ Z فيه إلو ميطار كوهان
+
+321
+00:31:36,330 --> 00:31:44,450
+ووحيد وكمان خاصية تانية إن ولا واحد من هذول متكرر
+
+322
+00:31:44,450 --> 00:31:48,390
+يعني اللي هو فيه اتنين من نفس الفئة لأ كل فئة إيش
+
+323
+00:31:48,390 --> 00:31:56,630
+مالة بمثلها واحد فهذا بنسميه من هنا بنعرف مفهوم
+
+324
+00:31:56,630 --> 00:32:02,640
+الـ Complete Residue Systemبنقول الآن أي أعداد R1
+
+325
+00:32:02,640 --> 00:32:08,720
+وR2 عند RS هيعمل لنا Complete Residue System Model
+
+326
+00:32:08,720 --> 00:32:16,300
+M إذا حققنا شرطين الشرط الأول أن ولا واحد من اللي
+
+327
+00:32:16,300 --> 00:32:24,350
+جوا يطابق الثانيأتنين أن أي عدد في الـ Z يجيب من
+
+328
+00:32:24,350 --> 00:32:29,810
+يمثله من هذه الأعداد يعني يجيب له واحد جواته بحيث
+
+329
+00:32:29,810 --> 00:32:36,090
+أنه N يطابق مين الـ URI مضله مين مضله N الآن ..
+
+330
+00:32:36,090 --> 00:32:43,250
+الآن .. الآن .. عنديالشروط أن يكون الـ Complete
+
+331
+00:32:43,250 --> 00:32:48,510
+Residue System واضحة أن ولا واحد بطابق التاني
+
+332
+00:32:48,510 --> 00:32:53,670
+الشرط التاني أن كل element in Z في واحد من هنا
+
+333
+00:32:53,670 --> 00:32:58,210
+يطاقوا مضلوا مين مضلوا عام هذه الشرطين المطلوبات
+
+334
+00:32:58,210 --> 00:33:05,990
+طيب الآن أجربكم كمثال عددي وستجد الموضوع الـ
+
+335
+00:33:05,990 --> 00:33:10,630
+familiar for you من اللي حكيناه في مبادئ الرياضيات
+
+336
+00:33:11,160 --> 00:33:17,400
+إيش هو؟ لو بدّي أجي أقول خلّينا نحكي واحد بده
+
+337
+00:33:17,400 --> 00:33:21,900
+يجيبلي Complete Residue System طبعا هذا هيمثل إيش
+
+338
+00:33:21,900 --> 00:33:27,700
+ماله؟ Complete Residue System ليش؟ لأن مش متطابقات
+
+339
+00:33:27,700 --> 00:33:31,140
+ولا واحد متطابق التاني وأي عدد في الـZ قلنا بيمثل
+
+340
+00:33:31,140 --> 00:33:35,840
+واحد من هذا وواحد وحيد إذا الأن لو بدنا نقول بدي
+
+341
+00:33:35,840 --> 00:33:39,080
+Complete Residue System مدهو مين؟ مدهو خمسة مثلا
+
+342
+00:33:39,900 --> 00:33:45,020
+على طول إيش هتقولوا ليه؟ Zero واحد واثنين وتلاتة
+
+343
+00:33:45,020 --> 00:33:49,960
+واربعة لو قلتلكم بدي complete residue system تاني
+
+344
+00:33:49,960 --> 00:33:58,820
+اللي هو إيش؟ خمسة، ستة، سبعة، ليش قلت هيك يا عبد؟
+
+345
+00:33:58,820 --> 00:34:03,740
+الكلام صحيح مية في المية، بس ليش قلت هيك؟أنت يعني
+
+346
+00:34:03,740 --> 00:34:09,000
+و كأنك قلت بدل ما أنا اللي يمثّلني هنا السفن بدي
+
+347
+00:34:09,000 --> 00:34:12,960
+يمثّلني إيه؟ زائد خمسة الخمسة و بدل ما يمثّلني
+
+348
+00:34:12,960 --> 00:34:16,460
+الواحد بدي يمثّلني إيه الستة و هذا السبعة و هذا
+
+349
+00:34:16,460 --> 00:34:21,460
+التمانية و هذا التسعة كلام مية في المية الآن فيه
+
+350
+00:34:21,460 --> 00:34:26,180
+غيره و أحد قال أنا بدي أشيل هذا و أكتب الخمسةأقول
+
+351
+00:34:26,180 --> 00:34:31,760
+له أه أبقى ليك بس بدك تبدل هذا السبعة برضه أه كل
+
+352
+00:34:31,760 --> 00:34:36,060
+ناشر بيعمل incomplete residue system وكأنه إذا
+
+353
+00:34:36,060 --> 00:34:39,520
+بتتذكر مش احنا نقول التطابقات equivalence relation
+
+354
+00:34:39,520 --> 00:34:45,900
+ال equivalence relation مدل 5 اللي هي 0 بساوي 0 1
+
+355
+00:34:45,900 --> 00:34:51,340
+2 إلى ما لا نهاية والواحد اللي هي عبارة عن اللي هي
+
+356
+00:34:51,340 --> 00:34:59,790
+من أين اللي جيبتهو عشرة فاهمين اه الواحد والستة
+
+357
+00:34:59,790 --> 00:35:05,090
+والحداشر إلى ما لا نهاية والتنين بساوي التنين
+
+358
+00:35:05,090 --> 00:35:10,090
+والسبعة إلى ما لا نهاية والتلاتة ويساوي اللي هو
+
+359
+00:35:10,090 --> 00:35:14,730
+تلاتة وتمانية إلى ما لا نهاية والاربعة بساوي
+
+360
+00:35:14,730 --> 00:35:18,810
+الاربعة والتسعة إلى ما لا نهاية ايش اللي بقوله
+
+361
+00:35:18,810 --> 00:35:23,440
+هان؟اللي بقوله وكأنه الـ Complete Residue System
+
+362
+00:35:23,440 --> 00:35:28,120
+كيف بتجوّن باجي أخد هدول الـ equivalence classes
+
+363
+00:35:28,120 --> 00:35:34,980
+تبعات مين؟ تبعات اللي هي العلاقة تطابق مدلوا مين؟
+
+364
+00:35:34,980 --> 00:35:38,240
+مدلوا خمسة، ما أحنا قلنا الـ equivalence التطابق
+
+365
+00:35:38,240 --> 00:35:40,280
+عبارة عن equivalence relation مدام equivalence
+
+366
+00:35:40,280 --> 00:35:42,700
+relation إذا بتولد equivalence classes ال
+
+367
+00:35:42,700 --> 00:35:47,510
+equivalence classes اللي إلهيهاوكأنه عشان أوجد الـ
+
+368
+00:35:47,510 --> 00:35:51,630
+Complete Residue System بدي أخد منها عنصر عشوائي
+
+369
+00:35:51,630 --> 00:35:56,170
+مااخدش غيره، مرة واحدة باخده ومنها عنصر عشوائي
+
+370
+00:35:56,170 --> 00:35:58,650
+ومنها عنصر عشوائي ومنها عنصر عشوائي ومنها عنصر
+
+371
+00:35:58,650 --> 00:36:04,490
+عشوائي هيكون إن إشماله Complete Residue System لأن
+
+372
+00:36:04,490 --> 00:36:08,670
+أكيد ولا واحد من هذول بطابق بعض، لأنه لو طابق بعض
+
+373
+00:36:08,670 --> 00:36:13,370
+لو دخل في نفس الـConveillance Classماشي الحال و
+
+374
+00:36:13,370 --> 00:36:18,830
+هدولة عمل انتج ذئب للزد مدام عمل انتج ذئب للزد
+
+375
+00:36:18,830 --> 00:36:24,110
+بناء عليه فبصير هذه الخمسة اللي أخدت من أماكن
+
+376
+00:36:24,110 --> 00:36:30,770
+مختلفة هيمثلن كل الزد ماضح؟ إذا مفهوم إيش معنى
+
+377
+00:36:30,770 --> 00:36:35,550
+complete residue system modulo اللي هو خمسة أو
+
+378
+00:36:35,550 --> 00:36:39,310
+مدوله ستة أو مدوله سبعة أو مدوله إلى آخرين أي
+
+379
+00:36:39,310 --> 00:36:39,770
+سؤال؟
+
+380
+00:36:42,680 --> 00:36:50,620
+طيب نيجي الآن .. نيجي الآن .. ننظر بزاوية أخرى لو
+
+381
+00:36:50,620 --> 00:36:55,880
+إيجي واحد و قاللي أنت بقال فيها محمد معايا إيجي
+
+382
+00:36:55,880 --> 00:37:03,940
+واحد قاللي أن R .. أن R1 وR2 عند RS قاللي أن هذا
+
+383
+00:37:03,940 --> 00:37:08,050
+عبارة عن Complete Residue System Modulo Mوقولّه
+
+384
+00:37:08,050 --> 00:37:11,090
+على طول ما زي ما أنت بتقول Complete Residue System
+
+385
+00:37:11,090 --> 00:37:17,450
+Modulo M ببشرك إنه أسهد إيه إيش بتساوي M فبنحكي
+
+386
+00:37:17,450 --> 00:37:22,630
+عنها إذا أي Complete Residue System Modulo M لازم
+
+387
+00:37:22,630 --> 00:37:28,910
+يكون عدده جد إيه إيش M من العناصر وإلا .. وإلا
+
+388
+00:37:28,910 --> 00:37:34,870
+حيصير في خلل عنده في التمثيل أو زيادة تكرار في
+
+389
+00:37:34,870 --> 00:37:40,370
+الناس اللي موجودين واضح أه؟معايا، نريد أن نثبت هذا
+
+390
+00:37:40,370 --> 00:37:51,010
+الكلام نظريتنا بتقول .. نظرية بتقول if .. أبو
+
+391
+00:37:51,010 --> 00:37:56,710
+سيم .. if S is .. S different integers R1 R2 لعند
+
+392
+00:37:56,710 --> 00:38:03,030
+R S S different integers R1 R2 R S form a complete
+
+393
+00:38:03,030 --> 00:38:09,030
+residue system modulo Mthen الـ S هذي مش هتساوي،
+
+394
+00:38:09,030 --> 00:38:13,750
+هتساوي الأمر. إذاً، ردد الـ Complete Residue
+
+395
+00:38:13,750 --> 00:38:20,070
+System Modulo M يجب و أصلاً لازم يطلع عدده بساوي
+
+396
+00:38:20,070 --> 00:38:21,870
+عدد المقياس.
+
+397
+00:38:24,230 --> 00:38:27,390
+يمكن برهين. شوفوا، صلوا على النبي عليه الصلاة
+
+398
+00:38:27,390 --> 00:38:33,120
+والسلام. أول حاجة بدي أثبتلكمإن الـ 0 و الـ 1 و
+
+399
+00:38:33,120 --> 00:38:36,520
+الـ 2 لعند الـ M نقص واحد إيش بتعمل ليه؟ Complete
+
+400
+00:38:36,520 --> 00:38:39,880
+Residue System Modulum أنا عموما أكيد أثبتته في
+
+401
+00:38:39,880 --> 00:38:46,140
+الأول بس بيتعيدلكم إياها الآن هو فرضية النظرية قال
+
+402
+00:38:46,140 --> 00:38:51,600
+لي R1 وR2 لعند Rs قاللي هذا عبارة عن Complete
+
+403
+00:38:51,600 --> 00:38:57,180
+Residue System Modulumين M، هيك ما أعطيني هو الآن
+
+404
+00:38:57,180 --> 00:39:06,110
+أول حاجة بدأ أثبتلكإن M0 و1 عند M ناقص واحد is a
+
+405
+00:39:06,110 --> 00:39:13,210
+complete residue system مضلمين مضلؤم عشان أثبت
+
+406
+00:39:13,210 --> 00:39:16,110
+complete residue system مضلؤم هذا بتدفت شغلتين
+
+407
+00:39:16,110 --> 00:39:21,350
+اللي هو ولا واحد بطابق الثاني أثبته إن لو أخدت A
+
+408
+00:39:21,350 --> 00:39:30,470
+وB جوا مش متساويتين إذا هيكون A لطبق B مضلمينمدلو
+
+409
+00:39:30,470 --> 00:39:38,330
+M معايا أه هذا واحد و أثبتنا أنه بال division
+
+410
+00:39:38,330 --> 00:39:46,130
+algorithm لكل Z element لكل N element in Z there
+
+411
+00:39:46,130 --> 00:39:52,950
+exist a unique Q و R such that اللي هو N تطابق ال
+
+412
+00:39:52,950 --> 00:40:00,780
+R مدلونيا مدلو M و ال R بين 0 و بين Mيعني كل واحد
+
+413
+00:40:00,780 --> 00:40:05,480
+في الـ A .. في الـ Z لجيتله واحد هان يمثله إذا هذا
+
+414
+00:40:05,480 --> 00:40:09,020
+أنا مويت عليه بشكل سريع لإنه أثبتته إذا صار عند
+
+415
+00:40:09,020 --> 00:40:12,940
+هذا إيش بيعمله؟ Complete Residue System Modulo M
+
+416
+00:40:12,940 --> 00:40:17,520
+وهي البرهان بشكل كامل وملخص صار عند الـ N صفر
+
+417
+00:40:17,520 --> 00:40:21,680
+وواحد واتنين وM نقص واحد إيش بيعمله؟ Form a
+
+418
+00:40:21,680 --> 00:40:27,540
+Complete Residue System Modulo M Modulo M الآن إيش
+
+419
+00:40:27,540 --> 00:40:36,030
+بده أثبت؟بدأ أثبت لكم بدأ أثبت لكم أن هذا الـ
+
+420
+00:40:36,030 --> 00:40:43,030
+Complete الـ R1 و الـ R2 و الـ RS هما عددهم M يعني
+
+421
+00:40:43,030 --> 00:40:51,010
+بدأ أثبت أن الـ S إيش بتساوي؟ بتساوي M الآن خُد
+
+422
+00:40:51,010 --> 00:40:57,450
+اللي هو الـ Complete Residue هذا System وخُد لي أي
+
+423
+00:40:57,450 --> 00:41:09,100
+RElement in R1 لعند RS ركز معايا خد أي R هنا معايا
+
+424
+00:41:09,100 --> 00:41:18,680
+الـ R اللي هنا R in Z في النهاية مدام R in Z إذا
+
+425
+00:41:18,680 --> 00:41:25,680
+بلاجئلها عنصر وحيد هو الموجودThere exists a unique
+
+426
+00:41:25,680 --> 00:41:32,520
+element A element in 0 و 1 لعند M نقص 1 بحيث أن R
+
+427
+00:41:32,520 --> 00:41:39,040
+يطابق الـ A مدلوا مين؟ مدلوا M إذا كل عنصر من هنا
+
+428
+00:41:39,040 --> 00:41:46,000
+هلجيله واحد و لو أخدت عنصر تاني هلجيله واحد مختلف
+
+429
+00:41:46,000 --> 00:41:51,150
+عن اللي لجيته هنالأن لو كان لجت له نفس العنصر
+
+430
+00:41:51,150 --> 00:41:56,030
+بيصير التنين هذا مالهن متطابقات وهذا يخالف أنه
+
+431
+00:41:56,030 --> 00:42:01,830
+complete residual system إذا
+
+432
+00:42:01,830 --> 00:42:06,960
+ما دام كل عنصر هنا فيه له صورة هنامعناته صار العدد
+
+433
+00:42:06,960 --> 00:42:12,480
+اللهانة اللي هي الـ S أصغر أو ساومين العدد اللهان
+
+434
+00:42:12,480 --> 00:42:16,460
+لأن كل واحد اللي جيتله أشمع له عنصر واحد وما تكررش
+
+435
+00:42:16,460 --> 00:42:21,430
+ماراحش اللي هو كمان واحد وروح لواحد تاني لنفسهإذا
+
+436
+00:42:21,430 --> 00:42:25,890
+راح لواحد تاني إذا أكيد هدولة لما انخلصتهم لأن كل
+
+437
+00:42:25,890 --> 00:42:30,690
+واحد لقيت له حد هنا صار عند الأصغر شاومين similar
+
+438
+00:42:30,690 --> 00:42:35,230
+لبنفس الأسلوب ما هو هذا برضه أيش معله complete
+
+439
+00:42:35,230 --> 00:42:41,690
+residual systemأذا لكل element R element in 0 و1
+
+440
+00:42:41,690 --> 00:42:46,210
+لعند الـ M نقص واحد بلا جيل واحد هار وواحد وحيد
+
+441
+00:42:46,210 --> 00:42:51,130
+element in R واحد لعند مين RS بحيث أن كون الاتنين
+
+442
+00:42:51,130 --> 00:42:55,990
+أشمالهم متطابقات مدام كل واحد له أنصر هنا معناته
+
+443
+00:42:55,990 --> 00:43:00,490
+سار اللي هو العدد اللي هنا الـ M أصغر أو يساوي
+
+444
+00:43:00,490 --> 00:43:03,890
+العدد اللي هناك اللي هي الـ S together الاتنتين
+
+445
+00:43:03,890 --> 00:43:09,980
+معناته أشماله Mتساوي إيش؟ تساوي قصة إذا صار عندي
+
+446
+00:43:09,980 --> 00:43:15,120
+للإعلان النهائي الآن إنه أي complete residue
+
+447
+00:43:15,120 --> 00:43:21,240
+system مدلؤام لازم يكون عدد عناصره إيه شماله أم من
+
+448
+00:43:21,240 --> 00:43:28,760
+العناصر سؤال لو كان في عندي الآن ستة Vintages
+
+449
+00:43:28,760 --> 00:43:37,350
+وكلهم in congruent لبعض وعددهم Mهل بيعمل الـ
+
+450
+00:43:37,350 --> 00:43:43,890
+Complete Residue System؟ كمان مرة عددهم
+
+451
+00:43:43,890 --> 00:43:51,110
+أم من العناصر ولا واحد congruent للتاني هل بيعمل
+
+452
+00:43:51,110 --> 00:43:54,850
+الـ Complete Residue System؟ أنا بقول أم، أه،
+
+453
+00:43:54,850 --> 00:44:01,370
+أكيد، أكيد لأن الشرط الثالث بيصير ضمنيا متحقق طيب،
+
+454
+00:44:01,370 --> 00:44:06,020
+لو كان في عندي، عندي أم من العناصروأي عنصر في Z
+
+455
+00:44:06,020 --> 00:44:10,960
+بيلاقيله واحد من اللي جوا congruent له هل بيعمل
+
+456
+00:44:10,960 --> 00:44:15,540
+الـ Complete Residual System Modulo M؟ ركزوا كمان
+
+457
+00:44:15,540 --> 00:44:20,380
+مرة بس كمان مرة، ركزوا تستعجلوا أشياء لو كان عند
+
+458
+00:44:20,380 --> 00:44:29,000
+الآن R واحد عند الـ RM يعني M من العناصر بحكي M من
+
+459
+00:44:29,000 --> 00:44:35,450
+العناصر وكان في عندي لكل element in Zبنجيل واحد
+
+460
+00:44:35,450 --> 00:44:41,130
+هنا وحيد بمثله اذا
+
+461
+00:44:41,130 --> 00:44:45,010
+برضه بيعمل complete residue system لإنه هيطلع
+
+462
+00:44:45,010 --> 00:44:49,570
+مباشرة كل هدوء الأشمالين are incongruent
+
+463
+00:44:52,080 --> 00:44:56,820
+إذا ممكن استبدال أي شرط من الشرطين بشرط عدد
+
+464
+00:44:56,820 --> 00:45:03,700
+العناصر يساوي المقياس هكذا خلصنا الـ Basic
+
+465
+00:45:03,700 --> 00:45:08,540
+Properties of congruences والمرة الجاية إن شاء
+
+466
+00:45:08,540 --> 00:45:13,280
+الله بناخد الـ Binary and الـ Decimal
+
+467
+00:45:13,280 --> 00:45:15,520
+Representations الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/cY0hXagA2Vc_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/cY0hXagA2Vc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..bf1a147e029664935d1b3bca43a56b62ae00a76d
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/cY0hXagA2Vc_raw.json
@@ -0,0 +1 @@
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112.29, "word": " خنتين", "probability": 0.9895833333333334}], "temperature": 1.0}, {"id": 5, "seek": 11962, "start": 113.3, "end": 119.62, "text": "معناته هو بده اللي هو الان في عندي رقم وفي عندي آخر خانتين اللي هي الأحد", "tokens": [2304, 3615, 8315, 47395, 31439, 47525, 3224, 13672, 1829, 31439, 2423, 7649, 8978, 18871, 16254, 12602, 4587, 2304, 4032, 41185, 18871, 16254, 19753, 34740, 16490, 7649, 2655, 9957, 13672, 1829, 39896, 16247, 24401], "avg_logprob": -0.30974264092305126, "compression_ratio": 1.4659090909090908, "no_speech_prob": 0.0, "words": [{"start": 113.3, "end": 113.98, "word": "معناته", "probability": 0.8121337890625}, {"start": 113.98, "end": 114.2, "word": " هو", "probability": 0.266357421875}, {"start": 114.2, "end": 114.56, "word": " بده", "probability": 0.406005859375}, {"start": 114.56, "end": 114.68, "word": " اللي", "probability": 0.757568359375}, {"start": 114.68, "end": 115.24, "word": " هو", "probability": 0.94970703125}, {"start": 115.24, "end": 116.08, 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{"start": 548.9, "end": 549.2, "word": " B", "probability": 0.7490234375}, {"start": 549.2, "end": 549.86, "word": " minus", "probability": 0.287841796875}, {"start": 549.86, "end": 550.6, "word": " واحد", "probability": 0.812255859375}, {"start": 550.6, "end": 551.34, "word": " اللي", "probability": 0.967041015625}, {"start": 551.34, "end": 551.66, "word": " بده", "probability": 0.78857421875}, {"start": 551.66, "end": 552.04, "word": " أثبت", "probability": 0.9327392578125}, {"start": 552.04, "end": 552.44, "word": " إنه", "probability": 0.57421875}, {"start": 552.44, "end": 552.94, "word": " هو", "probability": 0.84423828125}, {"start": 552.94, "end": 553.8, "word": " بيقسم", "probability": 0.82098388671875}, {"start": 553.8, "end": 554.22, "word": " العدد", "probability": 0.9697265625}, {"start": 554.22, "end": 554.46, "word": " هذا", "probability": 0.5986328125}, {"start": 554.46, "end": 554.64, "word": " F", "probability": 0.88671875}, {"start": 554.64, "end": 554.8, "word": " and", "probability": 0.053253173828125}, {"start": 554.8, "end": 555.2, "word": " F", "probability": 0.33837890625}, {"start": 555.2, "end": 555.82, "word": " اللي", "probability": 0.8681640625}, {"start": 555.82, "end": 556.0, "word": " هو", "probability": 0.9931640625}, {"start": 556.0, "end": 556.68, "word": " بيقسم", "probability": 0.9180908203125}, {"start": 556.68, "end": 557.08, "word": " اللي", "probability": 0.856201171875}, {"start": 557.08, "end": 557.24, "word": " هو", "probability": 0.97802734375}, {"start": 557.24, "end": 557.36, "word": " ال", "probability": 0.9072265625}, {"start": 557.36, "end": 557.62, "word": " S", "probability": 0.86474609375}], "temperature": 1.0}, {"id": 24, "seek": 58665, "start": 559.69, "end": 586.65, "text": "الآن لو أجيد اتطلعت للـ B هتلاقيها بتطابق الواحد مدنه مين؟ مدنه B-1 مدام الـ B تطابق الواحد مدنه B-1 إذا حسب نظرية سابقة هتكون B of B يطابق B of واحد مدنه مين؟ مدنه B-1 الـ B of B هذه مين هي؟", "tokens": [6027, 148, 48506, 45164, 5551, 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0.8312174479166666}, {"start": 571.63, "end": 571.83, "word": " الـ", "probability": 0.89306640625}, {"start": 571.83, "end": 571.95, "word": " B", "probability": 0.904296875}, {"start": 571.95, "end": 572.39, "word": " تطابق", "probability": 0.9456787109375}, {"start": 572.39, "end": 572.69, "word": " الواحد", "probability": 0.9913736979166666}, {"start": 572.69, "end": 572.99, "word": " مدنه", "probability": 0.9903564453125}, {"start": 572.99, "end": 573.09, "word": " B", "probability": 0.857421875}, {"start": 573.09, "end": 573.83, "word": "-1", "probability": 0.82763671875}, {"start": 573.83, "end": 574.11, "word": " إذا", "probability": 0.666015625}, {"start": 574.11, "end": 574.47, "word": " حسب", "probability": 0.9580078125}, {"start": 574.47, "end": 574.91, "word": " نظرية", "probability": 0.9439697265625}, {"start": 574.91, "end": 575.49, "word": " سابقة", "probability": 0.9873046875}, {"start": 575.49, "end": 576.53, "word": " هتكون", "probability": 0.7618001302083334}, {"start": 576.53, "end": 577.01, "word": " B", "probability": 0.55029296875}, {"start": 577.01, "end": 577.43, "word": " of", "probability": 0.8671875}, {"start": 577.43, "end": 577.93, "word": " B", "probability": 0.97607421875}, {"start": 577.93, "end": 579.21, "word": " يطابق", "probability": 0.97607421875}, {"start": 579.21, "end": 579.47, "word": " B", "probability": 0.96142578125}, {"start": 579.47, "end": 579.69, "word": " of", "probability": 0.9775390625}, {"start": 579.69, "end": 580.27, "word": " واحد", "probability": 0.794921875}, {"start": 580.27, "end": 581.37, "word": " مدنه", "probability": 0.991943359375}, {"start": 581.37, "end": 582.45, "word": " مين؟", "probability": 0.9890950520833334}, {"start": 582.45, "end": 582.77, "word": " مدنه", "probability": 0.990478515625}, {"start": 582.77, "end": 582.89, "word": " B", "probability": 0.94921875}, {"start": 582.89, "end": 583.61, "word": "-1", "probability": 0.90869140625}, {"start": 583.61, "end": 584.61, "word": " الـ", "probability": 0.971435546875}, {"start": 584.61, "end": 584.89, "word": " B", "probability": 0.8583984375}, {"start": 584.89, "end": 585.11, "word": " of", "probability": 0.98046875}, {"start": 585.11, "end": 585.29, "word": " B", "probability": 0.95556640625}, {"start": 585.29, "end": 585.53, "word": " هذه", "probability": 0.4423828125}, {"start": 585.53, "end": 585.77, "word": " مين", "probability": 0.9423828125}, {"start": 585.77, "end": 586.65, "word": " هي؟", "probability": 0.6478271484375}], "temperature": 1.0}, {"id": 25, "seek": 60946, "start": 588.18, "end": 609.46, "text": "تطابق الـ P of واحد مين هي الـ S modulo P minus واحد الان الصورة اتبحت P minus واحد بتجسم الان ايش تعني F اندول F الان تطابق السفر modulo مين P نقص واحد", "tokens": [2655, 9566, 16758, 4587, 2423, 39184, 430, 295, 36764, 24401, 3714, 9957, 39896, 2423, 39184, 318, 1072, 13455, 430, 3175, 36764, 24401, 2423, 7649, 31767, 13063, 3660, 1975, 2655, 3555, 33753, 430, 3175, 36764, 24401, 39894, 7435, 38251, 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S", "probability": 0.77197265625}, {"start": 591.38, "end": 592.2, "word": " modulo", "probability": 0.877685546875}, {"start": 592.2, "end": 592.72, "word": " P", "probability": 0.81689453125}, {"start": 592.72, "end": 593.08, "word": " minus", "probability": 0.60498046875}, {"start": 593.08, "end": 593.42, "word": " واحد", "probability": 0.986328125}, {"start": 593.42, "end": 594.1, "word": " الان", "probability": 0.4505615234375}, {"start": 594.1, "end": 594.62, "word": " الصورة", "probability": 0.97607421875}, {"start": 594.62, "end": 595.2, "word": " اتبحت", "probability": 0.77886962890625}, {"start": 595.2, "end": 597.62, "word": " P", "probability": 0.64794921875}, {"start": 597.62, "end": 599.08, "word": " minus", "probability": 0.8857421875}, {"start": 599.08, "end": 599.62, "word": " واحد", "probability": 0.9921875}, {"start": 599.62, "end": 600.52, "word": " بتجسم", "probability": 0.7473958333333334}, {"start": 600.52, "end": 600.96, "word": " الان", "probability": 0.92041015625}, {"start": 600.96, "end": 601.54, "word": " ايش", "probability": 0.7986653645833334}, {"start": 601.54, "end": 602.08, "word": " تعني", "probability": 0.8798828125}, {"start": 602.08, "end": 602.6, "word": " F", "probability": 0.837890625}, {"start": 602.6, "end": 603.0, "word": " اندول", "probability": 0.4733479817708333}, {"start": 603.0, "end": 603.36, "word": " F", "probability": 0.77880859375}, {"start": 603.36, "end": 604.36, "word": " الان", "probability": 0.95458984375}, {"start": 604.36, "end": 605.48, "word": " تطابق", "probability": 0.9859619140625}, {"start": 605.48, "end": 606.32, "word": " السفر", "probability": 0.87841796875}, {"start": 606.32, "end": 607.36, "word": " modulo", "probability": 0.86083984375}, {"start": 607.36, "end": 607.82, "word": " مين", "probability": 0.977294921875}, {"start": 607.82, "end": 608.74, "word": " P", "probability": 0.4921875}, {"start": 608.74, "end": 609.06, "word": " نقص", "probability": 0.8948567708333334}, {"start": 609.06, "end": 609.46, "word": " واحد", "probability": 0.99169921875}], "temperature": 1.0}, {"id": 26, "seek": 63947, "start": 610.35, "end": 639.47, "text": "واضح، أه؟ الـ N تطابق السفر و الـ S تطابق الـ S إذا أكيد اللي هو if and only if S تطابق السفر modulo B minus واحد وهذا يعني أن الـ B minus واحد بتجسم الـ S وهو المطلوب أي سؤال؟ اللي بعد، يلا الـ N ب application بسيط", "tokens": [2407, 46958, 5016, 12399, 5551, 3224, 22807, 2423, 39184, 426, 6055, 9566, 16758, 4587, 21136, 5172, 2288, 4032, 2423, 39184, 318, 6055, 9566, 16758, 4587, 2423, 39184, 318, 11933, 15730, 5551, 4117, 25708, 13672, 1829, 31439, 498, 293, 787, 498, 318, 6055, 9566, 16758, 4587, 21136, 5172, 2288, 1072, 13455, 363, 3175, 36764, 24401, 37037, 15730, 37495, 22653, 14739, 2423, 39184, 363, 3175, 36764, 24401, 39894, 7435, 38251, 2423, 39184, 318, 37037, 2407, 9673, 9566, 1211, 37746, 36632, 8608, 33604, 6027, 22807, 13672, 1829, 39182, 12399, 7251, 15040, 2423, 39184, 426, 4724, 3861, 4724, 3794, 1829, 9566], 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{"start": 620.19, "end": 621.13, "word": " modulo", "probability": 0.599365234375}, {"start": 621.13, "end": 621.29, "word": " B", "probability": 0.28466796875}, {"start": 621.29, "end": 621.67, "word": " minus", "probability": 0.34375}, {"start": 621.67, "end": 622.15, "word": " واحد", "probability": 0.81640625}, {"start": 622.15, "end": 622.81, "word": " وهذا", "probability": 0.8125}, {"start": 622.81, "end": 623.25, "word": " يعني", "probability": 0.98486328125}, {"start": 623.25, "end": 623.83, "word": " أن", "probability": 0.529296875}, {"start": 623.83, "end": 623.99, "word": " الـ", "probability": 0.8349609375}, {"start": 623.99, "end": 624.13, "word": " B", "probability": 0.8876953125}, {"start": 624.13, "end": 624.47, "word": " minus", "probability": 0.94580078125}, {"start": 624.47, "end": 625.05, "word": " واحد", "probability": 0.98779296875}, {"start": 625.05, "end": 626.05, "word": " بتجسم", "probability": 0.865234375}, {"start": 626.05, "end": 626.27, "word": " الـ", 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{"start": 638.73, "end": 639.47, "word": " بسيط", "probability": 0.99658203125}], "temperature": 1.0}, {"id": 27, "seek": 65332, "start": 640.54, "end": 653.32, "text": "بقول لي give a criterion for the divisibility of N by تلاتة and تمانية that depends on the digits of N when written in the base 9", "tokens": [3555, 39648, 32239, 976, 257, 46691, 337, 264, 25974, 2841, 295, 426, 538, 6055, 1211, 9307, 3660, 293, 46811, 7649, 10632, 300, 5946, 322, 264, 27011, 295, 426, 562, 3720, 294, 264, 3096, 1722], "avg_logprob": -0.3234374863760812, "compression_ratio": 1.168, "no_speech_prob": 0.0, "words": [{"start": 640.54, "end": 640.98, "word": "بقول", "probability": 0.5634765625}, {"start": 640.98, "end": 641.2, "word": " لي", "probability": 0.53125}, {"start": 641.2, "end": 641.76, "word": " give", "probability": 0.111083984375}, {"start": 641.76, "end": 641.98, "word": " a", "probability": 0.416748046875}, {"start": 641.98, "end": 642.6, "word": " criterion", "probability": 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الأساس اللي عندها ده أشماله عبارة عن 9 لو كان العدد مكتوب على صورة الأساس 9 ابحثلي عن اللي هو test لل divisibility by mean أول إشهر", "tokens": [3555, 39648, 32239, 45164, 9122, 2655, 3555, 8315, 18863, 3215, 3215, 11778, 995, 13672, 1829, 31439, 16247, 3794, 32277, 1722, 37495, 22653, 18863, 3215, 3215, 39896, 30544, 15844, 20328, 13063, 3660, 376, 20666, 3794, 995, 2407, 10632, 316, 376, 316, 1249, 376, 30767, 1829, 316, 502, 316, 1249, 1722, 5551, 4587, 9381, 10943, 30767, 1829, 316, 502, 1722, 30767, 1829, 316, 11633, 37495, 22653, 16247, 3794, 32277, 13672, 1829, 43242, 11296, 11778, 3224, 5551, 8592, 2304, 6027, 3224, 6225, 3555, 9640, 3660, 18871, 1722, 45164, 25961, 18863, 3215, 3215, 3714, 4117, 2655, 37746, 15844, 20328, 13063, 3660, 16247, 3794, 32277, 1722, 48127, 5016, 12984, 20292, 18871, 13672, 1829, 31439, 1500, 24976, 25974, 2841, 538, 914, 5551, 12610, 11933, 8592, 3224, 2288], "avg_logprob": -0.25204918985484076, "compression_ratio": 1.7838983050847457, 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"probability": 0.6552734375}, {"start": 4090.3, "end": 4090.96, "word": " remainder", "probability": 0.560546875}, {"start": 4090.96, "end": 4091.6, "word": " theorem", "probability": 0.40234375}, {"start": 4091.6, "end": 4092.72, "word": " الله", "probability": 0.716796875}, {"start": 4092.72, "end": 4093.06, "word": " يعطيكوا", "probability": 0.78720703125}, {"start": 4093.06, "end": 4093.46, "word": " العافية", "probability": 0.9319661458333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 4093.5619375, "duration_after_vad": 3947.7562499999813}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/cY0hXagA2Vc_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/cY0hXagA2Vc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a4fa0b9aad93e75c40626c1b811026e6ccd2cf97
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/cY0hXagA2Vc_raw.srt
@@ -0,0 +1,2944 @@
+1
+00:00:20,670 --> 00:00:26,770
+بسم الله الرحمن الرحيم المحاضرة اليوم هي عبارة عن
+
+2
+00:00:26,770 --> 00:00:31,470
+discussion لأربعة
+
+3
+00:00:31,470 --> 00:00:35,770
+تلاتة أو أربعة أربعة discussion لمادة ال linear
+
+4
+00:00:35,770 --> 00:00:41,310
+congruences and chinese remainder theorem وهي
+
+5
+00:00:41,310 --> 00:00:46,810
+المحاضرة رقم 18 في مساق نظرية الأعداد لطلبة
+
+6
+00:00:46,810 --> 00:00:53,360
+الجامعة الإسلاميةفي كليتي العلوم والتربية لقسم
+
+7
+00:00:53,360 --> 00:00:59,400
+رياضيات السؤال الأول اللي كان معاكم هو how to find
+
+8
+00:00:59,400 --> 00:01:03,660
+the last two digits of the number تسعة أس تسعة أس
+
+9
+00:01:03,660 --> 00:01:08,930
+تسعةبدنا اللي هو نحاول نعطيكوا الفكرة لحل السؤال
+
+10
+00:01:08,930 --> 00:01:15,470
+فيه hint في الكتاب معطيكم إياها إنه التسعة أس تسعة
+
+11
+00:01:15,470 --> 00:01:21,170
+تطابق التسعة وتمانين modulo مية
+
+12
+00:01:23,410 --> 00:01:28,790
+طبعا الـ hint اللي أمامنا ممكن بالقالة على السريع
+
+13
+00:01:28,790 --> 00:01:33,870
+9 اقص 9 تلاقي انه اخر رقمين في العدد اللي هي 89
+
+14
+00:01:33,870 --> 00:01:40,770
+يعني تطابق 89 مدنومية قبل ما نبدأ في الحل بس خلينا
+
+15
+00:01:40,770 --> 00:01:45,210
+نشوف اللي هو ايش .. ايش بده السؤال بالظبط بيقوللي
+
+16
+00:01:45,210 --> 00:01:51,530
+اودد اخر خنتين في العدد 9 اقص 9 اقص 9 معناته اخر
+
+17
+00:01:51,530 --> 00:01:57,920
+خنتينمعناته هو بده اللي هو الان في عندي رقم وفي
+
+18
+00:01:57,920 --> 00:02:02,330
+عندي آخر خانتين اللي هي الأحدوالعشرات بدّوا الرقم
+
+19
+00:02:02,330 --> 00:02:07,430
+اللي موجود هنا الرقم اللي موجود هنا معناته المتبقي
+
+20
+00:02:07,430 --> 00:02:13,290
+حين القسمة عالمية يعني بمعنى آخر بدّوا السؤال تسعة
+
+21
+00:02:13,290 --> 00:02:19,570
+أس تسعة أس تسعة تطابق ماذا مو دولومين مو دولومية
+
+22
+00:02:19,570 --> 00:02:24,750
+يعني بدنا رقم هنا مكوّن من خنتين يطابق هذا العدد
+
+23
+00:02:24,750 --> 00:02:28,830
+فيكون هنا أيه شمالهن خانة الأحد والعشرات للعدد
+
+24
+00:02:28,830 --> 00:02:34,260
+اللي عندناالآن خلّيني
+
+25
+00:02:34,260 --> 00:02:38,340
+أجرب ما نبدأ مباشرة في ال .. في ال .. في ال
+
+26
+00:02:38,340 --> 00:02:42,180
+congrance مدنومية خلّيني بس أحسب هذه الحسبة
+
+27
+00:02:42,180 --> 00:02:49,440
+البسيطة و هتعرفوا ليش تسعة تربيع الآن تطابق
+
+28
+00:02:49,440 --> 00:02:55,280
+مدنومين مدن عشرة التسعة تربيع هي واحد تمانين مظبوط
+
+29
+00:02:55,280 --> 00:03:00,140
+إذا نجدش بالنسبة للعشرة واحدالان ارفحها لقوة
+
+30
+00:03:00,140 --> 00:03:05,640
+تمانية لقوة كمان أربعة بيصير أس تمانية تطابق واحد
+
+31
+00:03:05,640 --> 00:03:12,680
+الان أس تسعة حطها بالجد ياش تسعة ماشي الحال إذا
+
+32
+00:03:12,680 --> 00:03:18,700
+صار العدد تسعة أس تسعة تسعة أس تسعة هو عبارة عن
+
+33
+00:03:18,700 --> 00:03:27,520
+اللي هوعشرة K زائد إيش زائد تسعة كيف هذا إيجا طبعا
+
+34
+00:03:27,520 --> 00:03:31,300
+احنا عارفين انه ايش معناته هذه معناته ان عشرة تقسم
+
+35
+00:03:31,300 --> 00:03:35,960
+تسعة اقص تسعة ناقص تسعة يعني بمعنى اخر ايش معنى
+
+36
+00:03:35,960 --> 00:03:42,140
+هذا تسعة اقص تسعة ناقص تسعة بتساوي عشرة K for some
+
+37
+00:03:42,140 --> 00:03:46,200
+K element in Z بمعنى اخر تسعة اقص تسعة ايش هتساوي
+
+38
+00:03:46,200 --> 00:03:53,690
+عشرة K زائد مين زائد تسعةماشي الحال اذا الان صيرنا
+
+39
+00:03:53,690 --> 00:04:00,390
+جاهزين لمية ليه بدي احسب تسعة اص تسعة اص تسعة
+
+40
+00:04:00,390 --> 00:04:06,150
+تطابق الان تسعة اص تسعة ايش لجيتها بتساوي عشرة كيه
+
+41
+00:04:06,150 --> 00:04:11,190
+زي التسعة يعني تسعة اص عشرة كيه زي التسعة يعني ايش
+
+42
+00:04:11,190 --> 00:04:17,690
+هذا عبارة عن ايش عبارة عن تسعة اص عشرة كيهوخلّينا
+
+43
+00:04:17,690 --> 00:04:23,650
+نفحّل القوة K في 9 أقص إيش 9 لأن بحسب مدنومين أنا
+
+44
+00:04:23,650 --> 00:04:30,710
+مدنومية عشان أشوف آخر خنتين الآن اتفجنا هذا عبارة
+
+45
+00:04:30,710 --> 00:04:39,370
+عن جداش عن 89 معايا اللي هو عبارة عن 8 9 مضروب في
+
+46
+00:04:39,370 --> 00:04:47,200
+9 أقص 10 أقص K طيب هذا بدي أحسبه مدنوميةعلى جهة لو
+
+47
+00:04:47,200 --> 00:04:53,480
+الـ G تتطلعت لـ 9 أُس اللي هي 9 جُلنا بتساوي 89
+
+48
+00:04:53,480 --> 00:05:00,500
+مدنوجة الدياشر 100 فالـ 89 برضه سابق نفسها مين هي
+
+49
+00:05:01,220 --> 00:05:05,700
+سالب 11 بالنسبة للـ 100 للـ 89 الان اضرب لهذه في
+
+50
+00:05:05,700 --> 00:05:10,420
+تسعة و هذه في تسعة تصبح تسعة اص عشرة تطابق ناقص
+
+51
+00:05:10,420 --> 00:05:14,820
+تسعة وتسعين ناقص تسعة وتسعين بالنسبة للمية ايش هي
+
+52
+00:05:14,820 --> 00:05:22,090
+عبارة عن واحد تطابق الواحد مدله ميةيعني الآن صار 9
+
+53
+00:05:22,090 --> 00:05:27,730
+أُس 10 عبارة عن 1 مدلومية يعني 9 أُس 10 كده برضه
+
+54
+00:05:27,730 --> 00:05:34,630
+مش هتساوي 1 مدلومية مدلومية يعني بمعنى آخر صارت
+
+55
+00:05:34,630 --> 00:05:38,430
+عندي 9 أُس 9 أُس 9 تطابق 89
+
+56
+00:05:41,090 --> 00:05:45,930
+مدلونية يعني بمعنى اخر صار the last two digits
+
+57
+00:05:45,930 --> 00:05:50,350
+بالنسبة للعدد تسعة وتسعة تسعة هو عبارة عن مين
+
+58
+00:05:50,350 --> 00:05:59,270
+تمانية تسعة يلا ايه بعده اطلع
+
+59
+00:05:59,270 --> 00:06:07,210
+لفوقالان السؤال الخامس السؤال الخامس فكرته مرت
+
+60
+00:06:07,210 --> 00:06:11,870
+علينا في النظريات فخلّيني على السريع أحكي فكرته
+
+61
+00:06:11,870 --> 00:06:18,350
+نحلله على السريع لأنه نفسه برهناه في نظريات سابقة
+
+62
+00:06:19,280 --> 00:06:24,600
+حين لما ضرهننا عن قابلية القسمة على 9 وقابلية
+
+63
+00:06:24,600 --> 00:06:29,020
+القسمة على 11 حلنا .. حل ال .. ال .. ال .. ال ..
+
+64
+00:06:29,020 --> 00:06:33,000
+تقريبا برهان نفس برهان أو مشابه للبرهان أو منطق
+
+65
+00:06:33,000 --> 00:06:37,760
+برهان سؤال 5 ايش بيقول السؤال 5؟ بيقول السؤال 5 لو
+
+66
+00:06:37,760 --> 00:06:43,430
+كان في عندي العدد Nمكتوب على صورة نظام العدل
+
+67
+00:06:43,430 --> 00:06:49,790
+الأساسي B يعني بمعنى أخر N عبارة عن AM بي أس M
+
+68
+00:06:49,790 --> 00:06:58,270
+زائد لما أصل عند A1 في B زائد A نوت بيقول لي
+
+69
+00:06:58,270 --> 00:07:05,360
+السؤال اثبت لياللي هو طبعا قبل أكيد الـ A0 و الـ
+
+70
+00:07:05,360 --> 00:07:09,480
+A1 اللي عند الـ AM الأعداد المستخدمة في نظام العد
+
+71
+00:07:09,480 --> 00:07:14,540
+اللي الأساسه بيه هتكون صفر واحد اتنين اللي عند B-
+
+72
+00:07:14,540 --> 00:07:19,200
+واحد زي العشر أشواء صفر واحد اتنين اللي عند التسعة
+
+73
+00:07:19,200 --> 00:07:23,460
+إذا العد الأساس بيه هتكون الـ A case تبعته بين
+
+74
+00:07:23,460 --> 00:07:30,480
+الصفر وأصغر أو ثومين B- واحدمعايا الان السؤال كانت
+
+75
+00:07:30,480 --> 00:07:36,480
+تالي ايش السؤال بيقول بيقول اثبت ان ال B ناقص واحد
+
+76
+00:07:36,480 --> 00:07:42,300
+تقسم ال N if and only if اللي هو ال B minus واحد
+
+77
+00:07:42,300 --> 00:07:49,600
+تقسم A naught زائد A واحد زائد A M معايا يا جماعة
+
+78
+00:07:49,600 --> 00:07:55,920
+هذا مش شابه للنظرية السابقة الان لو جينا لاحظنا
+
+79
+00:07:55,920 --> 00:08:03,430
+معينةلو جيت انت أخدت بي
+
+80
+00:08:03,430 --> 00:08:08,550
+of X البولنوميال بتساوي بتستقيها البولنوميال من
+
+81
+00:08:08,550 --> 00:08:13,630
+هذا اللي هو اللي عندي العدد عبارة عن A NOT زائد A1
+
+82
+00:08:13,630 --> 00:08:21,690
+في X زائد لما أصل عند A M X أُس M والـ A NOT والـ
+
+83
+00:08:21,690 --> 00:08:26,630
+A1 والـ A M زي ما هما موجودات في الأعلىلأ نلاحظ ما
+
+84
+00:08:26,630 --> 00:08:31,410
+يالي نلاحظ أن الـ N هذه اللي عندى اللى بدى أفحص
+
+85
+00:08:31,410 --> 00:08:35,990
+أنه B-1 تكسب الـ F و N دولة F B-1 تكسب الـ S الـ N
+
+86
+00:08:35,990 --> 00:08:44,310
+هذه عبارة عن B of .. of إيش؟ of B مظبوطة لا؟ B of
+
+87
+00:08:44,310 --> 00:08:49,410
+B إيش هتطلع؟ بساوة N و لو G تتطلعت للـ S هذه عبارة
+
+88
+00:08:49,410 --> 00:08:56,060
+عن مين؟ عن B of 1اللي هياش بتساوي بالساوي S إيش
+
+89
+00:08:56,060 --> 00:08:59,180
+علاقته في الموضوع هذا لأ علاقة قوية لإنه على
+
+90
+00:08:59,180 --> 00:09:05,900
+أساسها بده أشتغل الان ناقظ لو أجيت ال B طبعاً أنا
+
+91
+00:09:05,900 --> 00:09:11,660
+كل شغل مدنوين حيكون مدنو B minus واحد اللي بده
+
+92
+00:09:11,660 --> 00:09:16,680
+أثبت إنه هو بيقسم العدد هذا F and F اللي هو بيقسم
+
+93
+00:09:16,680 --> 00:09:24,370
+اللي هو ال Sالآن لو أجيد اتطلعت للـ B هتلاقيها
+
+94
+00:09:24,370 --> 00:09:32,390
+بتطابق الواحد مدنه مين؟ مدنه B-1 مدام الـ B تطابق
+
+95
+00:09:32,390 --> 00:09:37,930
+الواحد مدنه B-1 إذا حسب نظرية سابقة هتكون B of B
+
+96
+00:09:37,930 --> 00:09:45,530
+يطابق B of واحد مدنه مين؟ مدنه B-1 الـ B of B هذه
+
+97
+00:09:45,530 --> 00:09:52,720
+مين هي؟تطابق الـ P of واحد مين هي الـ S modulo P
+
+98
+00:09:52,720 --> 00:10:00,520
+minus واحد الان الصورة اتبحت P minus واحد بتجسم
+
+99
+00:10:00,520 --> 00:10:07,360
+الان ايش تعني F اندول F الان تطابق السفر modulo
+
+100
+00:10:07,360 --> 00:10:14,030
+مين P نقص واحدواضح، أه؟ الـ N تطابق السفر و الـ S
+
+101
+00:10:14,030 --> 00:10:18,630
+تطابق الـ S إذا أكيد اللي هو if and only if S
+
+102
+00:10:18,630 --> 00:10:24,130
+تطابق السفر modulo B minus واحد وهذا يعني أن الـ B
+
+103
+00:10:24,130 --> 00:10:31,830
+minus واحد بتجسم الـ S وهو المطلوب أي سؤال؟ اللي
+
+104
+00:10:31,830 --> 00:10:41,980
+بعد، يلا الـ N ب application بسيطبقول لي give a
+
+105
+00:10:41,980 --> 00:10:46,580
+criterion for the divisibility of N by تلاتة and
+
+106
+00:10:46,580 --> 00:10:51,660
+تمانية that depends on the digits of N when
+
+107
+00:10:51,660 --> 00:10:53,320
+written in the base 9
+
+108
+00:10:57,750 --> 00:11:03,610
+بقول لي لو كتبنا العدد دا اللي هو الأساس 9 يعني
+
+109
+00:11:03,610 --> 00:11:08,390
+العدد هيكون على صورة M بالساوية A M A Q M زي A 1 A
+
+110
+00:11:08,390 --> 00:11:14,090
+Q 9 أقصام زي A 1 9 زي A Note يعني الأساس اللي
+
+111
+00:11:14,090 --> 00:11:18,410
+عندها ده أشماله عبارة عن 9 لو كان العدد مكتوب على
+
+112
+00:11:18,410 --> 00:11:24,770
+صورة الأساس 9 ابحثلي عن اللي هو test لل
+
+113
+00:11:24,770 --> 00:11:30,170
+divisibility by mean أول إشهرby تلاتة تلاتة سهلة
+
+114
+00:11:30,170 --> 00:11:34,890
+لأن كل العداد من الان كلها بتجبه الجسم على تلاتة
+
+115
+00:11:34,890 --> 00:11:39,230
+لأن كلها فيها تسعات بظل مين اللي هيحكم ان العدد
+
+116
+00:11:39,230 --> 00:11:43,010
+هذا الكل بيجبه الجسم على تسعة ولا لأ على تلاتة ولا
+
+117
+00:11:43,010 --> 00:11:47,930
+لأ اللي هو مين الانوت اذا التلاتة بتجسم الان if
+
+118
+00:11:47,930 --> 00:11:54,170
+and only if التلاتة بتجسم الانوتطيب إذا هي ال test
+
+119
+00:11:54,170 --> 00:12:02,690
+المطلوب عندما تكتب الأمن على صورة اللي هو نظام عدد
+
+120
+00:12:02,690 --> 00:12:10,910
+عدد بالأساس 9 طيب اللي أنا بقوله او ددلي اللي هو
+
+121
+00:12:10,910 --> 00:12:16,910
+testللـ divisibility by تمانية عندما يُكتب الان
+
+122
+00:12:16,910 --> 00:12:24,810
+على صورة مين برضه عدد على نظام العد للأساس تسعة
+
+123
+00:12:24,810 --> 00:12:31,070
+هذا من النظرية اللي جابل بشوية اللي احنا كانت بي
+
+124
+00:12:31,970 --> 00:12:36,610
+اللي هي الاساس هنا عندنا تسعة إذا بيناقص واحد
+
+125
+00:12:36,610 --> 00:12:41,270
+تمانية إذا automatic هتنطق هنا إذا حسب البرهنة قبل
+
+126
+00:12:41,270 --> 00:12:46,270
+شوية اللي هو التمانية اللي هي تسعة ماقص واحد بتقسم
+
+127
+00:12:46,270 --> 00:12:50,650
+الان من الفرع a if and only if اللي هي التمانية
+
+128
+00:12:50,650 --> 00:12:55,610
+بتقسم main اللي هي مجموع ال a نص وال a واحد عند ال
+
+129
+00:12:55,610 --> 00:13:01,410
+a هذا ال testلـ Divisibility by 8 للعدد المكتوب
+
+130
+00:13:01,410 --> 00:13:10,270
+على أساس الأساس 9 طيب ما أعطيك مثال مقول لي هل
+
+131
+00:13:10,270 --> 00:13:15,370
+الانتجار هذا اللي مكتوب بالأساس 9 يقبل قسم ع تلاتة
+
+132
+00:13:15,370 --> 00:13:19,330
+وعلى تمانية ولا لأ ع تلاتة ما أنت عارف أخر أبني
+
+133
+00:13:19,330 --> 00:13:23,350
+الطل عالمين حسب اللي قلنا أخر واحد الستة من
+
+134
+00:13:23,350 --> 00:13:26,930
+المضاعفات التلاتة دون هذا بيقبل قسم عالمين ع تلاتة
+
+135
+00:13:26,930 --> 00:13:30,990
+فاهمينحسب الـ Test اللي قمنا به قليلًا لأن
+
+136
+00:13:30,990 --> 00:13:37,050
+الثمانية تجمع هذه الأعداد إذا تمانية تجسم من خلاص
+
+137
+00:13:37,050 --> 00:13:39,990
+بيقوم بجمع الجسم على ثمانية مجوحين هؤلاء اللي
+
+138
+00:13:39,990 --> 00:13:44,270
+جمعتهم ستجدوا 32 ثمانية تجسم على 32 إذن الثمانية
+
+139
+00:13:44,270 --> 00:13:51,150
+تجسم هذا العدد أي سؤال؟ نجي لسؤال سبعة
+
+140
+00:13:54,370 --> 00:14:01,130
+سؤال 7 برضه مش يابعه لما نضيع الوقت على الأسئلة دي
+
+141
+00:14:01,130 --> 00:14:04,850
+خلّيني
+
+142
+00:14:04,850 --> 00:14:11,730
+أخدها 7C و7A
+
+143
+00:14:11,730 --> 00:14:17,690
+و7D مشابهات لـ 7C هذه
+
+144
+00:14:17,690 --> 00:14:20,870
+معلومة انتوا بتعرفوها بقوللي
+
+145
+00:14:23,100 --> 00:14:28,780
+أحنا عشان .. عشان اللي هو نفحص قابلية القسم على
+
+146
+00:14:28,780 --> 00:14:34,220
+أربعة يعني نقول الأربعة بتجسم الان if and only if
+
+147
+00:14:34,970 --> 00:14:39,030
+الان الان الان هو عبارة عن عدد مكتوب على الصورة
+
+148
+00:14:39,030 --> 00:14:42,270
+العشرية خمسة ستة أربعة تلاتة اتنين واحد سبعة
+
+149
+00:14:42,270 --> 00:14:47,750
+تمانية واحد اتنين مثلا هذا العدد عشان تفحص قابلية
+
+150
+00:14:47,750 --> 00:14:55,320
+القسمة على اربعة بس بتتطلع لمين لاخر رقمينإذا آخر
+
+151
+00:14:55,320 --> 00:14:58,520
+رقامين اللي هو الرقم المتكون من آخر رقامين بيجبه
+
+152
+00:14:58,520 --> 00:15:01,120
+الجسم على أربعة معناته العدد بيجبه الجسم على أربعة
+
+153
+00:15:01,120 --> 00:15:06,200
+طيب إذا اللي بدهيا هو المطلوب أنه أربعة تقسم الان
+
+154
+00:15:06,200 --> 00:15:11,820
+F and only F اللي هو الأربعة بتجسم العدد اللي هو
+
+155
+00:15:11,820 --> 00:15:17,020
+مكوّن من آخر خانتين آخر خانتين اللي هو عشرة A1 زي
+
+156
+00:15:17,020 --> 00:15:25,690
+2 A0 إيش ال A1 و ال A0 الان تبعتناإيش بتساوي صورة
+
+157
+00:15:25,690 --> 00:15:29,810
+العامة إلها صورة العامة في النظام العشري كيف
+
+158
+00:15:29,810 --> 00:15:35,750
+كتبناها a m عشرة أقص م لما أصل عند a واحد في عشرة
+
+159
+00:15:35,750 --> 00:15:40,810
+زائد زائد مين زائد a نوت وال a نوت وال a واحد عند
+
+160
+00:15:40,810 --> 00:15:45,250
+ال a m أعداد بين أكبر بساوية سفر وأصغر بساوية تسعة
+
+161
+00:15:45,250 --> 00:15:55,300
+معايا أه الآن الأمر الأمر خيارنا بسيطلاحظ ان
+
+162
+00:15:55,300 --> 00:16:04,380
+الاربعة بتجسم الان if and only if ان اللي هو سفر
+
+163
+00:16:04,380 --> 00:16:13,100
+طابق الان مدنه مين مدنه اربعة مظبوط ولا لا؟ اكيد
+
+164
+00:16:13,100 --> 00:16:21,440
+طيب الان الان هذه مين هي؟ الان هذه ايش هي؟ عبارة
+
+165
+00:16:21,440 --> 00:16:31,120
+عنام عشرة وش سام زاد زاد ا واحد في عشرة زاد a note
+
+166
+00:16:31,120 --> 00:16:35,420
+هذا جون اشماله بطابق السفر فنقول ليه بطابق السفر
+
+167
+00:16:35,420 --> 00:16:44,340
+بطابق لاحظ ان الأرقام اتنين في مين اللي جابلها في
+
+168
+00:16:44,340 --> 00:16:50,190
+مية كل هذهاللي هي M عشرة أقسام M minus واحد عشرة
+
+169
+00:16:50,190 --> 00:16:54,090
+أقسام minus واحد لعند A اتنين في مية كلهم فيهم
+
+170
+00:16:54,090 --> 00:16:59,690
+ميات والمية بتجسم الأربعة إذا كلهم أشمال بالنسبة
+
+171
+00:16:59,690 --> 00:17:03,430
+للأربعة من مضاعفات الأربعة يعني كلهم سفر بالنسبة
+
+172
+00:17:03,430 --> 00:17:08,430
+للأربعة يعني هذا بطابق العشرة A واحد زائد مين
+
+173
+00:17:08,430 --> 00:17:14,770
+مودولو مين أربعةوهذا ايش يعني؟ F and والـ F طبعاً
+
+174
+00:17:14,770 --> 00:17:20,430
+هذا الكلام بطابق الصفر لإن الرقم هذا أصلا دائما
+
+175
+00:17:20,430 --> 00:17:25,290
+بطابق العشرة A واحد زائد A Note Modulo أربعة فإذا
+
+176
+00:17:25,290 --> 00:17:31,960
+F and والـ F الأربعة بتكسب عشر A واحد زائد Aوهكذا
+
+177
+00:17:31,960 --> 00:17:36,600
+اي سؤال انزلي على سؤال ستة مش معطيكم إياه الشكل
+
+178
+00:17:36,600 --> 00:17:40,520
+اللي كابلها كان معطيكم إياه بس مشطوع سؤال ستة فيه
+
+179
+00:17:40,520 --> 00:17:46,760
+فكرة جميلة ويمكن يكون فكرة متنوعة عن السؤال سبعة
+
+180
+00:17:46,760 --> 00:17:51,100
+لأنه سبعة أصلا زيه زي البرهين النظريات اللي
+
+181
+00:17:51,100 --> 00:17:56,520
+أخدناها نشوف أيش ستة بيقول خلينا نشرح ستة بالتفصيل
+
+182
+00:17:57,450 --> 00:18:00,730
+ونشوف كيف اللي هو السؤال بيحكي موجود في الكتاب
+
+183
+00:18:00,730 --> 00:18:04,970
+سؤال 6 طيب انتبهوا لسؤال 6 هنزلكوا جميعا كلنا على
+
+184
+00:18:04,970 --> 00:18:11,530
+الصفحه الحلول كلها هنزلها على الصفحه الان working
+
+185
+00:18:11,530 --> 00:18:18,410
+modulo 9 or 11 اللي بتبتاح نفسك له وبناسب السؤال
+
+186
+00:18:18,410 --> 00:18:22,750
+ركز معايا في اللي بحكيه كله find the missing
+
+187
+00:18:22,750 --> 00:18:29,250
+integersأو انتجر اللي هو in the calculations below
+
+188
+00:18:29,250 --> 00:18:36,570
+لان في كل فرع من الأسئلة ماعطيك اللي هو X مفقودة
+
+189
+00:18:36,570 --> 00:18:40,650
+سواء الـ X في جهة هذه أو في جهة هذه أو في الجهتين
+
+190
+00:18:40,650 --> 00:18:47,290
+وبدى نوجد مين قيمة هذه الـ Xالفكرة بيقول يا بتحل
+
+191
+00:18:47,290 --> 00:18:53,630
+مدلوا 9 يا مدلوا ايش 11 الفكرة انه احنا نشيل كل
+
+192
+00:18:53,630 --> 00:18:57,570
+المضاعفات التسعة او المضاعفات ال 11 من الرقم
+
+193
+00:18:57,570 --> 00:19:02,710
+الكبير لما نزغره لرقم صغير و بيصير معادلة اللي هو
+
+194
+00:19:02,710 --> 00:19:06,530
+عالدي و هادي و عالدي و هادي بس بأرقام قليلة و
+
+195
+00:19:06,530 --> 00:19:10,610
+بدلالة X و بتحل ال X بعدها ماشي الحالة نشوف اش
+
+196
+00:19:10,610 --> 00:19:15,410
+اللي بيقوله في عند السؤال كما يلي ايهماعطيك الرقم
+
+197
+00:19:15,410 --> 00:19:24,030
+ماعطيك هو خمسة واحد تمانية اربعة سفر مضروب في
+
+198
+00:19:24,030 --> 00:19:31,870
+اتنين سبعة تلاتة خمسة تمانية واحد اللي هو بساوي
+
+199
+00:19:31,870 --> 00:19:35,030
+واحد
+
+200
+00:19:35,030 --> 00:19:44,130
+اربعة واحد تمانية اتنين اربعةتلاتة اكس سفر اربعة
+
+201
+00:19:44,130 --> 00:19:48,610
+سفر معطيك
+
+202
+00:19:48,610 --> 00:19:52,870
+ان الرقامين هذين اشمال هين متساويين متساويين يعني
+
+203
+00:19:52,870 --> 00:19:56,290
+لو ضربت هذا الرقم في هذا الرقم هيطلع هذا الرقم منه
+
+204
+00:19:56,290 --> 00:20:00,110
+بدك تجيب مين بدك تجيب قيمة X بدون ما تضرب بدك توجد
+
+205
+00:20:00,110 --> 00:20:06,730
+قيمة X معايا؟ شوف الفكرة وين اجالك اشتغل يوم ودوله
+
+206
+00:20:06,730 --> 00:20:11,940
+تسعة يوم ودوله مين احداشرلو جيترا حبط على الرقم
+
+207
+00:20:11,940 --> 00:20:16,800
+هذا أول حاجة قبل ما أبدأ احنا قلنا ال .. ال .. ال
+
+208
+00:20:16,800 --> 00:20:21,700
+.. ال .. الأمن العدد بيجسم بالـ 11 إذا و فقط إذا
+
+209
+00:20:21,700 --> 00:20:27,700
+الـ T تبعت وبتجسم مين 11 معايا، إيش الـ T كانت؟
+
+210
+00:20:27,700 --> 00:20:30,680
+اللي هو الخانة الأولى، ناقص التانية، ناقص، زائد،
+
+211
+00:20:30,680 --> 00:20:33,180
+ناقص، زائد، ناقص، زائد، دون ضلم الشيء للآخر، مظبوط
+
+212
+00:20:33,180 --> 00:20:42,470
+ولا لأ؟ طيب، الآن العدد هذابتشوف لو جيت لحظة واحد
+
+213
+00:20:42,470 --> 00:20:46,310
+ناقص تمانية زائد خمسة ناقص ثلاثة زائد سبعة ناقص
+
+214
+00:20:46,310 --> 00:20:52,730
+اتنين هتلاقي العدد هذا ايش ماله بيساوي سفر لو حصل
+
+215
+00:20:52,730 --> 00:20:57,190
+ال test تبعه ال T تبعته ايش بتساوي سفر مفهوم مش ال
+
+216
+00:20:57,190 --> 00:21:02,710
+T إذا أكيد هذا بيكسب مين ال 11 مدام بيكسب ال 11
+
+217
+00:21:02,710 --> 00:21:08,850
+إذا هذا الرقمبطابق حصلت ضرب X من ال 11 إذا هذا
+
+218
+00:21:08,850 --> 00:21:14,010
+الرقم إيش ماله يطابق الصفر مدل مين مدل 11 إذا
+
+219
+00:21:14,010 --> 00:21:19,890
+المساوي إله هذا برضه هيطابق الصفر مدل إيش مدل 11
+
+220
+00:21:19,890 --> 00:21:30,030
+معناته الصفر يطابق ال 1 4 1 8 2 4 3 2 X 0 4 0 مدل
+
+221
+00:21:30,030 --> 00:21:37,440
+من 11 مظبوط ولا لأ؟ طيبالان انا شغله بدول 11 الان
+
+222
+00:21:37,440 --> 00:21:40,020
+احنا بنقول ان ال M بتجسم ال 11 فان دول M في ال T
+
+223
+00:21:40,020 --> 00:21:45,280
+تبعتها اشمالها بتجسم ال 11 اذا مدان هذا بتجسم ال
+
+224
+00:21:45,280 --> 00:21:50,640
+11 اذا ال T تبعته برضه بتجسم ال 11 يعني ال T تبعته
+
+225
+00:21:50,640 --> 00:21:55,660
+بطابق الصفر يعني ال T تبعته هذا بطابق ال Tأيش الـ
+
+226
+00:21:55,660 --> 00:21:59,860
+T؟ اللي هو سفر ناقص أربعة ناقص سفر زاد X ناقص
+
+227
+00:21:59,860 --> 00:22:04,320
+اتنين زاد تلاتة ناقص أربعة إلى آخره هذا كله جدّاش
+
+228
+00:22:04,320 --> 00:22:10,500
+محسوب أنا حاسبه هان هاي هذا كله قيمته عبارة عن
+
+229
+00:22:10,500 --> 00:22:18,500
+سالب تلاتاش سالب مين؟ X سالب موجب
+
+230
+00:22:18,500 --> 00:22:24,520
+سالب موجبسالب موجب سالب موجب الاخرين اللي هو عبارة
+
+231
+00:22:24,520 --> 00:22:30,560
+عن ايش يا شباب سالب تلتاش سالب X مدلمين واضحش اللي
+
+232
+00:22:30,560 --> 00:22:35,070
+عملتهالآن بدي أنجل الـ 13 الجهة الثانية أو الـ X
+
+233
+00:22:35,070 --> 00:22:39,250
+على الجهة الثانية بيصير X تطابق السلب 13 مدل 11
+
+234
+00:22:39,250 --> 00:22:44,750
+أنا بدي X، X هذه خانة، في الخانة هذه، هتكون بين
+
+235
+00:22:44,750 --> 00:22:49,730
+الصفر وبين 100 يعني الـ X أكبر أو يساوي صفر وأصغر
+
+236
+00:22:49,730 --> 00:22:54,410
+يساوي مين؟ تسعة، يعني السلب 13 تلزمنيش، إذا امين
+
+237
+00:22:54,410 --> 00:23:01,010
+اللي هيلزمني الآن، ضيف الـ 22، بتطلع كده؟موضله 11
+
+238
+00:23:01,010 --> 00:23:10,350
+إذا X بالظبط إيش هتساوي؟ هتساوي 9 واضح أه؟ أي
+
+239
+00:23:10,350 --> 00:23:14,330
+سؤال؟ اللي بعده نيجي للسؤال B شوف عليها بيه على
+
+240
+00:23:14,330 --> 00:23:23,560
+السريع معطيكاللي هو العدد 2 X 9 9 5 6 1 بساوي 3 في
+
+241
+00:23:23,560 --> 00:23:28,760
+5 2 3 زاد X الكل أشماله الكل تربية معايا يا شباب
+
+242
+00:23:28,760 --> 00:23:34,400
+طيب الآن طبعا من أول ما لاحظنا السؤال أكيد اللي هو
+
+243
+00:23:34,400 --> 00:23:39,920
+راح جابني أو سحبني باتجاه التسعة ليش؟ لأن هنا فيه
+
+244
+00:23:39,920 --> 00:23:44,170
+تلاتة أو تربية مانعته تسعةثلاثة مضروبة لأن المربع
+
+245
+00:23:44,170 --> 00:23:47,130
+بيصير تسعة إذا ما كان العدد يقبل القسم على تسعة
+
+246
+00:23:47,130 --> 00:23:51,550
+إذا صاحبه لازم اللي مساوي الوش برضه يقبل القسم على
+
+247
+00:23:51,550 --> 00:23:57,810
+تسعة إذا صار سهل الأمر إذا صار عندي الآن صار عندي
+
+248
+00:23:57,810 --> 00:24:06,150
+عندي اللي هو Bصار عندي اللي هو هذا سفر بالنسبة
+
+249
+00:24:06,150 --> 00:24:11,850
+للتسعة إذا السفر تطابق هذا سفر بالنسبة للتسعة إذا
+
+250
+00:24:11,850 --> 00:24:13,330
+هذا سفر بالنسبة للتسعة
+
+251
+00:24:18,620 --> 00:24:24,120
+ان التسعة بتكسب الان اف ان دولة اف الاس بتكسب
+
+252
+00:24:24,120 --> 00:24:29,520
+التسعة بتكسب الاس الاساس هي a note زي a واحد زي
+
+253
+00:24:29,520 --> 00:24:35,420
+اتنين زي am يعني مجموع اللي هي مين الخنات صح؟ إذا
+
+254
+00:24:35,420 --> 00:24:40,060
+هذا سفر بطابق اللي هو الرقم هذا مضله تسعة إذا
+
+255
+00:24:40,060 --> 00:24:47,510
+بطابق هذا كيف نعمله هذا اجمع واحد زي ستةزايد خمسة
+
+256
+00:24:47,510 --> 00:24:53,910
+زايد تسعتين زايد X زايد اتنين هذا كله مضله مين؟
+
+257
+00:24:53,910 --> 00:24:58,390
+مضله تسعة يطبع اجمعه للان تسعة و تسعة و تمانتاش
+
+258
+00:24:58,390 --> 00:25:03,750
+عشرين و خمسة و عشرين واحد اتنين و تلاتين زايد مين؟
+
+259
+00:25:03,750 --> 00:25:11,630
+X مضله تسعة شيل من اتنين و تلاتين ستة و تلاتين اه
+
+260
+00:25:11,630 --> 00:25:17,350
+بيصير سالب اربعةزاد X مدنه مين؟ مدنه تسعة طبعا ليش
+
+261
+00:25:17,350 --> 00:25:21,570
+انا هعمل السالب اربع عشان ننجلها بعد شوية يعني ليش
+
+262
+00:25:21,570 --> 00:25:26,950
+مااخدت مثلا اللي هو بس سبعة و عشرين عشان ماعرف
+
+263
+00:25:26,950 --> 00:25:32,850
+اعمل مرتين لذا صار عند ال X تطابق الأربعة مدنه
+
+264
+00:25:32,850 --> 00:25:40,710
+تسعة لذا ناخد X بالساوية
+
+265
+00:25:44,310 --> 00:25:51,110
+أي سؤال؟ لاحظ الآن الحل هذا مش لحاله أربعة و تلتاش
+
+266
+00:25:51,110 --> 00:25:55,310
+و كده و كده بس مين اللي .. اللي أنا بنسبني الـ X
+
+267
+00:25:55,310 --> 00:26:00,330
+اللي بين السفر و بين التسعة لإن أنا خيه أنا بدي
+
+268
+00:26:00,330 --> 00:26:07,460
+ماشي الحل اللي بعده؟مش دايما الدنيا هيك سهلة و
+
+269
+00:26:07,460 --> 00:26:10,520
+العدد اللي واحد من العددين بيقبل جسمها على 11 أو
+
+270
+00:26:10,520 --> 00:26:14,320
+بيقبل جسمها على 9 أحيانا لا بيقبل جسمها 9 ولا
+
+271
+00:26:14,320 --> 00:26:18,400
+بيقبل جسمها على 11 طب إيش بدى أسوي في حال بيقبلش
+
+272
+00:26:18,400 --> 00:26:22,640
+القسم على 9 أو بيقبلش القسم على 11 بناخد الطرف من
+
+273
+00:26:22,640 --> 00:26:25,780
+ال .. بناخد الطرفين كل واحد لحال ناخد الطرف الأول
+
+274
+00:26:25,780 --> 00:26:31,840
+و بنشيل منه كل التسعات أو كل إحد أعشاتوالطرف
+
+275
+00:26:31,840 --> 00:26:35,460
+الثاني بنشيل منه التسعات كلها أو الاحداشات كلها
+
+276
+00:26:35,460 --> 00:26:40,580
+وبنساو الطرفين وبنحل بنوجد قيمة X بنشوف هذا عمليا
+
+277
+00:26:40,580 --> 00:26:52,340
+الان نيجي لسؤال اللي عندى 2784X ساو X في 5569 الان
+
+278
+00:26:52,340 --> 00:26:59,800
+خليني أشوفطبعاً بدي أروح أنا باتجاه اللي هو التسعة
+
+279
+00:26:59,800 --> 00:27:04,560
+يعني ممكن تروح باتجاه الـ 11 بس انا يمكن ا ..
+
+280
+00:27:04,560 --> 00:27:07,660
+خلّيني أقول التسعة أقرب للنفس أسهل إلا إذا كان
+
+281
+00:27:07,660 --> 00:27:10,960
+طبعاً السؤال نفسه بقولك استخدم الـ 11 زي اللي
+
+282
+00:27:10,960 --> 00:27:14,620
+جابله هو بحكيلك إنه أنا بنفعني اللي احتاج فاهمين
+
+283
+00:27:14,620 --> 00:27:19,740
+إيش بحكيهم طيب لإنه التسعة تستها مجموع وامشي
+
+284
+00:27:19,740 --> 00:27:23,000
+الواحد ده كده و واحد ناقص و واحد ناقص بنفع بس
+
+285
+00:27:23,000 --> 00:27:26,690
+طبعاً يعني المجموع يمكن أسهلطيب شوفوا صلة على
+
+286
+00:27:26,690 --> 00:27:31,350
+النبي عليه الصلاة والسلام الآن ناخد رقم رقم من
+
+287
+00:27:31,350 --> 00:27:35,970
+هذول أول حاجة هذا الرقم 2 7 8 4 X هو عبارة عن
+
+288
+00:27:35,970 --> 00:27:39,310
+27840
+
+289
+00:27:39,310 --> 00:27:45,130
+زاد ال X مظبوط و هذا عبارة عن X مضروف في هذا الرقم
+
+290
+00:27:45,130 --> 00:27:49,170
+خلينا نشوف هذا و نشوف هذا نشوف إيش بنسوي مع
+
+291
+00:27:49,170 --> 00:27:49,630
+التانية
+
+292
+00:27:54,770 --> 00:28:05,370
+هذا C ناخد يا شباب عندي X مضروبة في خمسة خمسة ستة
+
+293
+00:28:05,370 --> 00:28:10,870
+تسعة بساوية او بطاقة او بساوية خلّيني أقول بطاقة
+
+294
+00:28:10,870 --> 00:28:16,390
+اكس فيه مضروبة الاهل هذا العدد ايش الفكرة اني بدي
+
+295
+00:28:16,390 --> 00:28:20,880
+اشيل التسعات منهلأن خمسة و خمسة عشرة و ستة و ست
+
+296
+00:28:20,880 --> 00:28:23,940
+عشرة و ست عشرة و ست عشرة و ست عشرة و ست عشرة و ست
+
+297
+00:28:23,940 --> 00:28:25,700
+عشرة و ست عشرة و ست عشرة و ست عشرة و ست عشرة و ست
+
+298
+00:28:25,700 --> 00:28:25,720
+عشرة و ست عشرة و ست عشرة و ست عشرة و ست عشرة و ست
+
+299
+00:28:25,720 --> 00:28:26,820
+عشرة و ست عشرة و ست عشرة و ست عشرة و ست عشرة و ست
+
+300
+00:28:26,820 --> 00:28:26,860
+عشرة و ست عشرة و ست عشرة و ست عشرة و ست عشرة و ست
+
+301
+00:28:26,860 --> 00:28:32,860
+عشرة و ست عشرة و ست عشرة و ست عشرة و ست عشرة و ست
+
+302
+00:28:32,860 --> 00:28:39,100
+عشرة و ست عشرة و ست عشرة
+
+303
+00:28:39,100 --> 00:28:46,120
+و ست عشرة و سعارفين ليش عملته هيك؟ عشان هذا سفر
+
+304
+00:28:46,120 --> 00:28:50,660
+بالنسبة لمين؟ بالنسبة للتسعة، إذا هذا بيصير طابق
+
+305
+00:28:50,660 --> 00:28:53,780
+يعني هذا العدد كتبته على الصورة هذه، شمعنا على
+
+306
+00:28:53,780 --> 00:28:57,860
+الصورة هذه عشان اللي هو كتبته العدد هو متبقي
+
+307
+00:28:57,860 --> 00:29:05,020
+بالقسمة على تسعة هذا بيصير طابق سبعة X بس modulo
+
+308
+00:29:05,020 --> 00:29:15,200
+مين؟ وهذا يطابق السفر modulo تسعةفهذا الطرف الأيمن
+
+309
+00:29:15,200 --> 00:29:22,880
+ليه دي الطرف الأيسر؟ 2 7 8 4 X إيش بيساوي هذا 2 7
+
+310
+00:29:22,880 --> 00:29:31,560
+8 4 0 زي 100 زي X صح ولا لأ؟الأن بدنا نشوف هذا
+
+311
+00:29:31,560 --> 00:29:37,500
+العدد الان هذا العدد اتنين سبعة تسعة وتمانية
+
+312
+00:29:37,500 --> 00:29:43,000
+سبعتاش سبعتاش واربعة وواحد وعشرين وواحد وعشرين يا
+
+313
+00:29:43,000 --> 00:29:46,280
+بد اضيفله يا بد انجزله اللي بدك هيه واحد وعشرين
+
+314
+00:29:46,280 --> 00:29:53,850
+واحد وعشرين اضيفله تلاتةدى فلوس 6 بيصير 27 صح؟ اذا
+
+315
+00:29:53,850 --> 00:29:59,050
+ان هذا بيصير عبارة عامة اتنين سبعة تمانية اربعة
+
+316
+00:29:59,050 --> 00:30:03,210
+قولنا ستة زاد اكس ماقص ستة اللي اضفتها بداية
+
+317
+00:30:03,210 --> 00:30:10,060
+اشيلها عشان العدد نفسه يطلع فاهمين اش سويتها؟هذا
+
+318
+00:30:10,060 --> 00:30:15,540
+العدد صفر بالنسبة للتسعة اذا انا .. معايا اه؟ اذا
+
+319
+00:30:15,540 --> 00:30:21,420
+أنا ده بطابق ال X ناقص ستة modulo تسعة هاي واحد
+
+320
+00:30:21,420 --> 00:30:28,360
+هاي اتنين من واحد و اتنين بيصير عندي الآن سبعة X
+
+321
+00:30:28,360 --> 00:30:38,340
+تطابق X ناقص ستة modulo تسعة modulo تسعةالآن بيصير
+
+322
+00:30:38,340 --> 00:30:45,260
+عبارة عن اجسم بيصير ماله 6x تطابق اللي هو سالب 6
+
+323
+00:30:45,260 --> 00:30:52,780
+مدنه 100 مدنه 9 بدك تجسم الجهتين على 6على .. مش
+
+324
+00:30:52,780 --> 00:30:55,780
+وشكلها، بتقسم الجهتين على ستة لما تقسم .. لا على
+
+325
+00:30:55,780 --> 00:31:00,280
+ستة، لما تقسم على ستة لازم تقسم التسعة على مين؟
+
+326
+00:31:00,280 --> 00:31:03,460
+على الـ greatest common divisor بين الستة والتسعة
+
+327
+00:31:03,460 --> 00:31:08,460
+اللي هو جديش، تلاتة فبصير عندك الآن الـ X تطابق
+
+328
+00:31:08,460 --> 00:31:14,640
+الناقص واحد modulo جديش modulo تلاتة الناقص واحد
+
+329
+00:31:14,640 --> 00:31:20,700
+مين هو؟ X بتطابق التنين modulo مين modulo تلاتة
+
+330
+00:31:21,460 --> 00:31:27,400
+لاحظ انه الاعداد انت بتاكي الاعداد بين مين ومين ال
+
+331
+00:31:27,400 --> 00:31:32,980
+X تبعك بين السفر وبين ايه ايش التسعة اكم X هنا
+
+332
+00:31:32,980 --> 00:31:39,430
+بتحقق بين السفر والتسعةعندك X بساوة 2 وخمسة و
+
+333
+00:31:39,430 --> 00:31:45,710
+تمانية و واحدة من هدولة لازم تحقق مش هيظبط كلها
+
+334
+00:31:45,710 --> 00:31:50,270
+واحدة منها لازم تحقق بسيط طب نعمل test بسيط بنيجي
+
+335
+00:31:50,270 --> 00:31:56,110
+بنضرب التنين في الطرق هنا مظبوط و هنا اتنين لو
+
+336
+00:31:56,110 --> 00:32:00,230
+اعوضنا ب X بساوة 2 بصير هذا اتنين هذا الرقم اللي
+
+337
+00:32:00,230 --> 00:32:04,470
+هنا لو ضربناه في اتنين من اول ضرب اتنين في تسعة مش
+
+338
+00:32:04,470 --> 00:32:08,820
+هولو بيصير خمسة لحد اشمالان تمانية بينما هنا إيش
+
+339
+00:32:08,820 --> 00:32:13,100
+يعني لو كان حتى الرقم قد ما يكون كبير بيانة العدل
+
+340
+00:32:13,100 --> 00:32:21,200
+واضح إذا أكيد مش الاتنين الآن تعالى الخمسة حط
+
+341
+00:32:21,200 --> 00:32:26,260
+الخمسة و أضرب الخمسة الآن خمسة فتسعة وخمسة واربعين
+
+342
+00:32:26,260 --> 00:32:30,480
+شكله هو اتأكد وضرب طلع هو التمانية حتى جهانش هو
+
+343
+00:32:30,480 --> 00:32:37,150
+إذا ال X أشبه الساوية اللي لدينا بالساويةأو في
+
+344
+00:32:37,150 --> 00:32:41,450
+تلات حاجات بس لأن هما solutions لمين للتطابق هو
+
+345
+00:32:41,450 --> 00:32:46,510
+هناك هذا تطابق هناك تساوي ماشي الحال فانت بالظبط
+
+346
+00:32:46,510 --> 00:32:50,610
+ده بتشوف مين اللي بساوي واضح اه خلينا نحلكم السؤال
+
+347
+00:32:50,610 --> 00:32:55,510
+الأخير دي برضه نثبت الفكرة عندي خمسمية واطمعاش في
+
+348
+00:32:55,510 --> 00:32:57,550
+هذا بساوي هذا اه
+
+349
+00:32:59,610 --> 00:33:03,750
+الان كيف بدك تشتغل بنفع؟ بدك تشتغل بالـ9 بنفع؟ بدك
+
+350
+00:33:03,750 --> 00:33:08,130
+تشتغل بالـ11 بنفع؟ يمكن هنا أنا بقى يعني هيك على
+
+351
+00:33:08,130 --> 00:33:13,010
+حلتي يعني اللي انت طلعت على طول اجا بالي لوحد هنا
+
+352
+00:33:13,010 --> 00:33:17,610
+واحد ممكن يجا باله الـ9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+353
+00:33:17,610 --> 00:33:18,630
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+354
+00:33:18,630 --> 00:33:24,690
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+355
+00:33:24,690 --> 00:33:24,690
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+356
+00:33:24,690 --> 00:33:24,690
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+357
+00:33:24,690 --> 00:33:24,690
+9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
+
+358
+00:33:25,120 --> 00:33:30,380
+تفشوف كيف يعني قولت هذا العدد واحد وطرحت منه واحد
+
+359
+00:33:30,380 --> 00:33:35,100
+بيصير العدد هذا يقبل قسم ال 11 ويبقى المين الواحد
+
+360
+00:33:35,100 --> 00:33:43,260
+بدكوا
+
+361
+00:33:43,260 --> 00:33:49,100
+نحل ب9 بحل ب9 بس عشان أنوع الحل أما بنفع ب9 ماشي
+
+362
+00:33:51,980 --> 00:33:56,000
+أي موجود هنا بـ 11 ماشي الحل الحلم بـ 9 الان
+
+363
+00:33:56,000 --> 00:34:02,100
+الواحد و كم سفر اعطينا كم سفر بالله لكي نخبره تسعة
+
+364
+00:34:02,100 --> 00:34:06,240
+أسفار ايش
+
+365
+00:34:06,240 --> 00:34:13,480
+بيساوي بيساوي تسعة تنتين تلاتة أربعة خمسة ستة سبعة
+
+366
+00:34:13,480 --> 00:34:17,780
+تمانية تسعة مش مشكلة ان الله يطير زيدي ايش زيدي
+
+367
+00:34:17,780 --> 00:34:24,090
+واحد صح؟مدره تسعة يعني هدولة بطاقة واحد مدنه مين
+
+368
+00:34:24,090 --> 00:34:29,070
+مدره تسعة اذا سهل هذا الموضوع ممكن اسأل كمان بغضب
+
+369
+00:34:29,070 --> 00:34:39,570
+نجي للبعده خمسة واحد اتنين في اليومين واحد اشترك
+
+370
+00:34:39,570 --> 00:34:44,870
+ومشتغل بضغط بسرعة اشتغل مرة واحدة مش مشكلة خمسة
+
+371
+00:34:44,870 --> 00:34:50,040
+خمسة تلاتة واحدأتنين خمسة بديش أخربط لإننا بنحلها
+
+372
+00:34:50,040 --> 00:34:55,000
+فشلنا جوابها الجد خمسمية و أتناشر خمسة و واحد ستة
+
+373
+00:34:55,000 --> 00:35:00,780
+ستة و اتنين تمامية تمامية مظبوط زود واحد بيصير و
+
+374
+00:35:00,780 --> 00:35:07,560
+ناقص واحد مظبوط بيصير هذا عبارة عن خمسمية و تلتاشر
+
+375
+00:35:07,560 --> 00:35:17,810
+ناقص واحد وصلنا في هذا مين هوخلّيني أعمل أول
+
+376
+00:35:17,810 --> 00:35:24,570
+لبعدين 1 X 5 3 1 2 5 هذا بطابق نعمله بطابق قبل مرة
+
+377
+00:35:24,570 --> 00:35:31,230
+الآن هذا صفر مظبوط إذن هذا سالب واحد مضروب في هذا
+
+378
+00:35:31,230 --> 00:35:38,970
+بطابق من العدد بطابق مجموعه لإنه بدي أشمله بطابق
+
+379
+00:35:38,970 --> 00:35:44,800
+اللي هو واحدزايد X زايد Modulo 9 Modulo 9 Modulo 9
+
+380
+00:35:44,800 --> 00:35:48,520
+Modulo 9 العدد بطابق مجموعه Modulo مين Modulo 9
+
+381
+00:35:48,520 --> 00:35:54,020
+زايد 5 زايد 3 زايد 1 زايد 2 زايد 5 ان شاء الله
+
+382
+00:35:54,020 --> 00:35:58,420
+مايكونوش خربطنا بيساوي اتفضل على العداد نعيد
+
+383
+00:35:58,420 --> 00:36:06,640
+Modulo 11 Modulo
+
+384
+00:36:06,640 --> 00:36:06,860
+9
+
+385
+00:36:09,670 --> 00:36:13,970
+الخطوة التالية هي الـ 17 أضافة
+
+386
+00:36:13,970 --> 00:36:20,090
+X لإيقاف X ناقص X
+
+387
+00:36:22,000 --> 00:36:29,120
+وهذا يطابق مين؟ واحد ناقص X موديلو تسعة لأنه ناقص
+
+388
+00:36:29,120 --> 00:36:32,160
+سبعتاش يتطابق مين؟ الواحد، اضيف تعالى للسبعتاش
+
+389
+00:36:32,160 --> 00:36:35,920
+اللي هو تسعتين تمانتاش، من سفر تسعة هذا يتطابق
+
+390
+00:36:35,920 --> 00:36:40,420
+مين؟ اللي هو واحد ناقص X وهذا يتطابق هذا، وهذا
+
+391
+00:36:40,420 --> 00:36:47,720
+بيساوي هذا، اذا فمين؟ اذا هاي واحد وهاي اتنين from
+
+392
+00:36:49,170 --> 00:37:02,160
+1 and 2 we get 1 يطابق 1-xThat is طبعا Modulo 9
+
+393
+00:37:02,160 --> 00:37:09,720
+جيب ال X إذا X تطابق السفر Modulo إيش Modulo 9 إذا
+
+394
+00:37:09,720 --> 00:37:16,980
+ال X بتساوي سفر Or ال X إيش بتساوي تسعة الآن سفر
+
+395
+00:37:16,980 --> 00:37:22,760
+هتلاجوه بظبطش فإيش بده يطلع تطلع تسعة
+
+396
+00:37:27,600 --> 00:37:40,320
+واضح أه؟ أي سؤال؟ اطلع للبعد ويلّا خلّيني .. إيش
+
+397
+00:37:40,320 --> 00:37:49,640
+هذا السؤال اللي بعده؟ ال problem أربعة تلاتة أنا
+
+398
+00:37:49,640 --> 00:37:53,800
+ماليش خطأ ده حلنا زيه كتير ال .. ال .. اه اطلع ..
+
+399
+00:37:53,800 --> 00:37:55,120
+اطلعنا على أربعة أربعة يلّا
+
+400
+00:37:59,240 --> 00:38:04,340
+لا حلنا هدولة اطلع الـ 4×4 انزل
+
+401
+00:38:04,340 --> 00:38:13,100
+انزل ماشي الحل الـ
+
+402
+00:38:13,100 --> 00:38:17,620
+congruences بتصور احنا أشبعناها حل مافيش داعي نحل
+
+403
+00:38:17,620 --> 00:38:24,910
+اللي هو خلينا بس نتطلع السريعالسؤال Solve the
+
+404
+00:38:24,910 --> 00:38:27,390
+following linear congruences الـ Linear
+
+405
+00:38:27,390 --> 00:38:30,970
+congruences صارت بالنسبة لنا سهلة وبدهية 25 نكس
+
+406
+00:38:30,970 --> 00:38:35,030
+الطابق الخمس عشر مدل وتسعة وعشرين الان بنيجي بنفحص
+
+407
+00:38:35,030 --> 00:38:37,270
+الخمسة عشرين والتسعة وعشرين عاملوا شتراك الأعلى
+
+408
+00:38:37,270 --> 00:38:40,230
+واحد إذا في إليها إيش ماله إليها unique solution
+
+409
+00:38:40,230 --> 00:38:45,450
+وبنبدأ نحل بتعرفوا تحله زي ما عملنا قبل شوية واضحة
+
+410
+00:38:45,450 --> 00:38:51,730
+ففيش داعي له اطلع لفوق السؤال الأول سهلاطلع اطلع
+
+411
+00:38:51,730 --> 00:38:56,410
+اطلع
+
+412
+00:38:56,410 --> 00:39:05,430
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+413
+00:39:05,430 --> 00:39:13,950
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+414
+00:39:14,580 --> 00:39:20,160
+أتنين using congruences Solve
+
+415
+00:39:20,160 --> 00:39:24,340
+the Diophantine equations below بدنا نستخدم اللي
+
+416
+00:39:24,340 --> 00:39:28,000
+هو ال congruences في حال مين؟ في حال ال
+
+417
+00:39:28,000 --> 00:39:32,020
+Diophantine equations معايا يا شباب؟ شوف عليها
+
+418
+00:39:32,020 --> 00:39:39,590
+إنها 4x زي 51y بساوة 9 شوف أشي اللي بدى أسويهبدي
+
+419
+00:39:39,590 --> 00:39:43,970
+اللي هو اشتغل شغلتين و بعدين ادويتهم مع بعض و هصلك
+
+420
+00:39:43,970 --> 00:39:48,610
+على الـ General solution اللي بالظبط كنا نوجده لما
+
+421
+00:39:48,610 --> 00:39:50,850
+كنا نحل الـ Different Time Equation بالطريقة اللي
+
+422
+00:39:50,850 --> 00:39:57,050
+احنا بنعرفها الآن الـ 4X ده يشغل على الـ Excel
+
+423
+00:39:57,050 --> 00:40:02,990
+الان الـ 4X على الطابق التسعة مدله مين؟ مدل 51 من
+
+424
+00:40:02,990 --> 00:40:07,430
+وين جبت هذه انا؟ اصلا الـ 51 هتقسم الـ 4X نقص 9
+
+425
+00:40:08,180 --> 00:40:12,320
+مظبوط يعني اربع اكس نقص تسعة بساوي واحد وخمسين في
+
+426
+00:40:12,320 --> 00:40:17,700
+some Y مظبوط ارجعنا لايه اشي مشابه لمين لدفن تاين
+
+427
+00:40:17,700 --> 00:40:25,380
+اكويتيك واضحش اللي سويته طيب الاربع اكس واحد
+
+428
+00:40:25,380 --> 00:40:31,560
+وخمسين معامل ال Yواجه هذه العصر لها، ايش بتصير؟
+
+429
+00:40:31,560 --> 00:40:39,240
+بتصير 51 بتجسم الـ 4X ناقص 9 يعني 4X ناقص 9 بساوي
+
+430
+00:40:39,240 --> 00:40:44,760
+51 في مين؟ في Y، ماشي الحال، ذات بتساوي 9، بدنا
+
+431
+00:40:44,760 --> 00:40:49,160
+نشوف الآن كل الـ X والـ Y اللي بحل ان هدولة بشكل
+
+432
+00:40:49,160 --> 00:40:52,360
+مشترك، بدحل هذه الحالة، وهذه الحالة، وبعدين اوجد
+
+433
+00:40:52,360 --> 00:40:58,040
+الحل المشترك، واثبتلك انه بطلع انه بالظبطزي اللي
+
+434
+00:40:58,040 --> 00:41:01,460
+هو الحل العادي اللي بنحله مباشرة بالـ D'Avantine
+
+435
+00:41:01,460 --> 00:41:07,840
+equation لأن 4x تطابق 9 من 51 التسعة خلت هي
+
+436
+00:41:07,840 --> 00:41:11,660
+أشمالها 60 فاهمين ليش لأن الأربعة بتروح معايا ال
+
+437
+00:41:11,660 --> 00:41:16,820
+60 بتطلع عند إيه 15 ال X تطابق 15 من 51 جسمت يعني
+
+438
+00:41:17,650 --> 00:41:24,050
+لأن X وطابق 15 ودره 51 إيش معناته أن 51 بتقسم X
+
+439
+00:41:24,050 --> 00:41:30,130
+نقص 15 إذا ساعة ال X إيش بتساوي 15 زائد 51 T
+
+440
+00:41:30,130 --> 00:41:36,070
+فاهمين و T element منين Z إذا ال X بتساوي 15 زائد
+
+441
+00:41:36,070 --> 00:41:44,420
+51 T و T و مالها في Zطيب، الآن هذا قيمة X بدوجة
+
+442
+00:41:44,420 --> 00:41:49,860
+قيمة مين؟ قيمة Y، هذا بدّي الـ X والـ Y اللي بحقق
+
+443
+00:41:49,860 --> 00:41:55,220
+هدولة مع بعضماشي لأن وجدت قيمة الـ X دم ده وجد مين
+
+444
+00:41:55,220 --> 00:42:01,940
+الآن قيمة ال Y قيمة ال Y بشكل شبيه 51Y تطابق
+
+445
+00:42:01,940 --> 00:42:07,000
+التسعة مدنه مين مدنه أربعة حلناها طلعت هندي Y
+
+446
+00:42:07,000 --> 00:42:11,420
+تطابق نقص واحد مدنه مين مدنه أربعة طلعت ال Y إيش
+
+447
+00:42:11,420 --> 00:42:16,720
+هتساوي حسب اللي هان نقص واحد زاد مين أربعة SS
+
+448
+00:42:16,720 --> 00:42:23,580
+المتنزد الآنبدي اللي x و ال y حل من هذه في نفس
+
+449
+00:42:23,580 --> 00:42:29,040
+الوقت فإيش برد بقى أسوي بعوض x و y في مين في هذه و
+
+450
+00:42:29,040 --> 00:42:33,340
+بشوف إيش علاقة أسب T و من العلاقة اللي هي الحل
+
+451
+00:42:33,340 --> 00:42:36,580
+المشترك بمعنى آخر أو قيمة المشترك اللي بتحل مع بعض
+
+452
+00:42:36,580 --> 00:42:43,040
+بيصير عندي 4x زي 51 y تساوي 9 if and only if عوضت
+
+453
+00:42:43,040 --> 00:42:48,760
+عن ال x قيمتها هيها و عن ال y قيمتها هيها بساوي 9
+
+454
+00:42:49,710 --> 00:42:55,130
+بسطها if and only if هذا المقدر ايش بيساوي بيساوي
+
+455
+00:42:55,130 --> 00:43:02,550
+سفر ضابط هذولهلاحظة عندي 4 فى 15 زي 51 فى T و 51
+
+456
+00:43:02,550 --> 00:43:07,810
+فى 4 اكيد ال 51 فى 4 و ال 4 فى 51 بطلع نفس الاشي و
+
+457
+00:43:07,810 --> 00:43:11,330
+بنشتغل F and only F يعني هتطلع معادل سهل البقص ده
+
+458
+00:43:11,330 --> 00:43:17,110
+هيطلع عندي 204 T زي 204 S إيش بيساوي سفر وهذا إيش
+
+459
+00:43:17,110 --> 00:43:21,960
+بقابل S إيش بتساوي سالب Tمدى مقاس بيتساوي سالب T
+
+460
+00:43:21,960 --> 00:43:27,120
+إذا صار عندي الحل المشترك اللي بيجمع X و Y هو
+
+461
+00:43:27,120 --> 00:43:32,880
+عبارة عن الحل X بتساوي 15 زايد 51 T and Y بيساوي
+
+462
+00:43:32,880 --> 00:43:40,200
+ناقص 1 ناقص 4T وهذا مين هو نفس الحل اللي بنحله
+
+463
+00:43:40,200 --> 00:43:43,440
+بالدايفونتين العادى والبكيات بنفس الأسلوب بطلع فوق
+
+464
+00:43:48,790 --> 00:43:54,210
+أطلع على نفسي .. اه سؤال تاني ايوة تلاتة اقف بس
+
+465
+00:43:54,210 --> 00:44:00,090
+فوق شوية انا عشان امرلكم على فكرة الأسئلة كلها
+
+466
+00:44:00,090 --> 00:44:04,430
+يعني بقدر الإمكان find all solutions of the linear
+
+467
+00:44:04,430 --> 00:44:11,210
+congruence تلاتة X تلاتة X نقل سبعة واحد وطابق ال
+
+468
+00:44:11,210 --> 00:44:19,750
+11 مضلوا مين؟ مضلوا 13 اه لان لاحظ ان هنااللاحظة
+
+469
+00:44:19,750 --> 00:44:24,530
+التالية انه
+
+470
+00:44:24,530 --> 00:44:29,970
+في عندى معادلة او congrance واحدة تطابق واحدة
+
+471
+00:44:29,970 --> 00:44:34,690
+وفيها ايش مجهولين احنا بنعرف انه جدلنا ال
+
+472
+00:44:34,690 --> 00:44:42,990
+congrance بمجهول واحد اه وبنعرف وعرفنا ان نحل
+
+473
+00:44:42,990 --> 00:44:51,480
+system عندى معادلتين او عندى تطابقتينتطابقتين بالـ
+
+474
+00:44:51,480 --> 00:44:54,620
+X والـ Y بنحلهم مع بعض ووجدنا الحل العام لهم،
+
+475
+00:44:54,620 --> 00:44:59,860
+نتذكرين، الآن هذا يعطيك بس إيش مالها، تطابق واحدة
+
+476
+00:44:59,860 --> 00:45:05,440
+بيقولك إيش الـ X و الـ Y اللي بيحققنها،
+
+477
+00:45:05,440 --> 00:45:10,280
+طبعا هو جايبها بطريقة يعني نقدر نحلها، لأنه الاشي
+
+478
+00:45:10,280 --> 00:45:16,620
+العام لها، الشغل العام لها، احنا ماتطلقناش لـ
+
+479
+00:45:17,670 --> 00:45:20,990
+Linear congruences في المتغيرين أو أكتر من
+
+480
+00:45:20,990 --> 00:45:26,850
+المتغيرين كل واحدة فيها أسليب الحل تبعتها نشوف هذه
+
+481
+00:45:26,850 --> 00:45:32,920
+3x-7 عايش بالطابق الـ 11 مدله 13 بدي أبسطهابصير
+
+482
+00:45:32,920 --> 00:45:36,460
+عندي الفكرة في الحل هنا أني بدوجة X بدلالة مين
+
+483
+00:45:36,460 --> 00:45:44,140
+بدلالة Y ماشي الحل و أعطي اللي هو الـ Y قيمة T و
+
+484
+00:45:44,140 --> 00:45:49,320
+أخليها هي تنطلق حرة تاخد القيم من سفر لعند نهاية
+
+485
+00:45:49,320 --> 00:45:54,680
+المدلو فبنكون أخدنا .. و بنوجد قيم Y المقابلة بكون
+
+486
+00:45:54,680 --> 00:45:58,720
+هيك أخدنا كل الـ incongruent solutions الباقي
+
+487
+00:45:58,720 --> 00:46:05,680
+هيكون congruent له طيب شوف كيفعندي ثلاثة X تطابق
+
+488
+00:46:05,680 --> 00:46:12,660
+سبعة Y مدل 11 نجلت السبعة هنا الآن السبعة Y صارت
+
+489
+00:46:12,660 --> 00:46:20,370
+إشمالها سالب ستة Y ماشي الـ 11 صار إشماله24 ماشي
+
+490
+00:46:20,370 --> 00:46:25,070
+الحالة إذا جسمت الجهتين على تلاتة بيصير X تطابق
+
+491
+00:46:25,070 --> 00:46:30,310
+نقص 2Y زائد 8 مضلومين مضل 13 طبعا التطابق هذه
+
+492
+00:46:30,310 --> 00:46:37,260
+اجبرت لطبيعتها ان اكتب ال X بدلالة 2 بدلالة Yالآن
+
+493
+00:46:37,260 --> 00:46:41,120
+hence all the solutions are given by solutions
+
+494
+00:46:41,120 --> 00:46:44,720
+الان بقدر أقول عنها إيش هي أن y تطابق ال T مدلوا
+
+495
+00:46:44,720 --> 00:46:51,540
+مين مدلوا تلات عشر و ال X إيش بتساوي تمانية ناقص
+
+496
+00:46:51,540 --> 00:46:54,440
+اللي هي اتنين y اللي هي اشت اتنين T مدلوا مين
+
+497
+00:46:54,440 --> 00:47:00,360
+مدلوا تلات عشر هذولة هم الحلمين لهذه التطابقةلأن
+
+498
+00:47:00,360 --> 00:47:03,980
+الـ Y تطابق B M T سميت الـ Y كأنه إشمالها T بس
+
+499
+00:47:03,980 --> 00:47:07,120
+مدلوا مين مدلوا تلات عشر وهذه X تطابق تمام يناقص
+
+500
+00:47:07,120 --> 00:47:12,320
+اتنين T مدلوا مين مدلوا تلات عشر الان ال .. ال ..
+
+501
+00:47:12,320 --> 00:47:16,380
+ال .. كل ال incongruent solutions هي كالتالي بتاخد
+
+502
+00:47:16,380 --> 00:47:23,180
+الان ال T الان بد ال incongruent ال T صفر واحد
+
+503
+00:47:23,180 --> 00:47:27,180
+اتنين عند اتن عشر لما بد ازيد بسير انقاش معاهم
+
+504
+00:47:27,180 --> 00:47:34,070
+جيبت اشي congruentالعند 12 فبصير عند الآن عوّضت هي
+
+505
+00:47:34,070 --> 00:47:40,610
+سفر X بسفر و Y بسفر و 1 و 2 و 3 و 4 و 5 لعند جداش
+
+506
+00:47:40,610 --> 00:47:46,090
+12 جيمة قيمة X المقابلة تمانية ناقص سفر طلعت
+
+507
+00:47:46,090 --> 00:47:50,230
+تمانية تمانية ناقص اتنين طلعت ستة و هكذا فدول اللي
+
+508
+00:47:50,230 --> 00:47:54,130
+هو عبارة عن الـ all incongruent solutions نيجي
+
+509
+00:47:54,130 --> 00:47:55,270
+للرابع اطلع للرابع
+
+510
+00:48:04,850 --> 00:48:08,530
+سؤال نبقى بقى يا شباب Solve each of the following
+
+511
+00:48:08,530 --> 00:48:13,510
+sets of simultaneous congruences بدنا نحل اللي هو
+
+512
+00:48:13,510 --> 00:48:19,850
+اللي هي ال system of linear congruences اللي
+
+513
+00:48:19,850 --> 00:48:24,230
+أمامنا قلنا اللي بيحللنا ال system أو بيساعدنا في
+
+514
+00:48:24,230 --> 00:48:27,390
+حل ال system اللي هي Chinese remainder theorem
+
+515
+00:48:27,390 --> 00:48:32,370
+نظرية البواقع الصينية الآن عشان أستخدم نظرية
+
+516
+00:48:32,370 --> 00:48:37,920
+البواقع الصينيةلازم تكون على الصورة هذه و لازم
+
+517
+00:48:37,920 --> 00:48:42,060
+يكون اللي إن الـ3 والـ5 والـ7 relative لـprime ناش
+
+518
+00:48:42,750 --> 00:48:46,990
+in pairs مظبوط كل تنتين مع بعضها شمالين اللي هي
+
+519
+00:48:46,990 --> 00:48:52,110
+relative liberal الان الحل المعروف مدام دولة سبعة
+
+520
+00:48:52,110 --> 00:48:55,410
+وخمسة و تلاتة relative liberal من pairs اذا it has
+
+521
+00:48:55,410 --> 00:49:00,090
+a unique solution modulo سبعة في خمسة في تلاتة
+
+522
+00:49:00,090 --> 00:49:03,610
+اللي هو modulo 105 ماشي الحال و الطريقة اللي احنا
+
+523
+00:49:03,610 --> 00:49:08,170
+عارفينها بنيجي هذه بنسميها A1 و الان واحد هي عبارة
+
+524
+00:49:08,170 --> 00:49:12,340
+عن خمسة في سبعةخمسة و تلاتين و الان واحد اللي هي
+
+525
+00:49:12,340 --> 00:49:17,260
+مين التلاتة small الان وين الحل بدنا نحل عشان نوجد
+
+526
+00:49:17,260 --> 00:49:20,600
+قيمة X اللي هي ان واحد X واحد تطابق الواحد مدل
+
+527
+00:49:20,600 --> 00:49:26,160
+ومين مدل ان واحد بيصير خمس و تلاتين تطابق خمس و
+
+528
+00:49:26,160 --> 00:49:29,180
+تلاتين X واحد تطابق الواحد مدل ومين مدلاتة منحلها
+
+529
+00:49:29,180 --> 00:49:33,980
+تطلع X واحد ايش بتساوي اتنين عرفنا A واحد وان واحد
+
+530
+00:49:33,980 --> 00:49:37,760
+و A و X واحد بنفس الطريقة بنحل اللي هي المتعلقة
+
+531
+00:49:37,760 --> 00:49:42,410
+بالثانية اللي هي ال A اتنين اتنينالـ N2 هي عبارة
+
+532
+00:49:42,410 --> 00:49:48,890
+عن 7×3 بـ 21 الـ N3 هي مين؟ الخمسة و بحل التطابق
+
+533
+00:49:48,890 --> 00:49:55,250
+N2 N2 X2 تطابق الواحد مدنه مين؟ مدنه الخمسة بحل
+
+534
+00:49:55,250 --> 00:49:59,350
+النار دي بتطلع عند X2 ساوي واحد بنفس الطريقة بعمل
+
+535
+00:49:59,350 --> 00:50:04,870
+لمين؟ لتالتة تلاتة اللي هي تلاتة و N3 small اللي
+
+536
+00:50:04,870 --> 00:50:10,830
+هي سبعة و N3 capital اللي هي 5×3 ب15الان و بحلل
+
+537
+00:50:10,830 --> 00:50:13,170
+تلاتة X ثلاثة الطابق واحد وبتطلع عندي X ثلاثة
+
+538
+00:50:13,170 --> 00:50:18,190
+بساوة واحد أخدت X ثلاثة الان من هذه و هذه و هذه و
+
+539
+00:50:18,190 --> 00:50:20,110
+هذه و هذه و هذه و هذه و هذه و هذه و هذه و هذه و
+
+540
+00:50:20,110 --> 00:50:20,290
+هذه و هذه و هذه و هذه و هذه و هذه و هذه و هذه و
+
+541
+00:50:20,290 --> 00:50:20,430
+هذه و هذه و هذه و هذه و هذه و هذه و هذه و هذه و
+
+542
+00:50:20,430 --> 00:50:25,290
+هذه و هذه و هذه و هذه و هذه و هذه و هذه و هذه و
+
+543
+00:50:25,290 --> 00:50:28,670
+هذه و هذه و هذه و هذه و هذه و هذه و هذه و هذه و
+
+544
+00:50:28,670 --> 00:50:28,810
+هذه و هذه و هذه و هذه و هذه و هذه و هذه و هذه و
+
+545
+00:50:28,810 --> 00:50:29,190
+هذه و هذه و هذه و هذه و هذه و هذه و هذه و هذه و
+
+546
+00:50:29,190 --> 00:50:29,190
+هذه و هذه و هذه و هذه و هذه و هذه و هذه و هذه و
+
+547
+00:50:29,190 --> 00:50:29,190
+هذه و هذه و هذه و هذه و هذه و هذه و هذه و هذه و
+
+548
+00:50:29,190 --> 00:50:33,090
+هذه و هذه و هذه و هذه و هذه و هذه و هذه و هذه و
+
+549
+00:50:33,090 --> 00:50:41,010
+هذه و هذهكدا 100% كلامك صحيح 100% نيجي لالي بعده
+
+550
+00:50:41,010 --> 00:50:45,910
+الآن هذه اللي هي الشغلاء اللي اعتدنا عليها في
+
+551
+00:50:45,910 --> 00:50:50,510
+الـChinese remainder theorem الآن ماتيني سؤال آخر
+
+552
+00:50:50,510 --> 00:50:55,690
+X تطابق الخمسة مدل 11 X تطابق الأربعة عشر مدل 29 X
+
+553
+00:50:55,690 --> 00:50:58,670
+تطابق الخمسة عشر مدل واحد و تلاتين برضه بنفس
+
+554
+00:50:58,670 --> 00:51:03,050
+الطريقة وفيش داعي ان هو انحل لإنه كل هنا relative
+
+555
+00:51:03,050 --> 00:51:07,190
+لبرامج دهخلّيني أمر على كل واحد لأن فيه .. في
+
+556
+00:51:07,190 --> 00:51:12,830
+شغلات فيها فكرة غير لأن برضه هذه الستة وحداشر
+
+557
+00:51:12,830 --> 00:51:16,030
+وسبعتاشر مافيش فيها مشكلة أو جلطة عنهم لأن كلهم
+
+558
+00:51:16,030 --> 00:51:23,090
+relative prime inverse نيجي لدي .. نيجي لدي .. دي
+
+559
+00:51:23,090 --> 00:51:27,600
+عند ..تطابق اتنين X تطابق الواحد modulo خمسة
+
+560
+00:51:27,600 --> 00:51:34,280
+modulo ستة modulo سبعة modulo احداش الآن نفس الاشي
+
+561
+00:51:34,280 --> 00:51:39,460
+اللي هي 11 و7 و6 و5 relatively prime and pairs
+
+562
+00:51:39,460 --> 00:51:45,760
+ولكن قبل ما نبدأ نطبق لازم اللي هو نجهز هذه تكون X
+
+563
+00:51:45,760 --> 00:51:49,780
+تطابق كذا و X تطابق كذا و X تطابق كذا و X تطابق
+
+564
+00:51:49,780 --> 00:51:54,300
+كذا و نكمل الحل زي ما عملنا واضح؟ اطلع لللي فوق
+
+565
+00:51:57,300 --> 00:52:03,260
+الان نجي لسؤال بعده Solve the linear congruences
+
+566
+00:52:03,260 --> 00:52:13,140
+17x طابق 3 modulo 2 في 3 في 5 في 7 كيف جاي لك؟ By
+
+567
+00:52:13,140 --> 00:52:19,440
+solving 17x طابق 3 modulo 2 modulo 3 modulo 5
+
+568
+00:52:19,440 --> 00:52:20,880
+modulo 7
+
+569
+00:52:23,640 --> 00:52:27,720
+برضه نفس الاشي الـ2 والـ3 والـ5 والـ7 relative
+
+570
+00:52:27,720 --> 00:52:33,280
+الـprime in pairs اذا اول اشي ايش بنسوي اللي هو
+
+571
+00:52:33,280 --> 00:52:39,540
+بنجهزه اللي هو X to top of كده هو بس انا يعني في
+
+572
+00:52:39,540 --> 00:52:46,420
+هذه في هذه عندى التلاتة بتصير سفر فعشانك بلزمش
+
+573
+00:52:46,420 --> 00:52:52,380
+اكمل خلاص بقعد جدي اتنين سفر وبشتغل فاهمين اه؟ اي
+
+574
+00:52:52,380 --> 00:52:59,590
+سؤال؟الى اللى بعده نجى لسؤال 15 فى ايه خلّينا ايه
+
+575
+00:52:59,590 --> 00:53:05,730
+موجود حلو برضه فى الاولانيات و هدوله للملحق 15 فيه
+
+576
+00:53:05,730 --> 00:53:13,430
+6 و فيه 14 بنرجعلهن خلّينا نشوف السؤال 6 و 14 و
+
+577
+00:53:13,430 --> 00:53:19,240
+بعدين بنروح ل 15 السؤال 6Find the smallest integer
+
+578
+00:53:19,240 --> 00:53:29,380
+a أكبر من 2 such that اتنين
+
+579
+00:53:29,380 --> 00:53:32,260
+بتقسم ال a والتلاتة بتقسم ال a زاد واحد والاربعة
+
+580
+00:53:32,260 --> 00:53:35,420
+بتقسم ال a زاد اتنين والخمسة بتقسم ال a زاد تلاتة
+
+581
+00:53:35,420 --> 00:53:39,660
+والستة بتقسم ال a زاد مين زاد اربعة الان هذي
+
+582
+00:53:39,660 --> 00:53:43,420
+بتحولها لمين ل congruences في الحالة الأولى ال a
+
+583
+00:53:43,420 --> 00:53:48,080
+في طابق الصفر مدنومينمدولة 2 في الحالة التانية a
+
+584
+00:53:48,080 --> 00:53:53,700
+تطابق الـ a شمالها ناقص واحد مدولة تلاتة صحيح؟
+
+585
+00:53:53,700 --> 00:53:57,020
+فاهمين؟ أصلها هي دي a تطابق ناقص واحد مدولة تلاتة
+
+586
+00:53:57,020 --> 00:54:02,580
+ليش؟ لأن التلاتة بتكسب من a زائد واحد واضح؟ الحالة
+
+587
+00:54:02,580 --> 00:54:06,380
+اللي بعدها اللي بعدها اللي هي a تطابق ناقص اتنين
+
+588
+00:54:06,380 --> 00:54:10,520
+مدولة مين؟ مدولة أربعة اللي بعدها a تطابق ناقص
+
+589
+00:54:11,580 --> 00:54:18,380
+تلاتة A تطابق ناقص أربعة مدلوا مين مدلوا ستة والـ
+
+590
+00:54:18,380 --> 00:54:23,180
+A تطابق ناقص تلاتة مدلوا خمسة واضح هيا الآن
+
+591
+00:54:23,180 --> 00:54:30,860
+حولناها ل system of linear congruences لأن Chinese
+
+592
+00:54:30,860 --> 00:54:36,040
+remainder term إيش مالها بتتعامل مع أن الكون كله
+
+593
+00:54:36,040 --> 00:54:40,200
+تنتهي relative to prime إيش انبارس فأنا إيش بسوي
+
+594
+00:54:41,140 --> 00:54:45,500
+بأتي و بتطلع الستراتيجية هي أن أجمع الـ Relative
+
+595
+00:54:45,500 --> 00:54:49,600
+prime in pairs و أحلل مع بعض وبتبقى الواحدة هناك
+
+596
+00:54:49,600 --> 00:54:53,100
+اللي بيطلع ال solution .. ال solution اللي بيطلع
+
+597
+00:54:53,100 --> 00:54:58,020
+بشوف انه بطابق .. بطابق هذيك ولا لاإذا بيطابقوا
+
+598
+00:54:58,020 --> 00:55:01,660
+خلاص بيكون هو ال solution يوم كله لو بيطابقوش يعني
+
+599
+00:55:01,660 --> 00:55:04,600
+جزء منه بيطابقه معناته بتدوجد ال solution نعم
+
+600
+00:55:04,600 --> 00:55:08,000
+بيكون هذا الجزء هو بيطابق الكل واضح يعني بتدوجد
+
+601
+00:55:08,000 --> 00:55:14,460
+الحل مين أنا الان الان شوف كيف عندي ال M أول حاجة
+
+602
+00:55:14,460 --> 00:55:24,260
+لو دي نطلعنا عندي modulo 3 وعندي modulo 6 و modulo
+
+603
+00:55:24,260 --> 00:55:30,310
+2وmodulo 4 هدولة فيها مشاكل مع بعض خلّيني بس أطلع
+
+604
+00:55:30,310 --> 00:55:35,910
+لأول إشي لفينة الـ2 وال4 لو جيت أطلعت للـA تطابق
+
+605
+00:55:35,910 --> 00:55:41,350
+نقص 2 modulo 4 والـA تطابق سفر modulo 2 هذا على
+
+606
+00:55:41,350 --> 00:55:47,250
+جهة سهل إن أنا أقرر فيها A تطابق أعطيني جديش؟ سفر
+
+607
+00:55:47,250 --> 00:55:52,950
+modulo 2 وA تطابق سلب 2 modulo 2 أنا بدي الحل
+
+608
+00:55:52,950 --> 00:55:57,600
+المشترك اللي بحل .. اللي بحل التنتينحلول هذه مين
+
+609
+00:55:57,600 --> 00:56:05,080
+هي؟ حلول هذه صفر و اتنين واربعة وستة و سالب اتنين
+
+610
+00:56:05,080 --> 00:56:08,820
+إلى ماله نهاية مظبوط ولا لأ؟ حلول هذه بس عشان
+
+611
+00:56:08,820 --> 00:56:14,880
+تتعرف ايش اللي بدنا نسويه سالب اتنين او اتنين وستة
+
+612
+00:56:14,880 --> 00:56:20,200
+واضح ان هذا جزء من اللي من اللي فوق يعني الحل
+
+613
+00:56:20,200 --> 00:56:25,860
+المشترك بين الجهتين مين هو؟ اللي تحتماشي الحال إذا
+
+614
+00:56:25,860 --> 00:56:33,940
+.. إذا هذه .. هذه بتغنيني عن هذه لإن الحل المشترك
+
+615
+00:56:33,940 --> 00:56:36,980
+بين الجهتين هذا و أنا بدي الحل مشترك يعني باخد
+
+616
+00:56:36,980 --> 00:56:40,900
+الحل اللي ياشي الأقل فبصير عندنا إيه؟ تطابق ناقص
+
+617
+00:56:40,900 --> 00:56:47,560
+اتنين مدلوا نين مدلوا أربعة الآن الخامسة مافيش
+
+618
+00:56:47,560 --> 00:56:54,410
+فيها مشكلة اكتبها إيه؟تطابق نقص لاتة modulo خمسة
+
+619
+00:56:54,410 --> 00:56:57,130
+لماذا أعمل ذلك؟ عشان أكبر استخدام الـChinese
+
+620
+00:56:57,130 --> 00:57:03,030
+remainder theorem نيجي الآن مين ومين؟ التلاتة
+
+621
+00:57:03,030 --> 00:57:10,250
+ومين؟ والستة الآن أمامي حلين باجي أنا طيرت الأربعة
+
+622
+00:57:10,250 --> 00:57:14,550
+بقى أقدر أدخل معاها التلاتة واللي بطلع بحله مع
+
+623
+00:57:14,550 --> 00:57:19,250
+مين؟ مع الستة لان ضال عندي إيش هال gate؟ اللي هي
+
+624
+00:57:19,250 --> 00:57:30,730
+نجّلني إياهاإيه تطابق مدونة 3 وإيه تطابق سلب 4
+
+625
+00:57:30,730 --> 00:57:35,390
+عمود لومين مدونة 6انت حوري بدك تعمل في هدولة
+
+626
+00:57:35,390 --> 00:57:39,070
+التنتين مع بعض زي أنا عاملي تحيان و تاخد اللي بتظل
+
+627
+00:57:39,070 --> 00:57:42,490
+بس بخاف اللي بتظل هذي و اللي بتظل هذي هتعمللي
+
+628
+00:57:42,490 --> 00:57:47,230
+مشكلة مع مين؟ مع الأربعة فمن رأس الدور أخدنا مين؟
+
+629
+00:57:47,230 --> 00:57:51,250
+أخدنا إيه؟ تطابق ناقص واحد مدوا مين؟ مدوا ثلاثة
+
+630
+00:57:51,250 --> 00:57:55,670
+الآن إيش الحل؟ أنا ببحث عن مين؟ عن الحل المشترك
+
+631
+00:57:55,670 --> 00:58:00,350
+بينهم كلهمهذه وهذه خلّصنا من إن الحل المشترك هو
+
+632
+00:58:00,350 --> 00:58:05,650
+مين هو اللي هي مدله أربعة يعني خلّصنا منها ضال إن
+
+633
+00:58:05,650 --> 00:58:10,390
+أبحث الحل المشترك هذه مع كل اللي ضايلات هذه
+
+634
+00:58:10,390 --> 00:58:14,330
+بتعمللي مشكلة مع الأربعة فأخدت هذولة التلاتة اللي
+
+635
+00:58:14,330 --> 00:58:18,650
+Relatively Branded Bears مع بعض بيطلعلي حل الحل
+
+636
+00:58:18,650 --> 00:58:23,610
+اللي بيطلعلي بيتشوفه مع هذه إذا هذا الحل بيحقق هذه
+
+637
+00:58:23,610 --> 00:58:28,800
+معناته هو الحل المشتركماحققش باخد المشترك بين هذه
+
+638
+00:58:28,800 --> 00:58:33,920
+وهذه بالطريقة اللي .. إيش؟ اللي حكيت فيها واضح؟
+
+639
+00:58:33,920 --> 00:58:40,060
+هنشوف كيف .. فلان هاي .. هنطلع لفوق اللي قولنا عنه
+
+640
+00:58:40,060 --> 00:58:42,160
+إن دولة بتشاينيز remainder theorem طالع .. طالع
+
+641
+00:58:42,160 --> 00:58:50,260
+عندي اللي هو ال X طابق 2 X طابق ال .. ال .. ال
+
+642
+00:58:50,260 --> 00:58:54,200
+command solution اه .. اه ال X طابق 2 مدل 100 مدل
+
+643
+00:58:54,200 --> 00:58:58,940
+60معايا؟ لأن X هو طابق اتنين مدرس ستين معناه ان X
+
+644
+00:58:58,940 --> 00:59:05,180
+ايش هيصير في صورتها؟ اتنين زائد ستين K فاهمين ليش؟
+
+645
+00:59:05,180 --> 00:59:10,320
+صاروا متعودين عليه هذا الآن X بتساوي اتنين زائد
+
+646
+00:59:10,320 --> 00:59:16,440
+ستين K الستين بالنسبة للستة صفر والتنين هي التنين
+
+647
+00:59:16,440 --> 00:59:20,760
+او التنين هي مين؟ سالف الأربعة إذا صارت ال X هذه
+
+648
+00:59:22,940 --> 00:59:27,780
+تحلّى مين لماقص أربعة مدلوا ستة إذا صارت حل
+
+649
+00:59:27,780 --> 00:59:33,160
+مشتركتين كلها إذا صار عند ال X تطابق اتنين مدلوا
+
+650
+00:59:33,160 --> 00:59:37,520
+مين مدلوا ستين نعود إلى سؤالنا الآن سؤالنا أيش
+
+651
+00:59:37,520 --> 00:59:41,060
+طالب خلّيه سؤالنا أيش طالب أنه بده أصغر أيه تحقق
+
+652
+00:59:41,060 --> 00:59:46,460
+ذلك أصغر أيه تحقق ذلك اللي هو طبعا أي شمع اللي
+
+653
+00:59:46,460 --> 00:59:53,520
+بديها أكبر من اتنين أيش طلعت على طول البعدإذا
+
+654
+00:59:53,520 --> 00:59:58,880
+العدد غير التنين اللي .. اللي بيحقق الشروط اللي ..
+
+655
+00:59:58,880 --> 01:00:02,380
+اللي حطها الخمسة أو الأربعة هو أبداً اتنين و ستة
+
+656
+01:00:02,380 --> 01:00:09,740
+اربع عشر عندي
+
+657
+01:00:09,740 --> 01:00:14,220
+a certain integer between واحد ألف و ألفينفي عندى
+
+658
+01:00:14,220 --> 01:00:19,120
+عدد بين الواحد ومين والألف وامتين ويقول لي leaves
+
+659
+01:00:19,120 --> 01:00:24,260
+the remainders هذا العدد اللى هو بيترك اللى هى ال
+
+660
+01:00:24,260 --> 01:00:29,080
+reminders التالية واحد واتنين وستة when divided by
+
+661
+01:00:29,080 --> 01:00:34,460
+تسعة وحداشر ومين وتلتاشر respectively الان ال
+
+662
+01:00:34,460 --> 01:00:37,940
+reminders بين واحد يعني بدى ال X اللى بين واحد
+
+663
+01:00:37,940 --> 01:00:43,000
+والف ومتين تحقق ميادةX remainderها واحد لما اجسم
+
+664
+01:00:43,000 --> 01:00:47,920
+عالمين تسعة و X طابق 2 مده 11 و X طابق 6 مده 2 مده
+
+665
+01:00:47,920 --> 01:00:52,000
+13 حل عادي by chinese remainder theorem لأن ما
+
+666
+01:00:52,000 --> 01:00:54,960
+دولة relative ل prime and pairs و بطلع عندي اللي
+
+667
+01:00:54,960 --> 01:00:59,940
+هو الرقم الرقم هذا اللي هو بديه بين واحد و بين الف
+
+668
+01:00:59,940 --> 01:01:04,940
+و متين X طابقه ال 838 مكون هو العدد اللي بديه اطلع
+
+669
+01:01:04,940 --> 01:01:05,280
+لفوق
+
+670
+01:01:08,000 --> 01:01:09,500
+خمسة عشر بنفس الأسلوب
+
+671
+01:01:39,850 --> 01:01:48,180
+المعادلات واضحة اطلع لفوق البعد على اللي جابلهطيب،
+
+672
+01:01:48,180 --> 01:01:52,340
+برضه نفس الاشي هذا ال .. بنفس .. نفس الفكرة بيه
+
+673
+01:01:52,340 --> 01:01:56,580
+find the integers having the remainder 2,3,4,5 لما
+
+674
+01:01:56,580 --> 01:02:00,280
+نجسمها by 3,4,5,6 بنفس الأسلوب اللي حكيته قبل شوية
+
+675
+01:02:00,280 --> 01:02:05,840
+اطلع فوق عشان نحل .. نحل سؤال عشرين نيجي لعشرين،
+
+676
+01:02:05,840 --> 01:02:10,080
+بنحل في سؤال عشرين واحد من هنا، بس find .. find
+
+677
+01:02:10,080 --> 01:02:15,320
+the solutions of each of the following systems of
+
+678
+01:02:15,320 --> 01:02:21,160
+linear congruencesهل في عندي اللي هو تطابقتين
+
+679
+01:02:21,160 --> 01:02:28,420
+بمجهولين XY وبدنا نوجد الحل العام لهم ماشي الحال
+
+680
+01:02:28,420 --> 01:02:34,810
+أو الحل المشترك لهم؟إذا بتتذكروا احنا كيف كنا نسوي
+
+681
+01:02:34,810 --> 01:02:39,830
+أول test نعمله كنا نقول نضرب اللي هو اللي كنا
+
+682
+01:02:39,830 --> 01:02:47,130
+نسميها دي A B C D وR وS بدون الأسماء مش مشكلة كناش
+
+683
+01:02:47,130 --> 01:02:52,370
+نقول ان معامل X في معامل Y ناقص معامل X في معامل Y
+
+684
+01:02:53,110 --> 01:02:56,810
+ماشي الحال و الأمن اللي عندي إذا العامل المشترك
+
+685
+01:02:56,810 --> 01:03:00,450
+اللي على بينهم بساوي واحد معناته هذا ال system فيه
+
+686
+01:03:00,450 --> 01:03:05,550
+إله اللي هو unique اللي هو solution ماشي الحال
+
+687
+01:03:05,550 --> 01:03:11,170
+مدنه مين مدنه الآن اتطلعي الآن خمسة في اتنين عشرة
+
+688
+01:03:11,730 --> 01:03:18,230
+نقص ثلاثة في ثلاثة تسعة والان سبعة هذا واحد وسبعة
+
+689
+01:03:18,230 --> 01:03:22,630
+لـ greatest common divisor بينهم ايش حيساوط اذا
+
+690
+01:03:22,630 --> 01:03:26,710
+اللي هو معادلة الناس معادلة ان في الهايونيكس
+
+691
+01:03:26,710 --> 01:03:30,390
+solution كيف موجد هذا ال solution اذا بتتذكروا
+
+692
+01:03:30,390 --> 01:03:39,380
+كتالي الان واضح انهعندنا هذا في الـ unique
+
+693
+01:03:39,380 --> 01:03:43,420
+solution اللي هو خمسة X انتبه عشان نرتب حالنا
+
+694
+01:03:43,420 --> 01:03:53,230
+تطابق الواحدmodulo 7 و3x زائد 2y وطابق الأربعة
+
+695
+01:03:53,230 --> 01:03:58,890
+modulo 7 قلنا بما أن الـ greatest common divisor
+
+696
+01:03:58,890 --> 01:04:04,470
+بين 5×2 عشرة ناطس 3×3 بتسعة اللي هي واحد والسبعة
+
+697
+01:04:04,470 --> 01:04:13,610
+بساوي واحد then the system has a unique solution
+
+698
+01:04:13,610 --> 01:04:20,100
+modulo السبعةلأن تـFind The Solution يعني يجب وجود
+
+699
+01:04:20,100 --> 01:04:24,080
+قيمة X ويوجد قيمة 100 Y قبل موجود الـ Solution
+
+700
+01:04:24,080 --> 01:04:27,720
+بدنا نحل التطابق اللي هو توصيلنا للـ Solution مين
+
+701
+01:04:27,720 --> 01:04:35,520
+التطابق كانت؟ اللي هي A D ناقص B C اللي هي هادي
+
+702
+01:04:35,520 --> 01:04:43,160
+اللي هي 1 في T تطابق الـ 1 modulo الـ N السبعة
+
+703
+01:04:43,160 --> 01:04:48,480
+تطابق الـ 1 modulo 100 modulo السبعةالآن بمعنى
+
+704
+01:04:48,480 --> 01:04:50,780
+العام المشترك اللي على بين الواحد والسبعة بساوي
+
+705
+01:04:50,780 --> 01:04:54,000
+واحد because it has a unique solution طلع هنا على
+
+706
+01:04:54,000 --> 01:04:59,960
+طول طلع الـ T تطابق الواحد مدنومين مدنوم سبعة على
+
+707
+01:04:59,960 --> 01:05:06,780
+طول take T بتساوي إيش الآن؟ واحد take T بتساوي
+
+708
+01:05:06,780 --> 01:05:10,900
+واحد لو أخدت كل الـ T أي T من مدنوم سبعة يعني
+
+709
+01:05:10,900 --> 01:05:14,810
+التمانية أو الكذا برضه بتلفعفاهمين علشان بقول هذا
+
+710
+01:05:14,810 --> 01:05:19,590
+لمين عشان اوجد ال X و ال Y ايش ال X كانت بتساوي ال
+
+711
+01:05:19,590 --> 01:05:27,830
+X تساوي او تطابق اللي هو كنا ناخد 2 في مين في واحد
+
+712
+01:05:27,830 --> 01:05:36,870
+ناقص تلاتة في أربعة باطماش فاهمين اللي هو عبارة عن
+
+713
+01:05:36,870 --> 01:05:49,950
+كده تطابق سالب عشرةموضوله سالب عشرة هذا في T تطابق
+
+714
+01:05:49,950 --> 01:05:58,190
+هذا الحل لهند الحيانة الحل موضوله إيش سبعة نيجي لل
+
+715
+01:05:58,190 --> 01:06:03,930
+Y اللي مش متابع ال Y مين ال Y نيجي لمعاملات X من
+
+716
+01:06:03,930 --> 01:06:11,410
+وين بدأنا احنا قبل شوية من فوق من تحت بدأنالأ
+
+717
+01:06:11,410 --> 01:06:17,650
+التانية بيبقى من فوق اللي هي خمسة فاربعة بعشرين
+
+718
+01:06:17,650 --> 01:06:25,050
+لازم واحدة من فوق واحدة من تحت تلاتة في
+
+719
+01:06:25,050 --> 01:06:32,870
+T مدلوا إياش مدلوا سبعة اللي عبارة عن العوض T بجد
+
+720
+01:06:32,870 --> 01:06:39,560
+إياش بواحد إذا من هذه عندي Xفاهمين عليها تطابق
+
+721
+01:06:39,560 --> 01:06:48,220
+سالب عشرة اللي هي بالطابق الاربعة مدنو سبعة واضحة
+
+722
+01:06:48,220 --> 01:06:55,680
+اللي بعدها Y بالطابق اللي هو عشرين نقص ثلاثة
+
+723
+01:06:55,680 --> 01:07:00,440
+سبعتاش سبعتاش في واحد التين لو جبناها مواصل سبعتاش
+
+724
+01:07:00,440 --> 01:07:10,500
+اللي هي بالطابق تلاتةموضله سبعة وهذا يعني الـ
+
+725
+01:07:10,500 --> 01:07:17,100
+Unique Required Solution طبعاً من أين جاء القوانين
+
+726
+01:07:17,100 --> 01:07:23,040
+اللي احنا حكيناها المرة الماضية انه جينا ضربنا هذا
+
+727
+01:07:23,040 --> 01:07:29,840
+في مثلا في اتنين وهذا ضربناه في ثلاثة وضيعه
+
+728
+01:07:29,840 --> 01:07:34,390
+وطرحناهمو جيبنا قيمة X و كذا و بعدين جيبنا قيمة Y
+
+729
+01:07:34,390 --> 01:07:38,710
+و اعتمادا على الـ T فالان اذا هذا اللي هو ال X
+
+730
+01:07:38,710 --> 01:07:41,230
+عندي هنا و ال Y دي اللي اخدناه بهذه الطريقة
+
+731
+01:07:41,230 --> 01:07:46,410
+اعتمادا على اللي حكينا المرة الماضية حين برهننا
+
+732
+01:07:46,410 --> 01:07:51,820
+النظريةبكون هيك احنا يعني بضل عندي اللي هو B و C
+
+733
+01:07:51,820 --> 01:07:58,300
+بنفس الطريقة بكون عندنا أنهينا لأن تقريبا معظم أو
+
+734
+01:07:58,300 --> 01:08:04,340
+كل المسائل المطلوبة في اللي هو Chapter 4 وعملنا
+
+735
+01:08:04,340 --> 01:08:10,300
+مراجعة كاملة لـ Linear congruences and the Chinese
+
+736
+01:08:10,300 --> 01:08:13,460
+remainder theorem الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/f_MGFKzXVQI_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/f_MGFKzXVQI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1b6e910504f24aa60f0d66df81606acd12399ce8
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/f_MGFKzXVQI_raw.json
@@ -0,0 +1 @@
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مباشرة فنشوف كيف، ايش اللي بحكيه الان let's prove", "tokens": [3224, 1863, 5172, 43042, 2423, 39184, 3769, 2747, 1114, 9886, 271, 284, 49374, 16095, 4724, 3794, 995, 2407, 3660, 413, 4032, 1863, 14851, 9778, 40448, 16490, 33546, 10632, 16472, 2423, 39184, 413, 8032, 2655, 7435, 38251, 36632, 14670, 289, 25939, 2486, 49374, 16095, 6156, 3224, 1863, 11242, 40228, 2423, 39184, 316, 9154, 25724, 3224, 2655, 9957, 4032, 29399, 30543, 3615, 16472, 2423, 39184, 413, 6055, 7435, 38251, 2423, 14407, 24401, 3714, 3555, 33599, 25720, 6156, 1863, 8592, 38688, 9122, 33911, 12399, 1975, 1829, 8592, 13672, 1829, 4724, 5016, 4117, 1829, 3224, 2423, 7649, 718, 311, 7081], "avg_logprob": -0.30380155622344657, "compression_ratio": 1.4700460829493087, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 100.74000000000001, "end": 101.72, "word": "هنفرض", "probability": 0.6163177490234375}, {"start": 101.72, "end": 101.92, "word": " الـ", "probability": 0.56072998046875}, {"start": 101.92, "end": 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الان بدي اعوض على الصورة مين الآن تلاتة K فبصير هذا عبارة عن اياش", "tokens": [6027, 7649, 4724, 47283, 3215, 9673, 28543, 9640, 13672, 7578, 43242, 7578, 16472, 6156, 7649, 30767, 16373, 3215, 36764, 24401, 6156, 7649, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 46599, 16254, 24525, 2304, 3224, 6225, 6055, 1211, 9307, 3660, 2423, 7649, 4724, 16254, 1975, 3615, 2407, 11242, 15844, 31767, 13063, 3660, 3714, 9957, 6024, 48506, 6055, 1211, 9307, 3660, 591, 6156, 3555, 9381, 13546, 23758, 6225, 3555, 9640, 3660, 18871, 1975, 1829, 33599], "avg_logprob": -0.30827702702702703, "compression_ratio": 1.7414965986394557, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 663.95, "end": 664.51, "word": "الان", "probability": 0.7958984375}, {"start": 664.51, "end": 668.01, "word": " باخد", "probability": 0.5785319010416666}, {"start": 668.01, "end": 668.45, "word": " المقدار", "probability": 0.8927408854166666}, {"start": 668.45, "end": 668.55, "word": " اللى", "probability": 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0.531982421875}, {"start": 2302.24, "end": 2302.24, "word": " ..", "probability": 0.050445556640625}, {"start": 2302.24, "end": 2302.46, "word": " اللي", "probability": 0.896728515625}, {"start": 2302.46, "end": 2302.82, "word": " هو", "probability": 0.98388671875}, {"start": 2302.82, "end": 2303.94, "word": " بدلالتهن", "probability": 0.759375}, {"start": 2303.94, "end": 2304.92, "word": " الـ", "probability": 0.78076171875}, {"start": 2304.92, "end": 2304.92, "word": " ..", "probability": 0.2215576171875}, {"start": 2304.92, "end": 2305.3, "word": " الـ", "probability": 0.9453125}, {"start": 2305.3, "end": 2305.3, "word": " ..", "probability": 0.048370361328125}, {"start": 2305.3, "end": 2305.46, "word": " الـ", "probability": 0.880615234375}, {"start": 2305.46, "end": 2305.76, "word": " Gresskow", "probability": 0.23043060302734375}, {"start": 2305.76, "end": 2305.86, "word": " من", "probability": 0.58349609375}, {"start": 2305.86, "end": 2305.94, "word": " الـ", "probability": 0.7281494140625}, {"start": 2305.94, "end": 2306.32, "word": " divisor", "probability": 0.662353515625}, {"start": 2306.32, "end": 2306.62, "word": " بين", "probability": 0.92578125}, {"start": 2306.62, "end": 2306.82, "word": " اللي", "probability": 0.97265625}, {"start": 2306.82, "end": 2307.12, "word": " هو", "probability": 0.9912109375}, {"start": 2307.12, "end": 2307.98, "word": " هذا", "probability": 0.8984375}, {"start": 2307.98, "end": 2308.4, "word": " ما", "probability": 0.35888671875}, {"start": 2308.4, "end": 2308.68, "word": " هو", "probability": 0.9443359375}, {"start": 2308.68, "end": 2309.18, "word": " جيبته", "probability": 0.919677734375}, {"start": 2309.18, "end": 2309.38, "word": " انت", "probability": 0.878173828125}, {"start": 2309.38, "end": 2309.6, "word": " بين", "probability": 0.94970703125}, {"start": 2309.6, "end": 2309.76, "word": " الـ", "probability": 0.8984375}, {"start": 2309.76, "end": 2309.86, "word": " A", "probability": 0.431884765625}, {"start": 2309.86, "end": 2309.92, "word": " و", "probability": 0.47314453125}, {"start": 2309.92, "end": 2310.0, "word": " الـ", "probability": 0.921630859375}, {"start": 2310.0, "end": 2310.16, "word": " B", "probability": 0.8095703125}, {"start": 2310.16, "end": 2310.78, "word": " بتجيبه", "probability": 0.93876953125}, {"start": 2310.78, "end": 2311.28, "word": " بدلالة", "probability": 0.91064453125}, {"start": 2311.28, "end": 2311.98, "word": " مين؟", "probability": 0.6971842447916666}, {"start": 2311.98, "end": 2312.04, "word": " الـ", "probability": 0.84912109375}, {"start": 2312.04, "end": 2312.2, "word": " A", "probability": 0.91943359375}, {"start": 2312.2, "end": 2312.24, "word": " و", "probability": 0.97900390625}, {"start": 2312.24, "end": 2312.3, "word": " الـ", "probability": 0.9130859375}, {"start": 2312.3, "end": 2312.4, "word": " B", "probability": 0.73876953125}, {"start": 2312.4, "end": 2312.9, "word": " فبصير", "probability": 0.8629150390625}, {"start": 2312.9, "end": 2313.2, "word": " كله", "probability": 0.96826171875}, {"start": 2313.2, "end": 2313.74, "word": " بدلالة", "probability": 0.989990234375}, {"start": 2313.74, "end": 2314.46, "word": " مين؟", "probability": 0.96826171875}, {"start": 2314.46, "end": 2314.7, "word": " الـ", "probability": 0.969482421875}, {"start": 2314.7, "end": 2314.8, "word": " A", "probability": 0.91552734375}, {"start": 2314.8, "end": 2314.92, "word": " و", "probability": 0.98388671875}, {"start": 2314.92, "end": 2315.0, "word": " الـ", "probability": 0.955810546875}, {"start": 2315.0, "end": 2315.08, "word": " B", "probability": 0.873046875}, {"start": 2315.08, "end": 2315.2, "word": " و", "probability": 0.94140625}, {"start": 2315.2, "end": 2315.32, "word": " الـ", "probability": 0.969482421875}, {"start": 2315.32, "end": 2315.48, "word": " C", "probability": 0.79833984375}, {"start": 2315.48, "end": 2315.96, "word": " فبتكون", "probability": 0.9681396484375}, {"start": 2315.96, "end": 2316.28, "word": " X", "probability": 0.916015625}, {"start": 2316.28, "end": 2316.42, "word": " و", "probability": 0.9658203125}, {"start": 2316.42, "end": 2316.68, "word": " Y", "probability": 0.84375}, {"start": 2316.68, "end": 2316.84, "word": " و", "probability": 0.9375}, {"start": 2316.84, "end": 2317.1, "word": " Z", "probability": 0.9912109375}, {"start": 2317.1, "end": 2317.7, "word": " هي", "probability": 0.9306640625}, {"start": 2317.7, "end": 2318.1, "word": " عبارة", "probability": 0.9970703125}, {"start": 2318.1, "end": 2318.34, "word": " عن", "probability": 0.9970703125}, {"start": 2318.34, "end": 2318.9, "word": " solutions", "probability": 0.378662109375}, {"start": 2318.9, "end": 2319.64, "word": " و", "probability": 0.429443359375}, {"start": 2319.64, "end": 2319.76, "word": " ال", "probability": 0.85302734375}, {"start": 2319.76, "end": 2320.12, "word": " solution", "probability": 0.6552734375}, {"start": 2320.12, "end": 2320.38, "word": " هي", "probability": 0.60888671875}, {"start": 2320.38, "end": 2320.48, "word": " و", "probability": 0.33349609375}, {"start": 2320.48, "end": 2320.82, "word": " موجود", "probability": 0.9407552083333334}, {"start": 2320.82, "end": 2321.18, "word": " كلها", "probability": 0.7529296875}, {"start": 2321.18, "end": 2321.8, "word": " موجودة", "probability": 0.92822265625}, {"start": 2321.8, "end": 2322.28, "word": " في", "probability": 0.94921875}, {"start": 2322.28, "end": 2322.5, "word": " ال", "probability": 0.92578125}, {"start": 2322.5, "end": 2322.62, "word": " ..", "probability": 0.8935546875}, {"start": 2322.62, "end": 2323.0, "word": " في", "probability": 0.77685546875}, {"start": 2323.0, "end": 2323.6, "word": " اللي", "probability": 0.92529296875}, {"start": 2323.6, "end": 2323.94, "word": " هو", "probability": 0.99609375}, {"start": 2323.94, "end": 2324.66, "word": " البابرة", "probability": 0.5770060221354166}, {"start": 2324.66, "end": 2326.04, "word": " يعني", "probability": 0.942626953125}, {"start": 2326.04, "end": 2326.4, "word": " هذه", "probability": 0.50390625}, {"start": 2326.4, "end": 2326.7, "word": " خلينا", "probability": 0.6702473958333334}, {"start": 2326.7, "end": 2326.96, "word": " نقول", "probability": 0.998046875}, {"start": 2326.96, "end": 2327.94, "word": " عبارة", "probability": 0.9964599609375}, {"start": 2327.94, "end": 2328.14, "word": " عن", "probability": 0.9921875}], "temperature": 1.0}, {"id": 94, "seek": 234812, "start": 2328.58, "end": 2348.12, "text": "يعني عبارة عن نماذج لأسئلة تعبر .. تعبر إلى حد ما عن الأفكار في هذا ال section وبظل عندكم انتوا اتكملوا باقي الأسئلة واتحولوا باقي الأسئلة عشان تغطوا باقي الأفكار مبارك الله فيكم", "tokens": [40228, 22653, 6225, 3555, 9640, 3660, 18871, 8717, 2304, 45636, 7435, 5296, 10721, 3794, 19986, 37977, 37279, 26890, 4386, 37279, 26890, 30731, 11331, 3215, 19446, 18871, 16247, 5172, 4117, 9640, 8978, 23758, 2423, 3541, 46599, 19913, 1211, 43242, 24793, 16472, 2655, 14407, 1975, 2655, 24793, 1211, 14407, 4724, 995, 38436, 16247, 3794, 19986, 37977, 4032, 9307, 5016, 12610, 14407, 4724, 995, 38436, 16247, 3794, 19986, 37977, 6225, 8592, 7649, 6055, 17082, 9566, 14407, 4724, 995, 38436, 16247, 5172, 4117, 9640, 3714, 3555, 9640, 4117, 21984, 8978, 24793], "avg_logprob": -0.14009233564138412, "compression_ratio": 1.8208092485549132, "no_speech_prob": 1.8715858459472656e-05, "words": [{"start": 2328.58, "end": 2329.2, "word": "يعني", "probability": 0.89892578125}, {"start": 2329.2, "end": 2331.22, "word": " عبارة", "probability": 0.9913330078125}, {"start": 2331.22, "end": 2331.6, "word": " عن", "probability": 0.9970703125}, {"start": 2331.6, "end": 2332.7, "word": " نماذج", "probability": 0.9764404296875}, {"start": 2332.7, "end": 2333.8, "word": " لأسئلة", "probability": 0.96982421875}, {"start": 2333.8, "end": 2334.54, "word": " تعبر", "probability": 0.901123046875}, {"start": 2334.54, "end": 2334.9, "word": " ..", "probability": 0.271240234375}, {"start": 2334.9, "end": 2336.0, "word": " تعبر", "probability": 0.850830078125}, {"start": 2336.0, "end": 2336.54, "word": " إلى", "probability": 0.875}, {"start": 2336.54, "end": 2336.88, "word": " حد", "probability": 0.995849609375}, {"start": 2336.88, "end": 2337.14, "word": " ما", "probability": 0.96875}, {"start": 2337.14, "end": 2337.92, "word": " عن", "probability": 0.98779296875}, {"start": 2337.92, "end": 2338.58, "word": " الأفكار", "probability": 0.990478515625}, {"start": 2338.58, "end": 2338.94, "word": " في", "probability": 0.9619140625}, {"start": 2338.94, "end": 2339.24, "word": " هذا", "probability": 0.95458984375}, {"start": 2339.24, "end": 2339.44, "word": " ال", "probability": 0.537109375}, {"start": 2339.44, "end": 2339.8, "word": " section", "probability": 0.84375}, {"start": 2339.8, "end": 2340.78, "word": " وبظل", "probability": 0.5574137369791666}, {"start": 2340.78, "end": 2341.16, "word": " عندكم", "probability": 0.986083984375}, {"start": 2341.16, "end": 2341.82, "word": " انتوا", "probability": 0.6861979166666666}, {"start": 2341.82, "end": 2342.68, "word": " اتكملوا", "probability": 0.90712890625}, {"start": 2342.68, "end": 2342.88, "word": " باقي", "probability": 0.8385416666666666}, {"start": 2342.88, "end": 2343.46, "word": " الأسئلة", "probability": 0.9935302734375}, {"start": 2343.46, "end": 2344.24, "word": " واتحولوا", "probability": 0.80498046875}, {"start": 2344.24, "end": 2344.38, "word": " باقي", "probability": 0.9326171875}, {"start": 2344.38, "end": 2344.8, "word": " الأسئلة", "probability": 0.9952392578125}, {"start": 2344.8, "end": 2345.12, "word": " عشان", "probability": 0.72900390625}, {"start": 2345.12, "end": 2345.56, "word": " تغطوا", "probability": 0.87060546875}, {"start": 2345.56, "end": 2345.72, "word": " باقي", "probability": 0.9596354166666666}, {"start": 2345.72, "end": 2346.3, "word": " الأفكار", "probability": 0.990234375}, {"start": 2346.3, "end": 2347.64, "word": " مبارك", "probability": 0.83197021484375}, {"start": 2347.64, "end": 2347.76, "word": " الله", "probability": 0.97216796875}, {"start": 2347.76, "end": 2348.12, "word": " فيكم", "probability": 0.9404296875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2348.326875, "duration_after_vad": 2267.461874999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/gsUWMBLCoZ8.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/gsUWMBLCoZ8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c2459b96d81dfa42f857b2d1bff7556d4c19fb82
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/gsUWMBLCoZ8.srt
@@ -0,0 +1,2391 @@
+1
+00:00:19,440 --> 00:00:25,020
+بسم الله الرحمن الرحيم المحاضرة رقم 14 في مساق
+
+2
+00:00:25,020 --> 00:00:29,960
+نظرية الأعداد لطلبة الجامعة الإسلامية قسم
+
+3
+00:00:29,960 --> 00:00:36,010
+الرياضيات لكلتا العلوم والتربية، هنكمل اللي بدأناه 
+
+4
+00:00:36,010 --> 00:00:38,150
+المرة الماضية الـ Linear congruences and the
+
+5
+00:00:38,150 --> 00:00:42,090
+Chinese remainder theorem حكينا المرة الماضية عن
+
+6
+00:00:42,090 --> 00:00:46,590
+الـ Linear congruences واليوم هنركز في حديثنا أو 
+
+7
+00:00:46,590 --> 00:00:51,650
+هنتحدث عن الـ Chinese remainder theorem حكينا 
+
+8
+00:00:51,650 --> 00:00:56,210
+المرة الماضية عن النظرية اللي بتقول إني لو كان
+
+9
+00:00:56,210 --> 00:01:02,930
+في عندي Linear congruence Ax تطابق الـ B modulo
+
+10
+00:01:04,530 --> 00:01:08,230
+AX  وطابق الـ B modulo N قلنا إنه لو كان العامل...
+
+11
+00:01:08,230 --> 00:01:13,090
+عشان أحل هذه التطابقة باجي بشوف العامل المشترك 
+
+12
+00:01:13,090 --> 00:01:16,270
+الأعلى بين الـ A و الـ N إذا كان العامل المشترك 
+
+13
+00:01:16,270 --> 00:01:20,630
+الأعلى بين الـ A و الـ N بيقسم الـ B معناته هذه هذا
+
+14
+00:01:20,630 --> 00:01:24,230
+solution بيقسم الـ B معناته مافيش أي solution
+
+15
+00:01:24,230 --> 00:01:28,930
+وقلنا إنه لو كان العامل المشترك الأعلى بين الـ A و
+
+16
+00:01:28,930 --> 00:01:35,340
+الـ N اللي هو بساوي D والـ D بتقسم الـ B إذا في
+
+17
+00:01:35,340 --> 00:01:40,000
+عندي D mutually incongruent solutions  مظلمين
+
+18
+00:01:40,000 --> 00:01:44,600
+مظلواً حيكون في هذه التطابق اللي هي عددها D من ال
+
+19
+00:01:44,600 --> 00:01:51,550
+solutions الغير متطابقة مظلمين مظلواً  واخدنا بعدها
+
+20
+00:01:51,550 --> 00:01:54,610
+Corollary كانت تقول لو كان العامل المشترك الأعلى
+
+21
+00:01:54,610 --> 00:02:01,290
+بين الـA و الـN بساوي 1 معناته إنه هو this has a
+
+22
+00:02:01,290 --> 00:02:07,450
+unique solution modulo N وحلينا مثال أو حلينا
+
+23
+00:02:07,450 --> 00:02:15,370
+تطابقه والآن وصلنا لعند التطابقه أو سؤال آخر اللي
+
+24
+00:02:15,370 --> 00:02:18,990
+هو solve the linear congruence 18X
+
+25
+00:02:20,350 --> 00:02:27,170
+18x تطابق 30
+
+26
+00:02:27,170 --> 00:02:30,850
+mod 42
+
+27
+00:02:30,850 --> 00:02:41,110
+solve الآن 
+
+28
+00:02:41,110 --> 00:02:48,130
+نحضر التطابق اللي أمامنا التطابق اللي أمامنا 18 X
+
+29
+00:02:48,130 --> 00:02:49,710
+وطبق الـ 30 مدل و 42 مدل و 42 مدل و 42 مدل و 42
+
+30
+00:02:49,710 --> 00:02:52,470
+مدل و 42 مدل و 42 مدل و 42 مدل و 42 مدل و 42 مدل و
+
+31
+00:02:52,470 --> 00:02:59,170
+42 مدل و 42 مدل و 42 مدل و 42 مدل و 42 مدل و 42
+
+32
+00:02:59,170 --> 00:02:59,530
+مدل و 42 مدل و 42 مدل و 42 مدل و 42 مدل و 42 مدل و
+
+33
+00:02:59,530 --> 00:02:59,610
+مدل و 42 مدل و 42 مدل و 42 مدل و 42 مدل و 42 مدل و
+
+34
+00:02:59,610 --> 00:03:12,730
+مدل و 32 مدل و 32 مدل و 32 مدل و 32 مدل و 32 مدل و
+
+35
+00:03:12,730 --> 00:03:17,400
+32 Incongruent solutions modulo minus 6 solutions
+
+36
+00:03:17,400 --> 00:03:19,920
+Incongruent modulo 40
+
+37
+00:03:25,840 --> 00:03:31,340
+زي ما قلنا الآن بنجسم اللي هو الطرفين على الستة
+
+38
+00:03:31,340 --> 00:03:34,560
+اللي جسمناها اللي هو العامل المشترك الأعلى لازم
+
+39
+00:03:34,560 --> 00:03:39,400
+يجسمه على مين؟ على 42 وقلنا هذا الكلام لازم يجسم
+
+40
+00:03:39,400 --> 00:03:43,180
+على 42 ولا مش شرط أنها تكون اللي هو اللي هي اللي 
+
+41
+00:03:43,180 --> 00:03:47,400
+بدك تطلعه بكافئ هذا واضح؟ وضربنا... أخذنا مثال
+
+42
+00:03:47,400 --> 00:03:57,000
+جسمنا على ستة بيصير عندك 3x تطابق 5 modulo 7 إذاً
+
+43
+00:03:57,000 --> 00:04:01,120
+خفّفنا عنا حتى من المقياس و بيسهّل علينا عملية
+
+44
+00:04:01,120 --> 00:04:07,320
+الحسابات الآن بنقول إيش هدفنا إحنا إنها بقيمة X 
+
+45
+00:04:07,320 --> 00:04:11,660
+يعني نجاعة DX لهذا لحالة وطابق كذا مدل السبعة
+
+46
+00:04:11,660 --> 00:04:20,380
+اللي عندي معايا؟ الآن إيش العدد القريب من السبعة و
+
+47
+00:04:20,380 --> 00:04:25,700
+اللي بيخليها DX؟ أو بيخلّيها حتى مضاعفات الـ X
+
+48
+00:04:25,700 --> 00:04:31,060
+ويطّلقلنا هنا عدد برضه بإضافة 7 أو طرح 7
+
+49
+00:04:31,060 --> 00:04:34,600
+يطلّقلنا برضه عدد نقدر نتعامل فيه مع العدد اللي
+
+50
+00:04:34,600 --> 00:04:38,260
+هنا، إيش معنى الحديث؟ اللي عن التلاتة X اللي عندي 
+
+51
+00:04:38,260 --> 00:04:43,600
+هذه أكيد هي التلاتة نفسها بالنسبة للسبعة نفسها هي 
+
+52
+00:04:43,600 --> 00:04:47,700
+الأربعة لأن التلاتة تطابق نقص أربعة تطابق نقص 
+
+53
+00:04:47,700 --> 00:04:51,500
+أربعة مضلة مين؟ مضلة سبعة إذا بدأت تبدل التلاتة من
+
+54
+00:04:51,500 --> 00:04:57,240
+مين؟ بـ 4 إذا صار عندي سالب 4 X تطابق هذا
+
+55
+00:04:57,240 --> 00:05:03,440
+استبدلتها بمن يطابقها الآن يجي للخمسة بدي أستبدلها
+
+56
+00:05:03,440 --> 00:05:07,460
+بإني أضيف سبعة وأطرح سبعة أو مضاعفات السبعة حسب
+
+57
+00:05:07,460 --> 00:05:11,300
+ما يلزمني هل جيت نفهم شو معادلة حسب ما يلزمني؟ لأن 
+
+58
+00:05:11,300 --> 00:05:14,810
+خمسة لو طرحنا منها سبعة بيصير سالب اتنين لأن سالب 
+
+59
+00:05:14,810 --> 00:05:19,070
+اتنين مع السالب أربعة نختصر السالب اتنين لكن بقال 
+
+60
+00:05:19,070 --> 00:05:24,470
+اتنينها فبدي كمان اللي هو عملية لكن ما أسهل لو قلت
+
+61
+00:05:24,470 --> 00:05:30,150
+سبعة وخمسة إيش شمالها اتماش لأن عند سرعة الخمسة
+
+62
+00:05:30,150 --> 00:05:36,130
+أكيد بالطبق اتماش مدنه مين مدنه سبعة إشمعنا
+
+63
+00:05:36,130 --> 00:05:38,270
+الاتماش حسبتها في دماغ الاتماش اللي هي علاقة
+
+64
+00:05:38,270 --> 00:05:40,530
+بالأربعة بعد الخطوة اللي بقى ده بقسم على أربعة
+
+65
+00:05:40,530 --> 00:05:48,010
+وبأرتاح واضح فبصير عندي الآن اتناش مدله مين مدله
+
+66
+00:05:48,010 --> 00:05:58,530
+سبعة واضح الآن هذا سبعة وعندي الأربعة اللي هو
+
+67
+00:05:58,530 --> 00:06:02,310
+الجواز كوم الـ divisor بينها وبين السبعة إيش إذا
+
+68
+00:06:02,310 --> 00:06:10,360
+بقسم وأنا مرتاح بصير عندي الآن ناقص X تطابقاللي هو
+
+69
+00:06:10,360 --> 00:06:18,300
+تلاتة مدله مين؟ مدله السبعة واضح أه؟ الآن هذه اضرب
+
+70
+00:06:18,300 --> 00:06:23,580
+اتجاه ثاني في ناقص بيصير عندي X ضرب جاز والجامعه
+
+71
+00:06:23,580 --> 00:06:28,460
+جاز ويقترح جاز القسمة بدك تأخد بإيه الاعتبار
+
+72
+00:06:28,460 --> 00:06:31,140
+ماكتكسم على مين؟ على العامل المشترك اللي هي على 
+
+73
+00:06:31,140 --> 00:06:36,360
+بين اللي يكون اللي هو اللي هو بين السبعة و... بين
+
+74
+00:06:36,360 --> 00:06:42,780
+الـ 42 و بين الـ 18 أو تقسم على كل المعادلة إذا كانت 
+
+75
+00:06:42,780 --> 00:06:48,180
+جائزة واضح اللي بحكيه في الـ C بالـ X في تطابق 
+
+76
+00:06:48,180 --> 00:06:52,280
+المعقص ثلاثة Modulo مين Modulo السبعة الـ X
+
+77
+00:06:52,280 --> 00:06:56,500
+بالطابق مين المعقص ثلاثة بالموجة بمين هي الأربعة
+
+78
+00:06:56,500 --> 00:07:01,400
+Modulo سبعة لأنه مقياس إيش سبعة يعني أنا بضيف سبعة
+
+79
+00:07:01,400 --> 00:07:08,960
+بطلع أربعة طيب شوفوا عليه الآن هذه هي الحلول لهذه
+
+80
+00:07:08,960 --> 00:07:18,880
+التطابقات انتبه عليها الآن هذه اللي طلعت عندي هي في
+
+81
+00:07:18,880 --> 00:07:23,100
+الواقع مجموعة أرقام عادة ذات مهام من الأرقام اللي
+
+82
+00:07:23,100 --> 00:07:28,260
+هي أربعة و11 و18
+
+83
+00:07:30,350 --> 00:07:44,110
+و25 و32 و39 و46 و53 وعالجهة الثانية ناقص ثلاثة
+
+84
+00:07:44,110 --> 00:07:50,170
+ناقص 10 ناقص ثلاثة ناقص 17 إلى مال نهاية
+
+85
+00:07:50,170 --> 00:07:55,610
+واضح هذه اللي هي عبارة عن set of solutions في Z
+
+86
+00:08:00,650 --> 00:08:08,050
+الآن هذا الـ set of solutions عبرنا عنها بالتطابق
+
+87
+00:08:08,050 --> 00:08:13,910
+و X تطابق 4 مضلوا 7 يعني في عندي only one solution
+
+88
+00:08:13,910 --> 00:08:21,370
+مضلمين مضلوا 7 لكن لو اطلعت فوق من بداية الحل عندي
+
+89
+00:08:21,370 --> 00:08:26,490
+في حسب اللي هان في عندي ستة من ال solutions
+
+90
+00:08:26,490 --> 00:08:44,310
+incongruent بس مضلمين مدن 42 مدن مين؟
+
+91
+00:08:44,310 --> 00:08:52,450
+مدن 42 مدن مين؟ مدن 42 مدن خذ أي ستة ورا بعضها
+
+92
+00:08:52,450 --> 00:08:57,890
+بيطلع إن هما الـ incongruent solutions مدن ومين؟
+
+93
+00:08:57,890 --> 00:09:03,650
+مدن 42 ومجاملهم بيصير مش congruent للي في جوا يعني 
+
+94
+00:09:03,650 --> 00:09:10,230
+بمعنى آخر هاخد الآن ال... ال... the only
+
+95
+00:09:10,230 --> 00:09:13,650
+incongruent
+
+96
+00:09:13,650 --> 00:09:16,590
+solutions
+
+97
+00:09:17,950 --> 00:09:25,190
+of هذه سميها star modulo 42R
+
+98
+00:09:27,470 --> 00:09:33,950
+من هنا الـ X تطابق الأربعة modulo من هنا من هنا 
+
+99
+00:09:33,950 --> 00:09:40,610
+يعني الأربعة والـ 11 والـ 18 والـ 25 والـ 32 والـ
+
+100
+00:09:40,610 --> 00:09:45,890
+39 يعني ال solutions بمعنى آخر هي التالي X تطابق
+
+101
+00:09:45,890 --> 00:09:53,790
+الأربعة modulo 42 X تطابق الـ 11 modulo 42 X تطابق 
+
+102
+00:09:53,790 --> 00:10:03,170
+الـ 18 modulo 42 X تطابق الـ 25 Modulo 42 X تطابق 
+
+103
+00:10:03,170 --> 00:10:12,470
+الـ 32 Modulo 39 X تطابق الـ 42 X تطابق الـ 39
+
+104
+00:10:12,470 --> 00:10:18,910
+Modulo 42 1,2,3,4,5,6 هدول الـ incongruent 
+
+105
+00:10:18,910 --> 00:10:23,010
+solutions للمعادلة الأصلية دا هذه عبارة عن طريقة
+
+106
+00:10:23,010 --> 00:10:31,010
+عرض للحلول اللي طلعت عند هذه أو هذه modulo 42 لما 
+
+107
+00:10:31,010 --> 00:10:36,130
+نعرض معها modulo 7 طلع بس one incongruent solution
+
+108
+00:10:36,130 --> 00:10:40,630
+مافيش غير unique solution بينما هنا طلع عندي 6
+
+109
+00:10:40,630 --> 00:10:46,950
+incongruent solutions modulo 42 لكن هدولة كلهم هم 
+
+110
+00:10:46,950 --> 00:10:52,890
+نفسها يعني الآن وكأنه خزّنت المعلومات هذه في هذه أو 
+
+111
+00:10:52,890 --> 00:10:56,930
+خزّنت المعلومات هذه في اللي هي طريقة العرض اللي 
+
+112
+00:10:56,930 --> 00:11:02,990
+عنده مدل 42 ولو أنت جربت... لو جربت تفرد هنا هذول 
+
+113
+00:11:02,990 --> 00:11:09,590
+هي عندك الأربعة ضيف له 42 ويطلع 46 هذا الـ 11 ضيف له
+
+114
+00:11:09,590 --> 00:11:13,350
+42 ويطلع 53 وهاكذا... أه وهاكذا وفي الجهة
+
+115
+00:11:13,350 --> 00:11:16,030
+الثانية نفس الشيء أي سؤال؟
+
+116
+00:11:18,530 --> 00:11:23,790
+من أين تريد أن تبدأ؟ من أين تريد أن تبدأ؟ لكن الـ 
+
+117
+00:11:23,790 --> 00:11:27,630
+Positive أقرب لنفسك فقط يعني من عندنا مقص لا
+
+118
+00:11:27,630 --> 00:11:34,050
+تبدأ، تحرر من عندنا مقص لا تبدأ، تحرر مثلما نعوّض
+
+119
+00:11:34,050 --> 00:11:36,830
+في معادلة، نعوض في معادلة ونعطيها Special
+
+120
+00:11:36,830 --> 00:11:42,710
+Solution واحد يروح ويعوّض في معادلة في X بساوية جدر 
+
+121
+00:11:42,710 --> 00:11:47,210
+الاثنين بقي بعيد عن نفس جذر الاثنين أو جذر الثلاثة أو
+
+122
+00:11:47,210 --> 00:11:51,790
+جذر السبعة بروح بعوّض عادة بما مثلاً بالصفر أسهله
+
+123
+00:11:51,790 --> 00:11:57,970
+إلا إذا كانت مقصودة مع الصفر وهكذا يعني أنت بتعوض
+
+124
+00:11:57,970 --> 00:12:02,830
+بما هو أو خلنا نقول تعرض بما تهوى نفسك أو خلنا 
+
+125
+00:12:02,830 --> 00:12:06,670
+نقول يهوى الآخرين هنا طبعاً الناس بترتاح أكثر لمين
+
+126
+00:12:06,670 --> 00:12:12,090
+للرقم الموجبة أما بنفع من عند ناقص ثلاثة تطلع أو
+
+127
+00:12:12,090 --> 00:12:15,830
+من ناقص 10 زي ما بدك يأتي الآن للجزء الثاني من
+
+128
+00:12:15,830 --> 00:12:19,470
+المحاضرة أو الجزء الأساسي في المحاضرة وهو Chinese
+
+129
+00:12:19,470 --> 00:12:24,410
+remained bar theorem نظرية الباقي الصينية نظرية
+
+130
+00:12:24,410 --> 00:12:31,170
+الباقي الصينية الآن نحكي عن نظرية الباقي الصينية
+
+131
+00:12:31,170 --> 00:12:40,370
+نذكر النظرية ونذكر برهانها وستجد برهانها هو فعلاً
+
+132
+00:12:41,550 --> 00:12:47,510
+الجزء العملي لحل الأسئلة يعني كيف بيبرهن كيف بده
+
+133
+00:12:47,510 --> 00:12:54,030
+يحل الأسئلة ركز معايا على النظرية إيش بتقول لأن ال
+
+134
+00:12:54,030 --> 00:12:57,750
+theorem هي Chinese remainder theorem اللي هو تقول 
+
+135
+00:12:57,750 --> 00:13:05,030
+ما يلي لو كان عندي N واحد و N اثنين عند N ر
+
+136
+00:13:05,030 --> 00:13:09,470
+positive integers كل اثنين مع بعض إيش مالهم؟ ال
+
+137
+00:13:09,470 --> 00:13:15,090
+relatively prime وبدأ أحل الـ system of equations
+
+138
+00:13:15,090 --> 00:13:19,950
+يعني الآن عرض علي اللي احنا طبعاً تعلمنا كيف نحل 
+
+139
+00:13:19,950 --> 00:13:22,530
+الـ linear congruence من النظرية اللي قبل شوية خدنا 
+
+140
+00:13:22,530 --> 00:13:26,750
+الأمثلة عليها الآن بتأخذ اللي هو مش اللي هو معادلة 
+
+141
+00:13:26,750 --> 00:13:31,830
+واحدة لـ system of اللي هو congruences يعني نظام
+
+142
+00:13:31,830 --> 00:13:36,730
+من الـ linear congruences و أحله أوجد الحل المشترك
+
+143
+00:13:36,730 --> 00:13:43,410
+لهم يعني بمعنى آخر عندي عرض علي X تطابق الواحد
+
+144
+00:13:43,410 --> 00:13:54,800
+modulo اللي هي N واحد و X تطابق اثنين modulo N2
+
+145
+00:13:54,800 --> 00:14:03,520
+لعند X تطابق AR modulo NR هذا System of Linear
+
+146
+00:14:03,520 --> 00:14:09,180
+Congruences بدي أبحث في حلول هذا الـ System الآن
+
+147
+00:14:09,180 --> 00:14:14,000
+النظرية بتقول لك ما هي ليه؟ لو كانت عندي العامل
+
+148
+00:14:14,000 --> 00:14:21,280
+المشترك الأعلى بين N1 وN2 وN1 وN3 وN2 وN3 لعند NR
+
+149
+00:14:22,140 --> 00:14:26,760
+كل اثنين مع بعض relatively prime يعني بمعنى آخر if
+
+150
+00:14:26,760 --> 00:14:31,100
+الـ greatest common divisor بين الـ Ni و الـ Nj
+
+151
+00:14:31,100 --> 00:14:42,760
+بيساوي واحد لكل i لا يساوي j then the system has
+
+152
+00:14:42,760 --> 00:14:49,340
+a unique solution modulo
+
+153
+00:14:50,560 --> 00:15:00,820
+N واحد في N اثنين لعند N R  a proof هذا
+
+154
+00:15:00,820 --> 00:15:07,060
+الـ solution حل لمين؟ لكل التطابقات simultaneously
+
+155
+00:15:07,060 --> 00:15:11,280
+solution لـ
+
+156
+00:15:11,280 --> 00:15:15,890
+N واحد N اثنين N R  بي positive integers such that
+
+157
+00:15:15,890 --> 00:15:18,810
+the greatest common divisor بين Ni و Nj 
+
+158
+00:15:18,810 --> 00:15:24,650
+بيساوي واحد for all i لا تساوي j، ركز معي، then the
+
+159
+00:15:24,650 --> 00:15:29,150
+system of linear congruences X تطابق A واحد، X
+
+160
+00:15:29,150 --> 00:15:31,950
+تطابق A اثنين modulo N واحد، modulo N اثنين عند X
+
+161
+00:15:31,950 --> 00:15:36,450
+تطابق AR modulo NR، has a simultaneous solution
+
+162
+00:15:37,270 --> 00:15:40,810
+which is unique modulo مين؟ modulo N واحد في N اثنين
+
+163
+00:15:40,810 --> 00:15:46,910
+فعند مين؟ N أقل إذا يوجد حل مشترك للـ system كله
+
+164
+00:15:46,910 --> 00:15:52,550
+و هذا الحل المشترك وحيد modulo مين؟ modulo حاصل ضرب
+
+165
+00:15:52,550 --> 00:15:55,870
+بين N واحد N اثنين لعند مين؟ N أقل إذا بتثبت شغلتين
+
+166
+00:15:55,870 --> 00:16:02,570
+أنه أول حاجة إنه في حل مشترك لهذه الاتنين اللي هو
+
+167
+00:16:02,570 --> 00:16:08,470
+هذا الحل المشترك وحيد modulo مين؟ و modulo N واحد و N
+
+168
+00:16:08,470 --> 00:16:10,210
+اثنين و N ثلاث و N أربع و N أربع و N أربع و N أربع
+
+169
+00:16:10,210 --> 00:16:10,690
+و N أربع و N أربع و N أربع و N أربع و N
+
+170
+00:16:10,690 --> 00:16:11,270
+أربع و N أربع و N أربع و N أربع و N أربع
+
+171
+00:16:11,270 --> 00:16:13,730
+و N أربع و N أربع و N أربع و N أربع و N
+
+172
+00:16:13,730 --> 00:16:15,150
+أربع و N أربع و N أربع و N أربع و N أربع
+
+173
+00:16:15,150 --> 00:16:16,810
+و N أربع و N أربع و N أربع و N أربع و N
+
+174
+00:16:16,810 --> 00:16:20,350
+أربع و N أربع و N أربع و N أربع و N أربع
+
+175
+00:16:20,350 --> 00:16:26,310
+و N أربع و N أربع و N أربع خليني أسمي N
+
+176
+00:16:26,310 --> 00:16:32,010
+بتساوي N واحد في N اثنين لعند N R يعني حاصل ضرب
+
+177
+00:16:32,010 --> 00:16:37,750
+المقاييس كلها بدي أسميها ن بدي أسميها N و خليني
+
+178
+00:16:37,750 --> 00:16:40,950
+أسمي الـ NK بتساوي
+
+179
+00:16:42,640 --> 00:16:48,500
+اللي هو الـ Mi هذه حاصل الضرب كله حاصل الضرب كله N
+
+180
+00:16:48,500 --> 00:16:57,120
+ما عدا الـ NKi Small يعني على سبيل المثال M1 هي
+
+181
+00:16:57,120 --> 00:17:06,400
+عبارة عن M2 في M3 لمّا أصل لـ NR M2 هي عبارة عن M1 في M3
+
+182
+00:17:06,400 --> 00:17:14,870
+لمّا أصل عن مين؟ لـ NR يعني بمعنى آخر الـ NKi Capital هي
+
+183
+00:17:14,870 --> 00:17:21,910
+عبارة عن كل الـ N بشيل منهن الـ NKi Small واضح صار
+
+184
+00:17:21,910 --> 00:17:26,550
+عندي بناء على هذا الحديث صار عندي الـ greatest common
+
+185
+00:17:26,550 --> 00:17:30,810
+divisor بين الـ NKi Capital و الـ NKi Small إيش
+
+186
+00:17:30,810 --> 00:17:38,310
+حسابها؟ ما فيش عامل ليش؟ لأنه أصلاً الـ NKi عبارة عن N
+
+187
+00:17:38,310 --> 00:17:43,450
+واحد N اثنين لعند MR مشهولة منها الـ NKi و أنا معرف
+
+188
+00:17:43,450 --> 00:17:49,550
+أنه الـ N واحد و الـ N اثنين لعند MR كلها Relatively
+
+189
+00:17:49,550 --> 00:17:57,390
+prime إذا ما ضلّ عامل بين الـ NKi و بين الـ N1 و
+
+190
+00:17:57,390 --> 00:18:01,610
+الـ N2 اللي عند الـ NR يعني ما ظلّ عامل بين الـ NKi
+
+191
+00:18:01,610 --> 00:18:07,310
+Capital اللي هي حاصل الـ N على الـ NKi و بين الـ NKi
+
+192
+00:18:07,310 --> 00:18:17,110
+إيه إيه؟ Small أي سؤال؟
+
+193
+00:18:17,110 --> 00:18:21,010
+طيب،
+
+194
+00:18:21,010 --> 00:18:24,720
+شوف صلى الله عليه وسلم النبي عليه الصلاة والسلام قبل ما
+
+195
+00:18:24,720 --> 00:18:32,620
+أعطيكم بين إيديكم الحل المشترك بدي أداة توصلني
+
+196
+00:18:32,620 --> 00:18:37,480
+إليه الأداة هي التالية بدي أثبت لكم .. بدي أحل لكم
+
+197
+00:18:37,480 --> 00:18:45,660
+الآن NKi في X تطابق الواحد modulo NKi بدي أحلها
+
+198
+00:18:45,660 --> 00:18:53,450
+السؤال هل هذه تحل؟ بما أن العامل المشترك الأعلى بين
+
+199
+00:18:53,450 --> 00:18:58,070
+الـ NKi Capital والـ NKi Small بيساوي واحد إذا 
+
+200
+00:18:58,070 --> 00:19:03,190
+بالنظرية الأولى تبعنا بدي يكون عندي this has a
+
+201
+00:19:03,190 --> 00:19:07,770
+unique solution modulo N modulo NKi سمي هذا الـ
+
+202
+00:19:07,770 --> 00:19:14,750
+solution لـ X since NKi و X بيساوي تطابق واحد modulo N
+
+203
+00:19:14,750 --> 00:19:26,820
+حتى then بعد هذا then has a unique solution modulo 
+
+204
+00:19:26,820 --> 00:19:35,680
+NKi إيش يعني؟ That is هذا يعني there exists integer
+
+205
+00:19:35,680 --> 00:19:40,440
+بيحقق إيش؟ المعادلة اللي بتطابقها سميها هذا there
+
+206
+00:19:40,440 --> 00:19:46,560
+exists Xk element in Z such that NKi في Xk تطابق
+
+207
+00:19:46,560 --> 00:19:54,180
+الواحد modulo NKi بما أن العامل المشترك
+
+208
+00:19:54,180 --> 00:19:58,540
+الأعلى بين الـ NKi و الـ NKi Small بيساوي واحد إذا هذه
+
+209
+00:19:58,540 --> 00:20:03,760
+التطابقة إلها إيش مالها؟ only one solution هذا الـ
+
+210
+00:20:03,760 --> 00:20:07,720
+solution سميته إيش اسمه؟ Xk إيش معناه solution
+
+211
+00:20:07,720 --> 00:20:14,960
+معناه يطابق كـ إيش مالها؟ بيحقق طرفي التطابقة بمعنى NKi
+
+212
+00:20:14,960 --> 00:20:20,920
+في Xk تطابق الواحد modulo مين؟ modulo NKi لأن النظرية
+
+213
+00:20:20,920 --> 00:20:26,480
+النظرية أنا أو النظرية اللي هو الكتاب بيقول ما 
+
+214
+00:20:26,480 --> 00:20:35,280
+يقول لي أنه لو أجيت أخذت X الآن وسميتها X بار و أجيت
+
+215
+00:20:35,280 --> 00:20:44,760
+أخذت الـ summation لـ Xi اللي طلعت هنا Xi و ضربت
+
+216
+00:20:44,760 --> 00:20:51,330
+في المعاملات هذول اللي هي الـ Ai اللي عندك و ضربتها
+
+217
+00:20:51,330 --> 00:20:57,210
+في الـ Ni هذه اللي ركبتها Ni من عند واحد
+
+218
+00:20:57,210 --> 00:21:03,290
+لعند R هتلاقي هذا هو الـ solution اللي أنت بتبحث
+
+219
+00:21:03,290 --> 00:21:08,430
+عنه يعني بمعنى آخر هتلاقي الـ X بار تطابق الـ A واحد
+
+220
+00:21:08,430 --> 00:21:13,200
+modulo N واحد و الـ X بار تطابق الـ A2 modulo N2 و الـ X 
+
+221
+00:21:13,200 --> 00:21:17,180
+بار تطابق الـ AR modulo NR بمعنى هو عبارة عن الـ
+
+222
+00:21:17,180 --> 00:21:22,400
+simultaneous solution للـ system اللي عندك و حكيت لك
+
+223
+00:21:22,400 --> 00:21:27,220
+إن هذا إيش مالها؟ وحيد modulo N في N واحد في N اثنين لعند
+
+224
+00:21:27,220 --> 00:21:32,240
+مين؟ لعند NR معالجة يا شباب؟ آه طيب صلّ على النبي 
+
+225
+00:21:32,240 --> 00:21:38,570
+عليه الصلاة والسلام الآن إذا مغلطي الـ X¯ بتساوي
+
+226
+00:21:38,570 --> 00:21:46,610
+summation Xi Ai Mi i من 1 لعند الـ R رايتي أن أثبت
+
+227
+00:21:46,610 --> 00:21:51,910
+لك إيدك إيش مالها؟ تطابق الـ A1 modulo N1 تطابق الـ A2
+
+228
+00:21:51,910 --> 00:21:57,030
+modulo N2 تطابق الـ AR modulo NR معناته إنه إيش مالها؟ عبارة عن الـ
+
+229
+00:21:57,030 --> 00:22:01,830
+simultaneous solution للـ system اللي
+
+230
+00:22:01,830 --> 00:22:02,250
+عندك
+
+231
+00:22:04,920 --> 00:22:13,680
+الآن ملاحظة على جنب .. لو أجينا لأي
+
+232
+00:22:13,680 --> 00:22:26,360
+i .. خليني أخذ اللي هو .. خليني
+
+233
+00:22:26,360 --> 00:22:27,300
+أكتب هنا لو نبحث
+
+234
+00:22:35,430 --> 00:22:46,610
+N واحد تطابق صفر modulo N واحد إيش رأيكم؟ ليش؟
+
+235
+00:22:46,610 --> 00:22:50,630
+N واحد مين هي؟
+
+236
+00:22:50,630 --> 00:22:58,930
+عبارة عن N اثنين، N ثلاث، N اثنين، N
+
+237
+00:22:58,930 --> 00:23:04,610
+أربع N i سميها و Ni إيش مالها؟ ليس واحد
+
+238
+00:23:07,360 --> 00:23:13,100
+واضح؟ آه عند N واحد تطابق صفر modulo Ni و i إيش مالها؟ 
+
+239
+00:23:13,100 --> 00:23:19,980
+ليست واحد يعني مثلاً خد اثنين الـ
+
+240
+00:23:19,980 --> 00:23:23,740
+N واحد تطابق صفر modulo N اثنين عارفين ليش؟ لأن
+
+241
+00:23:23,740 --> 00:23:29,480
+الـ N واحد إيش مالها؟ مضاعفات مين؟ N اثنين فاهمين
+
+242
+00:23:29,480 --> 00:23:34,640
+معنى الكلام؟ يعني الـ N اثنين بتقسم N واحد N ثلاث
+
+243
+00:23:36,300 --> 00:23:44,360
+N ثلاث تكسب عن واحد لأنه مضافة من الـ N ثلاث لكل 
+
+244
+00:23:44,360 --> 00:23:51,020
+i إيش مالها؟ ليست واحد لأن N واحد هذه إيش مالها؟ مضاعفات كل
+
+245
+00:23:51,020 --> 00:23:58,660
+المضاعفات هذه ما عدا N واحد N
+
+246
+00:23:58,660 --> 00:23:59,440
+اثنين
+
+247
+00:24:01,980 --> 00:24:09,180
+تطابق الـ Zero modulo Nj أو Ni i لا يساوي إيش؟
+
+248
+00:24:09,180 --> 00:24:18,040
+اثنين in general in general in general NKi تطابق
+
+249
+00:24:18,040 --> 00:24:27,760
+صفر modulo Ni الـ i إيش مالها؟ مش هي الـ k لسبب بسيط
+
+250
+00:24:27,760 --> 00:24:35,530
+إن الـ NKi أصلاً موجودة فيها كل الـ Mi's ما عدا الـ 
+
+251
+00:24:35,530 --> 00:24:40,670
+MKi Small يعني بمعنى آخر صارت الـ MKi هذه الـ 
+
+252
+00:24:40,670 --> 00:24:46,250
+Capital من مضاعفات مين؟ الـ Mi هذه إذا صارت الـ M
+
+253
+00:24:46,250 --> 00:24:49,810
+i تجسم الـ MKi معناه إن الـ MKi تطابق الصفر modulo
+
+254
+00:24:49,810 --> 00:24:57,410
+مين؟ Mi بدأنا نستخدم هذه إذا صارت هذه 
+
+255
+00:25:01,860 --> 00:25:11,100
+صار عندي هذا كل صفر modulo Mi ما عدا اللي هي
+
+256
+00:25:11,100 --> 00:25:18,420
+مين؟ لكل i لا تساوي مين؟ لا تساوي كم؟ ما عدا
+
+257
+00:25:18,420 --> 00:25:27,720
+الـ NKi Small يعني
+
+258
+00:25:27,720 --> 00:25:34,850
+الآن بدي أصفر كل اللي .. اللي عندي .. عندي الـ Mi
+
+259
+00:25:34,850 --> 00:25:44,630
+اللي هو صفر مع كلّهم ما عدا مع مين؟ الـ N اللي هي i 
+
+260
+00:25:44,630 --> 00:25:52,270
+الصغيرة ماشي؟ إذاً هذا بطابق .. قدحت النقطة هذه 
+
+261
+00:25:52,270 --> 00:25:55,350
+الـ Mi لأن كده بطابق الـ Mi modulo i، that's okay
+
+262
+00:25:56,620 --> 00:26:02,100
+الـ N و عشان تسهل على حالك سمي هذه i و هذه NKi لكل i
+
+263
+00:26:02,100 --> 00:26:09,880
+اللي تستخدم بيصير تطابق كل N هيتصفر ما عدا مين؟ الـ
+
+264
+00:26:09,880 --> 00:26:17,700
+NKi اللي هي الكبيرة و هيكون modulo الـ NKi الصغير
+
+265
+00:26:17,700 --> 00:26:33,970
+تطابق Xk Ak NKi مظبوط؟ modulo أي سؤال
+
+266
+00:26:33,970 --> 00:26:38,050
+واضح
+
+267
+00:26:38,050 --> 00:26:45,310
+آه طيب احنا ما احنا قلنا الـ NKi في الـ Xk إيش 
+
+268
+00:26:45,310 --> 00:26:51,750
+بالطابق modulo صح؟ لأن قلنا في solution لجماعة 
+
+269
+00:26:51,750 --> 00:26:54,910
+سمينا إيش اسمه؟ الـ Xk إذا هذا صار بطابق
+
+270
+00:26:58,260 --> 00:27:06,940
+الـ Ak في واحد modulo NKi هي و لا؟ أثبتناها دي NKi في
+
+271
+00:27:06,940 --> 00:27:11,480
+Xk إيش مالها؟ تطابق الواحد modulo و دولة NKi عوضت
+
+272
+00:27:11,480 --> 00:27:15,060
+عنها لبطء تطابق الـ Ak في الواحد modulo و دولة NKi
+
+273
+00:27:15,060 --> 00:27:21,200
+و ده إذا تعرفين الخواص و هذا تطابق الـ Ak modulo 
+
+274
+00:27:21,200 --> 00:27:29,050
+NKi هذا لكل K أخذناها لكل K إيش مالها؟ arbitrary آه
+
+275
+00:27:29,050 --> 00:27:34,810
+arbitrarily got fixed صار عندي الـ X بار تطابق الـ A
+
+276
+00:27:34,810 --> 00:27:41,230
+K modulo مين؟ modulo الـ Nk إذا for من البداية for
+
+277
+00:27:41,230 --> 00:27:47,130
+any fixed K أثبتنا هذا الكلام يعني بمعنى آخر صارت
+
+278
+00:27:47,130 --> 00:27:53,530
+الـ X بار إيش مالها؟ solution لها دولها يعني إيش 
+
+279
+00:27:53,530 --> 00:28:00,990
+مالها؟ صار simultaneous solution للـ system كله أي
+
+280
+00:28:00,990 --> 00:28:08,970
+سؤال؟ الآن .. الآن بدنا نثبت إيش؟ إنه Unique بدنا
+
+281
+00:28:08,970 --> 00:28:13,730
+نثبت أن هذا الـ Solution Unique مضمونين مضمون الآن
+
+282
+00:28:13,730 --> 00:28:22,250
+إيش هنقول؟ هنقول Suppose that في another solution
+
+283
+00:28:24,410 --> 00:28:27,330
+إذا الآن بدنا نثبت الـ uniqueness للـ solution
+
+284
+00:28:27,330 --> 00:28:40,750
+نقول suppose .. suppose .. suppose that X prime is
+
+285
+00:28:40,750 --> 00:28:44,790
+another solution
+
+286
+00:28:44,790 --> 00:28:50,630
+of the system ماشي؟
+
+287
+00:28:52,500 --> 00:28:58,320
+بنفترض أن الـ X' هو مصطلح آخر لـ System لكل K
+
+288
+00:28:58,320 --> 00:29:04,320
+بتساوي واحد لعند الـ R بيصير عند الـ X' X برايم
+
+289
+00:29:04,320 --> 00:29:12,100
+تطابق الـ A مدنومين عن
+
+290
+00:29:12,100 --> 00:29:17,320
+K لأنه مصطلح لكل الـ System وإحنا أثبتنا أن X'
+
+291
+00:29:17,920 --> 00:29:24,850
+برضه مصطلحه مظبوط؟ إذا عند الـ X' والـ AK والـ X'
+
+292
+00:29:25,030 --> 00:29:31,650
+كلهم إشمالا Concurrent مضمونين مضمون K هذا يعني
+
+293
+00:29:31,650 --> 00:29:39,050
+أنه صار عند الـ X' والـ X' Concurrent مضمونين
+
+294
+00:29:39,050 --> 00:29:45,040
+مضمون K صارت الـ x bar و الـ x prime و الـ x bar
+
+295
+00:29:45,040 --> 00:29:51,060
+congruent بدولة NK يعني الـ NK تجسم الـ x prime
+
+296
+00:29:51,060 --> 00:29:57,600
+ناقص x bar يعني
+
+297
+00:29:57,600 --> 00:30:06,540
+بمعنى آخر صار عندي ال N واحد تجسم ال x bar ناقص x 
+
+298
+00:30:06,540 --> 00:30:12,860
+prime ال N اتنين أو x prime ناقص x barم2 بتقسم الـ
+
+299
+00:30:12,860 --> 00:30:21,940
+X' نقص X¯ لعند ال MR بتقسم ال X' نقص X¯ لاحظ ميا
+
+300
+00:30:21,940 --> 00:30:29,220
+ليه ان براء واحد صارت من عوامل اللي هي ال X' ال X¯
+
+301
+00:30:29,220 --> 00:30:35,120
+و ال N2 من عواملهو الـ N1 و الـ N2 من الـ negative
+
+302
+00:30:35,120 --> 00:30:39,240
+لـ prime يعني هذا أخذ منه جزء و هذا أخذ منه جزء
+
+303
+00:30:39,240 --> 00:30:43,840
+ثاني مالوش علاقة فيه ونفس الأشياء MR كل مقاش مالي
+
+304
+00:30:43,840 --> 00:30:47,120
+من الـ negative لـ prime إذا كل واحد بياخد مكانه
+
+305
+00:30:47,120 --> 00:30:52,020
+من X prime نقص X bar ولا يتعدى على الآخر بمعنى آخر
+
+306
+00:30:52,020 --> 00:31:01,160
+حيكون عند N1 فN2 عند MR كلموجودين في مكان منفصل من
+
+307
+00:31:01,160 --> 00:31:08,300
+X'-X¯ يعني N1×N2×NR اللي هو كله على بعض و بقص مين
+
+308
+00:31:08,300 --> 00:31:18,740
+الـ X'-X¯ يعني
+
+309
+00:31:18,740 --> 00:31:22,760
+مثلًا على سبيل المثال لما نقعد أقول التنين بتقسم
+
+310
+00:31:22,760 --> 00:31:28,620
+12 والتلاتة بتقسم 12 ماشي الحال ان ان هدول التنين
+
+311
+00:31:28,620 --> 00:31:34,020
+relatively prime هذا عامل من 12 أخد نفسه التنين
+
+312
+00:31:34,020 --> 00:31:38,860
+هذا أخد نفسه التلاتة وليس بين العوامل إذا حصل
+
+313
+00:31:38,860 --> 00:31:43,120
+ضربهم بيبقى له محجوز هذا محجوز اللي إله وهذا
+
+314
+00:31:43,120 --> 00:31:46,960
+محجوز اللي إله منفصل بيصير بيكسل 100 أطلع عشان
+
+315
+00:31:46,960 --> 00:31:51,820
+التنين relatively prime واتبعتوا سهل لهم طيب
+
+316
+00:31:55,050 --> 00:32:00,790
+بنصارى ان دي غير الـ N واحد اللي هي الـ N بتجسم
+
+317
+00:32:00,790 --> 00:32:05,770
+الـ X برايم ناقص X bar N واحد في الـ N تلاتة عند
+
+318
+00:32:05,770 --> 00:32:12,710
+NR هي الـ N وهذا ايش يعني؟ هذا يعني أن x' تطابق الـ
+
+319
+00:32:12,710 --> 00:32:17,870
+x bar modulo n يعني بمعنى آخر في we have a unique
+
+320
+00:32:17,870 --> 00:32:22,130
+solution modulo إيش، modulo n يعني أي solution آخر
+
+321
+00:32:22,130 --> 00:32:29,670
+هيطلع كل درونت إليه modulo إيش، modulo n أي سؤال؟
+
+322
+00:32:29,670 --> 00:32:36,270
+طيب ناخد الآن تطبيق تطبيق على النظرية
+
+323
+00:32:41,090 --> 00:32:44,590
+بناخد مثال، شوفوا الآن، هتلاقونا في المثال، هنرتب
+
+324
+00:32:44,590 --> 00:32:52,350
+حالنا بأسلوب يعني بالظبط زي النظرية و هنرتب الحل
+
+325
+00:32:52,350 --> 00:32:55,870
+بطريقة معينة بحيث أنها تسير اللي هي طريقة خليني
+
+326
+00:32:55,870 --> 00:33:00,550
+أقول لغة مشتركة بيننا جميعا وتسهل علينا اللي هو
+
+327
+00:33:00,550 --> 00:33:07,400
+عملية إيجاد الحل الحل هي اللي مسحته هنا بديش امسحه
+
+328
+00:33:07,400 --> 00:33:13,000
+ال X bar هو مين الحل المشترك هيكون بساوي ال
+
+329
+00:33:13,000 --> 00:33:20,360
+summation XI AI MI I من عند واحد لعند R هذا
+
+330
+00:33:20,360 --> 00:33:24,840
+بيجمعته في السؤال وهذا أنا بكونه من المؤتة في
+
+331
+00:33:24,840 --> 00:33:31,240
+السؤال وهذا بجيبه من حل مين من حل MK XK تطابق
+
+332
+00:33:31,240 --> 00:33:38,390
+الواحد مدنه مين MK هي كل الجثة أيضاً صار الموضوع
+
+333
+00:33:38,390 --> 00:33:55,810
+سهل لنشوف كيف شوفوا
+
+334
+00:33:55,810 --> 00:33:58,090
+صلى الله على النبي يا جماعة عليه الصلاة والسلام صلى عليه
+
+335
+00:33:58,090 --> 00:34:01,930
+الصلاة والسلام محمد find بقول example example
+
+336
+00:34:05,480 --> 00:34:14,480
+Find the numbers which have the remainders 2 و3 و2
+
+337
+00:34:14,480 --> 00:34:22,900
+when divided by 3 و5 و7 respectively أوجد الأعداد
+
+338
+00:34:22,900 --> 00:34:29,380
+التي تحقق معنى مالي إيش بتحقق بالـDX اللي لما
+
+339
+00:34:29,380 --> 00:34:37,250
+أجسمها على 2 لما اجسمها على التلاتة يظل إيش؟ اتنين
+
+340
+00:34:37,250 --> 00:34:41,810
+اجسمها على الخمسة يظل جداش اجسمها على السبعة يظل
+
+341
+00:34:41,810 --> 00:34:49,290
+إيش؟ اتنين معين؟ أذكركم شغلة أن الأعداد التي لها
+
+342
+00:34:49,290 --> 00:34:51,570
+نفس ال remainder متطابقة
+
+343
+00:34:54,170 --> 00:35:01,530
+إذاً العدد نفسه يطابق اللي هو متبقي عندما يُقسم
+
+344
+00:35:01,530 --> 00:35:07,390
+على N يعني العدد اللي بدور عليه الـ X هذا لما بدّى
+
+345
+00:35:07,390 --> 00:35:12,510
+جسمه على 3 هيطابق اللي هو الـ remainder اللي متبقت
+
+346
+00:35:12,510 --> 00:35:17,830
+الاتنين مضلوا مين مضلوا 3 وهيطابق اللي هو التلاتة
+
+347
+00:35:17,830 --> 00:35:24,240
+مضلوا 7 مضلوا 5 وهيطابق التنين مضلوا مين واضحة
+
+348
+00:35:24,240 --> 00:35:33,340
+العدد يطابق remainder مدنه ما قسم عليه إذا صار
+
+349
+00:35:33,340 --> 00:35:38,360
+عندي الآن ترجمة هذا الـ X اللي بدور عليها يجب أن
+
+350
+00:35:38,360 --> 00:35:46,200
+تحقق مالي X تطابق اللي هو التنين مدنه تلاتة هذا
+
+351
+00:35:46,200 --> 00:35:51,480
+المقسم عليه وهذا ال remainder والـ X تطابق اللي هو
+
+352
+00:35:51,480 --> 00:36:01,380
+تلاتة موديلو خمسة و X تطابق اتنين موديلو سبعة إذا
+
+353
+00:36:01,380 --> 00:36:07,260
+صار في عندي الآن صار في عندي اللي هو ال three اللي
+
+354
+00:36:07,260 --> 00:36:11,140
+هو ال congruences أو linear congruences بدي احلهم
+
+355
+00:36:11,140 --> 00:36:17,900
+معا حلهم معا اجابته X bar بالساوية X واحد A واحد N
+
+356
+00:36:17,900 --> 00:36:20,820
+واحد زاد X اتنين A اتنين عن اتنين زاد X تلاتة A
+
+357
+00:36:20,820 --> 00:36:25,370
+تلاتة N تلاتة نعتبر هذه ا واحد وهذه اتنين وهذه
+
+358
+00:36:25,370 --> 00:36:29,670
+تلاتة ان واحد ا واحد وهذه ان واحد ان اتنين ان
+
+359
+00:36:29,670 --> 00:36:34,910
+تلاتة واضح؟ بتسمي التسميات اللي احنا عارفينها أول
+
+360
+00:36:34,910 --> 00:36:43,270
+حاجة الام ال capital ايش هي هتكون تلاتة في خمسة في
+
+361
+00:36:43,270 --> 00:36:48,390
+سبعة بيساوي تلاتة في خمسة بخمسة عشر أو سبعة في خمسة
+
+362
+00:36:48,390 --> 00:36:53,940
+بخمسة تلاتين في تلاتة مية وخمسة مظبوط؟ الآن عندي
+
+363
+00:36:53,940 --> 00:37:01,320
+خلّيني أجزّيها إلى تلات أجزاء هذه الان واحد .. ان
+
+364
+00:37:01,320 --> 00:37:06,340
+واحد .. ان واحد بساوية تلاتة ان واحد capital ..
+
+365
+00:37:06,340 --> 00:37:09,580
+انتبه عليها ان واحد بساوية تلاتة .. ان واحد
+
+366
+00:37:09,580 --> 00:37:15,280
+capital خمسة في سبعة خمسة و تلاتين الان ان اتنين
+
+367
+00:37:16,760 --> 00:37:20,620
+إيش هتساوي؟ خمسة الان اتنين كابيتال إيش هتساوي؟
+
+368
+00:37:20,620 --> 00:37:24,760
+ثلاثة في سبعة بواحد وعشرين الآن الان تلاتة small
+
+369
+00:37:24,760 --> 00:37:30,600
+سبعة الان تلاتة كابيتال إيش هتساوي؟ خمسة عشر واضح
+
+370
+00:37:30,600 --> 00:37:36,220
+أه؟ الآن ال A واحد تلخص كل معلوماتي ال A واحد
+
+371
+00:37:36,220 --> 00:37:44,720
+اتنين ال A اتنين تلاتة ال A تلاتة اتنين هذا اللي
+
+372
+00:37:44,720 --> 00:37:49,000
+هتلزمني وهذا اللي هتلزمني وهذا اللي هتلزمني وهذا
+
+373
+00:37:49,000 --> 00:37:53,380
+اللي هتلزمني وهذا اللي هتلزمني وهذا اللي هتلزمني
+
+374
+00:37:53,380 --> 00:37:54,400
+وهذا اللي هتلزمني وهذا اللي هتلزمني وهذا اللي
+
+375
+00:37:54,400 --> 00:37:54,800
+هتلزمني وهذا اللي هتلزمني وهذا اللي هتلزمني وهذا
+
+376
+00:37:54,800 --> 00:37:57,680
+اللي هتلزمني وهذا اللي هتلزمني وهذا اللي هتلزمني
+
+377
+00:37:57,680 --> 00:37:59,820
+وهذا اللي هتلزمني وهذا اللي هتلزمني وهذا اللي
+
+378
+00:37:59,820 --> 00:38:00,900
+هتلزمني وهذا اللي هتلزمني وهذا اللي هتلزمني وهذا
+
+379
+00:38:00,900 --> 00:38:04,220
+اللي هتلزمني وهذا اللي هتلزمني وهذا اللي هتلزمني
+
+380
+00:38:04,220 --> 00:38:08,050
+وهذا اللي الآن صار عندي الآن بدّى حل المعادلة الأولى
+
+381
+00:38:08,050 --> 00:38:15,010
+اللى هي N واحد X واحد تطابق الواحد modulo N واحد
+
+382
+00:38:15,010 --> 00:38:20,390
+معايا N واحد تبعتنا اللى هي خمسة و تلاتين X واحد
+
+383
+00:38:20,390 --> 00:38:28,770
+تطابق الواحد modulo جداش ثلاثة زي ما عتدنا الخمسة
+
+384
+00:38:28,770 --> 00:38:35,670
+و تلاتين اللي هي ناقصة عن الـ 36 واحد يعني بيطابق
+
+385
+00:38:35,670 --> 00:38:42,230
+الناقص واحد بيصير ناقص X واحد تطابق الواحد مدنه
+
+386
+00:38:42,230 --> 00:38:49,810
+مين؟ مدنه تلاتة واضحة؟ ليه هذي؟ لأن الـ 35 تطابق
+
+387
+00:38:49,810 --> 00:38:55,770
+الناقص واحد مدنه تلاتة لأن الـ 36 تلاتة بتكسبها
+
+388
+00:39:02,730 --> 00:39:07,630
+هذه اللي بنشتغل عليها هذي بنوجد ال XK دي بالك هذا
+
+389
+00:39:07,630 --> 00:39:16,530
+مفتاح الحل حكيته طيب الان وقيني بقول X1 إيش هي
+
+390
+00:39:17,660 --> 00:39:23,580
+عبارة عن X1 تطابق السالب واحد موضوعه تلاتة فالمهو
+
+391
+00:39:23,580 --> 00:39:27,900
+السالب واحد موضوعه تلاتة بتخليه وجه باحلى بس ليه
+
+392
+00:39:27,900 --> 00:39:34,400
+اجمالها اتنين فبخليها X1 تطابق التنين موضوعه تلاتة
+
+393
+00:39:34,400 --> 00:39:44,470
+إذا صارت الآن X1 عندي إيش متساوي X1 خُدها بتساوي 2
+
+394
+00:39:44,470 --> 00:39:50,810
+هاذي طبعا لو أخدت خمسة بنفع أخدت سبعة خمسة و
+
+395
+00:39:50,810 --> 00:39:56,850
+تلاتة تمانية بنفع فاهمين طيب شوفوا صلى على النبي
+
+396
+00:39:56,850 --> 00:40:00,010
+عليه الصلاة والسلام التاني بنفسه السنوبة اللي هي
+
+397
+00:40:00,010 --> 00:40:00,950
+واحد و عشرين
+
+398
+00:40:03,630 --> 00:40:12,990
+21N2 X2 تطابق الواحد modulo N2 X2
+
+399
+00:40:12,990 --> 00:40:15,990
+تطابق الواحد modulo 5 X2 تطابق الواحد modulo 5 X2
+
+400
+00:40:15,990 --> 00:40:20,250
+تطابق الواحد modulo 5 X2 تطابق الواحد modulo 5 X2
+
+401
+00:40:20,250 --> 00:40:30,240
+تطابق الواحد modulo 5 X2 تطابق الواحد modulo 5 إذا
+
+402
+00:40:30,240 --> 00:40:38,440
+صار عندي الـ X2 خدها X2 بتساوي واحد أو take خلينا
+
+403
+00:40:38,440 --> 00:40:44,120
+نقول نكون أضغط take X2 بتساوي واحد الآخرها دي برضه
+
+404
+00:40:44,120 --> 00:40:51,960
+نفس الاشي N3 X3 تطابق الواحد modulo اللي هو N ثلاثة
+
+405
+00:40:51,960 --> 00:40:56,840
+يعني الـ N ثلاثة جديش خمستائش X ثلاثة تطابق الواحد
+
+406
+00:40:56,840 --> 00:41:02,420
+مدله مين؟ سبعة اللي برضه الخمستائش جاهزة اللي هي
+
+407
+00:41:02,420 --> 00:41:06,020
+واحد لإنه شيف منها سبعتين تطلع واحد بصير X ثلاثة
+
+408
+00:41:06,020 --> 00:41:12,620
+معانا يا رامي X ثلاثة تطابق الواحد مدله سبعة إذا
+
+409
+00:41:12,620 --> 00:41:20,480
+إيش بدك تقول take X ثلاثة بساوي واحد الآن بدنا x
+
+410
+00:41:20,480 --> 00:41:30,520
+bar therefore therefore therefore x bar بتساوي إيش
+
+411
+00:41:30,520 --> 00:41:38,800
+بتساوي؟ اللي هو x summation xi ai ni i من عند واحد
+
+412
+00:41:38,800 --> 00:41:44,540
+لعين تلاتة ويساوي اللي هنا حسبوا معايا واحد اللي
+
+413
+00:41:44,540 --> 00:41:50,890
+هو اتنين في اتنين أربعة في تلاتة صح؟ في خمس و
+
+414
+00:41:50,890 --> 00:41:59,030
+تلاتين اه يعني اتنين في اتنين في خمس و تلاتين زائد
+
+415
+00:41:59,030 --> 00:42:09,750
+قولوا معي اكس واحد كده اكس اتنين واحد في تلاتة في
+
+416
+00:42:09,750 --> 00:42:18,290
+واحد و عشرين زائد واحد في كده في اتنين في خمستاشر
+
+417
+00:42:20,770 --> 00:42:25,310
+بطلع من قداش 233 المئتان و تلاتة و تلاتين المئتان و
+
+418
+00:42:25,310 --> 00:42:30,310
+تلاتة و تلاتين بيدخليهم ده زغيرهم طبعا كل حال جناش
+
+419
+00:42:30,310 --> 00:42:36,410
+ماله ليك solution موضوله مين موضوله ان قداش الآن
+
+420
+00:42:36,410 --> 00:42:45,830
+اللي هو يطابق شيل منه 105 تنتين بقال 23 موضوله 105 
+
+421
+00:42:46,850 --> 00:42:51,670
+إذا the solution of the system أو the unique
+
+422
+00:42:51,670 --> 00:43:01,910
+solution of the system is the unique solution of
+
+423
+00:43:01,910 --> 00:43:08,010
+the system is X X
+
+424
+00:43:08,010 --> 00:43:12,930
+تطابق 23 modulo 105
+
+425
+00:43:17,480 --> 00:43:31,040
+أي سؤال؟ لك
+
+426
+00:43:31,040 --> 00:43:38,440
+سبقها يعني، بعود، بس طويل وين المشكلة في وقتك؟
+
+427
+00:43:38,440 --> 00:43:48,110
+أنا؟ هذي أنت.. شيلت من الـ233 105 مرتين 210 أي
+
+428
+00:43:48,110 --> 00:43:52,670
+سؤال؟
+
+429
+00:43:52,670 --> 00:44:00,450
+أي سؤال؟ نجي لا؟ واضح، هو واضح الأمور، إيش عبد؟
+
+430
+00:44:00,450 --> 00:44:06,570
+طيب، نيجي نحل السؤال المثال الثاني، بقول Solve the
+
+431
+00:44:06,570 --> 00:44:11,630
+linear congruence 17x تطابق التسعة مدنه 276
+
+432
+00:44:20,750 --> 00:44:27,130
+بدي أحاول أوظف الـ Chinese remainder theorem لحل 
+
+433
+00:44:27,130 --> 00:44:31,390
+الـ linear congruence بس شوية أرقامها كبيرة أو
+
+434
+00:44:31,390 --> 00:44:38,170
+المدولة الصراحة كبيرة وإمكانية القسمة 
+
+435
+00:44:38,170 --> 00:44:47,130
+أو أن نشيل أعداد صعبة شوية لكن مش مستحيلة لكن احنا 
+
+436
+00:44:47,130 --> 00:44:55,110
+خلّينا نعتبر السؤال ك applications لإن نحل اللي هو
+
+437
+00:44:55,110 --> 00:44:58,910
+بواسطة Chinese remainder theorem للـ linear
+
+438
+00:44:58,910 --> 00:45:02,890
+congruence تُعطى إلينا اللي هي solve the linear
+
+439
+00:45:02,890 --> 00:45:10,610
+congruence 17x 17x تطابق وقول معايا 9
+
+440
+00:45:14,850 --> 00:45:23,940
+وبيدولها 276 شوف عليها الآن اللي عند الأمانة هذه إذا
+
+441
+00:45:23,940 --> 00:45:27,680
+بدحلها مرة واحدة بدحلها بالطريق اللي هو.. اللي
+
+442
+00:45:27,680 --> 00:45:32,600
+..اللي حكينا عليها قبل هيك بس الـ 276 الصعبة شوية
+
+443
+00:45:32,600 --> 00:45:36,800
+هتغلبني كثير في أني أضيف أو مثلا أطرح حيث أن أقدر 
+
+444
+00:45:36,800 --> 00:45:41,780
+أقسم وكده هتصير الأمور شوية.. شوية صعبة الآن مش
+
+445
+00:45:41,780 --> 00:45:46,940
+هذا هدف من السؤال السؤال هدفي أني أحول هذا لـ
+
+446
+00:45:46,940 --> 00:45:52,440
+System of Linear Congruences في النهاية بدي أوجد
+
+447
+00:45:52,440 --> 00:45:57,480
+الـ solution modulo 276 طبعا أكيد أكيد هو متأكد
+
+448
+00:45:57,480 --> 00:46:00,520
+إيه عشان هو عارف إنه اللي هو فيه الـ unique
+
+449
+00:46:00,520 --> 00:46:04,160
+solution modulo 276 ولو ما فيش بيكون متأكد عشان
+
+450
+00:46:04,160 --> 00:46:08,480
+أختصر وأصل إيش اللي فيه pH unique solution و
+
+451
+00:46:08,480 --> 00:46:11,000
+أستخدم ال mean اللي هنا congruence لأن الطرق
+
+452
+00:46:11,000 --> 00:46:15,850
+الثانية شوية أصعب معين؟ تشوفوا كيف لو جيت أخدت اللي
+
+453
+00:46:15,850 --> 00:46:19,010
+هو الـ17 والـ276 العامل المشترك الأعلى بينهما
+
+454
+00:46:19,010 --> 00:46:26,910
+شايكون واحد فنـشوف كيف واحد الـ276 انحللها اتنين 
+
+455
+00:46:26,910 --> 00:46:36,330
+سبعة ستة بتساوي تلاتة بتصير عندك تسعة اتنين صح؟ ع
+
+456
+00:46:36,330 --> 00:46:39,810
+تلاتة ع تلاتة دي اللي هي تسعة وده اتنين
+
+457
+00:46:42,890 --> 00:46:46,890
+ماشي الآن هذه ع تلاتة ما تجسمش إذا العالمية ما تجسم
+
+458
+00:46:46,890 --> 00:46:50,890
+باجسمش ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع
+
+459
+00:46:50,890 --> 00:46:52,110
+تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع
+
+460
+00:46:52,110 --> 00:46:53,430
+تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع
+
+461
+00:46:53,430 --> 00:46:54,890
+تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع
+
+462
+00:46:54,890 --> 00:46:58,970
+تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع
+
+463
+00:46:58,970 --> 00:46:59,750
+تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع تلاتة ع
+
+464
+00:46:59,750 --> 00:47:05,150
+تلاتة ع تلاتة ع تلاتة ع تلاتة
+
+465
+00:47:11,720 --> 00:47:18,140
+الـ L بدي أحولها لـ congruences ما حدش يقولي أحولها 
+
+466
+00:47:18,140 --> 00:47:20,980
+لتلاقي أي واحد هيها أو أي اتنين هيها أو أي تلاتة
+
+467
+00:47:20,980 --> 00:47:24,040
+هيها أو أي أربعة هيها بكون.. بكون.. أنا ما أعرفش
+
+468
+00:47:24,040 --> 00:47:27,020
+أطبق لأن she needs to be interfered مش بتقولليه
+
+469
+00:47:27,020 --> 00:47:31,260
+المقاييس لازم تكونها relatively prime إذا كيف بدي
+
+470
+00:47:31,260 --> 00:47:35,140
+آخذها relatively prime؟ أكيد حضوم التنقل لأقل
+
+471
+00:47:35,140 --> 00:47:42,820
+التنقل خلاص فبيصير عندي هذي أن واحد بيصير عندي اللي
+
+472
+00:47:42,820 --> 00:47:53,980
+هو 17x تطابق التسعة modulo 276 إيش معناتها 276 هذا
+
+473
+00:47:53,980 --> 00:48:02,780
+يكافئ if and only if 276 تقسم 17x ناقص 9 صح
+
+474
+00:48:06,420 --> 00:48:10,960
+if and only if if and only if هذا يطابق إيش الـ
+
+475
+00:48:10,960 --> 00:48:16,820
+276؟ اللي هي عبارة عن 3×4×23
+
+476
+00:48:16,820 --> 00:48:25,100
+بتقسم 17x ناقص مين؟ ناقص 9 وهذا يكافئ تماما لأن
+
+477
+00:48:25,100 --> 00:48:27,780
+كل هذه اللي كانت تمثلن مع بعض اللي ملتيف لبراين 
+
+478
+00:48:27,780 --> 00:48:33,940
+يكافئ أنه 3 تقسم 17x ناقص 9 وطوالنا عن هذه 
+
+479
+00:48:33,940 --> 00:48:46,500
+المعلومة الـ 4 تجسم 17x-9 والـ 23 تجسم 17x-9 هذا 
+
+480
+00:48:46,500 --> 00:48:54,680
+and في نفس الوقت هذا يعني if and only if 17x
+
+481
+00:48:54,680 --> 00:49:05,800
+تطابق 9 modulo 3 و17x تطابق 9 modulo 4 and 
+
+482
+00:49:07,440 --> 00:49:13,520
+17x تطابق التسعة modulo منين 23 إذا أنت حولت الآن
+
+483
+00:49:13,520 --> 00:49:18,960
+إلى سؤال من أسئلة مين اللي هو Chinese remainder
+
+484
+00:49:18,960 --> 00:49:26,000
+theorem صار عندي الآن ال
+
+485
+00:49:26,000 --> 00:49:30,160
+A1 بدي
+
+486
+00:49:30,160 --> 00:49:33,240
+أحولها جابل كل واحدة لمين
+
+487
+00:49:35,940 --> 00:49:40,420
+هذه صورتها عارفين صورتها؟ إيش الصورة العامة؟ X
+
+488
+00:49:40,420 --> 00:49:43,980
+وتطابق أ واحد X وتطابق أ اتنين X وتطابق أ تلاتة يعني
+
+489
+00:49:43,980 --> 00:49:48,780
+بدي أجهزها لسه مش جاهزة أن اسمي هذا أ واحد وذاك ده
+
+490
+00:49:48,780 --> 00:49:52,260
+الواحد جاهز وأن اتنين جاهز وأن تلاتة جاهز بس لسه
+
+491
+00:49:52,260 --> 00:49:58,300
+مش جاهزات مين هذي بنحولها الـ17 X جدية شمالها
+
+492
+00:49:58,300 --> 00:50:05,310
+التسعة بالطابق مين؟ الـ Zero فصارت خلاص ما خلصنا
+
+493
+00:50:05,310 --> 00:50:10,830
+منها دي صارت ال X شمالها Zero فاهمين آه؟ فعند ال X 
+
+494
+00:50:10,830 --> 00:50:27,030
+تطابق ال Zero Modulo تلاتة يعني حل هذه جاهز آه 
+
+495
+00:50:27,030 --> 00:50:34,150
+آه آه الآن 17x تطابق ال 9 مدله مين؟ مدله 4 الأربعة
+
+496
+00:50:34,150 --> 00:50:44,230
+هنا واحد وهنا واحد 16 و 8 بيصير x تطابق ال 1 مدله
+
+497
+00:50:44,230 --> 00:50:52,010
+4 مظبوط اللي بيعملوا؟ وهنا x اللي هو عند ال 23
+
+498
+00:50:55,890 --> 00:51:00,730
+لو عملنا كمان تلاتة و عشرين هي تلاتين اربعين
+
+499
+00:51:00,730 --> 00:51:09,030
+اربعين اربعين عندي
+
+500
+00:51:09,030 --> 00:51:16,510
+اربعين اكس تطابق اللي هو تلاتة و عشرين وتسعة اتنين
+
+501
+00:51:16,510 --> 00:51:22,430
+و تلاتين صح مو دولو تلاتة و عشرين نعمل هذه ها على
+
+502
+00:51:22,430 --> 00:51:29,750
+ثمانية ع ثمانية بيبقى خمسة و أربعة طب لو ضفنا كمان
+
+503
+00:51:29,750 --> 00:51:41,710
+شوية عليها تلاتة و عشرين لو ضربنا بيصير خمسة X ع
+
+504
+00:51:41,710 --> 00:51:47,130
+ثمانية تطابق اتنين وتلاتين على ثمانية كدهش بيبقى
+
+505
+00:51:47,130 --> 00:52:00,010
+أربعة مدوله تلاتة و عشرين بنخلّى دى ك X بيطلع
+
+506
+00:52:00,010 --> 00:52:10,570
+جديش 17 من 23 طرحنا يعني جديش بيطلع سالب ستة سالب
+
+507
+00:52:10,570 --> 00:52:19,910
+ستة بيظل عندنا تلاتة اه يعني خطوطين نعملها عندي
+
+508
+00:52:19,910 --> 00:52:25,450
+الآن بس بنصدر بقالك بس ممكن تولّبنا شوية ناخد جديش 
+
+509
+00:52:25,450 --> 00:52:35,730
+سالب سالب ستة X تسعة تسعة بتديه سير سهل صحيحلما
+
+510
+00:52:35,730 --> 00:52:38,730
+يبقى الـ 2 بيصير سهل لإنك بتضيف عليها دي كم بتصير؟
+
+511
+00:52:38,730 --> 00:52:45,030
+2 ده أسهلنا من الخمسة 6x بيصير إيش؟ سالب سالب ستة
+
+512
+00:52:45,030 --> 00:52:49,150
+و سبعة عشر بيطلع اللي هي متطابقة بيصير سالب 2x
+
+513
+00:52:49,150 --> 00:52:53,350
+تطابق جد إيش؟ تلاتة موضوله تلاتة و عشرين النيح
+
+514
+00:52:53,350 --> 00:52:56,990
+الان الـ 2 بيعرف يتصرف معاها اللي هو التلاتة و
+
+515
+00:52:56,990 --> 00:53:00,750
+عشرين بضيف له ده إيش؟ تلاتة و عشرين التلاتة بضيف
+
+516
+00:53:00,750 --> 00:53:03,150
+إلى تلاتة و عشرين بيصير زوجي بيصير تقسم على طول
+
+517
+00:53:03,150 --> 00:53:07,230
+اللي هو بيصير سالب اتنين X تطابق ستة و عشرين
+
+518
+00:53:07,230 --> 00:53:19,450
+مدنومين تلاتة و عشرين واضح اه بيصير X 
+
+519
+00:53:19,450 --> 00:53:26,270
+تلتاش مدنومين تلاتة و عشرين هذه سلب تلتاش يعني 
+
+520
+00:53:26,270 --> 00:53:34,080
+عشرة صح؟ أشر ولا لأ؟ إذا X تطابق العشرة مضرومين
+
+521
+00:53:34,080 --> 00:53:37,780
+مضوا تلاتة وعشرين يمكن اللي هديكي برضه نفس الفلعة
+
+522
+00:53:37,780 --> 00:53:40,340
+تانية خمسة ولا أربعة اللي جابله؟ سنة دكتور ما جسمنا
+
+523
+00:53:40,340 --> 00:53:44,580
+ع سنة ما اتنين اش ما جسمنا أشهر تلاتة وعشرين واحد
+
+524
+00:53:44,580 --> 00:53:46,960
+العامل الشتركي الأعلى بين الليهان وبين الليهان إيش
+
+525
+00:53:46,960 --> 00:53:53,310
+ماله؟ واحد اللي هنفس ال solution هو أنت بتجسم في
+
+526
+00:53:53,310 --> 00:53:56,490
+الواقع على.. اللي هو ال.. ال.. ال.. ال..
+
+527
+00:53:56,490 --> 00:53:58,830
+الأمن اللي.. اللي.. اللي هي المقياس بتجسمه على
+
+528
+00:53:58,830 --> 00:54:01,710
+الـ greatest common divisor بلزمش تجسمه على هدف
+
+529
+00:54:01,710 --> 00:54:05,650
+كله واضحش اللي بحكيه يعني أنا بدي اختصر هذا مثلا
+
+530
+00:54:05,650 --> 00:54:08,650
+من هن ستة و من هن ستة لكن عامله شركة العالم بين
+
+531
+00:54:08,650 --> 00:54:12,450
+هدف وهدف تلاتة بجسم التاني عالمين بس ع تلاتة و
+
+532
+00:54:12,450 --> 00:54:14,190
+بتكون تضمن له نفس ال solution
+
+533
+00:54:17,300 --> 00:54:21,280
+آه ما قولنا كيف اللي بقوله كيف نخسر إنه نجسم اللي 
+
+534
+00:54:21,280 --> 00:54:27,640
+هو كل المعادلة على الرقم اللي بحكيه مثلا على اللي 
+
+535
+00:54:27,640 --> 00:54:33,180
+هو ده نجسم هنا قبل قسم التنين على ستة إذا اللي هنا
+
+536
+00:54:33,180 --> 00:54:38,580
+في ستة بنجسم على ستة اللي هان اللي هان في اللي هو 
+
+537
+00:54:38,580 --> 00:54:43,280
+بس اتنين بنجسم على اتنين اللي هو بنقسم على العامل 
+
+538
+00:54:43,280 --> 00:54:49,740
+المشترك بين الـ 6 و بين الـ 23 بين الـ N و مين و
+
+539
+00:54:49,740 --> 00:54:58,760
+الـ A سميناها الـ N والـ A واضح هذا
+
+540
+00:54:58,760 --> 00:55:02,740
+الحسبة
+
+541
+00:55:02,740 --> 00:55:06,440
+اللي حسبناها اللي كنا.. احنا كان أمامنا أن هو
+
+542
+00:55:06,440 --> 00:55:14,630
+نضيف 17 جربنا نضيف 17 لـ 23 ناسف طلع 40 فصار عند
+
+543
+00:55:14,630 --> 00:55:22,550
+الرقم هنا بعيد شوية فقال اللي هو 6 17 ناقص 23 طلع
+
+544
+00:55:22,550 --> 00:55:27,410
+ناقص 6 شجعتنا ليش شجعتنا لإن هنا فيه 9 فالـ 3 
+
+545
+00:55:27,410 --> 00:55:32,070
+بنطيرها من هنا والـ 2 سهل التعامل لإن لو هنا زوجي 
+
+546
+00:55:32,070 --> 00:55:35,670
+بنقسم عليه مش زوجي هذا ما هو فردي بنضيفه على طول
+
+547
+00:55:35,670 --> 00:55:44,520
+بيطلع زوجي وبنقسم عليه مباشرة واضح آه أنت 
+
+548
+00:55:44,520 --> 00:55:48,180
+مش هي قدرت مش هي المهم إنه احنا كيف فكرنا آه كيف
+
+549
+00:55:48,180 --> 00:55:52,620
+فكرنا وإيش اللي بنسوي لإن الأرقام هتختلف لكن أنت 
+
+550
+00:55:52,620 --> 00:55:56,580
+بدك يصير في عندك اللي هو قول مهارة للوصول طبعا
+
+551
+00:55:56,580 --> 00:56:03,780
+الناس بتختلف من مهارتها من من شخص إلى شخص نكمل آه
+
+552
+00:56:04,870 --> 00:56:07,670
+لسه ما خلصناش السؤال لسه ما مدناش في ال.. في ال.. في 
+
+553
+00:56:07,670 --> 00:56:14,470
+الشيانيز المهندسيوري عندك الآن واحد نرجع لشغلنا
+
+554
+00:56:14,470 --> 00:56:22,590
+الأول أن تبعتنا الكبيرة إيش هتساوي اللي هي أو أن
+
+555
+00:56:22,590 --> 00:56:31,390
+واحد بيساوي تلاتة وأن اتنين بيساوي أربعة وأن تلاتة 
+
+556
+00:56:31,390 --> 00:56:38,670
+بيساوي تلاتة وعشرين عندي أن واحد capital بيساوي 
+
+557
+00:56:38,670 --> 00:56:43,950
+أربعة في تلاتة وعشرين هو الخلتين التانيات اضربواها
+
+558
+00:56:43,950 --> 00:56:53,730
+92 أن اتنين بيساوي تلاتة وعشرين في تلاتة تسعة وستين 
+
+559
+00:56:53,730 --> 00:57:02,670
+وأن تلاتة اللي هو أربعة في تلاتة باطن عشر الآن
+
+560
+00:57:04,490 --> 00:57:15,010
+أن الأصلية.. أن الأصلية بيساوي اللي هو ستة 
+
+561
+00:57:15,010 --> 00:57:19,670
+ثلاثة وتسعة وعشرون أكيد الـ 276 اللي بدنا 
+
+562
+00:57:19,670 --> 00:57:24,190
+فيها اه 276 اللي بدنا فيها وعشان اصلا احنا كل
+
+563
+00:57:24,190 --> 00:57:32,710
+الشغل 276 ماشي الان ان واحدة موجودة وبدنا مين اي
+
+564
+00:57:32,710 --> 00:57:40,130
+واحد A1 ماهي ساوية؟ صفر مافيش داعي أكمل هطلع صفر
+
+565
+00:57:40,130 --> 00:57:51,290
+اثنين بساوية واحد و ثلاثة بساوية عشرة نيجي نحل
+
+566
+00:57:51,290 --> 00:57:59,050
+هذه نحل هذه ايش اللي بدنا نحله؟ بدنا نحل NK X
+
+567
+00:57:59,880 --> 00:58:05,820
+K اليمين الان كيف في هذه الحالة N2 X2 تطابق الواحد
+
+568
+00:58:05,820 --> 00:58:14,740
+modulo N2 معايا شباب اه اللي هي N2 جديش أربعة X2
+
+569
+00:58:14,740 --> 00:58:21,860
+تطابق الواحد modulo 69
+
+570
+00:58:21,860 --> 00:58:29,160
+modulo جديش أربعة شيل 69 أربعاتها بيظهر واحد صح
+
+571
+00:58:32,410 --> 00:58:37,250
+بالـ C X2
+
+572
+00:58:37,250 --> 00:58:48,810
+تطابق الواحد مدوله أربعة يعني take X2 بساوي واحد
+
+573
+00:58:48,810 --> 00:58:54,650
+الأخيرة
+
+574
+00:58:54,650 --> 00:59:05,680
+عندي N ثلاثةX3 تطابق الواحد موضوله N ثلاثة لأن
+
+575
+00:59:05,680 --> 00:59:13,680
+ثلاثة جديش نعش X3 تطابق الواحد موضوله ثلاثة وعشرين
+
+576
+00:59:13,680 --> 00:59:19,800
+صحيح؟ بسهل يا عزيزي لما نضيف هناك إياه شماله ثلاثة
+
+577
+00:59:19,800 --> 00:59:24,040
+وعشرين بيصيرنا أربعة وعشرين وبتنقسم على طول بيصير
+
+578
+00:59:24,040 --> 00:59:33,950
+عندي تتنعشX3 تطابق الـ 24 modulo 23 عارفين ليش اه؟
+
+579
+00:59:33,950 --> 00:59:41,070
+نقسم الجهتين على 12 بصير X3 تطابق الـ 2 modulo 23
+
+580
+00:59:41,070 --> 00:59:47,130
+الآن take X3
+
+581
+00:59:47,130 --> 00:59:53,630
+بساوي 2 جمع الآن Xك بصير عند الـ X bar تبعتنا
+
+582
+00:59:57,770 --> 01:00:06,830
+The solution of star is
+
+583
+01:00:06,830 --> 01:00:16,390
+x bar بساوية لما تسميه x واحد a واحد n واحد زائد x
+
+584
+01:00:16,390 --> 01:00:22,230
+اثنين a اثنين n اثنين زائد x ثلاثة a ثلاثة n ثلاثة
+
+585
+01:00:22,230 --> 01:00:26,880
+ويساوي ما هي ال a واحد ايش طلعت من ده صفر إذا صفر
+
+586
+01:00:26,880 --> 01:00:36,980
+زائد X2 واحد في اثنين قداش واحد في تسعة وستين زائد
+
+587
+01:00:36,980 --> 01:00:47,080
+الثاني X3 اثنين في عشرة في اثنا عشر ويساوي تسعة وستين
+
+588
+01:00:47,080 --> 01:00:53,160
+زائد متين واربعين صح
+
+589
+01:00:53,160 --> 01:01:02,310
+اللي بنعمله؟ ثلاثمية وتسعة وادت وطابت جديش تلات و
+
+590
+01:01:02,310 --> 01:01:10,170
+ثلاثين ثلاثة و ثلاثين modulo اثنين سبعة ستة إذا ..
+
+591
+01:01:10,170 --> 01:01:15,170
+إذا عندي صعب
+
+592
+01:01:15,170 --> 01:01:20,610
+.. لا نزل بس دقيقة والله يا عزيزي الان ايش هو
+
+593
+01:01:20,610 --> 01:01:25,750
+السؤال اللي هو الـ congruence هذه صار اللي هو ال
+
+594
+01:01:25,750 --> 01:01:36,010
+unique solution لها عبارة عن اللي هو X طابق 33 modulo
+
+595
+01:01:36,010 --> 01:01:43,030
+و 276 معايا المرة
+
+596
+01:01:43,030 --> 01:01:51,570
+القادمة ان شاء الله أطلع لفكوم وصلنا عند نظرية 4 9
+
+597
+01:01:52,600 --> 01:01:58,180
+بنحاول نحل ال system of linear congruences وإلى
+
+598
+01:01:58,180 --> 01:01:59,120
+لقاء آخر
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/hGaju6zUWgU.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/hGaju6zUWgU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f5927a9e48a23aeacbab8ecde9f020c16e551990
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/hGaju6zUWgU.srt
@@ -0,0 +1,1649 @@
+1
+00:00:19,790 --> 00:00:25,130
+بسم الله الرحمن الرحيم محاضرة رقم 24 مساق نظرية
+
+2
+00:00:25,130 --> 00:00:30,050
+الأعداد طلاب الجامعة الإسلامية كلية العلوم وكلية
+
+3
+00:00:30,050 --> 00:00:38,520
+التربية، نكمل اليوم حديثنا عن ال five functions و
+
+4
+00:00:38,520 --> 00:00:43,480
+هنروح باتجاه إثبات الـ Euler's function اللي هي عبارة عن
+
+5
+00:00:43,480 --> 00:00:49,040
+generalization لـ Fermat's little theorem إذا 
+
+6
+00:00:49,040 --> 00:00:53,840
+بتتذكروا الـ Fermat's little theorem كانت تقول if
+
+7
+00:00:53,840 --> 00:01:04,200
+الـ b لا تقسم الـ a بدي يكون عندي a then A to the B
+
+8
+00:01:04,200 --> 00:01:10,900
+ناقص واحد تطابق الواحد modulo B هذه اللي كانت مين
+
+9
+00:01:10,900 --> 00:01:15,800
+هي الـ Fermat's little theorem الآن بدنا نروح
+
+10
+00:01:15,800 --> 00:01:22,800
+باتجاه تعميم لهذا النظرية بدنا نروح باتجاه أنه
+
+11
+00:01:22,800 --> 00:01:25,960
+نثبت أنه لو كان لـ Greatest common divisor بين
+
+12
+00:01:25,960 --> 00:01:31,480
+الـ A والـ B أو الـ A والـ N بساوي واحد then
+
+13
+00:01:32,840 --> 00:01:39,320
+الـ A to the Phi of N تطابق الواحد modulo N
+
+14
+00:01:39,320 --> 00:01:44,400
+modulo N فبتصير اللي هي في الـ Maths little theorem
+
+15
+00:01:44,400 --> 00:01:48,440
+حالة خاصة منها ليش حالة خاصة منها؟ لإن احنا المرة
+
+16
+00:01:48,440 --> 00:01:54,300
+الماضية قلنا أن Phi لـ Prime إيش هتساوي؟ P ناقص واحد
+
+17
+00:01:54,530 --> 00:02:00,110
+بناء عليه لو أثبتنا هذه بيصير عندي A طبعا modulo B
+
+18
+00:02:00,110 --> 00:02:05,650
+لا تقسم الـ A إذا العامل المشترك الأعلى بين الـ A و
+
+19
+00:02:05,650 --> 00:02:11,690
+الـ B بساوي واحد مظبوط ولا لا؟ إذا الشروط هذه
+
+20
+00:02:11,690 --> 00:02:17,230
+منطبقة إذا بيصير عندي a to the five of b يطابق
+
+21
+00:02:17,230 --> 00:02:22,350
+الواحد modulo مين؟ modulo b و ال five من مين؟ هي b
+
+22
+00:02:22,350 --> 00:02:25,430
+ناقص واحد فبتصير اللي هي لو أثبتنا الـ
+
+23
+00:02:25,430 --> 00:02:28,990
+generalization هذه اللي هي الـ Euler's theorem
+
+24
+00:02:28,990 --> 00:02:32,710
+بتكون اللي هي فرما حالة خاصة منها إذا نحن رايحين
+
+25
+00:02:32,710 --> 00:02:37,960
+بهذا الاتجاه، عشان نثبت هذا بلزمنا اللي هو لمّة
+
+26
+00:02:37,960 --> 00:02:44,960
+نبرهنها قبل ما نيجي نثبت النظرية إذا سبعة تلاتة
+
+27
+00:02:44,960 --> 00:02:50,340
+بيحكيلي عن الـ Euler's theorem ناخد اللي هو اللمّة قبل
+
+28
+00:02:50,340 --> 00:02:55,900
+ما نحكي عن الـ Euler's theorem اللمّة بتقول ما يلي
+
+29
+00:02:55,900 --> 00:03:05,650
+اللمّة بتقول لو كان عندي n أكبر من واحد وكان عندي
+
+30
+00:03:05,650 --> 00:03:09,150
+اللي هو a عدد صحيح بحيث أن الـ Greatest Common
+
+31
+00:03:09,150 --> 00:03:14,250
+Divisor بين الـ a والـ n بساوي واحد وكان عندي أيضا
+
+32
+00:03:14,250 --> 00:03:23,500
+اللي هو a واحد و a اتنين لعند الـ a Phi of n، لو كل
+
+33
+00:03:23,500 --> 00:03:31,180
+هذه كانت معطيات بحيث أن A1 وA2 وA Phi of N تمثل كل
+
+34
+00:03:31,180 --> 00:03:36,780
+الأعداد الـ relatively prime مع الـ N وأصغر أو 
+
+35
+00:03:36,780 --> 00:03:40,980
+تساوي N، الـ positive integers الأكبر ساوي
+
+36
+00:03:40,980 --> 00:03:46,360
+وأصغر ساوي N يعني هذول الأن مفترض أن أنا كل
+
+37
+00:03:47,610 --> 00:03:53,150
+الأعداد الـ relative prime مع الـ N وأصغر أو يساوي
+
+38
+00:03:53,150 --> 00:03:58,570
+N وأكبر أو يساوي 1، ماشي الحال؟ هذا المؤتمر إيش
+
+39
+00:03:58,570 --> 00:04:07,770
+النتيجة إذن إذن هذا لو جيت ضربت الـ A في الـ A1 والـ A
+
+40
+00:04:07,770 --> 00:04:14,180
+في الـ A2 وضربت الـ A في الـ A Phi of N، الأعداد اللي بتطلع
+
+41
+00:04:14,180 --> 00:04:21,980
+هذه هتكون congruent للأعداد هذه in some order، إيش
+
+42
+00:04:21,980 --> 00:04:27,540
+يعني؟ إن الـ A A1 هيكون بطابق واحد من هدول in some
+
+43
+00:04:27,540 --> 00:04:31,480
+order يعني مش شرط من طابق مين؟ A1 ممكن طابق مين؟ A2
+
+44
+00:04:31,480 --> 00:04:36,410
+A3، أي A من الموجودات عندنا، بيصير عندي أي واحد من
+
+45
+00:04:36,410 --> 00:04:40,370
+هذول مطابق واحد من اللي هي الأعداد اللي عندي يعني
+
+46
+00:04:40,370 --> 00:04:48,810
+عشان نفهم المثال لو جيت أخذت الـ a بتساوي التلاتة والـ n
+
+47
+00:04:48,810 --> 00:04:55,970
+بتساوي تمانية مثلا، عشان نفهم المثال معايا الـ n عدد
+
+48
+00:04:55,970 --> 00:05:01,710
+العامل المشترك الأعلى بين التلاتة والتمانية إيش بساوي؟ واحد
+
+49
+00:05:03,240 --> 00:05:07,120
+بدي اخذ كل الأعداد اللي أصغر أو يساوي تمانية الـ 
+
+50
+00:05:07,120 --> 00:05:09,720
+positive integers و relatively prime مع التمانية
+
+51
+00:05:09,720 --> 00:05:12,880
+مين هي relatively prime مع التمانية؟ الواحد
+
+52
+00:05:12,880 --> 00:05:20,400
+الاتنين لأ، التلاتة، الأربعة لأ، الخمسة، الستة لأ،
+
+53
+00:05:20,400 --> 00:05:25,240
+السبعة، هذول الأعداد اللي relatively prime مع اللي
+
+54
+00:05:25,240 --> 00:05:30,720
+هم التمانية أصغر أو يساوي من التمانية
+
+55
+00:05:32,720 --> 00:05:38,720
+الآن هذه شروط اللمّة بتقول لي إذا أنت لو جيت ضربت
+
+56
+00:05:38,720 --> 00:05:41,920
+اللي هي التلاتة، هذا العامل المشترك الأعلى بين
+
+57
+00:05:41,920 --> 00:05:45,480
+التلاتة والتمانية بساوي واحد، الأعداد اللي هتطلع عندك
+
+58
+00:05:45,480 --> 00:05:50,380
+اللي هي التلاتة، والتسعة، والخمسة عشر، والواحد وعشرين،
+
+59
+00:05:50,380 --> 00:05:56,720
+هذولة هيكون إيش مالهم؟ relatively prime، هذولة آسف
+
+60
+00:05:56,720 --> 00:06:01,180
+congruent لهذول in some order، إيش يعني؟ يعني
+
+61
+00:06:01,180 --> 00:06:06,080
+هتلاقي التلاتة لازم يطابق واحد من هدول، modulo مين؟
+
+62
+00:06:06,080 --> 00:06:10,340
+modulo تمانية، واضح إن التلاتة بتطابق مين؟ التلاتة
+
+63
+00:06:10,340 --> 00:06:19,060
+خلصنا، التسعة بتطابق مين؟ الواحد، الخمسة عشر بتطابق مين؟
+
+64
+00:06:19,060 --> 00:06:26,250
+السبعة، الواحد وعشرين هيتطابق مين؟ الخمسة، إذاً in
+
+65
+00:06:26,250 --> 00:06:31,310
+general هذا الكلام صحيح إنه لو كانت العامل المشترك
+
+66
+00:06:31,310 --> 00:06:35,010
+الأعلى بين الـ A والـ N بساوي واحد وكانت الـ A واحد
+
+67
+00:06:35,010 --> 00:06:39,010
+والـ A اتنين والـ A Phi of N عبارة عن اللي هي
+
+68
+00:06:39,010 --> 00:06:43,230
+الأعداد الـ relatively prime مع الـ N واللي أكبر أو
+
+69
+00:06:43,230 --> 00:06:48,010
+يساوي واحد والأصغر أو ساوي اللي هي N قطعاً هتطلع
+
+70
+00:06:48,010 --> 00:06:50,790
+عندي الـ a في الـ a1 والـ a في الـ a2 لعند الـ a
+
+71
+00:06:50,790 --> 00:06:55,850
+في الـ Phi of n، هذه الأعداد كل واحد congruent لواحد
+
+72
+00:06:55,850 --> 00:07:02,610
+من هذول in some order، واضح؟ نيجي الآن نبرهن
+
+73
+00:07:02,610 --> 00:07:08,090
+النظرية أو اللمّة نيجي نشوف كيف بدنا نبرهن هذه
+
+74
+00:07:08,090 --> 00:07:14,450
+اللمّة، الـ A1 ليس
+
+75
+00:07:14,450 --> 00:07:21,130
+شرط يطابق مين؟ لـ AA1 والـ A2 يطابق لـ AA2 يعني
+
+76
+00:07:21,130 --> 00:07:25,530
+ممكن يطابق لـ A1، يطابق هذه وهذه يطابق هذه وهذه
+
+77
+00:07:25,530 --> 00:07:29,650
+يطابق مثلًا واحدة يعني مش بنفس الـ order اللي
+
+78
+00:07:29,650 --> 00:07:34,350
+مكتوب فيه لأ مش بنفس الـ order اللي مكتوب فيه يعني
+
+79
+00:07:34,350 --> 00:07:38,560
+ممكن يكون زي ما شوفنا التلاتة كانت مع التلاتة مع
+
+80
+00:07:38,560 --> 00:07:42,020
+أنه التلاتة في الحالة الثانية الأولى وفي الحالة
+
+81
+00:07:42,020 --> 00:07:48,320
+الأولى الثانية هكذا واضح؟ آه
+
+82
+00:07:48,320 --> 00:07:53,460
+طيب، صلوا على النبي عليه الصلاة والسلام نيجي
+
+83
+00:07:53,460 --> 00:07:59,800
+للبراهين، البروف عشان
+
+84
+00:07:59,800 --> 00:08:07,590
+أثبت إنه اللي هو الـ A A1 الـ A A2 اللي عند الـ A Phi of N
+
+85
+00:08:07,590 --> 00:08:14,270
+are congruent modulo N to اللي هي A1 A2 A Phi of N in
+
+86
+00:08:14,270 --> 00:08:19,050
+some order بدي اعمل شغل ثاني أول حاجة بدي اثبت لك
+
+87
+00:08:19,050 --> 00:08:24,870
+إن هذول ولا واحد منهم بطابق ثاني يعني بمعنى آخر
+
+88
+00:08:24,870 --> 00:08:30,600
+هذول مختلفات modulo N، modulo N عشان ما يصير
+
+89
+00:08:30,600 --> 00:08:34,420
+اشتباه إنه يصير في عندي اثنين من هنا يطابق واحد من
+
+90
+00:08:34,420 --> 00:08:39,020
+هنا، فبيصير اللي هو مش كل واحد يطابق واحد وبس لأنه
+
+91
+00:08:39,020 --> 00:08:42,240
+عدد هدول Phi of N وعدد هدول برضه إيش مالهم؟ Phi of 
+
+92
+00:08:42,240 --> 00:08:47,100
+N إذاً أول حاجة أعملها إن أثبت لك إن كل هدول are
+
+93
+00:08:47,100 --> 00:08:50,960
+incongruent يعني ولا واحد بطابق الثاني modulo N
+
+94
+00:08:52,250 --> 00:08:56,650
+اثنين بدي أثبت لك إنه لو جيت أخذت أي واحد من هذول
+
+95
+00:08:56,650 --> 00:09:01,950
+هجيب له واحد من هنا يطابقه معناته خلصت إن سعر كل
+
+96
+00:09:01,950 --> 00:09:10,070
+واحد يطابق بس إيش واحد؟ ده نشوف، شوفوا أول حاجة بدي
+
+97
+00:09:10,070 --> 00:09:14,220
+نثبت هدول إن أنا incongruent، suppose not يعني
+
+98
+00:09:14,220 --> 00:09:18,240
+نفترض إن هدول اللي هو في اثنين منهم على الأقل
+
+99
+00:09:18,240 --> 00:09:24,340
+أشمالهم congruent إذا suppose that، suppose that
+
+100
+00:09:24,340 --> 00:09:33,540
+there exist a i، a ai و a aj element in a a1 لعند
+
+101
+00:09:33,540 --> 00:09:45,760
+الـ a a Phi of n such that الـ a ai يطابق الـ a aj modulo N
+
+102
+00:09:45,760 --> 00:09:50,580
+والـ i إيش مالها؟ مش هي الـ j ونصفها Contradiction
+
+103
+00:09:50,580 --> 00:09:58,540
+معايا؟ طيب الآن الكلام سهل ولسه مش سهل ليش؟ لإن
+
+104
+00:09:58,540 --> 00:10:02,800
+الـ A والـ N إيش مالهم؟ relatively prime، العامل
+
+105
+00:10:02,800 --> 00:10:05,680
+الشركي اللي عايز يبقى هنا مش مساوي، مدام relatively
+
+106
+00:10:05,680 --> 00:10:09,800
+prime إذاً اللي هو بقدر أقسمه على الجهتين فبيصير
+
+107
+00:10:09,800 --> 00:10:20,590
+عندي الـ Ai يطابق الـ Aj modulo N، modulo N إذا صار
+
+108
+00:10:20,590 --> 00:10:25,860
+فيه اثنين من هذول أشمالهم متطابقات وهذا مستحيل، اللي
+
+109
+00:10:25,860 --> 00:10:31,040
+هيكون متساويات ليش؟ لإن هذول أصلاً من A1 A2 لعند
+
+110
+00:10:31,040 --> 00:10:37,360
+A Phi of N اللي إنها incongruent لبعض، لإن هنا وهنا وهنا
+
+111
+00:10:37,360 --> 00:10:42,940
+وإن محصورين محصورين من اللي هو بين الواحد و N مين
+
+112
+00:10:42,940 --> 00:10:48,460
+الـ n و relatively prime مع بعض فإن دعم اللي أشمال الـ
+
+113
+00:10:48,460 --> 00:10:54,230
+complete residue system modulo N معايا إذا صارن إيش
+
+114
+00:10:54,230 --> 00:10:59,970
+مالهم كأي اثنين؟ إيش مالهم؟ هيكونن غير متطابقات
+
+115
+00:10:59,970 --> 00:11:05,350
+واضحة، هما أصلاً باعتبار كمان نظرة أخرى هما أصلاً
+
+116
+00:11:05,350 --> 00:11:13,930
+متبقيات من القسمة على N ودائماً اللي هو العدد بيكون
+
+117
+00:11:13,930 --> 00:11:23,170
+مطابق لمتبقى القسمة إله modulo المقسوم عليه واللي اللي
+
+118
+00:11:23,170 --> 00:11:27,250
+هما الـ remainders المختلفات بيكون أشمالًا M
+
+119
+00:11:27,250 --> 00:11:33,770
+congruent، طيب، so عند الـ A, I يطابق AJ modulo N وهذا
+
+120
+00:11:33,770 --> 00:11:38,670
+contradiction، therefore اللي هو الـ A في الـ A واحد
+
+121
+00:11:38,670 --> 00:11:41,970
+والـ A في الـ A اثنين عند الـ A في الـ Phi of N أشمالًا R
+
+122
+00:11:42,560 --> 00:11:48,060
+incongruent، لنثبت الآن إيش ماله إنه ناخد أي واحد
+
+123
+00:11:48,060 --> 00:11:55,340
+من هنا ونلاقيله واحد من هنا شوف، let
+
+124
+00:11:55,340 --> 00:12:11,620
+a في ai بأني fixed element m a a1 لعند الـ a a Phi of n
+
+125
+00:12:14,030 --> 00:12:21,310
+باشي، ناخد الـ a, a, i أي fixed element هنا الآن 
+
+126
+00:12:21,310 --> 00:12:27,610
+بدك تلاحظ أولاً إيش ماله إن الـ Greatest common divisor
+
+127
+00:12:27,610 --> 00:12:36,510
+بين الـ a والـ n بساوي واحد صح؟ مطلق
+
+128
+00:12:38,560 --> 00:12:42,120
+حاجة ثانية الـ Greatest Common Divisor بين الـ Ai
+
+129
+00:12:42,120 --> 00:12:47,920
+والـ N برضه إيش بساوي؟ ليش؟ لأنه إحنا ماخذين الـ
+
+130
+00:12:47,920 --> 00:12:52,020
+A1, A2, A Phi of N هي عبارة عن الأعداد اللي relatively
+
+131
+00:12:52,020 --> 00:12:59,200
+prime مع الـ N وأصغر أو ساوي N صحيح؟ إذن هدول مع
+
+132
+00:12:59,200 --> 00:13:05,150
+المعلومات مقطوعة من هنا الاثنين عشان تستخدمها بعد
+
+133
+00:13:05,150 --> 00:13:08,790
+شوية، لجدية، تستخدم الـ Divisor بين الـ A في الـ Ai
+
+134
+00:13:08,790 --> 00:13:13,650
+لما أخذناها المرة الماضية والآن برضه إيش هيساويها؟
+
+135
+00:13:13,650 --> 00:13:21,510
+هيساويها، هتخليها في الذاكرة معايا؟ طيب الآن الـ
+
+136
+00:13:21,510 --> 00:13:27,710
+AAi عبارة عن عدد صحيح بدي أقسمه على الـ N إذاً By
+
+137
+00:13:27,710 --> 00:13:32,880
+Division Algorithm، By Division Algorithm there
+
+138
+00:13:32,880 --> 00:13:40,000
+exists a unique B element in Z such that B أكبر أو
+
+139
+00:13:40,000 --> 00:13:45,880
+يساوي واحد وأصغر من مين؟ من N المتبقي هذا such
+
+140
+00:13:45,880 --> 00:13:55,240
+that اللي هو الـ A Ai هيساوي الـ B أو الـ N في Q 
+
+141
+00:13:55,240 --> 00:14:01,540
+there exists unique B و Q كمان زائد مين؟ زائد B
+
+142
+00:14:02,550 --> 00:14:09,730
+مظبوط أو لا؟ لأن إيش اللي سويته؟ قسمت الـ a ai على
+
+143
+00:14:09,730 --> 00:14:14,490
+مين؟ على n فالعندي unique remainder بيه الـ unique
+
+144
+00:14:14,490 --> 00:14:20,770
+اللي هو إيش؟ الـ quotient اللي هو اسمه q معايا إذا
+
+145
+00:14:20,770 --> 00:14:28,530
+صار عندي الـ an a ai يطابق مين؟ الـ b وهذه معناه
+
+146
+00:14:28,530 --> 00:14:31,570
+المثال اللي جابنا في الامتحان إنه دائما اللي هو
+
+147
+00:14:31,570 --> 00:14:38,070
+العدد والمتبقي اللي هو متطابقين موديلو المقسوم عليه
+
+148
+00:14:38,070 --> 00:14:45,130
+لأن افتكرك يا هلاها then صار عند الـA AI يطابق
+
+149
+00:14:45,130 --> 00:14:56,350
+الـB مديلو مين؟ مديلو N واضح اه؟ عندي يعني معنى آخر
+
+150
+00:14:56,350 --> 00:15:01,610
+الـ Greatest Common Divisor بين الـ A، AI و الـ N
+
+151
+00:15:01,610 --> 00:15:05,150
+هو نفسه الـ Greatest Common Divisor بين الـ B و M
+
+152
+00:15:05,150 --> 00:15:09,790
+و الـ N طيب، الـ Greatest Common Divisor بين الـ
+
+153
+00:15:09,790 --> 00:15:14,530
+AI و الـ N بساوي 1 إذا صار العام المشترك الأعلى
+
+154
+00:15:14,530 --> 00:15:19,550
+بين الـ B و الـ N، إيش بساوي؟ بساوي 1 إذا صار B
+
+155
+00:15:21,090 --> 00:15:25,370
+relative الـ prime مع الـ N ومحصور بين اللي هو
+
+156
+00:15:25,370 --> 00:15:31,790
+الواحد والـ N يعني من مين؟ B جاي من A1 A2 لعند مين؟
+
+157
+00:15:31,790 --> 00:15:37,890
+A5 N يعني الـ B element من A1 لعند الـ A5 N يعني
+
+158
+00:15:37,890 --> 00:15:42,890
+إيش اللي أثبتنا إنه أخدنا أي A AI fixed element هنا
+
+159
+00:15:42,890 --> 00:15:50,730
+ولقيناله إنه عنصر هنا يطابق مديلو مين؟ مديلو N إذا صار
+
+160
+00:15:50,730 --> 00:15:54,310
+عند المعلومتين مع بعض الأولى أن هذولا مختلفات
+
+161
+00:15:54,310 --> 00:15:59,010
+موديلؤا وأن كل واحد هنا في الواحد هنا صار أن هذولا
+
+162
+00:15:59,010 --> 00:16:08,070
+congruent لبعض in some order أي سؤال؟ نجلأ
+
+163
+00:16:08,070 --> 00:16:10,110
+اللي هي نظرية Eulers theorem
+
+164
+00:16:28,200 --> 00:16:36,080
+Euler's theorem if
+
+165
+00:16:36,080 --> 00:16:40,960
+الـ greatest common divisor بين الـ A والـ N بساوة
+
+166
+00:16:40,960 --> 00:16:50,240
+واحد then A to the five N يطابق الواحد مديلو مين؟
+
+167
+00:16:50,240 --> 00:16:51,100
+مديلو N
+
+168
+00:17:04,180 --> 00:17:08,340
+شوفوا الصلاة على النبي عليه الصلاة والسلام الآن
+
+169
+00:17:08,340 --> 00:17:11,660
+let
+
+170
+00:17:11,660 --> 00:17:25,860
+a1 و a2 لعند a5 and be the positive integers
+
+171
+00:17:25,860 --> 00:17:41,130
+less than and such that A less than N which are
+
+172
+00:17:41,130 --> 00:17:53,330
+relatively prime with N إيش اللي عملته؟ فرضت إن الـ
+
+173
+00:17:53,330 --> 00:17:57,970
+A1, A2, A5, N هذي أداء الوصول بتستخدم اللمبة ليش
+
+174
+00:17:57,970 --> 00:17:59,850
+كده إن أنا أعملها اللمبة اصلا اللمبة المعنى بتبقى
+
+175
+00:17:59,850 --> 00:18:02,850
+في نظرية بتستخدم اللي هي استخدمها في برهان نظرية
+
+176
+00:18:02,850 --> 00:18:08,730
+لاحقة أخدت a1 و a2 و a5n عبارة عن positive integers
+
+177
+00:18:08,730 --> 00:18:12,270
+less than .. positive integers اللي less than or
+
+178
+00:18:12,270 --> 00:18:17,130
+equal أن و relatively prime مع مين؟ معايا .. معايا
+
+179
+00:18:17,130 --> 00:18:24,570
+.. اه من النظرية اللي قبل بشوية then by لما اللي
+
+180
+00:18:24,570 --> 00:18:30,470
+قبل بشوية بكون ال a في ال a1 و ال a في ال a2 عند
+
+181
+00:18:30,470 --> 00:18:41,460
+ال a في ال a5n are congruent to الـ A1 لعند الـ A5N
+
+182
+00:18:41,460 --> 00:18:48,760
+in some order مظبوط؟ إذا صار كل واحد منها
+
+183
+00:18:48,760 --> 00:18:55,020
+congruent لواحد منها وكل واحد بس بيروح لوحده واضح؟
+
+184
+00:18:55,020 --> 00:19:02,360
+إذا أكيد حاصل ضرب هذول congruent لحاصل ضرب هذول إذا
+
+185
+00:19:02,360 --> 00:19:10,600
+صار عندي then ال a1 a2 لعند ال a5 of n يطابق
+
+186
+00:19:10,600 --> 00:19:14,100
+قولوا 
+
+187
+00:19:14,100 --> 00:19:25,840
+معايا a في a1 a في a2 لما أصل ل a في a5 of n مديلو
+
+188
+00:19:25,840 --> 00:19:30,580
+n طيب
+
+189
+00:19:31,310 --> 00:19:38,170
+الآن هذا يطابق يطابق الآن ال a هذه مضروبة في a
+
+190
+00:19:38,170 --> 00:19:40,950
+واحد و في a اتنين و في a five of n يعني مكررة
+
+191
+00:19:40,950 --> 00:19:47,110
+ماجداش five of n من المرات يعني بدها تسير هذه عندي
+
+192
+00:19:47,110 --> 00:19:54,770
+عبارة عن a أصفاه of n في a واحد لما أصل عند a five
+
+193
+00:19:54,770 --> 00:20:03,000
+of n مضروبين مضروبين طيب نحن عاملين بنقول العامل
+
+194
+00:20:03,000 --> 00:20:09,600
+المشترك الأعلى بين الـ A1 و الـ N1 و الـ A2 و الـ
+
+195
+00:20:09,600 --> 00:20:14,680
+N1 و الـ A5N و الـ NA شمالها صار إذن العامل
+
+196
+00:20:14,680 --> 00:20:21,140
+المشترك الأعلى بين الـ A1 لعند الـ A5N كله مع بعض
+
+197
+00:20:21,140 --> 00:20:26,450
+مع الـ N أيش برضه بساوي؟ إذا بصحّلي إيش أسوي؟ أجسم
+
+198
+00:20:26,450 --> 00:20:31,990
+الجهتين على مين؟ على هذا المقدار هانا بيضل Asian دي
+
+199
+00:20:31,990 --> 00:20:44,910
+واحد يطابق الـ A5N Modulo N وهو المطلوب أي
+
+200
+00:20:44,910 --> 00:20:47,930
+سؤال؟
+
+201
+00:20:47,930 --> 00:20:56,810
+الآن بتصير Fermat's حالة خاصة منها يعني بمعنى آخر
+
+202
+00:20:56,810 --> 00:21:03,570
+تصبح فرمات كورولا ري ل a large function اللي هي
+
+203
+00:21:03,570 --> 00:21:07,410
+بتقولك if b is a prime حكيتها قبل شوية and b لا
+
+204
+00:21:07,410 --> 00:21:10,350
+تقسم ال a إذا a to the b minus واحد يطابق الواحد
+
+205
+00:21:10,350 --> 00:21:17,560
+modulo b مديلو ب برايم وبلا تقسم الـA إذا العامل
+
+206
+00:21:17,560 --> 00:21:21,360
+المشترك الأعلى بين الـB والـA بساوي واحد إذا الـA
+
+207
+00:21:21,360 --> 00:21:27,280
+لازم تنطبق إذا A to the Phi of B يطابق الواحد
+
+208
+00:21:27,280 --> 00:21:32,180
+مضيلو B لكن الـPhi of B إيش بيساوي؟ إذا صار عندي A
+
+209
+00:21:32,180 --> 00:21:35,340
+to the B minus واحد يطابق الواحد مضيلو B وهو
+
+210
+00:21:35,340 --> 00:21:40,100
+المطلوب إذا صارت فرمات عذارة عن حالة خاصة من
+
+211
+00:21:40,100 --> 00:21:46,670
+Euler's theorem أو Corollary لإيه الارض فيه نفجر
+
+212
+00:21:46,670 --> 00:21:54,550
+الآن نوظف فرمات لحل بعض الأسئلة أو المسائل
+
+213
+00:21:54,550 --> 00:22:00,170
+الحسابية بقول
+
+214
+00:22:00,170 --> 00:22:08,450
+لي example example find
+
+215
+00:22:08,450 --> 00:22:24,240
+the last two digits of مثلا تلاتة to the اتنين اربع
+
+216
+00:22:24,240 --> 00:22:36,900
+ستة اتنين اللي هو خمسة ستة بكفي يعني بيقولي أو جد
+
+217
+00:22:36,900 --> 00:22:45,940
+اللي هو اخر الرقمين اخر رقمين لـ الرقم اللي عندي
+
+218
+00:22:45,940 --> 00:22:52,380
+نشوف إيش قصة اخر رقمين الآن لو جينا اخذنا اتنين
+
+219
+00:22:52,380 --> 00:22:56,760
+تلاتة أربعة خمسة واحد مثلا على سبيل المثال هذا
+
+220
+00:22:56,760 --> 00:23:01,720
+الرقم اخره مين؟ اخر رقمين؟ أشماله واحد خمسة يعني و
+
+221
+00:23:01,720 --> 00:23:04,720
+كأن الرقم هذا أو خمسة واحد هذا الرقم عبارة عن إيش؟
+
+222
+00:23:04,720 --> 00:23:16,710
+اتنين تلاتة أربعة ضرب مية صح؟ زي دياش 51 يعني هذا
+
+223
+00:23:16,710 --> 00:23:26,410
+الرقم نفسه 51 مديلو و إياش 100 لأن هدولة بالنسبالي
+
+224
+00:23:26,410 --> 00:23:33,210
+المية أشماله أسفار وكأنه وكأنه صار إنه عشان أوجد
+
+225
+00:23:33,210 --> 00:23:37,630
+ال last two digits السؤال بيصير اللي هو بطريقة
+
+226
+00:23:37,630 --> 00:23:44,680
+اخرى أو Deadly اللي هو المتبقي لهذا الرقم حين القسم
+
+227
+00:23:44,680 --> 00:23:50,860
+عالمية عالمية أو بمعنى آخر ماذا يطابق هذا الرقم
+
+228
+00:23:50,860 --> 00:23:59,450
+مديلو مية من الأعداد من واحد لتسعة وتسعين واضح؟ إذا
+
+229
+00:23:59,450 --> 00:24:02,770
+وكأنه صار لما يقولّك find the last two digits of
+
+230
+00:24:02,770 --> 00:24:09,690
+تلاتة أُس أُس كده بدي أوجب اللي هو هذا العدد يطابق
+
+231
+00:24:09,690 --> 00:24:16,470
+ماذا مديلو مية ماذا تعود على إيش؟ تعود على عدد من
+
+232
+00:24:16,470 --> 00:24:22,730
+واحد لمية أو المتبقي القسمة علامية واضح؟ إذا صارت
+
+233
+00:24:22,730 --> 00:24:29,270
+الأمور هيك واضحة وصار فيه إمكانية إنه نروح باتجاه
+
+234
+00:24:29,270 --> 00:24:34,810
+استغلال ما عرفتنا بـ Euler's theorem للوصول للحل
+
+235
+00:24:34,810 --> 00:24:42,810
+عندي أول حاجة اللي بدنا نيلها بقية سنين مية والعدد
+
+236
+00:24:42,810 --> 00:24:46,530
+اللي مرفوض للأسنين تلاتة وواضح إن الـ greatest
+
+237
+00:24:46,530 --> 00:24:51,830
+common divisor بين التلاتة والمية بساوي واحد
+
+238
+00:24:51,830 --> 00:25:00,730
+since then أكيد التلاتة to the file of مية يطابق
+
+239
+00:25:00,730 --> 00:25:06,410
+الواحد مديلو مجدياش مية ليش أخدنا الاليستيورم؟ لأنها
+
+240
+00:25:06,410 --> 00:25:11,490
+أصلا بتجيب للعدد يطابق مين؟ الواحد والواحد سهل في
+
+241
+00:25:11,490 --> 00:25:15,290
+الحسابات بتظل الباقي سهالات يعني بختار .. خلّيني
+
+242
+00:25:15,290 --> 00:25:20,980
+أقول باختصار الحسابات بشكل كبير جدا طيب الـ 1500
+
+243
+00:25:20,980 --> 00:25:27,840
+نحسمها إيش هتساوي؟ اللي هو عبارة عن 25 في 4 يعني
+
+244
+00:25:27,840 --> 00:25:34,760
+فيها 5 وفيها 2 إذا يعني 100 في 1 ماقص 5 في 1 ماقص
+
+245
+00:25:34,760 --> 00:25:44,500
+نص عارفين هالنظرية اللي هي بتطلع بتساوي 40 معايا؟
+
+246
+00:25:44,940 --> 00:25:50,160
+الآن ضال أطلّع للعدد هذا بشيل منه كل الأربعينات
+
+247
+00:25:50,160 --> 00:25:56,340
+أبوشوف إيش فيه أربعينات معايا حد يجسملي إنه هو
+
+248
+00:25:56,340 --> 00:26:03,600
+أشوف الآن اتنين أربعة ستة اتنين أربعة صفر أجسملي
+
+249
+00:26:03,600 --> 00:26:07,440
+على أربعين سيبك من الست عشر اللي بتضل شوف كده إيش
+
+250
+00:26:07,440 --> 00:26:08,340
+على الأقل على الأقل
+
+251
+00:26:18,770 --> 00:26:25,610
+Okay اللي هو .. انتبهت عليا هان؟ هو بده إيش ماله؟
+
+252
+00:26:25,610 --> 00:26:29,950
+اخر .. اخر .. اخر .. اخر .. اللي هو .. بده the
+
+253
+00:26:29,950 --> 00:26:34,530
+last two digits ماشي الحال؟ الآن يعني بده الواحد
+
+254
+00:26:34,530 --> 00:26:39,070
+وخمسين هان يعني وكأنه هذا العدد صار اللي هو مضروب
+
+255
+00:26:39,070 --> 00:26:44,920
+بيه زائد واحد وخمسين الـ 100 يجمعنا الـ 100 عساس إن
+
+256
+00:26:44,920 --> 00:26:49,320
+هذا يصبح من الـ 100 صفر وهو اللي يبقى الباق الـ
+
+257
+00:26:49,320 --> 00:26:54,680
+100 مية يعني خانتين هذين 6 1 5 6 6 ألف و 100 و 6 ألف
+
+258
+00:26:54,680 --> 00:27:02,770
+لو تلت خانات ألف ألف صحيح 5 1 5 6 هذا كم يطلع؟ 6 ستة
+
+259
+00:27:02,770 --> 00:27:07,690
+واحد خمسة ستة طيب انتبهوا الآن بيصير عندي تلاتة
+
+260
+00:27:07,690 --> 00:27:11,510
+أقصى اتنين أربع عشان مانضيعش الفكرة الاساسية ستة
+
+261
+00:27:11,510 --> 00:27:19,210
+اتنين خمسة ستة إيش ماله؟ بيساوي اللي هو اللي هو
+
+262
+00:27:19,210 --> 00:27:27,950
+تلاتة أقصى اربعين أقصى ستة واحد خمسة ستة فاهمين اه؟
+
+263
+00:27:27,950 --> 00:27:34,320
+في تلاتة أقصى ستة عشر إيش اللي عملته يا جماعة؟ هذا
+
+264
+00:27:34,320 --> 00:27:39,560
+العدد هذا العدد لو شيلته و كتبته بدلالة الأربعين
+
+265
+00:27:39,560 --> 00:27:50,660
+والمتبقي 16 معايا؟ مظبوط هيك الرقم؟ 61560 على 4
+
+266
+00:27:50,660 --> 00:27:54,960
+ولا على 40؟ على 40 مطلعته، مظبوط، مظبوط، مطلع على
+
+267
+00:27:54,960 --> 00:27:58,420
+40 هيك خليني أكمل، مطلع على 40 هيك، ماشي الحال؟
+
+268
+00:28:00,120 --> 00:28:04,560
+عشان ما اطلعش الفكرة هذا العدد بيساوي تلاتة أقصى
+
+269
+00:28:04,560 --> 00:28:08,040
+اربعين في هذا في هذا إيش مهم تلاتة أقصى اربعين
+
+270
+00:28:08,040 --> 00:28:12,220
+لإنه أنا عارف تلاتة أقصى اربعين إيش مالها؟ هذه five
+
+271
+00:28:12,220 --> 00:28:17,420
+of .. five of one hundred اربعين يعني هذه اعطتني
+
+272
+00:28:17,420 --> 00:28:24,560
+تلاتة أقصى اربعين يطابق الواحد مديلو مين؟ مية بيصير
+
+273
+00:28:24,560 --> 00:28:29,120
+عندي الآن هذا العدد يطابق هذا أو سوى وهذا يطابق
+
+274
+00:28:29,120 --> 00:28:36,360
+واحد أس ستة واحد خمسة ستة في تلاتة أس ستاش مديلو
+
+275
+00:28:36,360 --> 00:28:37,540
+مية
+
+276
+00:28:43,640 --> 00:28:48,600
+الآن بيصير عندي 3 أقصى 16 اللي هي سهلة الحساب تلاتة
+
+277
+00:28:48,600 --> 00:28:50,900
+فتلاتة ساعة تسعة وتسعة واحد و ثمانين اللي هي
+
+278
+00:28:50,900 --> 00:28:55,140
+عبارة عن واحد و ثمانين أقصى أش أقصى أربعة الواحد و
+
+279
+00:28:55,140 --> 00:28:57,760
+ثمانين أقصى أربعة بتطلع على الأقل على طول بسرعة أو
+
+280
+00:28:57,760 --> 00:29:02,800
+بتزغر اللي ناقص تسعة عشر أقصى أربعة اللي بدك تطلع
+
+
+
+281
+00:29:02,800 --> 00:29:06,720
+في الآخر آخر رقمين تطابق واحد وعشرين مدولين
+
+282
+00:29:06,720 --> 00:29:12,710
+مدولية بصير عندي الآن the last two digits of هذا
+
+283
+00:29:12,710 --> 00:29:22,230
+الرقم اللي هو عبارة عن قداش واحد وعشرين، أي سؤال؟
+
+284
+00:29:22,230 --> 00:29:35,010
+إجينا
+
+285
+00:29:35,010 --> 00:29:39,650
+هذا الآن، إيش سوينا؟ شلنا منه الأربعينات بمعنى آخر
+
+286
+00:29:39,650 --> 00:29:43,230
+قسّمناها على أربعين وشوفنا إيش المتبقي من القسمة الآن
+
+287
+00:29:43,230 --> 00:29:47,190
+المتبقي من القسمة على أربعين إيش طلع؟ ستة عشر فطلع
+
+288
+00:29:47,190 --> 00:29:51,990
+هذا الرقم عبارة عن هذا الرقم اللي عندي ثلاثة أربعة
+
+289
+00:29:51,990 --> 00:29:58,970
+ستة اثنين خمسة ستة بساول ستة واحد خمسة ستة مضروب 
+
+290
+00:29:58,970 --> 00:30:05,800
+في أربعين زاد إيش زاد؟ ستة عشر واضح فالآن ثلاثة أس
+
+291
+00:30:05,800 --> 00:30:09,140
+هذا المقدار بيساوي ثلاثة أس هذا المقدار يعني بمعنى
+
+292
+00:30:09,140 --> 00:30:15,120
+آخر ثلاثة في ثلاثة أس أربعة عشر هذا كله واحد لأن ثلاثة 
+
+293
+00:30:15,120 --> 00:30:19,260
+أس أربعين تطابق الواحد ب modulo الأربعين وبيظل
+
+294
+00:30:19,260 --> 00:30:22,540
+ثلاثة أس أربعة عشر اللي هي تطابق قداش؟ الواحد وعشرين
+
+295
+00:30:22,540 --> 00:30:30,240
+بالحسابات اليدوية أو الآلة نجي للي بعدها تطبيق آخر
+
+296
+00:30:38,380 --> 00:30:50,040
+Example آخر Example آخر خلّوكم
+
+297
+00:30:50,040 --> 00:30:57,380
+معايا وخلّينا نركز على أساس اللي هو تتضح الفكرة
+
+298
+00:30:57,380 --> 00:31:01,040
+عندي
+
+299
+00:31:04,310 --> 00:31:16,170
+let n be an odd integer إذا n is odd واحد n is odd
+
+300
+00:31:16,170 --> 00:31:23,850
+اثنين الآن فيش فيه خمسات الخمسة لتقسم مين الآن
+
+301
+00:31:23,850 --> 00:31:29,310
+الخمسة لتقسم الآن معايا
+
+302
+00:31:32,550 --> 00:31:43,870
+هذا مع بعض بقول لك إنه لازم الآن تقسم عدد خاناته 
+
+303
+00:31:43,870 --> 00:31:47,830
+كلها مكوّنة من واحد واحد واحد واحد يعني كل خاناته
+
+304
+00:31:47,830 --> 00:31:54,610
+واحد يعني بمعنى آخر واحد واحد some واحد عدد خمس
+
+305
+00:31:54,610 --> 00:31:57,670
+مرات ست مرات سبع مرات تمام مرات أشهر مرات حسب
+
+306
+00:31:57,670 --> 00:32:04,740
+العدد m واضح إذا الأعداد ال odd integers اللي مش
+
+307
+00:32:04,740 --> 00:32:11,900
+فيها خمسة في الآخر هتلاقي ال m بيجسم 2 هو عامل من 
+
+308
+00:32:11,900 --> 00:32:18,820
+عوامل اللي هو عدد اللي هو خاناته عبارة عن الواحد
+
+309
+00:32:18,820 --> 00:32:28,060
+واحد واحد واحد واضح الآن نشوف إيش الفكرة في الحل
+
+310
+00:32:28,060 --> 00:32:32,740
+طبعًا احنا قاعدين بنتعلم اللي هو خلّينا نقول
+
+311
+00:32:32,740 --> 00:32:38,820
+باتجاهات مختلفة أفكار مختلفة لتطبيق ال modulo عليها
+
+312
+00:32:38,820 --> 00:32:44,260
+توظيفها في حلها نشوف كيف اللي هو إيش اللي
+
+313
+00:32:44,260 --> 00:32:50,080
+بيقولوها solution اصبر
+
+314
+00:32:50,080 --> 00:32:56,520
+عليّ وخلّيك تفهم الفكرة الآن لو أجيت أخذت العامل
+
+315
+00:32:56,520 --> 00:33:00,680
+المشترك الأعلى للخمسة
+
+316
+00:33:00,680 --> 00:33:05,600
+مش فيها n مش موجودة .. مش .. ال n مش فيها خمسات
+
+317
+00:33:05,600 --> 00:33:09,800
+يعني بمعنى آخر العامل المشترك الأعلى بين الخمسة و
+
+318
+00:33:09,800 --> 00:33:16,820
+ال n واحد وال n فردي إذا مش فيها اثنينات يعني
+
+319
+00:33:16,820 --> 00:33:22,280
+بمعنى آخر العامل المشترك الأعلى بين الخمسة والآن
+
+320
+00:33:22,280 --> 00:33:28,360
+واحد والعشرة والآن إيش
+
+321
+00:33:28,360 --> 00:33:35,340
+مالها بيساوي واحد معايا العامل المشترك الأعلى بين
+
+322
+00:33:35,340 --> 00:33:38,720
+الآن والعشرة إيش بيساوي؟ يعني الآن مش فيها عشرة
+
+323
+00:33:38,720 --> 00:33:43,980
+تلاقت تعرف ليش العشرة العامل العامل المشترك الأعلى
+
+324
+00:33:45,470 --> 00:33:51,230
+بين العشرة والتسعة برضه إيش بيساوي؟ واحد إيش معنى
+
+325
+00:33:51,230 --> 00:33:55,710
+التسعة؟ هل جيت بتعرف ليش؟ لأنه أنا بدأت بالعدد في 
+
+326
+00:33:55,710 --> 00:34:00,550
+الآخر عشر أرقام إشي ماقص واحد يعني تسعات والتسعة
+
+327
+00:34:00,550 --> 00:34:04,430
+هذه هتلزمني إن أنا أحطها تحت فبيصير كل نقاش
+
+328
+00:34:04,430 --> 00:34:09,960
+وحدات ده نشوف كده العامل المشترك الأعلى بين العشرة
+
+329
+00:34:09,960 --> 00:34:14,220
+والآن واحد والعشرة والتسعة إيش بيساوي واحد إذا
+
+330
+00:34:14,220 --> 00:34:21,940
+أكيد العامل المشترك الأعلى بين العشرة والتسعة إن
+
+331
+00:34:21,940 --> 00:34:30,620
+إيش بيساوي؟ بيساوي واحد طيب إذا صارت فرمات جاهزة
+
+332
+00:34:30,620 --> 00:34:41,410
+إذا بيصير عندي اللي هو عشرة أس خمسة n مظبوط؟ عشرة
+
+333
+00:34:41,410 --> 00:34:46,450
+تسعة n بيساوي واحد العشرة بيتمثل لل a والتسعة n
+
+334
+00:34:46,450 --> 00:34:50,510
+بيتمثل لل n الجديدة فبيصير ال a to the five of n
+
+335
+00:34:50,510 --> 00:34:57,390
+يعني عشرة to the five of تسعة n تطابق الواحد
+
+336
+00:34:57,390 --> 00:35:03,870
+مدولية مدول تسعة n وأنا بدي التسعة n كمان الجد
+
+337
+00:35:03,870 --> 00:35:07,920
+تعرف ليش بدي تسعة n الآن إيش معناه هذا الكلام؟
+
+338
+00:35:07,920 --> 00:35:12,980
+معناه إن تسعة n تجسيم عشرة وده كده ماقص واحد أو
+
+339
+00:35:12,980 --> 00:35:20,240
+بمعنى آخر صار عندي الآن عشرة أس خمسة of تسعة n ماقص
+
+340
+00:35:20,240 --> 00:35:28,060
+واحد بيساوي تسعة n k for some k element in z
+
+341
+00:35:31,360 --> 00:35:36,640
+ال 9n هذا إيش معناه؟ إن ال 9n بتجسم العشرة the
+
+342
+00:35:36,640 --> 00:35:43,260
+five of 9n ناقص واحد أه مظبوط؟ إذا صار هذا بيساوي
+
+343
+00:35:43,260 --> 00:35:49,240
+هذا فصم number كيه معايا؟ واضح أه الآن هذا 
+
+344
+00:35:49,240 --> 00:35:53,640
+العدد أنا بدي ال n في الآخر تجسم مين؟ عدد في كل
+
+345
+00:35:53,640 --> 00:36:01,340
+واحدات الآن هذا العدد اللي بتطلعلي فرمات تسعات مش 
+
+346
+00:36:01,340 --> 00:36:06,740
+تسعات لهم عشرة قص كده وشيل منه واحد بيبقى لها
+
+347
+00:36:06,740 --> 00:36:11,120
+تسعات إذا عشان أحصل على اللي بديه يابن زمي كان
+
+348
+00:36:11,120 --> 00:36:17,800
+تسعة في الطريق وطلع فعلاً أصلاً الآن بيصير على تسعة 
+
+349
+00:36:17,800 --> 00:36:26,530
+بيساوي one في k يعني طلع هذا العدد كله واحد و
+
+350
+00:36:26,530 --> 00:36:33,210
+بيساوي n في k يعني بمعنى آخر من مضاعفات من ال n 
+
+351
+00:36:33,210 --> 00:36:42,130
+يعني صار عندك ال n بيجسم الواحد واحد لأ 
+
+352
+00:36:42,130 --> 00:36:45,570
+ما أعرفش أشوفه فيه لكل رقم فيه لعداده هل جيت مني أخذ
+
+353
+00:36:45,570 --> 00:36:53,550
+رقم هل جيت مني أخذ رقم خليني أنا أخذ أنثى لهم خد
+
+354
+00:36:53,550 --> 00:36:53,970
+ال n
+
+355
+00:37:01,000 --> 00:37:07,400
+خد ال n بتساوي سبعة ال n بتساوي سبعة بنتبق
+
+356
+00:37:07,400 --> 00:37:11,020
+عليها ليش بنتبق عليها؟ لأنه سبعة فردي وفيش فيها مين
+
+357
+00:37:11,020 --> 00:37:18,600
+خمسات ماشي الحل إذا حيكون عندي اللي هو العشرة عشرة 
+
+358
+00:37:18,600 --> 00:37:26,540
+أس five of ستة ثلاثة ناقص واحد على تسعة بيساوي 
+
+359
+00:37:26,540 --> 00:37:30,440
+سبعة في k مظبوط ولا لأ؟
+
+360
+00:37:34,030 --> 00:37:37,210
+معناه اللي إيه؟ ال five of ثلاثة وستين من اين
+
+361
+00:37:37,210 --> 00:37:41,250
+وجدها؟ five of ثلاثة وستين إيش five of ثلاثة و
+
+362
+00:37:41,250 --> 00:37:45,990
+ستين؟ بيساوي ثلاثة وستين فيها اللي هي ثلاثة وتسعة 
+
+363
+00:37:45,990 --> 00:37:51,510
+بس ثلاثة وسبعة بس اللي هي واحد ماقص تلت في واحد
+
+364
+00:37:51,510 --> 00:37:57,970
+ماقص سبعة مظبوط اللي بعمله؟ واضح ويساوي نحسبها
+
+365
+00:37:57,970 --> 00:38:01,330
+ثلاثة وستين في تلتين
+
+366
+00:38:02,870 --> 00:38:09,750
+في ستة على مين؟ على سبعة حيث الآن السبعة بتروح ..
+
+367
+00:38:09,750 --> 00:38:14,470
+أو الآن السبعة اللي بيبقى عنده سبعة بيبقى إيه
+
+368
+00:38:14,470 --> 00:38:20,810
+أشماله؟ تسعة وأنا واحد بيبقى قداش؟ اثنا عشر في ثلاثة
+
+369
+00:38:20,810 --> 00:38:27,030
+صح ولا لأ؟ ستة وثلاثين بيصير 
+
+370
+00:38:27,030 --> 00:38:34,300
+عشرة ال 36 ماقص واحد على مين؟ على تسعة بيساوي قداش
+
+371
+00:38:34,300 --> 00:38:39,740
+سبعة k الآن
+
+372
+00:38:39,740 --> 00:38:44,560
+بدنا نحسب عشرة قوى ستة وثلاثين أو 
+
+373
+00:38:44,560 --> 00:38:49,540
+شيل من هنا أه ستة وثلاثين سفر شيل من هنا قداش واحد
+
+374
+00:38:49,540 --> 00:38:55,440
+بيبقى هنا قداش؟ بيبقى التسعات بيبقى خمسة وثلاثين
+
+375
+00:38:55,440 --> 00:39:04,010
+أحد أو واحد بس ممكن تلاقي some of the properties 
+
+376
+00:39:04,010 --> 00:39:10,890
+of the phi function ده ناخذ بعض الخواص لمين؟ لل 
+
+377
+00:39:10,890 --> 00:39:15,010
+phi functions شوفوا صلوا على النبي عليه الصلاة
+
+378
+00:39:15,010 --> 00:39:21,690
+والسلام في عيننا اللي هي نظرية الأولى Gauss 
+
+379
+00:39:21,690 --> 00:39:22,930
+theorem
+
+380
+00:39:43,750 --> 00:39:49,630
+النظرية الأولى جاوس ثيوريم بتقول for each positive 
+
+381
+00:39:49,630 --> 00:39:53,930
+integer n أكبر أو يساوي واحد ال n بتساوي ال
+
+382
+00:39:53,930 --> 00:39:59,150
+summation لل phi of d دي بتقسم n يعني لو جيت حسبت 
+
+383
+00:39:59,150 --> 00:40:04,670
+أنت خد أي n أكبر أو يساوي واحد هتساوي ال summation
+
+384
+00:40:04,670 --> 00:40:14,350
+لل phi of d دي بتقسم n مجموعة ال divisors لل n دي 
+
+385
+00:40:14,350 --> 00:40:23,070
+بتقسم n هيساوي اللي هو مين؟ بساوي n أه summation لل
+
+386
+00:40:23,070 --> 00:40:27,270
+phi of d دي بتجسم n بساوي n احنا هناخد التفاصيل
+
+387
+00:40:27,270 --> 00:40:31,230
+المرة الجاية بس خلينا ناخذ نقام في العدد دي بس 
+
+388
+00:40:31,230 --> 00:40:37,620
+اللي هي لو أخدنا n بتساوي واحد n بتساوي واحد خد n
+
+389
+00:40:37,620 --> 00:40:42,120
+بتساوي واحد وحسب ليه ال summation لل phi دي دي 
+
+390
+00:40:42,120 --> 00:40:46,180
+بتجسم من الواحد واضح إنه ما فيش غير مين؟ اللي هو
+
+391
+00:40:46,180 --> 00:40:52,780
+phi واحد ويساوي إيش؟ واحد إيش
+
+392
+00:40:52,780 --> 00:41:01,370
+بتساوي n بتساوي n الآن n بتساوي 2 خد summation
+
+393
+00:41:01,370 --> 00:41:09,190
+phi of d دي بتقسم 2 ويساوي phi of واحد زائد phi
+
+394
+00:41:09,190 --> 00:41:14,650
+of اثنين صح ولا للم divisors للاثنين الواحد
+
+395
+00:41:14,650 --> 00:41:19,130
+والاثنين ويساوي واحد زائد واحد ويساوي اثنين ويساوي 
+
+396
+00:41:19,130 --> 00:41:23,350
+n الآن صمي خد n بتساوي سبعة مثلًا
+
+397
+00:41:27,150 --> 00:41:32,290
+أو خلّيني أخذ قبل ما هو عدد مش برايم ستة اللي عندي
+
+398
+00:41:32,290 --> 00:41:38,350
+summation phi d دي بتجسب الستة هو يساوي phi 
+
+399
+00:41:38,350 --> 00:41:47,630
+واحد زائد phi اثنين زائد phi ثلاثة زائد phi ستة
+
+400
+00:41:48,500 --> 00:41:53,480
+مظبوط ما يساوي phi واحد واحد phi اثنين واحد phi
+
+401
+00:41:53,480 --> 00:42:00,280
+ثلاثة اثنين phi ستة اللي هو قداش؟ اثنين مظبوط 
+
+402
+00:42:00,280 --> 00:42:04,480
+ما يساوي
+
+403
+00:42:04,480 --> 00:42:08,140
+نيجي
+
+404
+00:42:08,140 --> 00:42:17,410
+ناخد اثنين اللي هو n بتساوي سبعة summation phi of d
+
+405
+00:42:17,410 --> 00:42:23,690
+دي بتقسم سبعة ويساوي phi of واحد زائد phi of سبعة في 
+
+406
+00:42:23,690 --> 00:42:30,890
+غيرهم أكيد لأ long of prime أه صحيح ويساوي واحد كده 
+
+407
+00:42:30,890 --> 00:42:37,150
+إيش؟ واحدة ستة ويساوي سبعة الانفاصة ماشية phi of d
+
+408
+00:42:37,150 --> 00:42:42,850
+دي بتكسب ال prime أكيد سهلة إيش بتساوي اللي هو phi 
+
+409
+00:42:42,850 --> 00:42:47,450
+of واحد زيدي phi of ال p نفسها ويساوي عبارة عن 
+
+410
+00:42:47,450 --> 00:42:53,650
+واحد زيدي p ماينس واحد ويساوي اللي هو إيش؟ p فاضح 
+
+411
+00:42:53,650 --> 00:42:53,970
+أه
+
+412
+00:42:56,880 --> 00:43:00,340
+المرة الجاية إن شاء الله بنحكي في التفاصيل
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/hGaju6zUWgU_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/hGaju6zUWgU_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..023168f7253e7902a43fc0f1addc764e2cdb5072
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/hGaju6zUWgU_raw.json
@@ -0,0 +1 @@
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هذوله ان انا incongruent suppose not", "tokens": [9307, 1863, 9957, 47525, 3224, 1975, 12984, 3555, 2655, 23275, 16472, 3224, 45164, 10874, 36081, 1975, 9778, 3215, 2655, 1975, 1829, 36764, 24401, 9154, 8032, 8848, 12610, 3224, 8032, 7435, 26895, 3224, 36764, 24401, 9154, 34105, 4724, 9566, 16758, 4587, 3224, 20449, 8315, 47395, 16490, 1211, 9381, 2655, 16472, 3224, 8608, 3615, 2288, 28242, 36764, 24401, 4724, 9566, 16758, 4587, 4724, 3794, 1975, 1829, 8592, 36764, 24401, 11778, 3224, 8717, 8592, 38688, 13412, 38688, 14407, 1975, 12610, 11331, 26108, 3660, 47525, 3224, 8717, 12984, 3555, 2655, 8032, 8848, 12610, 3224, 16472, 1975, 8315, 834, 556, 894, 317, 7297, 406], "avg_logprob": -0.2229687537252903, "compression_ratio": 1.733695652173913, "no_speech_prob": 1.9669532775878906e-06, "words": [{"start": 532.25, "end": 532.75, "word": "اتنين", "probability": 0.6826171875}, {"start": 532.75, "end": 533.01, "word": " بده", "probability": 0.3804931640625}, {"start": 533.01, "end": 533.49, 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AJ مدن M وهذا contradiction therefore اللي هو الـA في الـA واحد والـA في الـA اتنين عند الـA في الـ5N إشمالًا R", "tokens": [3555, 30544, 3714, 9566, 16758, 4587, 32767, 2655, 3555, 4587, 7578, 25062, 38251, 11933, 43761, 3714, 3215, 1863, 9673, 4587, 9381, 20498, 47356, 4032, 6027, 20292, 13672, 1829, 8032, 15042, 2423, 39184, 39170, 443, 1616, 9673, 46456, 46538, 9307, 4724, 30544, 11933, 8592, 2304, 6027, 14111, 995, 376, 8882, 19226, 23032, 1829, 3555, 12399, 370, 43242, 2423, 39184, 32, 12399, 286, 23032, 995, 28671, 32759, 3714, 3215, 1863, 376, 37037, 15730, 34937, 4412, 13672, 1829, 31439, 2423, 39184, 32, 8978, 2423, 39184, 32, 36764, 24401, 16070, 39184, 32, 8978, 2423, 39184, 32, 1975, 2655, 1863, 9957, 43242, 2423, 39184, 32, 8978, 2423, 39184, 20, 45, 11933, 8592, 2304, 6027, 14111, 995, 497], "avg_logprob": -0.30973451327433627, "compression_ratio": 1.7244444444444444, "no_speech_prob": 1.7285346984863281e-06, "words": [{"start": 673.41, "end": 673.93, "word": "بكون", 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"end": 707.78, "word": " أي", "probability": 0.85107421875}, {"start": 707.78, "end": 708.06, "word": " واحد", "probability": 0.994140625}, {"start": 708.06, "end": 708.28, "word": " من", "probability": 0.98779296875}, {"start": 708.28, "end": 708.58, "word": " هنا", "probability": 0.96142578125}, {"start": 708.58, "end": 709.78, "word": " ونلاقيله", "probability": 0.61826171875}, {"start": 709.78, "end": 710.8, "word": " واحد", "probability": 0.990234375}, {"start": 710.8, "end": 711.0, "word": " من", "probability": 0.98486328125}, {"start": 711.0, "end": 711.26, "word": " هنا", "probability": 0.75146484375}, {"start": 711.26, "end": 712.18, "word": " شوف", "probability": 0.888427734375}, {"start": 712.18, "end": 715.34, "word": " let", "probability": 0.5673828125}, {"start": 715.34, "end": 717.32, "word": " a", "probability": 0.5595703125}, {"start": 717.32, "end": 717.52, "word": " في", "probability": 0.650390625}, {"start": 717.52, "end": 718.12, "word": " ai", "probability": 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divisor بين ال a و ال n بسوء واحد صح ملطق", "tokens": [3555, 33599, 1829, 8717, 47283, 3215, 2423, 257, 11, 257, 11, 741, 36632, 6806, 4478, 8032, 7649, 2423, 7649, 47525, 4117, 6055, 15040, 5016, 19913, 5551, 12610, 995, 13412, 2304, 6027, 1829, 16472, 2423, 6636, 2689, 25974, 284, 49374, 2423, 257, 4032, 2423, 297, 4724, 3794, 2407, 38207, 36764, 24401, 20328, 5016, 3714, 1211, 9566, 4587], "avg_logprob": -0.43585525479233056, "compression_ratio": 1.304054054054054, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 734.03, "end": 734.79, "word": "باشي", "probability": 0.4536539713541667}, {"start": 734.79, "end": 735.69, "word": " ناخد", "probability": 0.8016764322916666}, {"start": 735.69, "end": 735.87, "word": " ال", "probability": 0.66357421875}, {"start": 735.87, "end": 736.09, "word": " a,", "probability": 0.2333984375}, {"start": 736.19, "end": 736.33, "word": " a,", "probability": 0.6025390625}, {"start": 736.37, "end": 736.67, "word": " i", "probability": 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{"start": 746.37, "end": 746.75, "word": " common", "probability": 0.93994140625}, {"start": 746.75, "end": 747.61, "word": " divisor", "probability": 0.956298828125}, {"start": 747.61, "end": 748.19, "word": " بين", "probability": 0.83056640625}, {"start": 748.19, "end": 748.43, "word": " ال", "probability": 0.77490234375}, {"start": 748.43, "end": 748.81, "word": " a", "probability": 0.7958984375}, {"start": 748.81, "end": 749.99, "word": " و", "probability": 0.57421875}, {"start": 749.99, "end": 750.15, "word": " ال", "probability": 0.95703125}, {"start": 750.15, "end": 750.53, "word": " n", "probability": 0.9345703125}, {"start": 750.53, "end": 752.03, "word": " بسوء", "probability": 0.5457763671875}, {"start": 752.03, "end": 752.57, "word": " واحد", "probability": 0.94287109375}, {"start": 752.57, "end": 754.95, "word": " صح", "probability": 0.921875}, {"start": 754.95, "end": 756.51, "word": " ملطق", "probability": 0.467315673828125}], "temperature": 1.0}, {"id": 31, "seek": 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{"start": 1753.87, "end": 1753.99, "word": " هو", "probability": 0.98583984375}, {"start": 1753.99, "end": 1754.19, "word": " عبارة", "probability": 0.9854736328125}, {"start": 1754.19, "end": 1754.35, "word": " عن", "probability": 0.99560546875}, {"start": 1754.35, "end": 1755.33, "word": " قداشة", "probability": 0.52197265625}, {"start": 1755.33, "end": 1756.05, "word": " واحد", "probability": 0.898193359375}, {"start": 1756.05, "end": 1756.69, "word": " وعشرين،", "probability": 0.7460205078125}, {"start": 1756.69, "end": 1756.89, "word": " أي", "probability": 0.740234375}, {"start": 1756.89, "end": 1762.23, "word": " سؤال؟", "probability": 0.8480224609375}, {"start": 1762.23, "end": 1775.01, "word": " إجينا", "probability": 0.44324493408203125}, {"start": 1775.01, "end": 1775.69, "word": " هذا", "probability": 0.97119140625}, {"start": 1775.69, "end": 1776.27, "word": " الآن،", "probability": 0.7743326822916666}, {"start": 1776.27, "end": 1776.41, "word": " إيش", "probability": 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257396, "start": 2550.15, "end": 2573.97, "text": "واحد كده ايش؟ واحدة ستة ويساوي سبعة الانفاصة ماشية في of دي دي بتكسب ال prime اكيد سهلة ايش بتساوي اللي هو في of واحد زيدي في of ال بي نفسها ويساوي عبارة عن واحد زيدي بي ماينس واحد ويساوي اللي هو ايش بي فاضح اه", "tokens": [14407, 24401, 9122, 3215, 3224, 1975, 1829, 8592, 22807, 36764, 24401, 3660, 8608, 2655, 3660, 4032, 1829, 3794, 995, 45865, 8608, 3555, 27884, 2423, 7649, 5172, 33546, 3660, 3714, 33599, 10632, 8978, 295, 11778, 1829, 11778, 1829, 39894, 4117, 35457, 2423, 5835, 1975, 4117, 25708, 8608, 3224, 37977, 1975, 1829, 8592, 39894, 3794, 995, 45865, 13672, 1829, 31439, 8978, 295, 36764, 24401, 30767, 1829, 16254, 8978, 295, 2423, 4724, 1829, 8717, 36178, 11296, 4032, 1829, 3794, 995, 45865, 6225, 3555, 9640, 3660, 18871, 36764, 24401, 30767, 1829, 16254, 4724, 1829, 19446, 9957, 3794, 36764, 24401, 4032, 1829, 3794, 995, 45865, 13672, 1829, 31439, 1975, 1829, 8592, 4724, 1829, 6156, 46958, 5016, 1975, 3224], "avg_logprob": 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"probability": 0.5634765625}, {"start": 2556.55, "end": 2557.15, "word": " دي", "probability": 0.5989990234375}, {"start": 2557.15, "end": 2557.97, "word": " دي", "probability": 0.8349609375}, {"start": 2557.97, "end": 2558.43, "word": " بتكسب", "probability": 0.9381510416666666}, {"start": 2558.43, "end": 2558.61, "word": " ال", "probability": 0.47412109375}, {"start": 2558.61, "end": 2559.09, "word": " prime", "probability": 0.421875}, {"start": 2559.09, "end": 2559.59, "word": " اكيد", "probability": 0.7714029947916666}, {"start": 2559.59, "end": 2560.09, "word": " سهلة", "probability": 0.955078125}, {"start": 2560.09, "end": 2561.03, "word": " ايش", "probability": 0.8580729166666666}, {"start": 2561.03, "end": 2561.65, "word": " بتساوي", "probability": 0.9609375}, {"start": 2561.65, "end": 2562.35, "word": " اللي", "probability": 0.75244140625}, {"start": 2562.35, "end": 2562.53, "word": " هو", "probability": 0.96533203125}, {"start": 2562.53, "end": 2562.85, "word": " في", "probability": 0.69921875}, {"start": 2562.85, "end": 2563.17, "word": " of", "probability": 0.9052734375}, {"start": 2563.17, "end": 2563.83, "word": " واحد", "probability": 0.993896484375}, {"start": 2563.83, "end": 2564.33, "word": " زيدي", "probability": 0.656494140625}, {"start": 2564.33, "end": 2564.59, "word": " في", "probability": 0.87841796875}, {"start": 2564.59, "end": 2564.85, "word": " of", "probability": 0.92578125}, {"start": 2564.85, "end": 2565.07, "word": " ال", "probability": 0.67529296875}, {"start": 2565.07, "end": 2565.31, "word": " بي", "probability": 0.579833984375}, {"start": 2565.31, "end": 2566.39, "word": " نفسها", "probability": 0.99267578125}, {"start": 2566.39, "end": 2566.95, "word": " ويساوي", "probability": 0.84912109375}, {"start": 2566.95, "end": 2567.27, "word": " عبارة", "probability": 0.9879150390625}, {"start": 2567.27, "end": 2567.45, "word": " عن", "probability": 0.99267578125}, {"start": 2567.45, "end": 2567.81, "word": " واحد", "probability": 0.987548828125}, {"start": 2567.81, "end": 2568.19, "word": " زيدي", "probability": 0.8876953125}, {"start": 2568.19, "end": 2568.39, "word": " بي", "probability": 0.91015625}, {"start": 2568.39, "end": 2568.73, "word": " ماينس", "probability": 0.734375}, {"start": 2568.73, "end": 2569.29, "word": " واحد", "probability": 0.974609375}, {"start": 2569.29, "end": 2570.33, "word": " ويساوي", "probability": 0.96943359375}, {"start": 2570.33, "end": 2570.85, "word": " اللي", "probability": 0.9775390625}, {"start": 2570.85, "end": 2571.05, "word": " هو", "probability": 0.9794921875}, {"start": 2571.05, "end": 2571.47, "word": " ايش", "probability": 0.8430989583333334}, {"start": 2571.47, "end": 2572.47, "word": " بي", "probability": 0.923828125}, {"start": 2572.47, "end": 2573.65, "word": " فاضح", "probability": 0.7999674479166666}, {"start": 2573.65, "end": 2573.97, "word": " اه", "probability": 0.861328125}], "temperature": 1.0}, {"id": 98, "seek": 258034, "start": 2576.88, "end": 2580.34, "text": "المرة الجاية ان شاء الله بنحكي في التفاصيل", "tokens": [45340, 25720, 25724, 995, 10632, 16472, 13412, 16606, 21984, 44945, 5016, 4117, 1829, 8978, 16712, 5172, 33546, 26895], "avg_logprob": -0.18338816416891, "compression_ratio": 1.1159420289855073, "no_speech_prob": 0.0, "words": [{"start": 2576.88, "end": 2577.46, "word": "المرة", "probability": 0.76123046875}, {"start": 2577.46, "end": 2577.84, "word": " الجاية", "probability": 0.7284342447916666}, {"start": 2577.84, "end": 2577.96, "word": " ان", "probability": 0.64794921875}, {"start": 2577.96, "end": 2578.24, "word": " شاء", "probability": 0.987548828125}, {"start": 2578.24, "end": 2578.66, "word": " الله", "probability": 0.9560546875}, {"start": 2578.66, "end": 2579.56, "word": " بنحكي", "probability": 0.85162353515625}, {"start": 2579.56, "end": 2579.64, "word": " في", "probability": 0.9404296875}, {"start": 2579.64, "end": 2580.34, "word": " التفاصيل", "probability": 0.9757080078125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2580.5264375, "duration_after_vad": 2422.893749999986}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/hGaju6zUWgU_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/hGaju6zUWgU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..cb923cf22623e7bd844e4db90d9460479afda2a7
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/hGaju6zUWgU_raw.srt
@@ -0,0 +1,1648 @@
+1
+00:00:19,790 --> 00:00:25,130
+بسم الله الرحمن الرحيم محاضرة رقم 24 مساق نظرية
+
+2
+00:00:25,130 --> 00:00:30,050
+الاعداد طلاب الجامعة الإسلامية كلية العلوم وكلية
+
+3
+00:00:30,050 --> 00:00:38,520
+التربيةهنكمل اليوم حديثنا عن ال five functions و
+
+4
+00:00:38,520 --> 00:00:43,480
+هنروح باتجاه اثبات الارث فانكشن اللي هي عبارة عن
+
+5
+00:00:43,480 --> 00:00:49,040
+generalization ل Fermat's little theorem اذا
+
+6
+00:00:49,040 --> 00:00:53,840
+بتتذكروا ال Fermat's little theorem كانت تقول if
+
+7
+00:00:53,840 --> 00:01:04,200
+ال b لا تقسم ال a بدي يكون عندي a thenA to the B
+
+8
+00:01:04,200 --> 00:01:10,900
+minus واحد تطابق الواحد modulo B هذه اللي كانت مين
+
+9
+00:01:10,900 --> 00:01:15,800
+هي الـ Fermat's little theorem الآن بدنا نروح
+
+10
+00:01:15,800 --> 00:01:22,800
+باتجاه تعميم لهذا النظرية بدنا نروح باتجاه انه
+
+11
+00:01:22,800 --> 00:01:25,960
+نثبت انه لو كان لـ Greatest common divisor بين
+
+12
+00:01:25,960 --> 00:01:31,480
+الـA والـB او الـA والـN بسوء واحد then
+
+13
+00:01:32,840 --> 00:01:39,320
+الـ A to the Phi of N تطابق الواحد مُدُلُمين
+
+14
+00:01:39,320 --> 00:01:44,400
+مُدُلُن فبتصير اللي هي في الـ Maths little theorem
+
+15
+00:01:44,400 --> 00:01:48,440
+حالة خاصة منها ليش حالة خاصة منها لإن احنا المرة
+
+16
+00:01:48,440 --> 00:01:54,300
+الماضية قلنا أن Phi لـPrime إيش هتساوي P نقص واحدة
+
+17
+00:01:54,530 --> 00:02:00,110
+بناء عليه لو أثبتنا هذه بيصير عندي A طبعا مدان B
+
+18
+00:02:00,110 --> 00:02:05,650
+لا تقسم الـ A إذا العام المشترك الأعلى بين الـ A و
+
+19
+00:02:05,650 --> 00:02:11,690
+الـ B بساول واحد مظبوط ولا لا؟إذا الشروط هذه
+
+20
+00:02:11,690 --> 00:02:17,230
+منطبقة إذا بيصير عندي a to the five of b يطابق
+
+21
+00:02:17,230 --> 00:02:22,350
+الواحد modulo مين modulo b و ال five من مين هي b
+
+22
+00:02:22,350 --> 00:02:25,430
+minus واحد فبتصير اللي هي لو أثبتنا ال
+
+23
+00:02:25,430 --> 00:02:28,990
+generalization هذه اللي هي ال Euler's theorem
+
+24
+00:02:28,990 --> 00:02:32,710
+بتكون اللي هي فرمات حالة خاصة منها إذا نحن رايحين
+
+25
+00:02:32,710 --> 00:02:37,960
+بهذا الاتجاهعشان نثبت هذا بلزمنا اللي هو لمّة
+
+26
+00:02:37,960 --> 00:02:44,960
+نبرهنها قبل ما نيجي نثبت النظرية اذا سبعة تلاتة
+
+27
+00:02:44,960 --> 00:02:50,340
+بيحكيلي عن Euler's theorem ناخد اللي هو اللمّة قبل
+
+28
+00:02:50,340 --> 00:02:55,900
+ما نحكي عن Euler's theorem اللمّة بتقول ما يليه
+
+29
+00:02:55,900 --> 00:03:05,650
+اللمّة بتقول لو كان عندي n أكبر من واحدوكان عندى
+
+30
+00:03:05,650 --> 00:03:09,150
+اللى هو a زن انتجر بحيث ان الـ Greatest Common
+
+31
+00:03:09,150 --> 00:03:14,250
+Divisor بين الـ a والـ n بساوي واحد وكان عندى ايضا
+
+32
+00:03:14,250 --> 00:03:23,500
+اللى هو a واحد و a اتنين لعند ال a فاي of nلو كل
+
+33
+00:03:23,500 --> 00:03:31,180
+هذه كانت معطيات بحيث أن A1 وA2 وA5 of N تمثل كل
+
+34
+00:03:31,180 --> 00:03:36,780
+الأعداد الـ relatively prime مع الـ N وأصغر أو
+
+35
+00:03:36,780 --> 00:03:40,980
+تساومين الـ N الـ positive integers الأكبر ساوي
+
+36
+00:03:40,980 --> 00:03:46,360
+وأصغر ساومين الـ N يعني هذول الأن مفترض أن أنا كل
+
+37
+00:03:47,610 --> 00:03:53,150
+الأعداد الـ relative prime مع الـ N وأصغر أو يساوي
+
+38
+00:03:53,150 --> 00:03:58,570
+N وأكبر أو يساوي 1 ماشي الحال هذا المؤتمر ايش
+
+39
+00:03:58,570 --> 00:04:07,770
+النتيجة ذن ذن هذا لو جيت ضربة ال A في ال A1 وال A
+
+40
+00:04:07,770 --> 00:04:14,180
+في ال A2وضربت الـ A في الـ A5N الأعداد اللي بتطلع
+
+41
+00:04:14,180 --> 00:04:21,980
+هذه هتكون congruent للأعداد هذه in some order إيش
+
+42
+00:04:21,980 --> 00:04:27,540
+يعني؟ إن الـ A A1 هيكون بطابق واحد من هدول in some
+
+43
+00:04:27,540 --> 00:04:31,480
+order يعني مش شرط من طابق مين A1 ممكن طابق مين A2
+
+44
+00:04:31,480 --> 00:04:36,410
+A3 أي A من الموجودات عندنافبصير عندى اى واحد من
+
+45
+00:04:36,410 --> 00:04:40,370
+هذول مطابق واحد من اللى هى الاعداد اللى عندى يعنى
+
+46
+00:04:40,370 --> 00:04:48,810
+عسابى للمثال لو جيت اخدت ال a بتساوى التلاتة والان
+
+47
+00:04:48,810 --> 00:04:55,970
+بتساوى تمانية مثلا عسابى للمثال معايا الان العدل
+
+48
+00:04:55,970 --> 00:05:01,710
+المشترك الاعلى بين التلاتة والتمانية ايش بساوى احد
+
+49
+00:05:03,240 --> 00:05:07,120
+بدي أخد كل الأعداد اللي أصغر أو يساوي تمانية الـ
+
+50
+00:05:07,120 --> 00:05:09,720
+positive integers و relative librime مع التمانية
+
+51
+00:05:09,720 --> 00:05:12,880
+مين هي ال relative librime مع التمانية الواحد
+
+52
+00:05:12,880 --> 00:05:20,400
+الاتنين لأ التلاتة الأربعة لأ الخمسة الستة لأ
+
+53
+00:05:20,400 --> 00:05:25,240
+السبعة هذول الأعداد اللي relative librime مع اللي
+
+54
+00:05:25,240 --> 00:05:30,720
+هم التمانية أصغر أو يساوي من التمانية
+
+55
+00:05:32,720 --> 00:05:38,720
+الآن هذه شروط اللمّة بتقولّي إذا أنت لو إيجيد ضربة
+
+56
+00:05:38,720 --> 00:05:41,920
+اللي هي التلاتة هذا للعام المشترك الأعلى بين
+
+57
+00:05:41,920 --> 00:05:45,480
+التلاتة والتمن والسا وواحد الأعداد اللي هتطلع عندك
+
+58
+00:05:45,480 --> 00:05:50,380
+اللي هي التلاتة والتسعة والخمس عشر والواحد وعشرين
+
+59
+00:05:50,380 --> 00:05:56,720
+هذولة هيكون انقش مالهم relative prime هذولةأسف
+
+60
+00:05:56,720 --> 00:06:01,180
+congruent لحظوله in some order إيش يعني؟ يعني
+
+61
+00:06:01,180 --> 00:06:06,080
+هتلاقي التلاتة لازم يطابق واحد من هدول مدله مين؟
+
+62
+00:06:06,080 --> 00:06:10,340
+مدله تمانية واضح إن التلاتة بتابق مين التلاتة
+
+63
+00:06:10,340 --> 00:06:19,060
+خلصنا التسعة بتابق مين الواحد الخمسة عشر بتابق مين
+
+64
+00:06:19,060 --> 00:06:26,250
+السبعة الواحد وعشرين هيتابق مين الخمسةإذاً in
+
+65
+00:06:26,250 --> 00:06:31,310
+general هذا الكلام صحيح إنه لو كانت العامل المشترك
+
+66
+00:06:31,310 --> 00:06:35,010
+الأعلى بين ال A و ال N بساوي واحد و كانت ال A واحد
+
+67
+00:06:35,010 --> 00:06:39,010
+و ال A اتنين و ال A five N عبارة عن اللي هي
+
+68
+00:06:39,010 --> 00:06:43,230
+الأعداد ال relatively prime مع ال N و اللي أكبر أو
+
+69
+00:06:43,230 --> 00:06:48,010
+يساوي واحد و الأصغر أو ساوي اللي هي Nقطعاً هتطلع
+
+70
+00:06:48,010 --> 00:06:50,790
+عند الـ a في الـ a1 و الـ a في الـ a2 لعند الـ a
+
+71
+00:06:50,790 --> 00:06:55,850
+في الـ 5 of n هذه الأعداد كل واحد congruent لواحد
+
+72
+00:06:55,850 --> 00:07:02,610
+من هذوله in some order واضح نيجي الآن نبرهن
+
+73
+00:07:02,610 --> 00:07:08,090
+النظرية أو اللمة نيجي نشوف كيف بدنا نبرهن هذه
+
+74
+00:07:08,090 --> 00:07:14,450
+اللمةالـ A1 ليس
+
+75
+00:07:14,450 --> 00:07:21,130
+شرط الطابق مين لـ AA1 والـ A2 الطابق لـ AA2 يعني
+
+76
+00:07:21,130 --> 00:07:25,530
+ممكن الطابق لـ A1 الطابق هذه وهذه الطابق هذه وهذه
+
+77
+00:07:25,530 --> 00:07:29,650
+الطابق مثلًا واحدة يعني مش بنفس ال order اللي
+
+78
+00:07:29,650 --> 00:07:34,350
+مكتوب فيه لأ مش بنفس ال order اللي مكتبت فيه يعني
+
+79
+00:07:34,350 --> 00:07:38,560
+ممكن يكون زي ما شوفنا التلاتة كانتمع التلاتة مع
+
+80
+00:07:38,560 --> 00:07:42,020
+انه التلاتة في الحالة التانية الأولى وفي الحالة
+
+81
+00:07:42,020 --> 00:07:48,320
+الأولى التانية هكذا واضح اه
+
+82
+00:07:48,320 --> 00:07:53,460
+طيب صلوا على النبي عليه الصلاة والسلام نيجي
+
+83
+00:07:53,460 --> 00:07:59,800
+للبروهان البروف عشان
+
+84
+00:07:59,800 --> 00:08:07,590
+اثبت انه اللي هوالـ A A1 الـ A A2 اللي عند الـ A5N
+
+85
+00:08:07,590 --> 00:08:14,270
+are congruent modulo and to اللي هي A1 A2 A5N in
+
+86
+00:08:14,270 --> 00:08:19,050
+some order بدي اعمل شغل تاني اول حاجة بدي اثبتلك
+
+87
+00:08:19,050 --> 00:08:24,870
+ان هذولا ولا واحد منهم بطابق ثاني يعني بمعنى اخر
+
+88
+00:08:24,870 --> 00:08:30,600
+هذولا مختلفات modulo من modulo andعشان مايصير
+
+89
+00:08:30,600 --> 00:08:34,420
+اشتقار انه يصير في عندى اتنين من هنا بطابق واحد من
+
+90
+00:08:34,420 --> 00:08:39,020
+هنا فبصير اللي هو مش كل واحد بطابق واحد و بس لأنه
+
+91
+00:08:39,020 --> 00:08:42,240
+عدد هدولة five ان وعدد هدولة برضه ايه شماله five
+
+92
+00:08:42,240 --> 00:08:47,100
+ان اذا اول حاجة اعملها ان اثبتلك ان كل هدولة are
+
+93
+00:08:47,100 --> 00:08:50,960
+incongruent يعني ولا واحد بطابق الثاني مدل واحد
+
+94
+00:08:52,250 --> 00:08:56,650
+اتنين بده اثبتلك انه لو جيت اخدت اي واحد من هذوله
+
+95
+00:08:56,650 --> 00:09:01,950
+هجيله واحد من هنا بطابقه معناته خلصت انه سعر كل
+
+96
+00:09:01,950 --> 00:09:10,070
+واحد بطابق بس ايش واحد ده نشوف شوفوا اول حاجة بده
+
+97
+00:09:10,070 --> 00:09:14,220
+نثبت هذوله ان انا incongruent suppose notيعني
+
+98
+00:09:14,220 --> 00:09:18,240
+نفترض إن هدولة اللي هو فيه تمتين منهم على الأقل
+
+99
+00:09:18,240 --> 00:09:24,340
+أشمالهم congruent إذا suppose that suppose that
+
+100
+00:09:24,340 --> 00:09:33,540
+there exist a i a ai و a aj element in a a1 لعند
+
+101
+00:09:33,540 --> 00:09:45,760
+ال a a5n such that ال a aiيطابق الـ A AJ Modulo N
+
+102
+00:09:45,760 --> 00:09:50,580
+والـ I إيش ما لها مش هي الـ J ونصفها Contradiction
+
+103
+00:09:50,580 --> 00:09:58,540
+معايا؟ طيب الآن الكلام سهل ولسه مش سهل ليش؟ لإن
+
+104
+00:09:58,540 --> 00:10:02,800
+الـ A و الـ N إيش ما لهم Relative to Prime العامل
+
+105
+00:10:02,800 --> 00:10:05,680
+الشركي اللي عايز يبقى هنا مش مساوي مدام Relative
+
+106
+00:10:05,680 --> 00:10:09,800
+to Prime إذا اللي هو بقدر أجسمه على الجهتين فبصير
+
+107
+00:10:09,800 --> 00:10:20,590
+عندي الـ AIيطابق الـ A J modulo M modulo N إذا صار
+
+108
+00:10:20,590 --> 00:10:25,860
+فيه تنتين من هذول أشمالهممتطابقات وهذا مستحيل اللي
+
+109
+00:10:25,860 --> 00:10:31,040
+هيكون متساويات ليش؟ لإن هذولا أصلا من A1 A2 لعند
+
+110
+00:10:31,040 --> 00:10:37,360
+A5 N اللي إنها incongruent لبعض لإن يينا وينا وينا
+
+111
+00:10:37,360 --> 00:10:42,940
+وإن محصورات محصورات من اللي هو بين الواحد ودان مين
+
+112
+00:10:42,940 --> 00:10:48,460
+الان وrelative لبراين مع بعض فإن دعم اللي أشمل ال
+
+113
+00:10:48,460 --> 00:10:54,230
+complete residue system modulo Nمعايا إذا صارن إيش
+
+114
+00:10:54,230 --> 00:10:59,970
+مالهن كأي تنتين إيش مالين هيكونن غير متطابقات
+
+115
+00:10:59,970 --> 00:11:05,350
+واضحة هما أصلا باعتبار كمان نظرة أخرى هما أصلا
+
+116
+00:11:05,350 --> 00:11:13,930
+متبقيات من القسم على N ودائما اللي هو العددبكون
+
+117
+00:11:13,930 --> 00:11:23,170
+مطابق لمتبقى القسم إله مدن المقصوم عليه واللي اللي
+
+118
+00:11:23,170 --> 00:11:27,250
+هما الـRemembers المختلفات بكون إشمالًا M
+
+119
+00:11:27,250 --> 00:11:33,770
+congruent طيب، so عند الـA، I طاقة AJ مدن M وهذا
+
+120
+00:11:33,770 --> 00:11:38,670
+contradiction therefore اللي هو الـA في الـA واحد
+
+121
+00:11:38,670 --> 00:11:41,970
+والـA في الـA اتنين عند الـA في الـ5N إشمالًا R
+
+122
+00:11:42,560 --> 00:11:48,060
+incongruent لنثبت الأن إيش ماله إنه ناخد أي واحد
+
+123
+00:11:48,060 --> 00:11:55,340
+من هنا ونلاقيله واحد من هنا شوف let
+
+124
+00:11:55,340 --> 00:12:11,620
+a في ai بأني fixed element m a a1 لعند ال a a5
+
+125
+00:12:14,030 --> 00:12:21,310
+باشي ناخد ال a, a, i أي fixed element هان الان
+
+126
+00:12:21,310 --> 00:12:27,610
+بدك تلاحظ أولا شمالي ان ال greatest common divisor
+
+127
+00:12:27,610 --> 00:12:36,510
+بين ال a و ال n بسوء واحد صح ملطق
+
+128
+00:12:38,560 --> 00:12:42,120
+محاجة تانية الـ Greatest Common Divisor بين الـ AI
+
+129
+00:12:42,120 --> 00:12:47,920
+والـ N برضه إيش بساوي؟ ليش؟ لأنه إحنا ماخدين الـ
+
+130
+00:12:47,920 --> 00:12:52,020
+A1, A2, A5, N هي عبارة عن الأعداد اللي relatively
+
+131
+00:12:52,020 --> 00:12:59,200
+prime مع الـ N و أصغر أو ساوي N صحيح؟ إذن هدول مع
+
+132
+00:12:59,200 --> 00:13:05,150
+الملومات مقطاة من هنا التنتينعشان تستخدمها بعد
+
+133
+00:13:05,150 --> 00:13:08,790
+شوية لجدية تستخدم الـ Divisor بين الـ A في الـ AI
+
+134
+00:13:08,790 --> 00:13:13,650
+لما خدناها المرة الماضية والآن برضه ايش هيساويها؟
+
+135
+00:13:13,650 --> 00:13:21,510
+هيساويها، هتخليها في الذاكرة معايا؟ طيب الآن الـ
+
+136
+00:13:21,510 --> 00:13:27,710
+AAI عبارة عن انتجار بدي أجسمه على الـ N إذا By
+
+137
+00:13:27,710 --> 00:13:32,880
+Division Algorithm By Division Algorithmthere
+
+138
+00:13:32,880 --> 00:13:40,000
+exists a unique B element in Z such that B أكبر أو
+
+139
+00:13:40,000 --> 00:13:45,880
+يساوي واحد و أصغر من مين من N المتبقى هذا such
+
+140
+00:13:45,880 --> 00:13:55,240
+that اللي هو ال A AI هيساوي ال B أو ال N في Q
+
+141
+00:13:55,240 --> 00:14:01,540
+there exists unique B و Q كمان زائد مين زائد B
+
+142
+00:14:02,550 --> 00:14:09,730
+مظبوط او لا لان ايش اللي سويته قسمت ال a ai على
+
+143
+00:14:09,730 --> 00:14:14,490
+مين على n فالعندي unique remainder بيه ال unique
+
+144
+00:14:14,490 --> 00:14:20,770
+اللي هو ايش ال quotient اللي هو اسمه q معايا اذا
+
+145
+00:14:20,770 --> 00:14:28,530
+صار عندي ال an a ai يطابق مين ال bوهذه معناه
+
+146
+00:14:28,530 --> 00:14:31,570
+المثال اللي جابنا في الامتحان انه دائما اللي هو
+
+147
+00:14:31,570 --> 00:14:38,070
+العدد والمتبقي اللي هو متطابقين مودلو المقسوم عليه
+
+148
+00:14:38,070 --> 00:14:45,130
+لان افتكرك يا هلاها then صار عند الـA AI يطابق
+
+149
+00:14:45,130 --> 00:14:56,350
+الـB مدلو مين مدلو N واضح اه؟عندي يعني معنى آخر
+
+150
+00:14:56,350 --> 00:15:01,610
+الـ Greatest Common Divisor بين الـ A، AI و الـ N
+
+151
+00:15:01,610 --> 00:15:05,150
+هو نفسه الـ Greatest Common Divisor بين الـ B و M
+
+152
+00:15:05,150 --> 00:15:09,790
+و الـ N طيب، الـ Greatest Common Divisor بين الـ
+
+153
+00:15:09,790 --> 00:15:14,530
+AI و الـ N بساوي 1 إذا صار العام المشترك الأعلى
+
+154
+00:15:14,530 --> 00:15:19,550
+بين الـ B و الـ N، إيش بساوي؟ بساوي 1 إذا صار B
+
+155
+00:15:21,090 --> 00:15:25,370
+relative الـ prime مع الـ N ومحصور بين اللي هو
+
+156
+00:15:25,370 --> 00:15:31,790
+الواحد والـ N يعني من مين B جاي من A1 A2 لعند مين
+
+157
+00:15:31,790 --> 00:15:37,890
+A5 N يعني الـ B element من A1 لعند الـ A5 N يعني
+
+158
+00:15:37,890 --> 00:15:42,890
+أش اللي أثبتنا أنه أخدنا أي A AI fixed element هنا
+
+159
+00:15:42,890 --> 00:15:50,730
+ولقيناله أنه عنصر هنا يطارق مدله مين مدله Nإذا صار
+
+160
+00:15:50,730 --> 00:15:54,310
+عند المعلومتين مع بعض الأولى أن هذولا مختلفات
+
+161
+00:15:54,310 --> 00:15:59,010
+مودلؤا وأن كل واحد هنا في الواحد هنا صار أن هذولا
+
+162
+00:15:59,010 --> 00:16:08,070
+congruent لبعض in some order أي سؤال نجلأ
+
+163
+00:16:08,070 --> 00:16:10,110
+اللي هي نظرية Ehlers theorem
+
+164
+00:16:28,200 --> 00:16:36,080
+Euler's theorem if
+
+165
+00:16:36,080 --> 00:16:40,960
+الـ greatest common divisor بين الـ A والـ N بساوة
+
+166
+00:16:40,960 --> 00:16:50,240
+واحد then A to the five N تطابق الواحد مدلومين
+
+167
+00:16:50,240 --> 00:16:51,100
+مدلوين
+
+168
+00:17:04,180 --> 00:17:08,340
+شوفوا الصلاة على النبي عليه الصلاة والسلام الان
+
+169
+00:17:08,340 --> 00:17:11,660
+let
+
+170
+00:17:11,660 --> 00:17:25,860
+a1 و a2 لعند a5 and be the positive integers
+
+171
+00:17:25,860 --> 00:17:41,130
+less than and such thatA less than N which are
+
+172
+00:17:41,130 --> 00:17:53,330
+relatively prime with N ايش اللي عملته فرضت ان الـ
+
+173
+00:17:53,330 --> 00:17:57,970
+A1, A2, A5, N هذي أداء الوصول بتستخدم اللمبة ليش
+
+174
+00:17:57,970 --> 00:17:59,850
+كده ان انا اعملها اللمبة اصلا اللمبة المعنى بتبقى
+
+175
+00:17:59,850 --> 00:18:02,850
+في نظرية بتستخدم اللي هي استخدمها في برهان نظرية
+
+176
+00:18:02,850 --> 00:18:08,730
+لاحقةأخدت a1 و a2 و a5n عبارة عن positive integers
+
+177
+00:18:08,730 --> 00:18:12,270
+less than .. positive integers اللي less than or
+
+178
+00:18:12,270 --> 00:18:17,130
+equal أن و relatively prime مع مين؟ معايا .. معايا
+
+179
+00:18:17,130 --> 00:18:24,570
+.. اه من النظرية اللي قبل بشوية then by لما اللي
+
+180
+00:18:24,570 --> 00:18:30,470
+قبل بشوية بكون ال a في ال a1 و ال a في ال a2 عند
+
+181
+00:18:30,470 --> 00:18:41,460
+ال a في ال a5nare congruent to الـ A1 لعند الـ A5N
+
+182
+00:18:41,460 --> 00:18:48,760
+in some order مظبوط؟ إذا صار كل واحد منها
+
+183
+00:18:48,760 --> 00:18:55,020
+congruent لواحد منها وكل واحد بس بروح لوحد واضح؟
+
+184
+00:18:55,020 --> 00:19:02,360
+إذا أكيد حاصل جرب هذول congruent لحاصل جرب هذولإذا
+
+185
+00:19:02,360 --> 00:19:10,600
+صار عند ا then ال a1 a2 لعند ال a5 of n تطابق
+
+186
+00:19:10,600 --> 00:19:14,100
+قولوا
+
+187
+00:19:14,100 --> 00:19:25,840
+معايا a في a1 a في a2 لما أصل ل a في a5 of n مدلوا
+
+188
+00:19:25,840 --> 00:19:30,580
+n طيب
+
+189
+00:19:31,310 --> 00:19:38,170
+الان هذا بطابق بطابق الان ال a هذه مضروبة في a
+
+190
+00:19:38,170 --> 00:19:40,950
+واحد و في a اتنين و في a five of n يعني مكررة
+
+191
+00:19:40,950 --> 00:19:47,110
+ماجداش five of n من المرات يعني بدها تسير هذه عندى
+
+192
+00:19:47,110 --> 00:19:54,770
+عبارة عن a أصفاه of n في a واحد لما أصل عند a five
+
+193
+00:19:54,770 --> 00:20:03,000
+of n مضنونين مضرعينطيب نحن عاملة بنقول العامل
+
+194
+00:20:03,000 --> 00:20:09,600
+المشترك الأعلى بين الـ A1 و الـ N1 و الـ A2 و الـ
+
+195
+00:20:09,600 --> 00:20:14,680
+N1 و الـ A5N و الـ NA شمالها صار إذن العامل
+
+196
+00:20:14,680 --> 00:20:21,140
+المشترك الأعلى بين الـ A1 لعند الـ A5N كله مع بعض
+
+197
+00:20:21,140 --> 00:20:26,450
+مع الـ N أيش برضه بساوي؟إذا بصحّلي إيش أسوي أجسم
+
+198
+00:20:26,450 --> 00:20:31,990
+الجهتين على مين على هذا المقدار هانا بيضل Asian دي
+
+199
+00:20:31,990 --> 00:20:44,910
+واحد يطابق الـ A5N Modulo N وهو المطلوب أي
+
+200
+00:20:44,910 --> 00:20:47,930
+سؤال؟
+
+201
+00:20:47,930 --> 00:20:56,810
+الآن بتصير Formats حالة خاصة منهايعني بمعنى أخر
+
+202
+00:20:56,810 --> 00:21:03,570
+تصبح فرمات كورولا ري ل a large function اللي هي
+
+203
+00:21:03,570 --> 00:21:07,410
+بتقولك if b is a prime حكيتها قبل شوية and b لا
+
+204
+00:21:07,410 --> 00:21:10,350
+تقسم ال a إذا a to the b minus واحد تطابق الواحد
+
+205
+00:21:10,350 --> 00:21:17,560
+modulo bمدن بي برايم وبلا تقسم الـA إذا العامل
+
+206
+00:21:17,560 --> 00:21:21,360
+المشترك الأعلى بين الـB والـA بساوي واحد إذا الـA
+
+207
+00:21:21,360 --> 00:21:27,280
+لازم تنطبق إذا A to the Phi of B لطابق الواحد
+
+208
+00:21:27,280 --> 00:21:32,180
+مضلوا B لكن الـPhi of B إيش بيساوي إذا صار عندي A
+
+209
+00:21:32,180 --> 00:21:35,340
+to the B minus واحد لطابق الواحد مضلوا B وهو
+
+210
+00:21:35,340 --> 00:21:40,100
+المطلوب إذا صارت فرمات عذارة عن حالة خاصة من
+
+211
+00:21:40,100 --> 00:21:46,670
+Euler's theorem أو Corollaryلإيه الارض فيه نفجر
+
+212
+00:21:46,670 --> 00:21:54,550
+الآن نوظف فرمات لحل بعض الأسئلة أو المسائل
+
+213
+00:21:54,550 --> 00:22:00,170
+الحسابية بقول
+
+214
+00:22:00,170 --> 00:22:08,450
+لي example example find
+
+215
+00:22:08,450 --> 00:22:24,240
+the lastTwo digits of مثلا تلاتة to the اتنين اربع
+
+216
+00:22:24,240 --> 00:22:36,900
+ستة اتنين اللي هو خمسة ستة بكفي يعني بيقولي او جد
+
+217
+00:22:36,900 --> 00:22:45,940
+اللي هو اخر الرقمينأخر رقمين لـ الرقم اللي عندي
+
+218
+00:22:45,940 --> 00:22:52,380
+نشوف أيش قصة أخر رقمين الآن لو جينا أخدنا اتنين
+
+219
+00:22:52,380 --> 00:22:56,760
+تلاتة أربعة خمسة واحد مثلا على سبيل المثال هذا
+
+220
+00:22:56,760 --> 00:23:01,720
+الرقم أخره مين أخر رقمين أشمالا واحد خمسة يعني و
+
+221
+00:23:01,720 --> 00:23:04,720
+كأن الرقم هذا أو خمسة واحد هذا الرقم عبارة عن إيش
+
+222
+00:23:04,720 --> 00:23:16,710
+اتنين تلاتة أربعة درب ميةصح؟ زي دياش 51 يعني هذا
+
+223
+00:23:16,710 --> 00:23:26,410
+الرقم نفسه 51 مدن و إياش 100 لأن هدولة بالنسبالي
+
+224
+00:23:26,410 --> 00:23:33,210
+المية أشمالها أسفار وكأنه وكأنه صار أنه عشان أوجد
+
+225
+00:23:33,210 --> 00:23:37,630
+ال last two digits السؤال بيصير اللي هو بطريقة
+
+226
+00:23:37,630 --> 00:23:44,680
+أخرىأو Deadly اللي هو المتبقي لهذا الرقم حين القسم
+
+227
+00:23:44,680 --> 00:23:50,860
+عالميا عالميا أو بمعنى أخر ماذا يطابق هذا الرقم
+
+228
+00:23:50,860 --> 00:23:59,450
+مدنومية من الأعداد من واحد لتسعة وتسعينواضح؟ إذا
+
+229
+00:23:59,450 --> 00:24:02,770
+وكأنه صار لما يقولّك find the last two digits of
+
+230
+00:24:02,770 --> 00:24:09,690
+تلاتة أُس أُس كده بدي أوجب اللي هو هذا العدد يطابق
+
+231
+00:24:09,690 --> 00:24:16,470
+ماذا مدنومية الماذا تعود على إيش تعود على عدد من
+
+232
+00:24:16,470 --> 00:24:22,730
+واحد لمي أو المتبقى القسمة علامية واضح؟ إذا صارت
+
+233
+00:24:22,730 --> 00:24:29,270
+الأمور هيكواضحة وصار فيه إمكانية إنه نروح باتجاه
+
+234
+00:24:29,270 --> 00:24:34,810
+استغلال ما عرفتنا بـ Euler's theorem للوصول للحل
+
+235
+00:24:34,810 --> 00:24:42,810
+عندي أول حاجة اللي بدنا نياله بقيا سنين مية والعدد
+
+236
+00:24:42,810 --> 00:24:46,530
+اللي مرفوض للأسنين ثلاثة وواضح إن الـ greatest
+
+237
+00:24:46,530 --> 00:24:51,830
+common divisor بين الثلاثة والمية بساوي عاش واحد
+
+238
+00:24:51,830 --> 00:25:00,730
+sincethen أكيد التلاتة to the file of مية بطابق
+
+239
+00:25:00,730 --> 00:25:06,410
+الواحد مدل مجدياش مية ليش أخدنا الاليستيورم لأنها
+
+240
+00:25:06,410 --> 00:25:11,490
+أصلا بتجيب للعدد بطابق مين الواحد والواحد سيل في
+
+241
+00:25:11,490 --> 00:25:15,290
+الحسابات بتظل الباقي سهلات يعني بختار .. خلّيني
+
+242
+00:25:15,290 --> 00:25:20,980
+أقول باختصر الحسابات بشكل كبير جداطيب الـ 1500
+
+243
+00:25:20,980 --> 00:25:27,840
+نحسمها إيش هتساوي اللي هو عبارة عن 25 في 4 يعني
+
+244
+00:25:27,840 --> 00:25:34,760
+فيها 5 و فيها 2 إذا يعني 100 في 1 ماقص 5 في 1 ماقص
+
+245
+00:25:34,760 --> 00:25:44,500
+نص عارفين هالنظرية اللي هي بتطلع بتساوي 40 معايا؟
+
+246
+00:25:44,940 --> 00:25:50,160
+الآن ضال أطلّع للعدد هذا بشيل منه كل الأربعينات
+
+247
+00:25:50,160 --> 00:25:56,340
+أبوشوف إيش فيه أربعينات معايا حد يجسملي أنه هو
+
+248
+00:25:56,340 --> 00:26:03,600
+أشوف الآن اتنين أربعة ستة اتنين أربعة سفر اجسملي
+
+249
+00:26:03,600 --> 00:26:07,440
+على أربعين سيبك من الست عشر اللي بتضل شوف كده إيش
+
+250
+00:26:07,440 --> 00:26:08,340
+على الأقل على الأقل
+
+251
+00:26:18,770 --> 00:26:25,610
+Okay اللي هو .. انتبهت عليا هان؟ هو بده إيش ماله؟
+
+252
+00:26:25,610 --> 00:26:29,950
+آخر .. آخر .. آخر .. آخر .. اللي هو .. بده the
+
+253
+00:26:29,950 --> 00:26:34,530
+last two digits ماشي الحال؟ الآن يعني بده الواحد
+
+254
+00:26:34,530 --> 00:26:39,070
+وخمسين هان يعني وكأنه هذا العدد صار اللي هو مضروف
+
+255
+00:26:39,070 --> 00:26:44,920
+بيه زائد واحد وخمسينالـ 100 يجمعنا الـ 100 عساس ان
+
+256
+00:26:44,920 --> 00:26:49,320
+هذا يصبح من الـ 100 صفر وهو اللي يبقى الباق الـ
+
+257
+00:26:49,320 --> 00:26:54,680
+100 مياني خانتين هذين 6 1 5 6 6 ألف و 100 و 6 ألف
+
+258
+00:26:54,680 --> 00:27:02,770
+لو تلت خانات ألف ألف صحيح 5 1 5 6 هذا كم يطلع 6ستة
+
+259
+00:27:02,770 --> 00:27:07,690
+واحد خمسة ستة طيب انتبهوا الان بيصير عندي تلاتة
+
+260
+00:27:07,690 --> 00:27:11,510
+اقصى اتنين اربع عشان مانضيعش الفكرة الاساسية ستة
+
+261
+00:27:11,510 --> 00:27:19,210
+اتنين خمسة ستة ايش ماله بيساوي اللي هو اللي هو
+
+262
+00:27:19,210 --> 00:27:27,950
+تلاتة اقصى اربعين اقصى ستة واحد خمسة ستة فاهمين اه
+
+263
+00:27:27,950 --> 00:27:34,320
+في تلاتة اقصى ستة عشرأيش اللي عملته يا جماعة هذا
+
+264
+00:27:34,320 --> 00:27:39,560
+العدد هذا العدد لو شيلته و كتبته بدلالة الأربعين
+
+265
+00:27:39,560 --> 00:27:50,660
+والمتبقى 16 معايا؟ مظبوط هيك الرقم؟ 61560 على 4
+
+266
+00:27:50,660 --> 00:27:54,960
+ولا على 40؟ على 40 مطلحت، مظبوط، مظبوط، مطلع على
+
+267
+00:27:54,960 --> 00:27:58,420
+40 هيك خليني أكمل، مطلع على 40 هيك، ماشي الحال؟
+
+268
+00:28:00,120 --> 00:28:04,560
+عشان ما اطلعشي الفكرة هذا العدد بيساوي تلاتة اقصى
+
+269
+00:28:04,560 --> 00:28:08,040
+اربعين في هذا في هذا ايش مهم تلاتة اقصى اربعين
+
+270
+00:28:08,040 --> 00:28:12,220
+لإنه انا عارف تلاتة اقصى اربعين ايش مالها هذه five
+
+271
+00:28:12,220 --> 00:28:17,420
+of .. five of one hundred اربعين يعني هذه اعطتني
+
+272
+00:28:17,420 --> 00:28:24,560
+تلاتة اقصى اربعين تطابق الواحد مضنوا مين؟ ميةبصير
+
+273
+00:28:24,560 --> 00:28:29,120
+عندي الآن هذا العدد بطابق هذا أو سوى وهذا بطابق
+
+274
+00:28:29,120 --> 00:28:36,360
+واحد أس ستة واحد خمس ستة في تلاتة أس ستاش مدلوا
+
+275
+00:28:36,360 --> 00:28:37,540
+مية
+
+276
+00:28:43,640 --> 00:28:48,600
+الان بيصير عندى 3 اقص 16 اللى هى سهلة الحساب تلاتة
+
+277
+00:28:48,600 --> 00:28:50,900
+فتلاتة ساعة تسعة و تسعة واحد و تمانين اللى هى
+
+278
+00:28:50,900 --> 00:28:55,140
+عبارة عن واحد و تمانين اقص اش اقص اربعة الواحد و
+
+279
+00:28:55,140 --> 00:28:57,760
+تمانين اقص اربعة بتطلح على الاقل على طول بسرعة او
+
+280
+00:28:57,760 --> 00:29:02,800
+بتزغر اللى ناقص تسعة عشر اقص اربعة اللى بدك تطلع
+
+281
+00:29:02,800 --> 00:29:06,720
+في الاخر اخر رقمين تطابق واحد و عشرين مدلومين
+
+282
+00:29:06,720 --> 00:29:12,710
+مدلوميةبصير عندي الآن the last two digits of هذا
+
+283
+00:29:12,710 --> 00:29:22,230
+الرقم اللي هو عبارة عن قداشة واحد وعشرين، أي سؤال؟
+
+284
+00:29:22,230 --> 00:29:35,010
+إجينا
+
+285
+00:29:35,010 --> 00:29:39,650
+هذا الآن، إيش سوينا؟شيلنا منه الاربعينات بمعنى اخر
+
+286
+00:29:39,650 --> 00:29:43,230
+جسمناها على اربعين وشوفنا ايش متبقى القسمة الان
+
+287
+00:29:43,230 --> 00:29:47,190
+المتبقى من القسمة على اربعين ايش طال ستة عشر فاطلع
+
+288
+00:29:47,190 --> 00:29:51,990
+هذا الرقم عبارة عن هذا الرقم اللي عندي تلاتة اربعة
+
+289
+00:29:51,990 --> 00:29:58,970
+ستة اتنين خمسة ستة بساول ستة واحد خمسة ستة مضروب
+
+290
+00:29:58,970 --> 00:30:05,800
+في اربعين زاد ايش زاد ستة عشر واضحفالآن تلاتة أس
+
+291
+00:30:05,800 --> 00:30:09,140
+هذا المقدار بيساوي تلاتة أس هذا المقدار يعني بمعنى
+
+292
+00:30:09,140 --> 00:30:15,120
+أخر تلاتة في تلاتة أس اتتاش هذا كله واحد لأن تلاتة
+
+293
+00:30:15,120 --> 00:30:19,260
+أس اربعين تطابق الواحد ب firm ال الارس و بيظل
+
+294
+00:30:19,260 --> 00:30:22,540
+تلاتة أس اتتاش اللي هي طابقة قداش الواحد وعشرين
+
+295
+00:30:22,540 --> 00:30:30,240
+بالحسابات اليدوية أو الألة نجي للي بعدها تطبيق آخر
+
+296
+00:30:38,380 --> 00:30:50,040
+Example آخر Example آخر خلوكم
+
+297
+00:30:50,040 --> 00:30:57,380
+معايا وخلّينا نركز على أساس اللي هو تتضح الفكرة
+
+298
+00:30:57,380 --> 00:31:01,040
+عندي
+
+299
+00:31:04,310 --> 00:31:16,170
+let n be an odd integer اذا ن is odd واحد ن is odd
+
+300
+00:31:16,170 --> 00:31:23,850
+اتنين الان فيش فيه خمسات الخمسة لتقسم مين الان
+
+301
+00:31:23,850 --> 00:31:29,310
+الخمسة لتقسم الان معايا
+
+302
+00:31:32,550 --> 00:31:43,870
+هذا مع بعض بقول لك انه لازم الان تقسم عدد خاناته
+
+303
+00:31:43,870 --> 00:31:47,830
+كلها مكوّنة من واحد واحد واحد واحد يعني كل خاناته
+
+304
+00:31:47,830 --> 00:31:54,610
+واحد يعني بمعنى اخر واحد واحد some واحد عدد خمس
+
+305
+00:31:54,610 --> 00:31:57,670
+مرات ست مرات سبع مرات تمام مرات اشهر مرات حسب
+
+306
+00:31:57,670 --> 00:32:04,740
+العدد M واضحإذا الأعداد ال odd integers اللي مش
+
+307
+00:32:04,740 --> 00:32:11,900
+فيها خمسة في الآخر هتلاقي ال M بيجسم 2 هو عامل من
+
+308
+00:32:11,900 --> 00:32:18,820
+عوامل اللي هو عدد اللي هو خاناته عبارة عن الواحد
+
+309
+00:32:18,820 --> 00:32:28,060
+واحد واحد واحد واضح الانشوف ايش الفكرة في الحل
+
+310
+00:32:28,060 --> 00:32:32,740
+طبعا احنا قاعدين بنتعلم اللي هو خلّينا نقول
+
+311
+00:32:32,740 --> 00:32:38,820
+باتجاهات مختلفة أفكار مختلفة لتطبيق ال الارث في رم
+
+312
+00:32:38,820 --> 00:32:44,260
+عليها توظيفها في حلها نشوف كيف اللي هو ايش اللي
+
+313
+00:32:44,260 --> 00:32:50,080
+بيقولوها solution اصبر
+
+314
+00:32:50,080 --> 00:32:56,520
+عليّ وخلّيك تفهم الفكرة الانلو أجيت أخدت العامل
+
+315
+00:32:56,520 --> 00:33:00,680
+المشترك الأعلى الخمسة
+
+316
+00:33:00,680 --> 00:33:05,600
+مش فيها N مش موجودة .. مش .. الـ N مش فيها خمسات
+
+317
+00:33:05,600 --> 00:33:09,800
+يعني بمعنى أخر العامل المشترك الأعلى بين الخمسة و
+
+318
+00:33:09,800 --> 00:33:16,820
+الـ N واحد و الـ N قُبط إذا مش فيها اتنينات يعني
+
+319
+00:33:16,820 --> 00:33:22,280
+بمعنى أخر العامل المشترك الأعلى بين الخمسةوالان
+
+320
+00:33:22,280 --> 00:33:28,360
+واحد والتمين والان واحد يعني العشرة والان ايش
+
+321
+00:33:28,360 --> 00:33:35,340
+مالها بساو واحد معايا العامل المشترك الاعلى بين
+
+322
+00:33:35,340 --> 00:33:38,720
+الان والعشرة ايش بيساوي يعني الان مش فيها عشرة
+
+323
+00:33:38,720 --> 00:33:43,980
+تلجت تعرفي ليش العشرة العامل العامل المشترك الاعلى
+
+324
+00:33:45,470 --> 00:33:51,230
+بين العشرة والتسعة برضه إيش بيساوي؟ واحد إيش معنى
+
+325
+00:33:51,230 --> 00:33:55,710
+التسعة؟ هل جيت بتعرف ليش؟ لأنه أنا بدأت بالعدد في
+
+326
+00:33:55,710 --> 00:34:00,550
+الآخر عشر عقص إشي ماقص واحد، يعني تسعات، والتسعة
+
+327
+00:34:00,550 --> 00:34:04,430
+هذه هتلزمني إن أنا أحطها تحت، فبيصير كل نقاش
+
+328
+00:34:04,430 --> 00:34:09,960
+وحدات، ده نشوف كدهالعامل المشترك الأعلى بين العشرة
+
+329
+00:34:09,960 --> 00:34:14,220
+والان واحد والعشرة والتسعة ايش بيساوي واحد اذا
+
+330
+00:34:14,220 --> 00:34:21,940
+اكيد العامل المشترك الأعلى بين العشرة والتسعة ان
+
+331
+00:34:21,940 --> 00:34:30,620
+ايش بيساوي بيساوي واحد طيب اذا صارت فرمات جاهزة
+
+332
+00:34:30,620 --> 00:34:41,410
+اذا بيصير عندي اللي هوعشرة أو خمسة N، مظبوط؟ عشرة
+
+333
+00:34:41,410 --> 00:34:46,450
+تسعة N بيساوي واحد العشرة بيتمثل للـA والتسعة N
+
+334
+00:34:46,450 --> 00:34:50,510
+بيتمثل للـN الجديدة فبيصير الـA to the five of N
+
+335
+00:34:50,510 --> 00:34:57,390
+يعني عشرة to the five of تسعة N تطابق الواحد
+
+336
+00:34:57,390 --> 00:35:03,870
+مضلونية مضلو تسعة N وانا بدي التسعة N كمان الجد
+
+337
+00:35:03,870 --> 00:35:07,920
+تعرف ليش بدي تسعة Nالأن إيش معناته هذا الكلام؟
+
+338
+00:35:07,920 --> 00:35:12,980
+معناته إن تسعة N تجسيم عشرة وده كده ماقص واحد أو
+
+339
+00:35:12,980 --> 00:35:20,240
+بمعنى آخر صار عندي الآن عشرة أصفاي of تسعة N ماقص
+
+340
+00:35:20,240 --> 00:35:28,060
+واحد بساوي تسعة N K for some K element in Z
+
+341
+00:35:31,360 --> 00:35:36,640
+الـ 9N هذا إيش معناته؟ إن الـ 9N بتجسم العشرة The
+
+342
+00:35:36,640 --> 00:35:43,260
+five of 9N ناقص واحد، أه؟ مظبوط؟ إذا صار هذا بساوي
+
+343
+00:35:43,260 --> 00:35:49,240
+هذا فصم number كيه؟ معايا؟ واضح، أه؟ الآن هذا
+
+344
+00:35:49,240 --> 00:35:53,640
+العدد أنا بدي الـ N في الآخر تجسم مين؟ عدد في كل
+
+345
+00:35:53,640 --> 00:36:01,340
+واحدات الآن هذا العدد اللي بتطلعلي فرمات، تسعاتمش
+
+346
+00:36:01,340 --> 00:36:06,740
+تسعات لهم عشرة قص كده وشيل منه واحد بيبقى لها
+
+347
+00:36:06,740 --> 00:36:11,120
+تسعات اذا عشان احصل على اللي بديه يابن زمي كان
+
+348
+00:36:11,120 --> 00:36:17,800
+تسعة في الطريق وطلقت فعلا اصلا الان بيصير على تسعة
+
+349
+00:36:17,800 --> 00:36:26,530
+بساوي one في K يعني طلع هذا العدد كله واحداتو
+
+350
+00:36:26,530 --> 00:36:33,210
+بيساوي N في K يعني بمعنى أخر من المضاعفات من الـ N
+
+351
+00:36:33,210 --> 00:36:42,130
+يعني صار عندك الـ N بيجسم الواحد واحد لأ
+
+352
+00:36:42,130 --> 00:36:45,570
+ماعرفش أشوفه فيه لكل رقم فيه لعداده هل جيت مني أخد
+
+353
+00:36:45,570 --> 00:36:53,550
+رقم؟ هل جيت مني أخد رقم؟ خليني أنا أخد أنثى لهم خد
+
+354
+00:36:53,550 --> 00:36:53,970
+الـ N
+
+355
+00:37:01,000 --> 00:37:07,400
+خُد الـ N بتساوي سبعة الـ N بتساوي سبعة بنتبق
+
+356
+00:37:07,400 --> 00:37:11,020
+عليها ليش بنتبق عليها لأنه سبعة قُد وفيش فيها مين
+
+357
+00:37:11,020 --> 00:37:18,600
+خمسات ماشي الحل إذا حيكون عندي اللي هو العشرة عشرة
+
+358
+00:37:18,600 --> 00:37:26,540
+أُس five of ستة تلاتة ناقص واحد على تسعة بساوي
+
+359
+00:37:26,540 --> 00:37:30,440
+سبعة في K مظبوط ولا لأ؟
+
+360
+00:37:34,030 --> 00:37:37,210
+معناه اللي ايه؟ الـ five of تلاتة و ستين من اين
+
+361
+00:37:37,210 --> 00:37:41,250
+وجدها؟ five of تلاتة و ستين ايش five of تلاتة و
+
+362
+00:37:41,250 --> 00:37:45,990
+ستين؟ بسعر تلاتة و ستين فيها اللي هي تلاتة و تسعة
+
+363
+00:37:45,990 --> 00:37:51,510
+بس تلاتة و سبعة بس اللي هي واحد ماقص تلت في واحد
+
+364
+00:37:51,510 --> 00:37:57,970
+ماقص سبعة، مظبوط اللي بعمله؟ واضح، واساوي، نحسبها
+
+365
+00:37:57,970 --> 00:38:01,330
+تلاتة و ستين في تلتين
+
+366
+00:38:02,870 --> 00:38:09,750
+في ستة على مين؟ على سبعة حيث الآن السبعة بتروح ..
+
+367
+00:38:09,750 --> 00:38:14,470
+او الآن السبعة اللي بيبقى عنده سبعة بيبقى إيه
+
+368
+00:38:14,470 --> 00:38:20,810
+اشماله؟ تسعة وانا واحد بيبقى قداش؟ اتناشر في تلاتة
+
+369
+00:38:20,810 --> 00:38:27,030
+صح ولا لأ؟ ستة و تلاتين بيصير
+
+370
+00:38:27,030 --> 00:38:34,300
+عشرةالـ 36 ماقص واحد على مين على تسعة بيساوي جداش
+
+371
+00:38:34,300 --> 00:38:39,740
+سبعة كيه الآن
+
+372
+00:38:39,740 --> 00:38:44,560
+بدنا نحسب عشرة عقل ستة وتلاتين او
+
+373
+00:38:44,560 --> 00:38:49,540
+شيل من هنا اه ستة وتلاتين سفر شيل من هنا جداش واحد
+
+374
+00:38:49,540 --> 00:38:55,440
+بيبقى هنا جداش بيبقى التسعات بيبقى الخمس وتلاتين
+
+375
+00:38:55,440 --> 00:39:04,010
+احدة او واحدبس ممكن تلاقي some of the properties
+
+376
+00:39:04,010 --> 00:39:10,890
+of the phi function ده ناخد بعض الخواص لمين للـ
+
+377
+00:39:10,890 --> 00:39:15,010
+phi functions شوفوا صلوا على النبي عليه الصلاة
+
+378
+00:39:15,010 --> 00:39:21,690
+والسلام في عيننا اللي هي نظرية الأولى Joules
+
+379
+00:39:21,690 --> 00:39:22,930
+theorem
+
+380
+00:39:43,750 --> 00:39:49,630
+النظرية الأولى جاوس تيريم بتقول for each positive
+
+381
+00:39:49,630 --> 00:39:53,930
+integer n أكبر الساعة واحدالـ N بتساوي الـ
+
+382
+00:39:53,930 --> 00:39:59,150
+summation للـ Phi of D دي بتقسم N يعني لو جيت حسبت
+
+383
+00:39:59,150 --> 00:40:04,670
+أنت خد أي N أكبر أو سوى واحد هتساوي الـ summation
+
+384
+00:40:04,670 --> 00:40:14,350
+للـ Phi of D دي بتقسم N مجموعة ال divisors لل N دي
+
+385
+00:40:14,350 --> 00:40:23,070
+بتقسم N هيساوياللي هو مين؟ بساول n اه summation لل
+
+386
+00:40:23,070 --> 00:40:27,270
+five of d دي بتجسم n بساول n احنا هناخد التفاصيل
+
+387
+00:40:27,270 --> 00:40:31,230
+المرة الجاية بس خلينا ناخد نقام في العدد دي بس
+
+388
+00:40:31,230 --> 00:40:37,620
+اللي هي لو أخدنا n بتساوي واحدان بتساوي واحد خد ان
+
+389
+00:40:37,620 --> 00:40:42,120
+بتساوي واحد وحسب ليه ال summation لل five دي دي
+
+390
+00:40:42,120 --> 00:40:46,180
+بتجسم من الواحد واضح انه مافيش غير مين اللي هو
+
+391
+00:40:46,180 --> 00:40:52,780
+five واحد ويساوي إياش واحد إياش
+
+392
+00:40:52,780 --> 00:41:01,370
+بتساوي ان بتساوي انالأن أن بتساوى 2 خُد summation
+
+393
+00:41:01,370 --> 00:41:09,190
+فاي of دي دي بتقسم 2 ويساوي فاي of واحد زائد فاي
+
+394
+00:41:09,190 --> 00:41:14,650
+of اتنين صح ولا للميديو ديفانزور للتنين الواحد
+
+395
+00:41:14,650 --> 00:41:19,130
+والتنين ويساوي واحد زائد واحد ويساوي اتنين ويساوي
+
+396
+00:41:19,130 --> 00:41:23,350
+أن الآن صمي خد أن بتساوي سبعة مثلا
+
+397
+00:41:27,150 --> 00:41:32,290
+أو خلّيني أخد قبل ما هو عدد مش برايم ستة اللي عندى
+
+398
+00:41:32,290 --> 00:41:38,350
+summation فايف دي دي بتجسب الستة هو يساوي فايف
+
+399
+00:41:38,350 --> 00:41:47,630
+واحد زاد فايف اتنين زاد فايف تلاتة زاد فايف ستة
+
+400
+00:41:48,500 --> 00:41:53,480
+مظبوط مايساوي five واحد واحد five اتنين واحد five
+
+401
+00:41:53,480 --> 00:42:00,280
+تلاتة اتنين five ستة اللي هو قداش اتنين مظبوط
+
+402
+00:42:00,280 --> 00:42:04,480
+مايساوي
+
+403
+00:42:04,480 --> 00:42:08,140
+نيجي
+
+404
+00:42:08,140 --> 00:42:17,410
+ناخد اتنين اللي هو nبتساوي سبعة summation في of دي
+
+405
+00:42:17,410 --> 00:42:23,690
+دي بتقسم سبعة ويساوي في of واحد زاد في of سبعة في
+
+406
+00:42:23,690 --> 00:42:30,890
+غيرهم أكيد لأ long of prime أه صحيح ويساويواحد كده
+
+407
+00:42:30,890 --> 00:42:37,150
+ايش؟ واحدة ستة ويساوي سبعة الانفاصة ماشية في of دي
+
+408
+00:42:37,150 --> 00:42:42,850
+دي بتكسب ال prime اكيد سهلة ايش بتساوي اللي هو في
+
+409
+00:42:42,850 --> 00:42:47,450
+of واحد زيدي في of ال بي نفسها ويساوي عبارة عن
+
+410
+00:42:47,450 --> 00:42:53,650
+واحد زيدي بي ماينس واحد ويساوي اللي هو ايش بي فاضح
+
+411
+00:42:53,650 --> 00:42:53,970
+اه
+
+412
+00:42:56,880 --> 00:43:00,340
+المرة الجاية ان شاء الله بنحكي في التفاصيل
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/iOr4UuxtU-4.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/iOr4UuxtU-4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c94f315e1829fadf5ac405e8d405bef27f9f4e6e
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/iOr4UuxtU-4.srt
@@ -0,0 +1,1707 @@
+1
+00:00:19,440 --> 00:00:25,280
+بسم الله الرحمن الرحيم المحاضرة التاسعة في مساق
+
+2
+00:00:25,280 --> 00:00:29,760
+نظرية الأعداد لطلبة قسم رياضيات بالجامعة الإسلامية
+
+3
+00:00:29,760 --> 00:00:37,120
+كليتي العلوم والتربية هنكمل الحديث حول خواص
+
+4
+00:00:37,120 --> 00:00:41,420
+الأعداد الأولية أو some properties of primes
+
+5
+00:00:41,420 --> 00:00:44,960
+والجزء الثاني من المحاضرة هيكون اللي هو the theory
+
+6
+00:00:44,960 --> 00:00:50,680
+of congruences أو نظرية التطابقات. نكمل اللي اتحدثنا
+
+7
+00:00:50,680 --> 00:00:55,160
+فيه المرة الماضية اللي هي بعض خواص الأعداد الأولية
+
+8
+00:00:55,160 --> 00:01:00,120
+الخاصية الأولى اللي هناخدها اللمّة اللي هناخدها اللمّة بتقول ما
+
+9
+00:01:00,120 --> 00:01:05,220
+يليه The product of two or more integers of the
+
+10
+00:01:05,220 --> 00:01:09,760
+form أربعة M زائد واحد is of the same form. يعني الآن
+
+11
+00:01:09,760 --> 00:01:15,560
+لو كان في عندي اللي هو عددين على صورة أربعة M زائد 
+
+12
+00:01:15,560 --> 00:01:20,720
+واحد. نفترض أربعة K زائد واحد. يعني عددين على نفس
+
+13
+00:01:20,720 --> 00:01:24,790
+الصورة اللي هي أربعة M زائد واحد. اللي هو حيكون حاصل
+
+14
+00:01:24,790 --> 00:01:28,130
+ضربهم هنا برضه على صورة أربعة M زائد واحد أو أربعة
+
+15
+00:01:28,130 --> 00:01:32,590
+M زائد واحد أو أربعة K زائد واحد for some K element in
+
+16
+00:01:32,590 --> 00:01:40,690
+Z. الآن بدنا نبرهنها. برهان بسيط proof الآن let اللي
+
+17
+00:01:40,690 --> 00:01:44,070
+هو العدد الأول أربعة M زائد واحد. والعدد الثاني أربعة
+
+18
+00:01:44,070 --> 00:01:48,410
+K زائد واحد. وضربناهم في بعض أربعة M زائد واحد في
+
+19
+00:01:48,410 --> 00:01:53,990
+أربعة K زائد واحد. الإدعاء أنه هيكون على صورة أربعة Q
+
+20
+00:01:53,990 --> 00:01:58,830
+زائد واحد. يعني بمعنى آخر، العدد المتبقي لما نقسمه 
+
+21
+00:01:58,830 --> 00:02:03,800
+على أربعة ويتبقى واحد. نضربه في عدد ثاني برضه اللي
+
+22
+00:02:03,800 --> 00:02:07,620
+هو لما نقسمه على أربعة ومتبقي واحد هيطلع حاصل
+
+23
+00:02:07,620 --> 00:02:11,540
+الضرب هو عبارة عن عدد لما نقسمه على أربعة ومتبقي
+
+24
+00:02:11,540 --> 00:02:20,680
+واحد. ويساوي اللي هو أربعة في 16 KM زائد أربعة M
+
+25
+00:02:20,680 --> 00:02:26,860
+زائد أربعة K زائد واحد. مظبوط؟ هدول كلها فيها
+
+26
+00:02:26,860 --> 00:02:31,540
+أربعات. خد الأربعة المشترك تصير أربعة في أربعة KM
+
+27
+00:02:32,190 --> 00:02:38,310
+زائد M زائد K الكل زائد إيش؟ واحد. هذا كله  ضمن 
+
+28
+00:02:38,310 --> 00:02:45,110
+تجاويف AQ في Z. ويساويها على صورة 4Q زائد 1. إذا 
+
+29
+00:02:45,110 --> 00:02:50,290
+حاصل ضرب أي عددين على صورة 4M زائد 1 بيطلع برضه على
+
+30
+00:02:50,290 --> 00:02:54,870
+صورة 4Q زائد 1. ولو ضربناهم في كمان عدد على نفس
+
+31
+00:02:54,870 --> 00:02:59,450
+الصورة هيطلع نفس الشيء. إذا حاصل ضرب any finite
+
+32
+00:02:59,450 --> 00:03:06,090
+number of integers of the form 4k زائد 1 is of the
+
+33
+00:03:06,090 --> 00:03:11,610
+same form أي is of the form 4k أو 4q زائد 1 for
+
+34
+00:03:11,610 --> 00:03:15,730
+some q element in z. هذا اللي ما بدنا نوظفها و
+
+35
+00:03:15,730 --> 00:03:20,710
+نستخدمها في إثبات النظرية 3.6 اللي هي النظرية اللي
+
+36
+00:03:20,710 --> 00:03:25,350
+بتقول لي there is an infinite number of primes of
+
+37
+00:03:25,350 --> 00:03:31,240
+the form 4n زائد 3. إذا هذه النظرية بتقول لي أنه عدد
+
+38
+00:03:31,240 --> 00:03:34,680
+الأعداد اللي على صورة الأولية اللي على صورة أربعة n
+
+39
+00:03:34,680 --> 00:03:41,140
+زائد ثلاثة هيكون infinite number of primes. احنا 
+
+40
+00:03:41,140 --> 00:03:46,680
+أثبتنا قبل هيك أنه عدد الأعداد الأولية is infinite
+
+41
+00:03:46,680 --> 00:03:52,160
+number. البرهان تقريبا له نفس الروح. إيش قال 
+
+42
+00:03:52,160 --> 00:04:01,180
+النظرية كمان مرة؟ النظرية بتقول there نظريتنا there
+
+43
+00:04:01,180 --> 00:04:18,720
+is an infinite number of primes of the form 4K
+
+44
+00:04:18,720 --> 00:04:25,040
+زائد 3. في عندي عدد لانهائي من الأعداد الأولية
+
+45
+00:04:25,040 --> 00:04:32,570
+الأولية 4K زائد ثلاثة. معي؟ شوف البرهان بنفس
+
+46
+00:04:32,570 --> 00:04:37,910
+الأسلوب اللي برهننا فيه اللي هو نظرية أنه فيه عدد
+
+47
+00:04:37,910 --> 00:04:42,710
+لانهائي من الأعداد الأولية. نفترض أنه في عندي finite
+
+48
+00:04:42,710 --> 00:04:47,570
+number of the primes of this form. وبنصل
+
+49
+00:04:47,570 --> 00:04:56,020
+لـ contradiction. نقول suppose that there is a finite
+
+50
+00:04:56,020 --> 00:05:11,160
+number of primes of the form أربعة K زائد ثلاثة.
+
+51
+00:05:11,160 --> 00:05:17,180
+ماشي الحال. نفترض أن في عندنا عدد نهائي من الأعداد
+
+52
+00:05:17,180 --> 00:05:23,700
+الأولية الأولية الأربعة K زائد ثلاثة. say they are
+
+53
+00:05:23,700 --> 00:05:30,120
+نفترض إن هما مين بالظبط؟ مين هما؟ Q1 وQ2 عند مين؟ Qs 
+
+54
+00:05:30,120 --> 00:05:34,460
+مثلا. إذا افترضنا إنه في عندي بس عدد نهائي من
+
+55
+00:05:34,460 --> 00:05:37,620
+الأعداد الأولية اللي على صورة أربعة K زائد ثلاثة.
+
+56
+00:05:37,620 --> 00:05:45,000
+وسميتهم بالظبط مين هما؟ Q1 وQ2 عند مين؟ Qs. الآن now
+
+57
+00:05:45,000 --> 00:05:52,340
+إيش بده ياخذ؟ بياخذ اللي هو عدد بيركبه تركيبة معينة من
+
+58
+00:05:52,340 --> 00:05:57,580
+خلاله بيصل أنه اللي هو واحد من هدول بيقسم الواحد
+
+59
+00:05:57,580 --> 00:06:01,700
+ومن ثم نصل أنه صار اللي هو الـ prime is one. وهذا
+
+60
+00:06:01,700 --> 00:06:04,980
+بيصير contradiction. نشوف كيف بنفس الأسلوب اللي
+
+61
+00:06:04,980 --> 00:06:08,660
+عملنا فيه اللي هو نظرية النظرية الأصلية في اللي هو
+
+62
+00:06:08,660 --> 00:06:13,640
+there are infinite number of primes. now consider
+
+63
+00:06:13,640 --> 00:06:20,120
+العدد n بتساوي اللي هو اضرب هدول كلهم في بعض.
+
+64
+00:06:20,120 --> 00:06:26,180
+Q1 في Q2 لعند Qs. أنا حددت يعني الأعداد على صورة
+
+65
+00:06:26,180 --> 00:06:28,780
+مين؟ أربعة K زائد ثلاثة أو أربعة K زائد واحد لغاية
+
+66
+00:06:28,780 --> 00:06:33,740
+بعد شوية. إذا بدي أضرب هدول في أربعة وأطرح من هنا
+
+67
+00:06:33,740 --> 00:06:39,240
+إيش؟ واحد. ماشي الحال. ليش طرحت واحد؟ عشان بعد شوية
+
+68
+00:06:39,240 --> 00:06:42,920
+أعمل combination معين وأصل أن الـ .. الـ .. الـ
+
+69
+00:06:42,920 --> 00:06:45,840
+prime اللي عندي بيكسب منين ماقص واحد وأصل لـ
+
+70
+00:06:45,840 --> 00:06:48,960
+contradiction. ماشي. طيب قلت أربعة دكتور في الفيلم
+
+71
+00:06:48,960 --> 00:06:52,860
+كلها هلجيتي Q1 في Q2 عندك Qs وضربت 
+
+72
+00:06:52,860 --> 00:06:56,720
+الفيلم مين في أربعة؟ هي عدد ركبته أنا وطرحت منه
+
+73
+00:06:56,720 --> 00:07:02,540
+واحد. آه ليش هيك؟ على أساس إن هذا العدد N اللي هو في
+
+74
+00:07:02,540 --> 00:07:07,760
+الآخر بيصل من خلاله لإبرهيم بيكسل مين؟ الواحد وفي
+
+75
+00:07:07,760 --> 00:07:10,980
+نفس الوقت هذا العدد اللي كتبته هو في الواقع على
+
+76
+00:07:10,980 --> 00:07:17,370
+صورة أربعة K زي التلاتة. ليش؟ شوف كيف بيساوي أربعة
+
+77
+00:07:17,370 --> 00:07:23,830
+في Q1 في Q2 لعند QS ناقص واحد لكل ايه
+
+78
+00:07:23,830 --> 00:07:32,830
+شماله. مظبوط. الآن اضرب هذه أربعة Q1 لعند QS 
+
+79
+00:07:32,830 --> 00:07:39,990
+ناقص أربعة زائد ثلاثة تطلع إيش؟ -1 واضح. إذا صار
+
+80
+00:07:39,990 --> 00:07:44,530
+الرقم الآن العدد اللي عندي n إيش شماله على صورة
+
+81
+00:07:44,530 --> 00:07:54,270
+4k زي آدمين زي التلاتة. طيب أي سؤال؟ صار العدد عندي
+
+82
+00:07:54,270 --> 00:08:02,070
+الآن هذا على صورة 4k زي التلاتة. الآن عندي الـ Q1
+
+83
+00:08:02,070 --> 00:08:11,010
+والـ Q2 عند الـ Qs عبارة عن odd numbers. أكيد آه؟
+
+84
+00:08:11,010 --> 00:08:17,010
+odd لأن كلها على صورة 4K زي 3. والآن هذا الـ odd
+
+85
+00:08:17,010 --> 00:08:22,710
+number حصلت
+
+86
+00:08:22,710 --> 00:08:29,130
+ضرب صار odd مضروب في أربعة مضروب في أربعة صار even لأن
+
+87
+00:08:29,130 --> 00:08:33,090
+مطروح من واحد بيصير عياشه. إذا هذا الآن عبارة عن odd
+
+88
+00:08:33,090 --> 00:08:40,210
+مدام الآن odd إذا الآن اللي عندي هذا هو عبارة عن
+
+89
+00:08:40,210 --> 00:08:46,390
+odd number على هذه الصورة. والآن هذا أكبر من واحد.
+
+90
+00:08:46,390 --> 00:08:51,180
+أكيد. ليش أكبر من واحد؟ أكيد لأن هدول على صورة
+
+91
+00:08:51,180 --> 00:08:55,820
+الـ primes. هدول على صورة 4K زي التلاتة يعني أكيد
+
+92
+00:08:55,820 --> 00:08:59,520
+... أكيد هدول في منهم التلاتة والخمسة والسبعة وكذا
+
+93
+00:08:59,520 --> 00:09:04,380
+لما نضربهم في بعض هيطلع رقم أكبر من ... من ... من ...
+
+94
+00:09:04,380 --> 00:09:06,720
+من ... من اثنين أكبر من ثلاثة أو أكبر من أربعة
+
+95
+00:09:06,720 --> 00:09:10,820
+الأخيرين. لما أطرح منه واحد أكيد بيضل شماله أكبر من
+
+96
+00:09:10,820 --> 00:09:15,060
+واحد. يعني إذا صار عندي الآن عبارة عن عدد أكبر من
+
+97
+00:09:15,060 --> 00:09:15,340
+واحد.
+
+98
+00:09:18,110 --> 00:09:21,950
+بقدر أكتبه على صورة n و product of the primes
+
+99
+00:09:21,950 --> 00:09:30,810
+سميهم R1 R2 لعند Rt مثلا. معي؟ طيب صار
+
+100
+00:09:30,810 --> 00:09:36,490
+الآن هذا n is odd وحللته على صورة product of the
+
+101
+00:09:36,490 --> 00:09:40,990
+primes. طبعا كل الـ primes اللي هنا هيكونوا odd لأن 
+
+102
+00:09:40,990 --> 00:09:44,550
+لو واحد فيه even معناته صار الآن n شماله is even
+
+103
+00:09:44,550 --> 00:09:49,470
+واحنا الآن تبعنا n شماله is odd. مدام الـ Rs اللي
+
+104
+00:09:49,470 --> 00:09:55,430
+هنا is odd إذا هدول الـ primes اللي هنا يا على صورة
+
+105
+00:09:55,430 --> 00:10:03,590
+4k زائد 1 يا 4k زائد ثلاثة. الآن لو كانوا كلهم
+
+106
+00:10:03,590 --> 00:10:08,150
+على صورة 4k زائد 1 حسب النظرية اللي قبلت بشوية
+
+107
+00:10:08,150 --> 00:10:14,010
+هيكون الـ product برضه على صورة 4k زائد 1. كمان مرة
+
+108
+00:10:14,010 --> 00:10:20,410
+الآن هذا n odd إذاً الـ primes كلهم اللي فيه n 
+
+109
+00:10:20,410 --> 00:10:26,430
+أُدمعناته صار الـ primes R1, R2, Rt يا على صورة 4K
+
+110
+00:10:26,430 --> 00:10:33,710
+زائد 1 يا 4K زائد 3. الآن أنا بقول لو كان كلهم على
+
+111
+00:10:33,710 --> 00:10:38,130
+صورة 4K زائد 1 معناته حاصل ضربهم هيطلع 4K زائد إيش؟
+
+112
+00:10:38,130 --> 00:10:43,390
+واحد. لكن الـ n بقيت مع صورة 4K زائد 3. إذن في
+
+113
+00:10:43,390 --> 00:10:49,960
+واحد منهم على الأقل على صورة 4K زائد 3. إذا صار في
+
+114
+00:10:49,960 --> 00:10:55,380
+عندنا واحد منهم سميه RK مثلا أو RN أو Rn من اللي
+
+115
+00:10:55,380 --> 00:11:05,280
+بدك إيها Rn على صورة مين؟ 4K زائد 3. بمعنى إن RK صار
+
+116
+00:11:05,280 --> 00:11:11,440
+منين؟ واحد من الـ Q1 وQ2 لعند Qs. لأنه احنا فرضنا إن
+
+117
+00:11:11,440 --> 00:11:15,380
+كل الأعداد الـ primes اللي في الدنيا اللي على صورة
+
+118
+00:11:15,380 --> 00:11:22,480
+4K زي 3 هي Q1 وQ2 لعند Qs. إذا صار الـ Rm واحد من
+
+119
+00:11:22,480 --> 00:11:29,820
+هدول. مدام واحد منهم إذا أكيد الـ Rm هيجسم Q1 في Q2
+
+120
+00:11:29,820 --> 00:11:38,710
+لعند Qs. ومنه على طول بيعطيني الـ Rm بكسم الأربعة 
+
+121
+00:11:38,710 --> 00:11:46,790
+في Q1 لعند QS. لكن من جهة أخرى الـ n بتساوي R1 R2
+
+122
+00:11:46,790 --> 00:11:52,930
+لعند الـ Rt وRm واحد منهم. إذا الـ Rm صار بيكسم منه
+
+123
+00:11:52,930 --> 00:12:01,810
+برضه الـ n كم مرة؟ الـ Rm واحد من هدول. ماشي الحال؟
+
+124
+00:12:01,810 --> 00:12:06,010
+إذا الـ Rm بيجسم مين صار؟ لأن الـ n product في 
+
+125
+00:12:06,010 --> 00:12:08,970
+هذه القولة كلها. إذا صار عندي الـ Rm بيجسم الـ n
+
+126
+00:12:08,970 --> 00:12:12,390
+وبيجسم اللي هو هذا المقدار. إذا بيجسم أي linear
+
+127
+00:12:12,390 --> 00:12:17,370
+combination بينهم. إذا الـ Rm بيجسم اللي هو أربعة
+
+128
+00:12:17,370 --> 00:12:25,570
+Q1 لعند QS ناقص مين؟ الـ n هذا على بعضه. مين هو؟
+
+129
+00:12:25,570 --> 00:12:29,250
+هذا على بعضه ليش ثلاثة؟
+
+130
+00:12:32,700 --> 00:12:39,500
+أربعة Q1 لعند QS ناقص أربعة زائد ناقص واحد.
+
+131
+00:12:39,500 --> 00:12:43,860
+الواحد. إيش بيطلع يعني؟ الأرقام إيش مالها؟ بتكسب من
+
+132
+00:12:43,860 --> 00:12:49,200
+الواحد. إذا الأرقام إيش بتساوي؟ وهذا contradiction
+
+133
+00:12:49,200 --> 00:12:54,080
+لأن الأرقام is a prime. therefore our first
+
+134
+00:12:54,080 --> 00:12:59,930
+assumption is not true. so there are infinite number
+
+135
+00:12:59,930 --> 00:13:05,750
+of primes of the form mean أربعة K زائد ثلاثة. تطلع
+
+136
+00:13:05,750 --> 00:13:12,810
+لفوق. الآن معلومة أخيرة في الـ section هي اللي بدنا
+
+137
+00:13:12,810 --> 00:13:18,230
+نعمل الـ section هذا بس. الـ theorem الأخيرة theorem
+
+138
+00:13:18,230 --> 00:13:25,170
+ثلاثة سبعة بدون مروحانة. الـ ضرورية
+
+139
+00:13:26,290 --> 00:13:34,610
+هي كما يلي. خذ 
+
+140
+00:13:34,610 --> 00:13:40,210
+الآن a,b element in z وافترض أن الـ Greatest
+
+141
+00:13:40,210 --> 00:13:46,910
+common divisor بين a وb هو 1 معايا؟
+
+142
+00:13:49,030 --> 00:13:53,690
+واخد اللي هي الـ sequence أو الأعداد على صورة A A
+
+143
+00:13:53,690 --> 00:13:59,870
+زائد B A زائد ثلاثة B A زائد أربعة B إلى ما لا نهاية
+
+144
+00:13:59,870 --> 00:14:07,610
+الأعداد على هذه الصورة ماشي الحال اه
+
+145
+00:14:07,610 --> 00:14:16,590
+اه لأ لأ كله بالمظبوط A زائد 2 بس أنا ناسيها
+
+146
+00:14:25,380 --> 00:14:30,980
+هذه الآن الأعداد اللي بيحكي في النظرية بيقول أن
+
+147
+00:14:30,980 --> 00:14:35,460
+و شمالها there are infinite number of primes في
+
+148
+00:14:35,460 --> 00:14:41,220
+داخلها فاضي؟ إذا النظرية هي كالتالي F لـ Greatest
+
+149
+00:14:41,220 --> 00:14:47,310
+common divisor بين الـA و الـB يساوي 1 ثم يكون هناك
+
+150
+00:14:47,310 --> 00:14:53,030
+عدد محدود من الـ Primes من هذه السيكوانس A وA زائد
+
+151
+00:14:53,030 --> 00:14:57,470
+B وA زائد 2B وA زائد 3B وA زائد 4B إلى ما لا نهاية
+
+152
+00:14:57,470 --> 00:15:01,990
+هذا بس من اللي يعرف النص النظرية هذا ليه يعني إن
+
+153
+00:15:01,990 --> 00:15:04,870
+هنا Primes مش شرط يكون هنا Primes كلها
+
+154
+00:15:08,840 --> 00:15:13,600
+لأنه مثال بسيط خد ثلاثة والسبعة مثلا ثلاثة والسبعة
+
+155
+00:15:13,600 --> 00:15:17,940
+مجموعها مش ماله اللي هو عشرة مش برايم لكن في
+
+156
+00:15:17,940 --> 00:15:20,680
+هذول في داخلها ماله في infinite number of the
+
+157
+00:15:20,680 --> 00:15:25,300
+primes بكون عندنا ال homework ثلاثة ثلاثة هيك
+
+158
+00:15:25,300 --> 00:15:28,400
+بنكون خلصنا chapter ثلاثة يوم السبت إن شاء الله
+
+159
+00:15:28,400 --> 00:15:33,710
+نعمل discussion ل chapter ثلاثة ضروري تيجي درسين
+
+160
+00:15:33,710 --> 00:15:40,190
+chapter 3 ومطلعين على الأسئلة وحلين الأسئلة بقدر
+
+161
+00:15:40,190 --> 00:15:44,430
+الإمكان نيجي للجزء الثاني من المحاضرة الجزء الثاني
+
+162
+00:15:44,430 --> 00:15:48,490
+اللي هو the theory of congruences أو نظرية
+
+163
+00:15:48,490 --> 00:15:53,550
+التطابقات ال chapter 4 عنوانه the theory of
+
+164
+00:15:53,550 --> 00:15:59,050
+congruences سنبدأ بالقسم الثاني ببعض properties of
+
+165
+00:15:59,050 --> 00:16:02,930
+congruences بعض اللي هي الخواص الأساسية لل
+
+166
+00:16:02,930 --> 00:16:09,970
+congruences خلّينا نشوف إيش اللي بنقصده في ال
+
+167
+00:16:09,970 --> 00:16:14,970
+congruences وماذا يعني إيه تطابق is congruent to
+
+168
+00:16:14,970 --> 00:16:19,990
+be مدلولاً الآن طبعاً هذا اللي هو the theory of
+
+169
+00:16:19,990 --> 00:16:24,640
+congruences أساس أنظمة العد اللي احنا بنعرف النظام
+
+170
+00:16:24,640 --> 00:16:27,780
+العد الثنائي أو الثلاثي أو الرباعي أو العشري تبعنا إلى
+
+171
+00:16:27,780 --> 00:16:36,060
+آخره فنشوف كيف الآن a تطابق b modulo n إيش بتعني
+
+172
+00:16:36,060 --> 00:16:43,720
+أو a is congruent to b modulo n a تطابق b بالنسبة
+
+173
+00:16:43,720 --> 00:16:51,260
+للمقياس n إيش بتعني يا ضياء؟ بتعنيها بتعني أنه اللي
+
+174
+00:16:51,260 --> 00:16:59,690
+هو القاسم الـ A ناقص B بنقول عن العدد A أنه
+
+175
+00:16:59,690 --> 00:17:04,130
+بيطابق الـ B modulo N إذا و فقط إذا الـ N بيقسم الـ
+
+176
+00:17:04,130 --> 00:17:13,370
+A ناقص B وبنقول عن العدد A is incongruent للـ
+
+177
+00:17:13,370 --> 00:17:21,110
+B modulo N A is not congruent أو is incongruent
+
+178
+00:17:21,110 --> 00:17:29,550
+modulo أو B modulo N بيعني أن N لا تقسم من الـ A
+
+179
+00:17:29,550 --> 00:17:34,510
+ناقص B أو مش من عوامل الـ A ناقص B نيجي الآن ناخد 
+
+180
+00:17:34,510 --> 00:17:39,490
+بعض الأمثلة العددية اللي بتوضح الأمر وخلّينا نشوف
+
+181
+00:17:39,490 --> 00:17:46,010
+نربطها بالأنظمة العددية اللي بنعرفها وبين النظرية
+
+182
+00:17:46,010 --> 00:17:51,310
+اللي هيقلبها نحكي عنها نيجي ناخد أول شيء اللي هو
+
+183
+00:17:51,310 --> 00:17:59,390
+مقياس اثنين Modulo اثنين Modulo اثنين بالمناسبة
+
+184
+00:17:59,390 --> 00:18:03,550
+هذا مثال اللي هو A تطابق B Modulo N مثال بناخده في
+
+185
+00:18:03,550 --> 00:18:08,790
+مبادئ رياضيات مثال على ال equivalence relation
+
+186
+00:18:08,790 --> 00:18:13,130
+وبناخد أمثلة ونشوف ونثبت أنه equivalence relation
+
+187
+00:18:13,130 --> 00:18:16,270
+ومن ثم بناخد أمثلة عددية بنوجد ال equivalence
+
+188
+00:18:16,270 --> 00:18:22,800
+classes في كل حالة ماشي الحال طيب الآن خلّينا ناخد
+
+189
+00:18:22,800 --> 00:18:29,720
+اللي هو إيش الأعداد اللي بتطابق مثلا الواحد
+
+190
+00:18:29,720 --> 00:18:34,140
+modulo اثنين إيش الأعداد اللي بتطابق الواحد
+
+191
+00:18:34,140 --> 00:18:39,700
+modulo اثنين كيف بفحص؟ بفحص إنه بدي الاثنين يقسم
+
+192
+00:18:39,700 --> 00:18:44,920
+الـB ناقص واحد أو الواحد ناقص B مش فارقة الـB
+
+193
+00:18:44,920 --> 00:18:51,170
+ناقص واحد من الأعداد اللي بتقسم الـB-1 الفردية؟
+
+194
+00:18:51,170 --> 00:18:56,050
+كلها ثلاثة وخمسة وسبعة وتسعة وحدعشر ومن
+
+195
+00:18:56,050 --> 00:18:59,810
+الجهة الثانية ناقص واحد إلى آخر إيه إذا وكأنه اللي
+
+196
+00:18:59,810 --> 00:19:06,430
+بتطابق الواحد ومقياس الاثنين هي واحد نفسها وثلاثة
+
+197
+00:19:06,430 --> 00:19:13,250
+وخمسة وسبعة وتسعة وناقص واحد الـodd numbers
+
+198
+00:19:13,250 --> 00:19:21,240
+والناقص واحد والناقص ثلاثة إلى ما لا نهاية الآن لو
+
+199
+00:19:21,240 --> 00:19:26,720
+جينا لأي اثنين مع بعض من هنا الواحد
+
+200
+00:19:26,720 --> 00:19:32,400
+بيطابق الكل وكل واحد هنا بيطابق الآخرين لو جيت السبعة
+
+201
+00:19:32,400 --> 00:19:36,600
+و الخمسة هتلاقي السبعة تطابق الخمسة موديلو اثنين
+
+202
+00:19:36,600 --> 00:19:43,040
+ليش؟ لأنه حاصل طرح بيطلع مين عدد زوجي واضح، إذا كل
+
+203
+00:19:43,040 --> 00:19:50,680
+هذول بيطابق بعض أي سؤال نيجي الآن هذول لو اجينا
+
+204
+00:19:50,680 --> 00:19:52,980
+بقى طبعا الاثنين واضح مش فيها ولا الأربعة ولا
+
+205
+00:19:52,980 --> 00:19:56,940
+الستة فبنشوف الاثنين بتطابق مين أو الأربعة بتطابق
+
+206
+00:19:56,940 --> 00:20:01,420
+مين يعني الآن بدي أسأل الأربعة بتطابق مين مثلا
+
+207
+00:20:01,420 --> 00:20:08,880
+modulo الاثنين يعني بدي الأعداد بيه اللي اثنين
+
+208
+00:20:08,880 --> 00:20:14,510
+بتقسم أربعة ناقص B أكيد هتقول الأربعة نفسها وهتقول
+
+209
+00:20:14,510 --> 00:20:17,630
+الاثنين نفسها وهتقول الستة وهتقول الثمانية و
+
+210
+00:20:17,630 --> 00:20:20,290
+الناقص اثنين والناقص أربعة إذا كل الأعداد مين
+
+211
+00:20:20,290 --> 00:20:27,430
+الزوجية إذا صار عندي الآن مقياس الاثنين الأربعة
+
+212
+00:20:27,430 --> 00:20:33,050
+تطابق نفسها تطابق الاثنين تطابق الأربعة تطابق ناقص
+
+213
+00:20:33,050 --> 00:20:38,160
+الاثنين تطابق اللي هو الستة إلى ما لا نهاية وكأنه
+
+214
+00:20:38,160 --> 00:20:43,900
+مقياس الاثنين .. مقياس الاثنين الآن قسم ليه؟ الزد
+
+215
+00:20:43,900 --> 00:20:51,960
+إلى جزئين اللي هو جزء كلهم بيطابق بعض وجزء اللي
+
+216
+00:20:51,960 --> 00:20:57,800
+هو برضه آخر بيطابق بعض لكن هذول لا يتطابقون وكأنه
+
+217
+00:20:57,800 --> 00:21:00,480
+فصلّي الزد أو اعمليها نوعين
+
+218
+00:21:03,920 --> 00:21:08,340
+الآن لو اجينا خلّي المرحلة دي هرجعلها اجينا ناخد
+
+219
+00:21:08,340 --> 00:21:13,340
+مدولها مين؟ مدولها ثلاثة مثلاً لو اجينا بدنا الأعداد
+
+220
+00:21:13,340 --> 00:21:22,940
+اللي هو إيش بيطابق الواحد مدولها مين؟ مدولها ثلاثة الآن
+
+221
+00:21:22,940 --> 00:21:29,920
+مين اللي بيفحصها ثلاثة بتقسم بيه ناقص واحد أول
+
+222
+00:21:29,920 --> 00:21:35,760
+حاجة الواحد بيطابق حاله بعدين مين عشان بيناقص واحد
+
+223
+00:21:35,760 --> 00:21:41,320
+يطلع إيش منه من مضاعفات الثلاثه اللي كل مرة بيفيه
+
+224
+00:21:41,320 --> 00:21:46,600
+إيش ثلاثة بيطلع أربعة سبعة وعشرة وهنا إيش منه نقص
+
+225
+00:21:46,600 --> 00:21:56,510
+اثنين إلى هالنهاية الآن واضح إن اللي عندي هنالو
+
+226
+00:21:56,510 --> 00:22:01,510
+طلعت عليهم هيطلع إن الأعداد اللي لو قسمتهم على
+
+227
+00:22:01,510 --> 00:22:07,150
+ثلاثة بزيد إيش؟ واحد، ماشي الحال؟ طيب نيجي إلى
+
+228
+00:22:07,150 --> 00:22:11,010
+كلهم لو قسمتهم على ثلاثة إيش باقيهم بزيد؟ واحد وكأن
+
+229
+00:22:11,010 --> 00:22:16,330
+كل الأعداد اللي باقيهم زي بعض متطابقات بالنسبة
+
+230
+00:22:16,330 --> 00:22:22,890
+لمين؟ اللي مقسم عليه؟ واضح اه؟ الآن نيجي واضح إن
+
+231
+00:22:22,890 --> 00:22:27,390
+الاثنين مش موجودة هنا بدنا نشوف اللي هو اثنين بيطابق
+
+232
+00:22:27,390 --> 00:22:32,850
+مين مدولها مين يعني بدنا نشوف مين الثلاثه بتقسم بيه
+
+233
+00:22:32,850 --> 00:22:38,150
+ناقص اثنين إيش ال B بيه؟ أول شيء اثنين غير اثنين خمسة و
+
+234
+00:22:38,150 --> 00:22:46,490
+ثمانية فاهمين؟ هو نفس الشيء من الجهة الأخرى معايا؟
+
+235
+00:22:46,490 --> 00:22:50,390
+الآن في
+
+236
+00:22:50,390 --> 00:22:55,440
+أعداد لسه مش موجودة اللي هو مين مثلا الثلاثه نفسها
+
+237
+00:22:55,440 --> 00:23:01,560
+مظبوط الآن بدنا نشوف الثلاثه تطابق مين مدولها مين
+
+238
+00:23:01,560 --> 00:23:06,700
+مدولها ثلاثة هتطلع مين الثلاثه والستة والتسعة
+
+239
+00:23:06,700 --> 00:23:11,860
+والاثناعشر والجهة الثانية اللي هو صفر ناقص ثلاثة
+
+240
+00:23:11,860 --> 00:23:18,550
+إلى ما لا نهاية وكأنه .. وكأنه الـ Z بواصفة المقياس
+
+241
+00:23:18,550 --> 00:23:23,470
+ثلاثة جزّقناها إلى ثلاثة أجزاء هي الجزء الأول اللي
+
+242
+00:23:23,470 --> 00:23:28,910
+باقي له واحد لما نقسمها على ثلاثة والجزء الثاني
+
+243
+00:23:28,910 --> 00:23:33,070
+اللي باقي له اثنين والجزء الثالث اللي باقي له
+
+244
+00:23:33,070 --> 00:23:40,220
+إيش؟ صفر معايا؟ وهذا اللي بيقودنا لأنظمة العد لنظام
+
+245
+00:23:40,220 --> 00:23:44,600
+العد الثنائي بنعتبر هؤلاء الأرقام concurrent لبعض
+
+246
+00:23:44,600 --> 00:23:50,780
+فبناخد عددين مثلّنهم اللي هو بنبدأ بالـ 0 و 100 و 1
+
+247
+00:23:51,450 --> 00:23:56,330
+ولما العدد يكبر عن الواحد بيصير خانة ثانية يبقى
+
+248
+00:23:56,330 --> 00:24:00,610
+يشبه الأربعة للأربعة وهكذا هذا اللي هو اللي .. اللي ..
+
+249
+00:24:00,610 --> 00:24:03,130
+اللي .. اللي .. اللي كنا نحكي عنه نظام العددين
+
+250
+00:24:03,130 --> 00:24:07,490
+الثنائي من ال .. من المقياس ثلاثة نقدر نحكي عن نظام
+
+251
+00:24:07,490 --> 00:24:12,410
+العد الثلاثي من أعداده الأساسية صفر واحد واثنين
+
+252
+00:24:12,880 --> 00:24:16,880
+أيضًا اللي هو نظام تبعنا العدد العشري اللي هو
+
+253
+00:24:16,880 --> 00:24:22,320
+modulo 10 هيكون عشرة فبتصير اللي هي الأعدادنا
+
+254
+00:24:22,320 --> 00:24:27,880
+اللي هي صفر واحد واثنين لعند مين؟ لعند إيش؟ لعند
+
+255
+00:24:27,880 --> 00:24:37,090
+التسعة الآن واضح إن كل واحد من هذول باقي القسمة
+
+256
+00:24:37,090 --> 00:24:41,310
+على ثلاثة زي بعض وهنا باقي القسمة على ثلاثة زي بعض
+
+257
+00:24:41,310 --> 00:24:43,370
+وهنا باقي القسمة على ثلاثة زي بعض
+
+258
+00:24:46,960 --> 00:24:53,080
+بيقودنا لإنه نروح باتجاه نظرية بدنا نثبتها أن for
+
+259
+00:24:53,080 --> 00:24:58,080
+an arbitrary a و b element in z a is congruent to
+
+260
+00:24:58,080 --> 00:25:03,080
+b modulo n if and only if a and b شمالهم have the
+
+261
+00:25:03,080 --> 00:25:09,220
+same remainder when they divided by mean by n يعني
+
+262
+00:25:09,220 --> 00:25:15,560
+A تطابق B مدولوا إذا وفقط إذا كان الـ A والـ B لهم
+
+263
+00:25:15,560 --> 00:25:22,760
+نفس المتبقي عندما يقسم كل منهما على N واضح؟
+
+264
+00:25:22,760 --> 00:25:35,160
+انبروا الآن
+
+265
+00:25:35,160 --> 00:25:37,960
+بتفترض صحبوز
+
+266
+00:25:43,490 --> 00:25:50,310
+that A is congruent to B modulo of N modulo of A
+
+267
+00:25:50,310 --> 00:25:51,110
+modulo of N modulo of A modulo of N modulo of A
+
+268
+00:25:51,110 --> 00:25:54,210
+modulo of N modulo of A modulo of N modulo of A
+
+269
+00:25:54,210 --> 00:25:56,710
+modulo of N modulo of A modulo of N modulo of A
+
+270
+00:25:56,710 --> 00:26:00,770
+modulo of N modulo of A modulo of N modulo of A
+
+271
+00:26:00,770 --> 00:26:04,430
+modulo
+
+272
+00:26:04,430 --> 00:26:08,270
+of N modulo of N modulo of N modulo of N modulo of
+
+273
+00:26:08,270 --> 00:26:08,310
+N modulo of N modulo of N modulo of N modulo of N
+
+274
+00:26:08,310 --> 00:26:10,110
+modulo of N modulo of N modulo of N modulo of N
+
+275
+00:26:10,110 --> 00:26:13,960
+modulo of N modulo of N modulo of N مظبوط؟ ومنه
+
+276
+00:26:13,960 --> 00:26:24,600
+على طول أن a ناقص b يساوي k في n for some k
+
+277
+00:26:24,600 --> 00:26:32,980
+element in integer z واضح اه؟ الآن بدنا ننجل هذا على
+
+278
+00:26:32,980 --> 00:26:42,910
+الجهة الثانية a بتساوي b زائد k في n الآن أنا غلط
+
+279
+00:26:42,910 --> 00:26:46,930
+دي اروح وين ان اثبت لك ان a و b لما نيجي نقسمهم على n
+
+280
+00:26:46,930 --> 00:26:51,790
+الى نفس الـ remainder اقسم الآن b على مين؟ على 
+
+281
+00:26:51,790 --> 00:27:03,190
+عندي اللي هو b هتساوى q في n by dividing algorithm
+
+282
+00:27:03,190 --> 00:27:10,230
+زائد r أكبر أو يساوى صفر و أصغر من مين؟ من N أيش 
+
+283
+00:27:10,230 --> 00:27:15,350
+عملت يا جماعة جسمت ال B على مين؟ على ال N طلع ناتج
+
+284
+00:27:15,350 --> 00:27:20,510
+القسمة Q وهو وحيد وطلع عندي متبقى القسمة بين 0 و بين
+
+285
+00:27:20,510 --> 00:27:25,290
+N وهو وحيد ماشي الحال؟ طيب لأن بتثبتلك ان متبقى
+
+286
+00:27:25,290 --> 00:27:29,910
+القسمة بين ال A و ال M برضه هيطلع مين؟ اللي هو R
+
+287
+00:27:29,910 --> 00:27:36,610
+عوضتها عوضتها إذا من اللي هو هي عندي مثلاً واحد وهي
+
+288
+00:27:36,610 --> 00:27:45,870
+اثنين from واحد and اثنين we have أيش we have a
+
+289
+00:27:45,870 --> 00:27:54,670
+بتساوي qn زائد r مكان ال b زائد
+
+290
+00:27:54,670 --> 00:27:59,750
+k فعلاً ويساوي جمع لي اللي هي اللي فيها الـ n مع بعض
+
+291
+00:27:59,750 --> 00:28:09,210
+بيصير k زائد Q فـ N زائد مين زائد R أصبح الآن لـ A على 
+
+292
+00:28:09,210 --> 00:28:15,650
+صورة اللي هو ناتج القسمة اللي هو Q زائد K ومتبقى 
+
+293
+00:28:15,650 --> 00:28:19,970
+القسمة مين؟ R والـ R طبعاً بين مين مين؟ بين R أكبر
+
+294
+00:28:19,970 --> 00:28:25,670
+أو يساوى صفر وأصغر من مين؟ هذا يعني أنه متبقى القسمة
+
+295
+00:28:25,670 --> 00:28:31,030
+للـ A على الـ N هو R وفي الأصل عندي متبقى القسمة
+
+296
+00:28:31,800 --> 00:28:36,240
+للـ B على ال N هو ال R إذا ال A و ال B have the
+
+297
+00:28:36,240 --> 00:28:44,180
+same remainder إذا hence أو therefore A و B have
+
+298
+00:28:44,180 --> 00:28:54,840
+the same remainder when they divided by N أي سؤال؟
+
+299
+00:29:02,900 --> 00:29:07,980
+طيب conversely .. conversely بدنا نفترض أن a و b
+
+300
+00:29:07,980 --> 00:29:12,820
+اللي نفسه ال remainder  و نثبت للجميع أن they are
+
+301
+00:29:12,820 --> 00:29:26,020
+congruent modulo n إذن conversely
+
+302
+00:29:26,020 --> 00:29:31,280
+صباز
+
+303
+00:29:32,700 --> 00:29:44,600
+that a بتساوي b في q في n زائد r أكبر يساوي صفر
+
+304
+00:29:44,600 --> 00:29:47,900
+أصغر من n سميها q واحد
+
+305
+00:29:50,380 --> 00:29:56,320
+B بتساوي Q2 في N زائد R وR أكبر يساوي صفر وأصغر من 
+
+306
+00:29:56,320 --> 00:30:00,860
+مين N أشي اللي فرضناه فرضنا إنه إنه لما جسمنا ال A
+
+307
+00:30:00,860 --> 00:30:04,720
+على ال N طلع اللي هو remainder R لما جسمنا ال B
+
+308
+00:30:04,720 --> 00:30:07,000
+على ال N طلع اللي هو remainder R يعني A وB have
+
+309
+00:30:07,000 --> 00:30:09,900
+the same remainder لأن الانتباه أن هما congruent
+
+310
+00:30:09,900 --> 00:30:21,980
+modulo N modulo N الآن A minus B معايا بتساويQ واحد
+
+311
+00:30:21,980 --> 00:30:29,820
+ناقص Q اتنين فان والـ r واحد مع الـ r وهذا يعني أيش
+
+312
+00:30:29,820 --> 00:30:37,640
+and so الـ and تجسم a minus b hence a is congruent
+
+313
+00:30:37,640 --> 00:30:48,790
+to b modulo أي سؤال أي استفسار طيب ناخد الآن خواص
+
+314
+00:30:48,790 --> 00:30:53,190
+أخرى from congruences الخواص اللي حكينا عنها في 
+
+315
+00:30:53,190 --> 00:30:57,950
+الأول أنه اللي هي علاقة الـ congruence هذه بتعمل
+
+316
+00:30:57,950 --> 00:31:03,770
+equivalence relation يعني بمعنى آخر هتكون اللي هو 
+
+317
+00:31:03,770 --> 00:31:10,910
+symmetric و transitive و reflexive، مظبوط؟ وهنا
+
+318
+00:31:10,910 --> 00:31:15,920
+خواص أخرى أيضًا، نيجي نتطلع الخواص واحدة واحدةلأن
+
+319
+00:31:15,920 --> 00:31:21,380
+let n أكبر من 0 be fixed and a و b و c be
+
+320
+00:31:21,380 --> 00:31:27,160
+arbitrary integers then خاصية الأولى أن a تطابق
+
+321
+00:31:27,160 --> 00:31:30,960
+نفسها modulo n اللي هي أيش بنسميها reflexive
+
+322
+00:31:30,960 --> 00:31:37,400
+الواحدة
+
+323
+00:31:37,400 --> 00:31:40,700
+trivial case أكبر من واحد معايا
+
+324
+00:31:44,930 --> 00:31:50,370
+الـ A تطابق بي modulo n modulo لأن في حالة الواحد 
+
+325
+00:31:50,370 --> 00:31:58,530
+كل الدنيا أشمالها متطابقات modulo واحد
+
+326
+00:31:58,530 --> 00:32:07,840
+يقسم A-B modulo الواحد modulo الواحد بيكسب مين متحققة
+
+327
+00:32:07,840 --> 00:32:11,640
+يعني يعني بنفع نقول أن أكبر من أيش من صفر وبنفع
+
+328
+00:32:11,640 --> 00:32:14,980
+نقول أن أكبر أو يساوى واحد فاحنا طبعاً عساس أنه
+
+329
+00:32:14,980 --> 00:32:18,100
+نكسب الواحد ما احنا والـ general case بنقول أن أكبر
+
+330
+00:32:18,100 --> 00:32:22,580
+أو يساوى واحد أو بنقول أن أكبر من مين من صفر يعني
+
+331
+00:32:22,580 --> 00:32:26,180
+لما أكتب أن أكبر من صفر معناته أنها أيش أن أكبر
+
+332
+00:32:26,180 --> 00:32:31,320
+أو يساوى واحد فمافيش نفس الشي يعني في الكتاب أنا
+
+333
+00:32:31,320 --> 00:32:35,720
+أكبر مساوية واحد هنا أنا أكبر من السبب إذا اه وحتى 
+
+334
+00:32:35,720 --> 00:32:41,980
+لو مساوية عندي بس
+
+335
+00:32:41,980 --> 00:32:51,280
+A تطابق B modulo مين modulo واحد هذه دائماً صحيح
+
+336
+00:32:51,280 --> 00:32:56,940
+ليش تريد ده ال case عشان هناك A واحد تقسم A minus
+
+337
+00:32:56,940 --> 00:32:57,260
+B
+
+338
+00:33:04,530 --> 00:33:10,280
+الخواص اللي عندنا الخاصية الأولى أيش هيقولوا معايا 
+
+339
+00:33:10,280 --> 00:33:14,460
+اللي هي أيش اللي هي reflexive اللي A تطابق A
+
+340
+00:33:14,460 --> 00:33:18,880
+modulo n الخاصية الثانية اللي هي مين؟ Symmetric A
+
+341
+00:33:18,880 --> 00:33:23,320
+تطابق B يعطينا B تطابق A الخاصية الثالثة اللي هي 
+
+342
+00:33:23,320 --> 00:33:27,800
+أيش؟ Transitive A تطابق B وB تطابق C إذن A تطابق
+
+343
+00:33:27,800 --> 00:33:32,820
+مين؟ C هذه الثلاثة احنا بنبرهنين حتى في المبادئ
+
+344
+00:33:33,610 --> 00:33:39,690
+الآن خاصية ثالثة لو A تطابق B modulo n و C تطابق D
+
+345
+00:33:39,690 --> 00:33:48,350
+modulo n إذا A زائد C تطابق B زائد D modulo n  و أيضاً A
+
+346
+00:33:48,350 --> 00:33:56,870
+في C تطابق B في D modulo n واضحة لأن الخاصية الخامسة
+
+347
+00:33:56,870 --> 00:34:01,170
+هي حالة خاصة من الخاصية مين اللي هي اللي جابلها 
+
+348
+00:34:01,170 --> 00:34:05,370
+حالة خاصة بإنه أخد اللي هو الـ C تطابق الـ C
+
+349
+00:34:05,370 --> 00:34:10,510
+modulo N كيف؟ جالك الـ A تطابق B modulo N إذا A 
+
+350
+00:34:10,510 --> 00:34:12,370
+زائد C تطابق B زائد C
+
+351
+00:34:16,640 --> 00:34:20,000
+اللي بعد هي a في c تطابق b في b في c يعني برهان 
+
+352
+00:34:20,000 --> 00:34:24,520
+هذه اللي هو حالة اعتماد على اللي four بتقول since
+
+353
+00:34:24,520 --> 00:34:29,040
+c تطابق c modulo n إذا by four بتطلع اللي هي خمسة 
+
+354
+00:34:29,040 --> 00:34:34,020
+بواضح طيب اللي بعد هو اللي هو a تطابق b modulo n
+
+355
+00:34:34,020 --> 00:34:38,140
+يؤدي إلى ان a to the k تطابق b to the k modulo n 
+
+356
+00:34:38,140 --> 00:34:46,810
+لكل mean لكل k element in N أي سؤال؟ طيب نيجي
+
+357
+00:34:46,810 --> 00:34:50,130
+نبرهن .. شوفوا أيش اللي بدنا نبرهنه أيش اللي بدنا
+
+358
+00:34:50,130 --> 00:34:54,530
+نبرهنه دي 
+
+359
+00:34:54,530 --> 00:35:01,570
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+360
+00:35:01,570 --> 00:35:02,190
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+361
+00:35:02,190 --> 00:35:04,410
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+362
+00:35:04,410 --> 00:35:06,310
+دي دي دي دي دي دي دي
+
+363
+00:35:12,510 --> 00:35:19,030
+بنشوف هذا بيعطينا انه a تطابق c modulo n ماشي إذا
+
+364
+00:35:19,030 --> 00:35:24,810
+بيقول suppose that كده إذا من التعريف مباشرة then
+
+365
+00:35:26,270 --> 00:35:31,630
+اللي هو n تقسم a minus b و الثانية n تقسم b
+
+366
+00:35:31,630 --> 00:35:35,490
+minus c إذن بتقسم أي linear combination بينهم الـ n
+
+367
+00:35:35,490 --> 00:35:39,030
+الـ linear combination اللي بيخدم ليه بدي أطير الـ b
+
+368
+00:35:39,030 --> 00:35:42,030
+من هنا و الـ b من هنا عشان أوجد العلاقة بين الـ a و
+
+369
+00:35:42,030 --> 00:35:48,670
+الـ c إذن hence n بتقسم ال a minus b زائد b minus c
+
+370
+00:35:48,670 --> 00:35:53,050
+اللي هو هذا على بعضه اللي عبارة عن مين a minus c إذن
+
+371
+00:35:53,050 --> 00:36:01,660
+هذا يعني الـ A تطابق C Modulo N هذه خاصية مين 
+
+372
+00:36:01,660 --> 00:36:06,440
+لترانزيتف خاصية لترانزيتف نيجي نبرهن مين كمان
+
+373
+00:36:06,440 --> 00:36:12,200
+نبرهن أربعة لأن خمس حالة خاصة من مين من أربعة الآن
+
+374
+00:36:12,200 --> 00:36:19,880
+أربعة أيش أربعة بتقول أن A A
+
+375
+00:36:19,880 --> 00:36:30,880
+تطابق B Modulo N وC تطابق دي modulo n بدنا شغل تاني
+
+376
+00:36:30,880 --> 00:36:36,300
+الـ a زائد و الـ a ضرب ماشي الحال نيجي لمين أول شيء
+
+377
+00:36:36,300 --> 00:36:43,640
+للجمع لأن هذا أيش بتعني أن n بتقسم a minus b
+
+378
+00:36:43,640 --> 00:36:50,840
+وهذا أيش بتعني n بتقسم c minus d الآن بدنا نحصل على
+
+379
+00:36:50,840 --> 00:36:55,460
+الجمع الجمع المباشر اللي بيجيب و لا لأ إذا صار
+
+380
+00:36:55,460 --> 00:37:00,020
+عندي N بتجسم A linear combination بينهم اللي هو A
+
+381
+00:37:00,020 --> 00:37:07,980
+minus B زائد C minus D هذا على بعض N بتجسم A زائد 
+
+382
+00:37:07,980 --> 00:37:18,000
+C ناقص B زائد D مظبوط؟ وهذا اللي هو اللي بدنا أنه 
+
+383
+00:37:18,000 --> 00:37:30,290
+A زائد C تطابق بي زائد دي modulo n الآن أي سؤال طيب
+
+384
+00:37:30,290 --> 00:37:39,230
+نيجي لمين الآن للضرب نيجي للضرب أيش
+
+385
+00:37:39,230 --> 00:37:46,430
+غرضه إيه a في c و b في مين في d شوفوا عندي N بتقسم A
+
+386
+00:37:46,430 --> 00:37:52,330
+-B و N بتقسم C-D إذا الـ N بتقسم أي Linear
+
+387
+00:37:52,330 --> 00:37:57,430
+combination بينهم أنا بدي اللي هو أحصل عالميا على 
+
+388
+00:37:57,430 --> 00:38:05,370
+A في C فهضرب هذه في C، مظبوط؟ فبيصير الآن C في A-B
+
+389
+00:38:05,370 --> 00:38:11,450
+زائد الآن أنا .. الآن بدي أخلي AC، مظبوط؟
+
+390
+00:38:14,090 --> 00:38:19,170
+فـ الآن طلعت عندي هنا C في B بديش إياها C في B فـ الآن
+
+391
+00:38:19,170 --> 00:38:23,710
+عشان أطير C في B بضربها دي في مين؟ في B بيه بيه
+
+392
+00:38:23,710 --> 00:38:26,910
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+393
+00:38:26,910 --> 00:38:27,110
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+394
+00:38:27,110 --> 00:38:27,830
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+395
+00:38:27,830 --> 00:38:30,710
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+396
+00:38:30,710 --> 00:38:35,470
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بي
+
+397
+00:38:36,130 --> 00:38:42,410
+عشان احصل على AC ضربت هدف C لكن نشأ عندي هنا CB CB
+
+398
+00:38:42,410 --> 00:38:47,610
+بقدر طيّرها من هنا A ضرب هدف مين؟ في B فصار عندي
+
+399
+00:38:47,610 --> 00:38:51,550
+الآن N بتجسم هذا المقدار في هذا المقدار هذا عبارة
+
+400
+00:38:51,550 --> 00:39:01,810
+عن أيش؟ يعني N بتجسم CA نقص CB زي BC نقص CBC مع CB
+
+401
+00:39:01,810 --> 00:39:09,190
+بيروحوا مع بعض إذا أنت بتكسب AC نقص CD معناته ان AC
+
+402
+00:39:09,190 --> 00:39:18,630
+تطابق CD Modulo B Modulo
+
+403
+00:39:18,630 --> 00:39:22,270
+مين Modulo يعني كلامكم صحيح من لئة باللئة إذا
+
+404
+00:39:22,270 --> 00:39:27,510
+الخاصية هذه برضه أيش مالها متحقق وصح لها دلعندي
+
+405
+00:39:30,260 --> 00:39:39,340
+بنثبت ان إذا A تطابق B modulo N و A K تطابق
+
+406
+00:39:39,340 --> 00:39:44,320
+الـ BK modulo N لكل K مالها بالـ induction أكيد
+
+407
+00:39:44,320 --> 00:39:48,320
+مالها بالـ induction و الـ induction تبعها برضه سهل
+
+408
+00:39:48,320 --> 00:39:59,110
+نعم نشوف اللي هو الـ induction لـ اللي هو الخاصية
+
+409
+00:39:59,110 --> 00:40:02,890
+الأخيرة عند
+
+410
+00:40:02,890 --> 00:40:11,050
+a تطابق b modulo n بدنا نثبت أنه بادي الى a k
+
+411
+00:40:11,050 --> 00:40:22,600
+تطابق b k modulo n for every k element in N الآن
+
+412
+00:40:22,600 --> 00:40:26,480
+اللي هي أخر مغطى a تطابق b modulo n بيعطيني a to
+
+413
+00:40:26,480 --> 00:40:31,360
+the k تطابق b modulo k لكل k element in N اللي هو
+
+414
+00:40:31,360 --> 00:40:39,560
+بينين by induction الآن for n بيساوي واحد أو for k
+
+415
+00:40:39,560 --> 00:40:43,560
+بيساوي واحد it is trivial لأن هي معطى أصلاً الآن
+
+416
+00:40:43,560 --> 00:40:48,660
+إذا بدنا نقول suppose that اللي هي star
+
+417
+00:40:51,230 --> 00:40:58,230
+is true for k بتساوي M مثلاً ماشي الحال وبدأ أثبت لـ
+
+418
+00:40:58,230 --> 00:41:03,570
+M زائد واحد معايا اه إذا مادام true for k بتساوي M
+
+419
+00:41:03,570 --> 00:41:10,110
+إذا then A to the M تطابق B to the M modulo N
+
+420
+00:41:10,110 --> 00:41:17,410
+معايا لكن بط But إن A تطابق الـ B modulo N 
+
+421
+00:41:17,410 --> 00:41:21,910
+وبالنظرية اللي قبل بشوية اللي بقى خمسة التماثل مع
+
+422
+00:41:21,910 --> 00:41:27,670
+بعض إذا A to the M في A اللي هي M زائد واحد تطابق 
+
+423
+00:41:27,670 --> 00:41:32,950
+الـ B أقسم في B اللي هو M زائد واحد modulo N إذا
+
+424
+00:41:32,950 --> 00:41:35,930
+صارت اللي هي Star is true for M زائد واحد
+
+425
+00:41:35,930 --> 00:41:40,390
+Therefore Star is true for any M أو for any K
+
+426
+00:41:40,390 --> 00:41:45,290
+element والمرة القادمة إن شاء الله بنكمل وبكون
+
+427
+00:41:45,290 --> 00:41:48,590
+عندنا discussion لـ chapter 3 
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/iOr4UuxtU-4_postprocess.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/iOr4UuxtU-4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..df885979e5ea886b146b9c0a9695ddce748c496d
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/iOr4UuxtU-4_postprocess.srt
@@ -0,0 +1,1708 @@
+1
+00:00:19,440 --> 00:00:25,280
+بسم الله الرحمن الرحيم المحاضرة التاسعة في مساق
+
+2
+00:00:25,280 --> 00:00:29,760
+نظرية الأعداد لطلبة قسم رياضيات بالجامعة الإسلامية
+
+3
+00:00:29,760 --> 00:00:37,120
+كليتي العلوم والتربية هنكمل الحديث حول خواص
+
+4
+00:00:37,120 --> 00:00:41,420
+الأعداد الأولية أو some properties of primes
+
+5
+00:00:41,420 --> 00:00:44,960
+والجزء الثاني من المحاضرة هيكون اللي هو the theory
+
+6
+00:00:44,960 --> 00:00:50,680
+of congruences أو نظرية التطابقاتنكمل اللي اتحدثنا
+
+7
+00:00:50,680 --> 00:00:55,160
+فيه المرة الماضية اللي هي بعض خواص الأعداد الأولية
+
+8
+00:00:55,160 --> 00:01:00,120
+الخاصية الأولى اللمّة هناخد اللمّة اللمّة بتقول ما
+
+9
+00:01:00,120 --> 00:01:05,220
+يليهThe product of two or more integers of the
+
+10
+00:01:05,220 --> 00:01:09,760
+form أربع M زائد واحد is the same form يعني الآن
+
+11
+00:01:09,760 --> 00:01:15,560
+لو كان في عندى اللي هو عددين على صورة أربع M زائد
+
+12
+00:01:15,560 --> 00:01:20,720
+واحد نفترض أربع K زائد واحد يعني عددين على نفس
+
+13
+00:01:20,720 --> 00:01:24,790
+الصورة اللي هي أربع M زائد واحداللي هو حيكون حاصل
+
+14
+00:01:24,790 --> 00:01:28,130
+درب هنا برضه على صورة اربعة M زائد او احد او اربعة
+
+15
+00:01:28,130 --> 00:01:32,590
+M زائد او اربعة K زائد واحد for some K element in
+
+16
+00:01:32,590 --> 00:01:40,690
+Z الآن بدنا نبرهنها بورنا بسيط بروف الان letاللي
+
+17
+00:01:40,690 --> 00:01:44,070
+هو العدد الأول أربعا زائد واحد والعدد التاني أربعة
+
+18
+00:01:44,070 --> 00:01:48,410
+كزائد واحد وضرب ليهم في بعض أربعا زائد واحد في
+
+19
+00:01:48,410 --> 00:01:53,990
+أربع كزائد واحد الإدعاء أنه هيكون على صورة أربعة Q
+
+20
+00:01:53,990 --> 00:01:58,830
+زائد واحد يعني بمعنى آخر العدد المتبقي لما نقسمه
+
+21
+00:01:58,830 --> 00:02:03,800
+على أربعة ويتبقى واحد نضربه في عدد تانيبرضه اللي
+
+22
+00:02:03,800 --> 00:02:07,620
+هو لما نقسمه على أربعة ومتبقي واحد هيطلع حاصل
+
+23
+00:02:07,620 --> 00:02:11,540
+الدرب هو عبارة عن عدد لما نقسمه على أربعة ومتبقي
+
+24
+00:02:11,540 --> 00:02:20,680
+واحد ويساوي اللي هو أربعة ست عشر KM زائد أربعة M
+
+25
+00:02:20,680 --> 00:02:26,860
+زائد أربعة K زائد واحد مظبوط هدولة كلها فيها
+
+26
+00:02:26,860 --> 00:02:31,540
+أربعات خد الأربعة المشترك تصير أربعة في أربعة KM
+
+27
+00:02:32,190 --> 00:02:38,310
+زائد M زائد K الكل زائد إيش واحد هذا كله صمم
+
+28
+00:02:38,310 --> 00:02:45,110
+تجاروين AQ في Z ويسواها على صورة 4Q زائد 1 إذا
+
+29
+00:02:45,110 --> 00:02:50,290
+حاصل ضرب أي عددين على صورة 4M زائد 1 بطلع برضه على
+
+30
+00:02:50,290 --> 00:02:54,870
+صورة 4Q زائد 1 ولو ضربناهم في كمان عدد على نفس
+
+31
+00:02:54,870 --> 00:02:59,450
+الصورة هيطلع نفس الشيء إذا حاصل ضرب any finite
+
+32
+00:02:59,450 --> 00:03:06,090
+numberof integers of the form 4k زائد 1 is of the
+
+33
+00:03:06,090 --> 00:03:11,610
+same form أي is of the form 4k أو 4q زائد 1 for
+
+34
+00:03:11,610 --> 00:03:15,730
+some q limit in z هذا اللي ما بدنا نوظفها و
+
+35
+00:03:15,730 --> 00:03:20,710
+نستخدمها في إثبات النظرية 3.6 اللي هي النظرية اللي
+
+36
+00:03:20,710 --> 00:03:25,350
+بتقول لي there is an infinite number of primes of
+
+37
+00:03:25,350 --> 00:03:31,240
+the form 4n زائد 3 إذا هذا النظرية بتقول لي أنهعدد
+
+38
+00:03:31,240 --> 00:03:34,680
+الأعداد اللي على صورة الأولية اللي على صورة أربعان
+
+39
+00:03:34,680 --> 00:03:41,140
+زائد تلاتة هيكون infinite number of primes احنا
+
+40
+00:03:41,140 --> 00:03:46,680
+أثبتنا قبل هيك انه عدد الأعداد الأولية is infinite
+
+41
+00:03:46,680 --> 00:03:52,160
+number البورمان تقريبا له نفس الروح ايش قال
+
+42
+00:03:52,160 --> 00:04:01,180
+النظرية كمان مرة النظرية بتقولthere نظريتنا there
+
+43
+00:04:01,180 --> 00:04:18,720
+is an infinite number of primes of the form 4K
+
+44
+00:04:18,720 --> 00:04:25,040
+زائد 3 في عندى عدد لنهائى من الاعداد الاولية
+
+45
+00:04:25,040 --> 00:04:32,570
+العصورية 4Kزائد تلاتة معايا؟ شوف البرهان بنفس
+
+46
+00:04:32,570 --> 00:04:37,910
+الأسلوب اللي برهننا فيه اللي هو نظرية أنه فيه عدد
+
+47
+00:04:37,910 --> 00:04:42,710
+لانهاء من الأعداد الأولية نفترض أنه في عنده finite
+
+48
+00:04:42,710 --> 00:04:47,570
+number of the primes of this form وبنصل
+
+49
+00:04:47,570 --> 00:04:56,020
+لcontradiction نقول سبوزthat there is a finite
+
+50
+00:04:56,020 --> 00:05:11,160
+number of primes of the form أربعة K زائد تلاتة
+
+51
+00:05:11,160 --> 00:05:17,180
+ماشي الحال نفترض أن في عندنا عدد نهائي من الأعداد
+
+52
+00:05:17,180 --> 00:05:23,700
+الأولية العصورية الأربعة K زائد تلاتةsay they are
+
+53
+00:05:23,700 --> 00:05:30,120
+نفرض إن هما مين بالظبط مين هما Q1 وQ2 عند مين AQS
+
+54
+00:05:30,120 --> 00:05:34,460
+مثلا إذا انفرضنا إنه في عندي بس عدد نهائي من
+
+55
+00:05:34,460 --> 00:05:37,620
+الأعداد الأولية اللي عصورة أربعة K زائد تلاتة
+
+56
+00:05:37,620 --> 00:05:45,000
+وسميتهم بالظبط مين هما Q1 وQ2 عند مين AQS الآن now
+
+57
+00:05:45,000 --> 00:05:52,340
+إيش بده أخدبتاخد اللي هو عدد ركبه تركيبه معينة من
+
+58
+00:05:52,340 --> 00:05:57,580
+خلاله أصل أنه اللي هو واحد من هدولة بقسم الواحد
+
+59
+00:05:57,580 --> 00:06:01,700
+ومن ثم نصل أنه صار اللي هو الـ prime is one وهذا
+
+60
+00:06:01,700 --> 00:06:04,980
+بيصير contradiction نشوف كيف بنفس الأسلوب اللي
+
+61
+00:06:04,980 --> 00:06:08,660
+عملنا فيه اللي هو نظرية النظرية الأصلية في اللي هو
+
+62
+00:06:08,660 --> 00:06:13,640
+there are infinite number of primes now consider
+
+63
+00:06:13,640 --> 00:06:20,120
+العدد n بتساوياللي هو اضرب لها دولة كل الهن في بعض
+
+64
+00:06:20,120 --> 00:06:26,180
+Q1 في Q2 لعندي Qs أنا حديث يعني الأعداد على صورة
+
+65
+00:06:26,180 --> 00:06:28,780
+مين أربعة K زايد تلتة أو أربعة K زايد واحد لغاية
+
+66
+00:06:28,780 --> 00:06:33,740
+بعد شوية إذا بدي أضرب هن في أربعة واطرح من هنا
+
+67
+00:06:33,740 --> 00:06:39,240
+إياش واحد ماشي الحال ليش طرحت واحد عساس بعد شوية
+
+68
+00:06:39,240 --> 00:06:42,920
+أعمل combination معين و أصل أن ال .. ال .. الـ
+
+69
+00:06:42,920 --> 00:06:45,840
+prime اللي عندي بيكسب منين ماقص واحد و أصل لا
+
+70
+00:06:45,840 --> 00:06:48,960
+contradictionماشي طيب قلت أربعة دكتور في الفيلم
+
+71
+00:06:48,960 --> 00:06:52,860
+كلها هلجيتي Q واحد في Q اتنين عندك U S وضربت
+
+72
+00:06:52,860 --> 00:06:56,720
+الفيلم مين في أربعة هي عدد ركّبته أنا وطرحت منه
+
+73
+00:06:56,720 --> 00:07:02,540
+واحد آه ليش هيك على أساس إن هذا العدد N اللي هو في
+
+74
+00:07:02,540 --> 00:07:07,760
+الآخر أصل من خلاله لإبراهيم بيكسل مين الواحد وفي
+
+75
+00:07:07,760 --> 00:07:10,980
+نفس الوقت هذا العدد اللي كتبته هو في الواقع على
+
+76
+00:07:10,980 --> 00:07:17,370
+صورة أربعة K زي التلاتة ليش؟ شوف كيف بيساويأربعة
+
+77
+00:07:17,370 --> 00:07:23,830
+في Q واحد في Q اتنين لعندي QS ناقص واحد لكل ايه
+
+78
+00:07:23,830 --> 00:07:32,830
+شماله مظبوط الان اضرب هذه اربعة Q واحد لعندي QS
+
+79
+00:07:32,830 --> 00:07:39,990
+ناقص اربعة زائد تلاتة تطلع ايهاش-1 واضح اذا صار
+
+80
+00:07:39,990 --> 00:07:44,530
+الرقم الان العدد اللي عندي ان ايه شماله على صورة
+
+81
+00:07:44,530 --> 00:07:54,270
+4k زي ادمين زي التلاتة طيب اي سؤال صار العدد عندي
+
+82
+00:07:54,270 --> 00:08:02,070
+الان هذا على صورة 4k زي التلاتة الان عنديالـ Q1
+
+83
+00:08:02,070 --> 00:08:11,010
+والـ Q2 عند الـ Qs عبارة عن odd numbers أكيد أه؟
+
+84
+00:08:11,010 --> 00:08:17,010
+odd لأن كلنا على صورة 8 4K زي 3 والآن هذا ال odd
+
+85
+00:08:17,010 --> 00:08:22,710
+number حصلت
+
+86
+00:08:22,710 --> 00:08:29,130
+ضرب صار odd مضروف في 4مضروف فاربع سار even لأن
+
+87
+00:08:29,130 --> 00:08:33,090
+مطرح من واحد بيصير عياشه إذا هذا الان عبارة عن odd
+
+88
+00:08:33,090 --> 00:08:40,210
+مدام الان odd إذا الان اللي عندي هذا هو عبارة عن
+
+89
+00:08:40,210 --> 00:08:46,390
+odd number على هذه الصورة والان هذا أكبر من واحد
+
+90
+00:08:46,390 --> 00:08:51,180
+أكيدليش أكبر من واحد أكيد لأن هذولة على صورة
+
+91
+00:08:51,180 --> 00:08:55,820
+الـprimes هذولة على صورة 4K زي التلاتة يعني أكيد
+
+92
+00:08:55,820 --> 00:08:59,520
+.. أكيد هذولة في من التلاتة والخمسة والسبعة وكذا
+
+93
+00:08:59,520 --> 00:09:04,380
+لما نقضرهم في بعض هيطلع رقم أكبر من .. من .. من ..
+
+94
+00:09:04,380 --> 00:09:06,720
+من .. من اتنين أكبر من تلاتة أو أكبر من أربعة
+
+95
+00:09:06,720 --> 00:09:10,820
+الاخرين لما أطرح منه واحد أكيد بيضل أشماله أكبر من
+
+96
+00:09:10,820 --> 00:09:15,060
+واحد يعني إذا صار عندي الآن عبارة عن عدد أكبر من
+
+97
+00:09:15,060 --> 00:09:15,340
+واحد
+
+98
+00:09:18,110 --> 00:09:21,950
+بقدر أكتبه على صورة n و product of the primes
+
+99
+00:09:21,950 --> 00:09:30,810
+سميهم الواحد اتنين عدمين RT مثلا معايا؟ طيب صار
+
+100
+00:09:30,810 --> 00:09:36,490
+الان هذا n is odd و حللته على صورة product of the
+
+101
+00:09:36,490 --> 00:09:40,990
+primes طبعا كل الprimes اللي هنا هيكون ال odd لأن
+
+102
+00:09:40,990 --> 00:09:44,550
+لو واحد فيه even معناته صار الان إيه شماله is even
+
+103
+00:09:44,550 --> 00:09:49,470
+و احنا الان تبعنا إيه شماله is oddمدام الـ Rs اللي
+
+104
+00:09:49,470 --> 00:09:55,430
+هنا is odd إذا هذولة الـ prize اللي هنا ياها صورة
+
+105
+00:09:55,430 --> 00:10:03,590
+4k زائد 1 يا 4k زائد 2، تلاتة الآن لو كانوا كلهم
+
+106
+00:10:03,590 --> 00:10:08,150
+على صورة 4k زائد 1 حسب النظرية اللي جابلت بشوية
+
+107
+00:10:08,150 --> 00:10:14,010
+هيكون ال product برضه على صورة 4k زائد 1 كمان مرة
+
+108
+00:10:14,010 --> 00:10:20,410
+الآن هذا unoddإذاً الـ Primes كلهم اللي فيه إيه
+
+109
+00:10:20,410 --> 00:10:26,430
+أُدمعناته صار الـprimes R1,R2,RT يا على صورة 4K
+
+110
+00:10:26,430 --> 00:10:33,710
+زائد 1 يا 4K زائد 3 الآن أنا بقول لو كان كلهم على
+
+111
+00:10:33,710 --> 00:10:38,130
+صورة 4K زائد 1 معناته حاصل دورفن هيطلع 4K زائد إيش
+
+112
+00:10:38,130 --> 00:10:43,390
+واحد لكن الألقى بقيت مع صورة 2 4K زائد 3 إذن في
+
+113
+00:10:43,390 --> 00:10:49,960
+واحد منهم عن أقل على صورة 2 4K زائد 3إذا صار في
+
+114
+00:10:49,960 --> 00:10:55,380
+عندهم واحد منهم سميه RK مثلا أو RN أو RN من اللي
+
+115
+00:10:55,380 --> 00:11:05,280
+بدكيها RN على صورة مين؟ 4K زائد 3بمعنى إن RK سار
+
+116
+00:11:05,280 --> 00:11:11,440
+منين و 1 من الـ Q1 و Q2 عندين لأنه احنا فرضين إن
+
+117
+00:11:11,440 --> 00:11:15,380
+كل الأعداد الـ Primes اللي في الدنيا اللي ع صورة
+
+118
+00:11:15,380 --> 00:11:22,480
+4K زي 3 هي Q1 و Q2 عندين QS إذا صار الـ RM 1 من
+
+119
+00:11:22,480 --> 00:11:29,820
+هذول مدام 1 منهم إذا أكيد الـ RM هيجسم Q1 في Q2
+
+120
+00:11:29,820 --> 00:11:38,710
+لعند Q2 Sومنه على طول بيعطيني الـ RM بكسم الأربعة
+
+121
+00:11:38,710 --> 00:11:46,790
+في Q1 لعند QS لكن من جهة أخرى الـ M بتساوي R1 R2
+
+122
+00:11:46,790 --> 00:11:52,930
+لعند الـ RT وRM واحد منهم إذا الـ RM صار بيكسم منه
+
+123
+00:11:52,930 --> 00:12:01,810
+برضه الـ M كم مرة الـ M RM واحد من هدولماشي الحال
+
+124
+00:12:01,810 --> 00:12:06,010
+إذا الـ RM بيجسم مين صار؟ لأن الـ N productive في
+
+125
+00:12:06,010 --> 00:12:08,970
+هذه القولة كلها إذا صار عندي الـ RM بيجسم الـ N
+
+126
+00:12:08,970 --> 00:12:12,390
+وبيجسم اللي هو هذا المقدار إذا بيجسم أي linear
+
+127
+00:12:12,390 --> 00:12:17,370
+combination بينهم إذا الـ RM بيجسم اللي هو أربعة
+
+128
+00:12:17,370 --> 00:12:25,570
+Q1 لعندي QS ناقص مين الـ N هذا على بعضه مين هو؟
+
+129
+00:12:25,570 --> 00:12:29,250
+هذا على بعضه ليش تلاتة؟
+
+130
+00:12:32,700 --> 00:12:39,500
+أربعة Q واحد لان دي QS ناقص أربعة Q ناقص ناقص واحد
+
+131
+00:12:39,500 --> 00:12:43,860
+الواحد ايش بيطلع يعني الأرقام أيش مالها بتكسب من
+
+132
+00:12:43,860 --> 00:12:49,200
+الواحد إذا الأرقام أيش بتساوي وهذا contradiction
+
+133
+00:12:49,200 --> 00:12:54,080
+لأن أرقام is a prime therefore our first
+
+134
+00:12:54,080 --> 00:12:59,930
+assumptionis not true so there are infinite number
+
+135
+00:12:59,930 --> 00:13:05,750
+of primes of the form mean أربعة K زائد تلاتة تطلع
+
+136
+00:13:05,750 --> 00:13:12,810
+لفوق الآن معلومة أخيرة في ال section هي اللي بدنا
+
+137
+00:13:12,810 --> 00:13:18,230
+نعمل ال section هذا بس ال theorem الأخيرة theorem
+
+138
+00:13:18,230 --> 00:13:25,170
+تلاتة السبعة بدون مروحانة الوضرية
+
+139
+00:13:26,290 --> 00:13:34,610
+هي كما يلي خد
+
+140
+00:13:34,610 --> 00:13:40,210
+الآن a,b element in z وافترض ان الـ Greatest
+
+141
+00:13:40,210 --> 00:13:46,910
+common divisor بين a وb هو 1 معايا؟
+
+142
+00:13:49,030 --> 00:13:53,690
+واخد اللي هي الـ sequence أو الاعداد على صورة A A
+
+143
+00:13:53,690 --> 00:13:59,870
+زائد B A زائد تلتة B A زائد أربعة B إلى ما لنهاية
+
+144
+00:13:59,870 --> 00:14:07,610
+الاعداد على هذه الصورة ماشي الحال اه
+
+145
+00:14:07,610 --> 00:14:16,590
+اه لأ لأ كله بالمظبوط A زائد 2 بس أنا منسيها
+
+146
+00:14:25,380 --> 00:14:30,980
+هذه الأيان الأعداد اللي بيحكي في النظرية بيقول ان
+
+147
+00:14:30,980 --> 00:14:35,460
+و شمالها there are infinite number of primes في
+
+148
+00:14:35,460 --> 00:14:41,220
+داخلها فاشي؟ إذا النظرية هي كالتالي F لـ Greatest
+
+149
+00:14:41,220 --> 00:14:47,310
+common divisor بين الـA و الـB بساوة 1ثم يكون هناك
+
+150
+00:14:47,310 --> 00:14:53,030
+عدد محدد من الـ Primes من هذه السيكوانس A وA زائد
+
+151
+00:14:53,030 --> 00:14:57,470
+B وA زائد 2B وA زائد 3B وA زائد 4B إلى مالا نهاية
+
+152
+00:14:57,470 --> 00:15:01,990
+هذا بس من اللي يعرف النص النظرية هذا ليه يعني إن
+
+153
+00:15:01,990 --> 00:15:04,870
+هنا Primes مش شرط يكون هنا Primes كلها
+
+154
+00:15:08,840 --> 00:15:13,600
+لأنه مثال بسيط خد تلاتة والسبعة مثلا تلاتة والسبعة
+
+155
+00:15:13,600 --> 00:15:17,940
+مجموح إنهاش ماله اللي هو عشرة مش برايم لكن في
+
+156
+00:15:17,940 --> 00:15:20,680
+هذولة في داخلها ماله في infinite number of the
+
+157
+00:15:20,680 --> 00:15:25,300
+primes بكون عندنا ال homework تلاتة تلاتة هيك
+
+158
+00:15:25,300 --> 00:15:28,400
+بنكون خلصنا chapter تلاتة يوم السبت إن شاء الله
+
+159
+00:15:28,400 --> 00:15:33,710
+نعمل discussion ل chapter تلاتةفضروري تيجي درسين
+
+160
+00:15:33,710 --> 00:15:40,190
+chapter 3 ومطلعين على الأسئلة وحلين الأسئلة بقدر
+
+161
+00:15:40,190 --> 00:15:44,430
+الإمكان نيجي للجزء الثاني من المحاضرة الجزء الثاني
+
+162
+00:15:44,430 --> 00:15:48,490
+اللي هو the theory of congruences أو نظرية
+
+163
+00:15:48,490 --> 00:15:53,550
+التطابقات ال chapter 4 عنوانه the theory of
+
+164
+00:15:53,550 --> 00:15:59,050
+congruencesسنبدأ بالقسم الثاني باسك بروبارتيز of
+
+165
+00:15:59,050 --> 00:16:02,930
+congruences بعض اللي هي الخواص الأساسية لل
+
+166
+00:16:02,930 --> 00:16:09,970
+congruences خلّينا نشوف إيش اللي بنقصده في ال
+
+167
+00:16:09,970 --> 00:16:14,970
+congruences وماذا يعني إيه تطابق is congruent to
+
+168
+00:16:14,970 --> 00:16:19,990
+be مدلؤاً الآن طبعاً هذا اللي هو the theory of
+
+169
+00:16:19,990 --> 00:16:24,640
+congruences أساس أنظمة العداللي احنا بنعرف النظام
+
+170
+00:16:24,640 --> 00:16:27,780
+العد السناء أو الثلاث أو الربع أو العشري تبعنا إلى
+
+171
+00:16:27,780 --> 00:16:36,060
+آخره فنشوف كيف الان a تطابق بي modulo n ايش بتعني
+
+172
+00:16:36,060 --> 00:16:43,720
+او a is congruent to b modulo n a تطابق بي بالنسبة
+
+173
+00:16:43,720 --> 00:16:51,260
+للمقياس n ايش بتعني ياضيا ابنعنيها بتعني انه اللي
+
+174
+00:16:51,260 --> 00:16:59,690
+هو الامرتقسم الـ A minus B بنقول عن العدد A أنه
+
+175
+00:16:59,690 --> 00:17:04,130
+بطابق الـ B modulo N إذا و فقط إذا الـ N بيجسمين
+
+176
+00:17:04,130 --> 00:17:13,370
+الـ A minus B وبنقول عن العدد A is incongruent للـ
+
+177
+00:17:13,370 --> 00:17:21,110
+B modulo N A is not congruent أو is incongruent
+
+178
+00:17:21,110 --> 00:17:29,550
+moduloأو B modulo N بيعني أن N لا تقسم من الـ A
+
+179
+00:17:29,550 --> 00:17:34,510
+minus B أو مش من عوام الـ A minus B نيجي الأن ناخد
+
+180
+00:17:34,510 --> 00:17:39,490
+بعض الأمثلة العددية اللي بتوضح الأمر وخلّينا نشوف
+
+181
+00:17:39,490 --> 00:17:46,010
+نربطها بالأنظمة العدد اللي بنعرفها و بين النظرية
+
+182
+00:17:46,010 --> 00:17:51,310
+اللي هيقلحها نحكي عنها نيجي ناخد أول إشياللي هو
+
+183
+00:17:51,310 --> 00:17:59,390
+مقياس اتنين Modulo اتنين Modulo اتنين بالمناسبة
+
+184
+00:17:59,390 --> 00:18:03,550
+هذا مثال اللي هو A تطابق V Modulo N مثال بناخده في
+
+185
+00:18:03,550 --> 00:18:08,790
+مبادئ رياضيات مثال على ال equivalence relation
+
+186
+00:18:08,790 --> 00:18:13,130
+وبناخد أمثلة ونشوف ونثبت انه equivalence relation
+
+187
+00:18:13,130 --> 00:18:16,270
+ومن ثم بناخد أمثلة عددية بنوجد ال equivalence
+
+188
+00:18:16,270 --> 00:18:22,800
+classes في كل حالة ماشي الحالة طيبالآن خلّينا ناخد
+
+189
+00:18:22,800 --> 00:18:29,720
+اللي هو إيش الأعداد اللي بالطابق مثلا الواحد
+
+190
+00:18:29,720 --> 00:18:34,140
+modulo اتنين إيش الأعداد اللي بالطابق الواحد
+
+191
+00:18:34,140 --> 00:18:39,700
+modulo اتنين كيف بافحص؟ بافحص إنه بدي التمين يقسم
+
+192
+00:18:39,700 --> 00:18:44,920
+الـB minus واحد أو الواحد minus B مش فارقة الـB
+
+193
+00:18:44,920 --> 00:18:51,170
+minus واحدمين الأعداد اللي بتجسم الـP-1 الفردية؟
+
+194
+00:18:51,170 --> 00:18:56,050
+كلها التلاتة والخمسة والسبعة والتسعة والحداشر ومن
+
+195
+00:18:56,050 --> 00:18:59,810
+الجهة الثانية ناقص واحد إلى آخر إيه إذا وكأنه اللي
+
+196
+00:18:59,810 --> 00:19:06,430
+بتطابق الواحد ومقياس الاتنين هي واحد نفسها وتلاتة
+
+197
+00:19:06,430 --> 00:19:13,250
+وخمسة وسبعة وتسعة وناقص واحد الـodd numbers
+
+198
+00:19:13,250 --> 00:19:21,240
+والناقص واحد والناقص تلاتةإلى مانا نهاية الان لو
+
+199
+00:19:21,240 --> 00:19:26,720
+جينا لأي اتنين مع بعض من هنا الواحد
+
+200
+00:19:26,720 --> 00:19:32,400
+طابق الكل وكل واحد هنا بطابق الآخرين لو جيت السبعة
+
+201
+00:19:32,400 --> 00:19:36,600
+و الخمسة هتلاقي السبعة تطابق الخمسة موجودة اتنين
+
+202
+00:19:36,600 --> 00:19:43,040
+ليش؟ لأنه حاصل طرح بطلع مين عدد زوجي واضح، إذا كل
+
+203
+00:19:43,040 --> 00:19:50,680
+هذولة بطابق بعضأي سؤال نيجي الآن هدولة لو اجينا
+
+204
+00:19:50,680 --> 00:19:52,980
+بقى طبعا الاتنين واضح مش فيها ولا الأربعة ولا
+
+205
+00:19:52,980 --> 00:19:56,940
+الستة فبنشوف الاتنين بتابق مين أو الأربعة بتابق
+
+206
+00:19:56,940 --> 00:20:01,420
+مين يعني الآن بدي أسأل الأربعة بتابق مين مثلا
+
+207
+00:20:01,420 --> 00:20:08,880
+modulo الاتنين يعني بدي الأعداد بيه اللي اتنين
+
+208
+00:20:08,880 --> 00:20:14,510
+بتقسم أربعة ناقصB أكيد هتقول الأربعة نفسها و هتقول
+
+209
+00:20:14,510 --> 00:20:17,630
+التنين نفسها و هتقول الستة و هتقول التمانية و
+
+210
+00:20:17,630 --> 00:20:20,290
+الناقص اتنين و الناقص أربعة إذا كل الإعداد مين
+
+211
+00:20:20,290 --> 00:20:27,430
+الزوجية إذا صار عندي الآن مقياس التنين الأربعة
+
+212
+00:20:27,430 --> 00:20:33,050
+تطابق نفسها تطابق التنين تطابق السفر تطابق ناقص
+
+213
+00:20:33,050 --> 00:20:38,160
+التنين تطابق اللي هو الستة إلى مال نهايةوكأنه
+
+214
+00:20:38,160 --> 00:20:43,900
+مقياس التنين .. مقياس التنين الآن قسم ليه؟ الزد
+
+215
+00:20:43,900 --> 00:20:51,960
+إلى جزئين اللي هو جزء كلهم بتارقن بعض و جزء اللي
+
+216
+00:20:51,960 --> 00:20:57,800
+هو برضه آخر بتارقن بعض لكن هذولا لا يتارقنين وكأنه
+
+217
+00:20:57,800 --> 00:21:00,480
+فصلّي الزد أو اعمليها نوعين
+
+218
+00:21:03,920 --> 00:21:08,340
+الآن لو اجينا خلّي المراحة ده هرجعلها اجينا ناخد
+
+219
+00:21:08,340 --> 00:21:13,340
+مدنه مين؟ مدنه تلاتة مثلاً لو اجينا بدنا الأعداد
+
+220
+00:21:13,340 --> 00:21:22,940
+اللي هو إيش بطابق الواحد مدنه مين؟ مدنه تلاتة الآن
+
+221
+00:21:22,940 --> 00:21:29,920
+مين اللي بيفحصلنا تلاتة تجسم بيه ماقص واحد أول
+
+222
+00:21:29,920 --> 00:21:35,760
+حاجة الواحد بطابق حالهبعدين مين عشان بيناقص واحد
+
+223
+00:21:35,760 --> 00:21:41,320
+يطلع أش منه من مضاعفات التلاتة اللي كل مرة بيفيه
+
+224
+00:21:41,320 --> 00:21:46,600
+أش تلاتة بيطلع أربعة سبعة وعشرة وهنا أش منه نقص
+
+225
+00:21:46,600 --> 00:21:56,510
+اتنين إلى هالنهاية الآن واضح انه اللي عندي هنالو
+
+226
+00:21:56,510 --> 00:22:01,510
+طلعت عليهم هيطلع إن الأعداد اللي لو قسمتهم على
+
+227
+00:22:01,510 --> 00:22:07,150
+تلاتة بزيد إيش؟ واحد، ماشي الحال؟ طيب نيجي إلى
+
+228
+00:22:07,150 --> 00:22:11,010
+كلهم لو قسمتهم على تلاتة إيش مانوا بزيد؟ واحد وكأن
+
+229
+00:22:11,010 --> 00:22:16,330
+كل الأعداد اللي متبقيهم زي بعض متطابقات بالنسبة
+
+230
+00:22:16,330 --> 00:22:22,890
+لمين اللي مقسم عليه؟ واضح أه؟ الآن نيجي واضح إن
+
+231
+00:22:22,890 --> 00:22:27,390
+الاتنين مش موجودة هنابدنا نشوف اللي هو اتنين يطابق
+
+232
+00:22:27,390 --> 00:22:32,850
+مين مدنه مين يعني بدنا نشوف مين التلاتة تجسم بيه
+
+233
+00:22:32,850 --> 00:22:38,150
+نقص اتنين ايش ال بيه؟ اولش اتنين غير اتنين خمسة و
+
+234
+00:22:38,150 --> 00:22:46,490
+تمانية فاهمين؟ هو نفس الاشي من الجهة الأخرى معايا؟
+
+235
+00:22:46,490 --> 00:22:50,390
+الآن في
+
+236
+00:22:50,390 --> 00:22:55,440
+أعداد لسه مش وجودةاللي هو مين مثلا التلاتة نفسها
+
+237
+00:22:55,440 --> 00:23:01,560
+مظبوط الآن بدنا نشوف التلاتة الطابق مين مدوا مين
+
+238
+00:23:01,560 --> 00:23:06,700
+مدوا تلاتة هتطلع مين التلاتة والستة والتسعة
+
+239
+00:23:06,700 --> 00:23:11,860
+والاطماعش والجهة الثانية اللي هو صفر ناقص ثلاثة
+
+240
+00:23:11,860 --> 00:23:18,550
+إلى ما لا نهايةوكأنه .. وكأنه الـ Z بواصفة المقياس
+
+241
+00:23:18,550 --> 00:23:23,470
+ثلاثة جزّقناها إلى تلت أجزاء هي الجزء الأول اللي
+
+242
+00:23:23,470 --> 00:23:28,910
+المتبقى له واحد لما نقسمها تلاتة والجزء الثاني
+
+243
+00:23:28,910 --> 00:23:33,070
+اللي المتبقى له اتنين والجزء الثالث اللي متبقى له
+
+244
+00:23:33,070 --> 00:23:40,220
+اياش سفرمعايا وهذا اللي بيقودنا لأنظمة العد لنظام
+
+245
+00:23:40,220 --> 00:23:44,600
+العد الثنائي بنعتبر هؤلاء الأقام concurrent لبعض
+
+246
+00:23:44,600 --> 00:23:50,780
+فبناخد عددين مثلنهم اللي هو بنبدأ بالـ 0 و 100 و 1
+
+247
+00:23:51,450 --> 00:23:56,330
+ولما العدد يكبر عن الواحد بيصير خانة تانية يبقى
+
+248
+00:23:56,330 --> 00:24:00,610
+يشبه السفر للسفر وهكذا هذا اللي هو اللي .. اللي ..
+
+249
+00:24:00,610 --> 00:24:03,130
+اللي .. اللي .. اللي كنا نحكي عنه نظام العدنين
+
+250
+00:24:03,130 --> 00:24:07,490
+اثنائي من ال .. من المقياس ثلاثة نقدر نحكي عن نظام
+
+251
+00:24:07,490 --> 00:24:12,410
+العد الثلاثي من أعداده الأساسية صفر واحد واثنين
+
+252
+00:24:12,880 --> 00:24:16,880
+أيضًا اللي هو نظام تبعنا العدل العشري اللي هو
+
+253
+00:24:16,880 --> 00:24:22,320
+modulo 100 هيكون عشرة فبتصير اللي هي الأعدادنا
+
+254
+00:24:22,320 --> 00:24:27,880
+اللي هي سفر واحد واثنين لعند مين لعند إيش لعند
+
+255
+00:24:27,880 --> 00:24:37,090
+التسعة الآن واضح إن كل واحد من هذولةباقي القسمة
+
+256
+00:24:37,090 --> 00:24:41,310
+على ثلاثة زي بعض وهنا باقي القسمة على ثلاثة زي بعض
+
+257
+00:24:41,310 --> 00:24:43,370
+وهنا باقي القسمة على ثلاثة زي بعض
+
+258
+00:24:46,960 --> 00:24:53,080
+بقودنا لإنه نروح باتجاه نظرية بدنا نثبتها انه for
+
+259
+00:24:53,080 --> 00:24:58,080
+an arbitrary a و b element in z a is congruent to
+
+260
+00:24:58,080 --> 00:25:03,080
+b modulo n if and only if a and b إشمالهم have the
+
+261
+00:25:03,080 --> 00:25:09,220
+same remainder when they divided by mean by nيعني
+
+262
+00:25:09,220 --> 00:25:15,560
+A تطابق B مدلؤا إذا وفقط إذا كان الـ A والـ B الهي
+
+263
+00:25:15,560 --> 00:25:22,760
+النفس المتبقى عندما يقسم كل منهما على N باضح؟
+
+264
+00:25:22,760 --> 00:25:35,160
+انبردوا الآن
+
+265
+00:25:35,160 --> 00:25:37,960
+بتفترض صبوز
+
+266
+00:25:43,490 --> 00:25:50,310
+that A is congruent to B modulo of B modulo of A
+
+267
+00:25:50,310 --> 00:25:51,110
+modulo of B modulo of A modulo of B modulo of A
+
+268
+00:25:51,110 --> 00:25:54,210
+modulo of B modulo of A modulo of B modulo of A
+
+269
+00:25:54,210 --> 00:25:56,710
+modulo of B modulo of A modulo of B modulo of A
+
+270
+00:25:56,710 --> 00:26:00,770
+modulo of B modulo of A modulo of B modulo of A
+
+271
+00:26:00,770 --> 00:26:04,430
+modulo
+
+272
+00:26:04,430 --> 00:26:08,270
+of B modulo of B modulo of B modulo of B modulo of
+
+273
+00:26:08,270 --> 00:26:08,310
+B modulo of B modulo of B modulo of B modulo of B
+
+274
+00:26:08,310 --> 00:26:10,110
+modulo of B modulo of B modulo of B modulo of B
+
+275
+00:26:10,110 --> 00:26:13,960
+modulo of B modulo of B modulo of B modمظبوط؟ ومنه
+
+276
+00:26:13,960 --> 00:26:24,600
+على طول أنه a minus b بساوي k في n for some k
+
+277
+00:26:24,600 --> 00:26:32,980
+element in mean nz واضح أه؟ الآن بدنا ننجل هذا على
+
+278
+00:26:32,980 --> 00:26:42,910
+الجهة الثانية a بتساوي b زي مين k في nالان انا غلط
+
+279
+00:26:42,910 --> 00:26:46,930
+دي اروح وين ان اثبتلك ان a و b لما نينجس من على n
+
+280
+00:26:46,930 --> 00:26:51,790
+الى نفس الـ remainder اجسمني الان بي على مين؟ على
+
+281
+00:26:51,790 --> 00:27:03,190
+n by dividing algorithm عندي اللي هو b هتسوى q في
+
+282
+00:27:03,190 --> 00:27:10,230
+n زائد r اكبر او سوى سفر و ازهر من مين؟من N أيش
+
+283
+00:27:10,230 --> 00:27:15,350
+عملت يا جماعة جسمت ال B على مين؟ على ال N طلع ناتج
+
+284
+00:27:15,350 --> 00:27:20,510
+القسمة Q وهو وحيد وطلع عند متبق القسمة بين 0 و بين
+
+285
+00:27:20,510 --> 00:27:25,290
+N وهو وحيد ماشي الحال؟ طيب لان بتثبتلك ان متبق
+
+286
+00:27:25,290 --> 00:27:29,910
+القسمة بين ال A و ال M برضه هيطلع مين؟ اللي هو R
+
+287
+00:27:29,910 --> 00:27:36,610
+عوضتها عوضتها اذا من اللي هو هي عندي مثلا واحد وهي
+
+288
+00:27:36,610 --> 00:27:45,870
+اتنين fromواحد and اتنين we have ايش we have a
+
+289
+00:27:45,870 --> 00:27:54,670
+بتساوي qn زائد r مكان ال b زائد
+
+290
+00:27:54,670 --> 00:27:59,750
+k فعلا ويساوي جمعلي اللي هي اللي فيها الان مع بعض
+
+291
+00:27:59,750 --> 00:28:09,210
+بيصير kزاد Q فـ N زاد مين زاد R أصبح الأن لـ A على
+
+292
+00:28:09,210 --> 00:28:15,650
+صورة اللي هو ناتج القسمة اللي هو Q زاد K ومتبقى
+
+293
+00:28:15,650 --> 00:28:19,970
+القسمة مين؟ R والـ R طبعا بين مين مين؟ بين R أكبر
+
+294
+00:28:19,970 --> 00:28:25,670
+شهر سفر وأصغر من مين؟ هذا يعني أنه متبقى القسمة
+
+295
+00:28:25,670 --> 00:28:31,030
+للـ A على الـ N هو R وفي الأصل عندي متبقى القسمة
+
+296
+00:28:31,800 --> 00:28:36,240
+للـ B على ال N هو ال R إذا ال A و ال B have the
+
+297
+00:28:36,240 --> 00:28:44,180
+same remainder إذا hence أو therefore A و B have
+
+298
+00:28:44,180 --> 00:28:54,840
+the same remainder when they divided by N أي سؤال؟
+
+299
+00:29:02,900 --> 00:29:07,980
+طيب conversely .. conversely بدنا نفترض أن a و b
+
+300
+00:29:07,980 --> 00:29:12,820
+اللي نفسه الميندر و نصر للهن الشمال هن they are
+
+301
+00:29:12,820 --> 00:29:26,020
+congruent modulo n إذن conversely
+
+302
+00:29:26,020 --> 00:29:31,280
+صباز
+
+303
+00:29:32,700 --> 00:29:44,600
+that a بتساوي b في q في n زائد r أكبر يساوي صفر
+
+304
+00:29:44,600 --> 00:29:47,900
+أصغر من n سميها q واحد
+
+305
+00:29:50,380 --> 00:29:56,320
+B بتساوي Q2 في N زائد R وR أكبر يساوي سفر وأصغر من
+
+306
+00:29:56,320 --> 00:30:00,860
+مين N أشي اللي فرضناه فرضنا إنه إنه لما جسمنا ال A
+
+307
+00:30:00,860 --> 00:30:04,720
+على ال N طلع اللي هو remainder R لما جسمنا ال B
+
+308
+00:30:04,720 --> 00:30:07,000
+على ال N طلع اللي هو remainder R يعني A وB have
+
+309
+00:30:07,000 --> 00:30:09,900
+the same remainder لإن الانتباه أن هما congruent
+
+310
+00:30:09,900 --> 00:30:21,980
+مضلوا N مضلوا N الآن A minus B معايا بساويQ واحد
+
+311
+00:30:21,980 --> 00:30:29,820
+نقص Q اتنين فان والار واحد مع الار وهذا يعني ايش
+
+312
+00:30:29,820 --> 00:30:37,640
+and so ال and تجسم a minus b hence a is congruent
+
+313
+00:30:37,640 --> 00:30:48,790
+to b modulo اي سؤال اي استفسار طيبناخد الآن خواص
+
+314
+00:30:48,790 --> 00:30:53,190
+أخرى from congruences الخواص اللي حكينا عنها في
+
+315
+00:30:53,190 --> 00:30:57,950
+الأول أنه اللي هي علاقة الـ congruence هذه بتعمل
+
+316
+00:30:57,950 --> 00:31:03,770
+equivalence relation يعني بمعنى آخر هتكون اللي هو
+
+317
+00:31:03,770 --> 00:31:10,910
+symmetric و transitive و reflexive، مظبوط؟ و هنا
+
+318
+00:31:10,910 --> 00:31:15,920
+خواص أخرى أيضًا، نيجي نتطلع الخواص واحدة واحدةلأن
+
+319
+00:31:15,920 --> 00:31:21,380
+let n أكبر من 0 be fixed and a و b و c be
+
+320
+00:31:21,380 --> 00:31:27,160
+arbitrary integers then خاصية الأولى أن a تطابق
+
+321
+00:31:27,160 --> 00:31:30,960
+نفسها مضلمين n اللي هي إيش بنسميها reflexive
+
+322
+00:31:30,960 --> 00:31:37,400
+الواحدة
+
+323
+00:31:37,400 --> 00:31:40,700
+trivial case أكبر من واحدة معايا
+
+324
+00:31:44,930 --> 00:31:50,370
+الـ A تطابق بي مضلونيين مضلون لأن في حالة الواحد
+
+325
+00:31:50,370 --> 00:31:58,530
+كل الدنيا أشمالها متطابقات الواحد
+
+326
+00:31:58,530 --> 00:32:07,840
+يقسم A-Bمحالة mode الواحد الواحد بيكسب مين متحققة
+
+327
+00:32:07,840 --> 00:32:11,640
+يعني يعني بنفع نقول أن أكبر من إياش من سفر وبنفع
+
+328
+00:32:11,640 --> 00:32:14,980
+نقول أن أكبر أو يساوي واحد فاحنا طبعا عساس أنه
+
+329
+00:32:14,980 --> 00:32:18,100
+نكسب الواحد ماحنا و ال general case بنقول أن أكبر
+
+330
+00:32:18,100 --> 00:32:22,580
+أو يساوي واحد أو بنقول أن أكبر من مين من سفر يعني
+
+331
+00:32:22,580 --> 00:32:26,180
+لما أكتب أن أكبر من سفر معناته أنها إياش أن أكبر
+
+332
+00:32:26,180 --> 00:32:31,320
+أو يساوي واحدفمافيش نفس الاشي يعني في الكتاب انا
+
+333
+00:32:31,320 --> 00:32:35,720
+اكبر مساوية واحد هنا انا اكبر من السبب اذا اه وحتى
+
+334
+00:32:35,720 --> 00:32:41,980
+لو مساوية عندى بس
+
+335
+00:32:41,980 --> 00:32:51,280
+A تطابق B modulo مين modulo واحد هذه دائما صحيح
+
+336
+00:32:51,280 --> 00:32:56,940
+ليش تريد ده ال case عشان هناك A واحد تقسم A minus
+
+337
+00:32:56,940 --> 00:32:57,260
+B
+
+338
+00:33:04,530 --> 00:33:10,280
+الخواص اللي عندنا الخاصية الأولى ايش هيقولوا معايا
+
+339
+00:33:10,280 --> 00:33:14,460
+اللي هي إيش اللي هي reflexive اللي A تطابق A
+
+340
+00:33:14,460 --> 00:33:18,880
+مدلقاً الخاصية التانية اللي هي مين؟ Symmetric A
+
+341
+00:33:18,880 --> 00:33:23,320
+تطابق B يعطينا B تطابق H A الخاصية الثالثة اللي هي
+
+342
+00:33:23,320 --> 00:33:27,800
+إيش؟ Transitive A تطابق B وB تطابق C إذن A تطابق
+
+343
+00:33:27,800 --> 00:33:32,820
+مين؟ C هذه الثلاثة احنا بنبرهنين حتى في المبادئ
+
+344
+00:33:33,610 --> 00:33:39,690
+الان خاصية ثالثة لو A تطابق B مدلوعا و C تطابق D
+
+345
+00:33:39,690 --> 00:33:48,350
+مدلوعا اذا A زاد C تطابق B زاد D مدلوعا و ايضا A
+
+346
+00:33:48,350 --> 00:33:56,870
+في C تطابق B في D مدلوعا واضحلأن الخاصية الخامسة
+
+347
+00:33:56,870 --> 00:34:01,170
+هي حالة خاصة من الخاصية مين اللي هي اللي جابلها
+
+348
+00:34:01,170 --> 00:34:05,370
+حالة خاصة بإنه أخد اللي هو الـ C تطابق الـ C
+
+349
+00:34:05,370 --> 00:34:10,510
+modulo N كيف؟ جالك الـ A تطابق B modulo N إذا A
+
+350
+00:34:10,510 --> 00:34:12,370
+زائد C تطابق B زائد C
+
+351
+00:34:16,640 --> 00:34:20,000
+اللي بعد هي a في c تطابق b في b في c يعني برهان
+
+352
+00:34:20,000 --> 00:34:24,520
+هذه اللي هو حالة اعتماد على اللي four بتقول since
+
+353
+00:34:24,520 --> 00:34:29,040
+c تطابق c modulo n اذا by four بتطلع اللي هي خمسة
+
+354
+00:34:29,040 --> 00:34:34,020
+باضح طيب اللي بعد هو اللي هو a تطابق b modulo n
+
+355
+00:34:34,020 --> 00:34:38,140
+يؤدي إلى ان a to the k تطابق b to the k modulo n
+
+356
+00:34:38,140 --> 00:34:46,810
+لكل mean لكل k element in and أي سؤال؟طيب نجي
+
+357
+00:34:46,810 --> 00:34:50,130
+نبرهن .. شوفوا إيش اللي بدنا نبرهنه إيش اللي بدنا
+
+358
+00:34:50,130 --> 00:34:54,530
+نبرهنه دي
+
+359
+00:34:54,530 --> 00:35:01,570
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+360
+00:35:01,570 --> 00:35:02,190
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+361
+00:35:02,190 --> 00:35:04,410
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+362
+00:35:04,410 --> 00:35:06,310
+دي دي دي دي دي دي دي
+
+363
+00:35:12,510 --> 00:35:19,030
+بنشوف هذا بيعطينا انه ايه تطابق c مدلؤا ماشي اذا
+
+364
+00:35:19,030 --> 00:35:24,810
+بيقول suppose that كده اذا من التعريف باشرة then
+
+365
+00:35:26,270 --> 00:35:31,630
+اللي هو n تقسم a minus b and التانية n تقسم b
+
+366
+00:35:31,630 --> 00:35:35,490
+minus c إذن بتقسم أي linear combination بينه ال n
+
+367
+00:35:35,490 --> 00:35:39,030
+ال linear combination اللي بيخدم ليه بدي أطير ال b
+
+368
+00:35:39,030 --> 00:35:42,030
+من هنا و ال b من هنا عشان أوجد اللاقة بين ال a و
+
+369
+00:35:42,030 --> 00:35:48,670
+ال c إذن hence n بتقسم ال a minus b زائد b minus c
+
+370
+00:35:48,670 --> 00:35:53,050
+اللي هو هذا ع بعضه اللي عبارة عن مين a minus c إذن
+
+371
+00:35:53,050 --> 00:36:01,660
+هذا يعنيالـ A تطابق C Modulo N هذه خاصية مين
+
+372
+00:36:01,660 --> 00:36:06,440
+لترانزيتف خاصية لترانزيتف نيجي نبرهن مين كمان
+
+373
+00:36:06,440 --> 00:36:12,200
+نبرهن أربعة لأن خمس حالة خاصة من مين من أربعة الأن
+
+374
+00:36:12,200 --> 00:36:19,880
+أربعة أيش أربعة بتقول أن A A
+
+375
+00:36:19,880 --> 00:36:30,880
+تطابق B Modulo N وCوطابق دي modulo n بدنا شغل تاني
+
+376
+00:36:30,880 --> 00:36:36,300
+ال a زائد وال a ضرب ماشي الحال نيجي لمين أولشي
+
+377
+00:36:36,300 --> 00:36:43,640
+للجامعة لأن هذا إيش بتعني أن n بتقسم a minus b
+
+378
+00:36:43,640 --> 00:36:50,840
+وهذا إيش بتعني n بتقسم c minus dالان بدنا نحصل على
+
+379
+00:36:50,840 --> 00:36:55,460
+الجمع الجمع المباشر اللي بيجيب و لا لأ إذا صار
+
+380
+00:36:55,460 --> 00:37:00,020
+عندي N بتجسم A لنا combination بينهم اللي هو A
+
+381
+00:37:00,020 --> 00:37:07,980
+minus B زائد C minus D هذا على بعض N بتجسم A زائد
+
+382
+00:37:07,980 --> 00:37:18,000
+C ماقص B زائد D مظبوط؟ وهذا اللي هو اللي بدنا أنه
+
+383
+00:37:18,000 --> 00:37:30,290
+A زائد Cتطابق بي زائد دي مدله الان أي سؤال طيب
+
+384
+00:37:30,290 --> 00:37:39,230
+نيجي لمين الآن للضرب نيجي للضرب ايش
+
+385
+00:37:39,230 --> 00:37:46,430
+غرض ايه a في c و b في مين في dشوفوا عندي N بتقسم A
+
+386
+00:37:46,430 --> 00:37:52,330
+-B و N بتقسم C-D إذا الـ N بتقسم أي Linear
+
+387
+00:37:52,330 --> 00:37:57,430
+combination بينهم أنا بدي اللي هو أحصل عالميا على
+
+388
+00:37:57,430 --> 00:38:05,370
+A في C فهضرب هذه في C، مظبوط؟ فبصير الآن C في A-B
+
+389
+00:38:05,370 --> 00:38:11,450
+زاد الآن أنا .. الآن بدي أخلي AC، مظبوط؟
+
+390
+00:38:14,090 --> 00:38:19,170
+فالان طلعت عندي هنا C في B بديش إياها C في B فالان
+
+391
+00:38:19,170 --> 00:38:23,710
+عشان أطير C في B بضربها دي في مين؟ في B بيه بيه
+
+392
+00:38:23,710 --> 00:38:26,910
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+393
+00:38:26,910 --> 00:38:27,110
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+394
+00:38:27,110 --> 00:38:27,830
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+395
+00:38:27,830 --> 00:38:30,710
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+396
+00:38:30,710 --> 00:38:35,470
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بي
+
+397
+00:38:36,130 --> 00:38:42,410
+عشان احصل على AC ضربت هدف C لكن نشأ عندي هنا CB CB
+
+398
+00:38:42,410 --> 00:38:47,610
+بقدر طيّرها من هنا A ضرب هدف مين؟ في B فصار عندي
+
+399
+00:38:47,610 --> 00:38:51,550
+الان N بتجسم هذا المقدار في هذا المقدار هذا عبارة
+
+400
+00:38:51,550 --> 00:39:01,810
+عن إيش؟ يعني N بتجسم CA نقص CB زي BC نقص CBC مع CB
+
+401
+00:39:01,810 --> 00:39:09,190
+بروحن مع بعض اذا انت بتكسب AC نقص CD معناته ان AC
+
+402
+00:39:09,190 --> 00:39:18,630
+تطابق CD Modulo B Modulo
+
+403
+00:39:18,630 --> 00:39:22,270
+مين Modulo يعني كلامكم صحيح من لئة باللئة اذا
+
+404
+00:39:22,270 --> 00:39:27,510
+الخاصية هذه برضه ايش مالها متحقق وصح لها دلعندي
+
+405
+00:39:30,260 --> 00:39:39,340
+بنثبت ان اذا A تطابق B modulo N و A K تطابق
+
+406
+00:39:39,340 --> 00:39:44,320
+الـ BK modulo N لكل K مالها بالinduction اكيد
+
+407
+00:39:44,320 --> 00:39:48,320
+مالها بالinduction و ال induction تبعها برضه سهل
+
+408
+00:39:48,320 --> 00:39:59,110
+نعم تنشوف اللي هو ال induction ل اللي هوالخاصية
+
+409
+00:39:59,110 --> 00:40:02,890
+الأخيرة عند
+
+410
+00:40:02,890 --> 00:40:11,050
+a تطابق b modulo n بدنا نثبت انه بادى الى a k
+
+411
+00:40:11,050 --> 00:40:22,600
+تطابق b k modulo n for every k element in Nالان
+
+412
+00:40:22,600 --> 00:40:26,480
+اللي هي أخر مغطى a تطابق b modulo n بيعطيني a to
+
+413
+00:40:26,480 --> 00:40:31,360
+the k تطابق b modulo k لكل k element in n اللي هو
+
+414
+00:40:31,360 --> 00:40:39,560
+بينين by induction الان for n بيساوي واحد او for k
+
+415
+00:40:39,560 --> 00:40:43,560
+بيساوي واحد it is trivial لأن هي معطى أصلا الان
+
+416
+00:40:43,560 --> 00:40:48,660
+إذا بدنا نقول suppose that اللي هي star
+
+417
+00:40:51,230 --> 00:40:58,230
+is true for k بتساوي M مثلا ماشي الحال وبدأ أثبت ل
+
+418
+00:40:58,230 --> 00:41:03,570
+M زائد واحد معايا اه اذا مادام true for k بتساوي M
+
+419
+00:41:03,570 --> 00:41:10,110
+اذا then A to the M تطابق B to the M modulo N
+
+420
+00:41:10,110 --> 00:41:17,410
+معايا لكن بطBut ان A تطابق الـ B modulo N
+
+421
+00:41:17,410 --> 00:41:21,910
+وبالنظرية اللي قبل بشوية اللي بقى خمسة التمتال مع
+
+422
+00:41:21,910 --> 00:41:27,670
+بعض اذا A to the M في A اللي هي M زائد واحد تطابق
+
+423
+00:41:27,670 --> 00:41:32,950
+الـ B أقسم في B اللي هو BM زائد واحد modulo N إذا
+
+424
+00:41:32,950 --> 00:41:35,930
+صارت اللي هي Star is true for M زائد واحد
+
+425
+00:41:35,930 --> 00:41:40,390
+Therefore Star is true for any M أو for any K
+
+426
+00:41:40,390 --> 00:41:45,290
+elementوالمرة القادمة ان شاء الله بنكمل وبكون
+
+427
+00:41:45,290 --> 00:41:48,590
+عندنا discussion ل chapter 3
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/qytPH80aNtM_postprocess.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/qytPH80aNtM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..daade9bcc904547c070065399cb4996b4594358e
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/qytPH80aNtM_postprocess.srt
@@ -0,0 +1,3252 @@
+1
+00:00:21,040 --> 00:00:25,860
+بسم الله الرحمن الرحيم المحاضرة رقم 26 مساق نظرية
+
+2
+00:00:25,860 --> 00:00:30,380
+الاعداد طلاب طالبات الجامعة الإسلامية كلية العلوم
+
+3
+00:00:30,380 --> 00:00:35,680
+والتربية قسم رياضيات اليوم ان شاء الله هيكون في
+
+4
+00:00:35,680 --> 00:00:42,800
+عنا مرادعة او مناقشة لأسئلة شبطة الخمسة وهو حول
+
+5
+00:00:42,800 --> 00:00:48,220
+Fermat's theorem وWilson's
+
+6
+00:00:48,220 --> 00:00:55,810
+theoremنبدأ في خمسة اتنين للأسئلة المطلوبة أن
+
+7
+00:00:55,810 --> 00:01:02,170
+السؤال الأول السؤال الأول يقول ما يلي use Fermat
+
+8
+00:01:02,170 --> 00:01:06,990
+theorem Fermat theorem to verify that سبعة عشر
+
+9
+00:01:06,990 --> 00:01:12,970
+divides أحداش أثنية وأربعة زائد واحد نثبت أنه سبعة
+
+10
+00:01:12,970 --> 00:01:15,590
+عشر تقسم لحداش
+
+11
+00:01:21,470 --> 00:01:28,710
+اشان نثبت اللي هو ان السبعتاش تقسم ل 11 أس 104
+
+12
+00:01:28,710 --> 00:01:38,820
+زائد 1بيعني ذلك إنه نثبت إن 11 قسمية وأربعة تطابق
+
+13
+00:01:38,820 --> 00:01:45,520
+الناقص واحد أو بمعنى زائد واحد تطابق السفر modulo
+
+14
+00:01:45,520 --> 00:01:50,780
+17 هذا اللي بدنا نثبته أو بمعنى آخر بدنا نثبت إن
+
+15
+00:01:50,780 --> 00:01:58,370
+11 قسمية وأربعة تطابق الناقص واحد modulo 17الان
+
+16
+00:01:58,370 --> 00:02:03,770
+نذكركم فرماتس فيرم فرماتس فيرم بتقول ماهي ليه لو
+
+17
+00:02:03,770 --> 00:02:11,730
+كان عند بي ال zebrain و بي لا تقسم العدد a أي
+
+18
+00:02:11,730 --> 00:02:16,530
+integer a بي لا تقسم a فبدي يكون عندي a to the b
+
+19
+00:02:16,530 --> 00:02:26,180
+minus واحد تطابق الواحد modulo اللي هوهذه اللي هي
+
+20
+00:02:26,180 --> 00:02:30,120
+Fermat's theorem وفي عندنا الـ Corollary لـ Fermat
+
+21
+00:02:30,120 --> 00:02:35,780
+اللي هي بتقولنا أي element in Z بكون A to the B
+
+22
+00:02:35,780 --> 00:02:42,600
+تطابق الـ A Modulo B هذه اللي هي النتيجتين المهمين
+
+23
+00:02:42,600 --> 00:02:48,880
+المهمتين في اللي هو خمسة اتنين ندى الآن نشوف ايش
+
+24
+00:02:48,880 --> 00:02:58,920
+الفكرة عندي اللي هو By Fermat's theoremSense 17
+
+25
+00:02:58,920 --> 00:03:07,020
+لتقسم الـ 11 then 11 to the P minus واحد اللي هي
+
+26
+00:03:07,020 --> 00:03:18,420
+16 تطابق الواحد modulo 17 اقرب رقم ل ال 104 اللي
+
+27
+00:03:18,420 --> 00:03:26,340
+هو 96 96 كيف نجيبه 11 أُس 16 أُس 6اللي هو عبارة عن
+
+28
+00:03:26,340 --> 00:03:33,720
+96 تطابق الواحد modulo 17 أنا بدي 104 فبنضرب
+
+29
+00:03:33,720 --> 00:03:43,830
+الجهتين في 11 أس 8الرقم اللي احنا 11104 تطابق ال
+
+30
+00:03:43,830 --> 00:03:50,550
+11 قص 8 modulo 17 هذا اللي هو عبارة عن مين الرقم
+
+31
+00:03:50,550 --> 00:03:59,030
+اللي احنا 11104 تطابق ال 11 قص 8 modulo 17 الان
+
+32
+00:03:59,030 --> 00:04:04,670
+بدنا نبدأ نوجد ال 11 قص 8 ال 11 قص 8 حسبته سهل ان
+
+33
+00:04:04,670 --> 00:04:15,090
+شاء اللهالآن 11 تربيع اللي هو عبارة عن 121 121 او
+
+34
+00:04:15,090 --> 00:04:22,910
+ممكن اللي هو أسهلنا ل 11 modulo 17 نشوف ايش بتطابق
+
+35
+00:04:22,910 --> 00:04:30,030
+يمكن أسهلنا كمان لو قلبنا ل 11 تربيع تطابق اللي هو
+
+36
+00:04:30,030 --> 00:04:35,930
+ماقص 6 تربيعلأن الـ 11 تطابق النقطة 6 مدوله 17
+
+37
+00:04:35,930 --> 00:04:42,330
+اللي هو عبارة عن 36 اللي هو بالنسبة للـ 17 36
+
+38
+00:04:42,330 --> 00:04:50,350
+عبارة عن 2 34 17 في 2 و 34 زاد 2 اذا مدله اللي هو
+
+39
+00:04:50,350 --> 00:04:55,230
+17 صار عند ال 11 تربيه اللي هو عبارة عن جداش عن
+
+40
+00:04:55,230 --> 00:05:06,550
+اتنين صار الآن من اي اتنين وهي عند واحدfrom واحد
+
+41
+00:05:06,550 --> 00:05:18,090
+and اتنين بيصير عندي الـ 11 قص 104 تطابق ال 11 قص
+
+42
+00:05:18,090 --> 00:05:25,300
+8 اللي هي 11 قص 2 قص 4الـ 11 أُس 2 كده شفناها
+
+43
+00:05:25,300 --> 00:05:34,000
+بيساوي 2 وهي ساوي 2 أُس 4 2 أُس 4 عبارة عن 16 الـ
+
+44
+00:05:34,000 --> 00:05:40,900
+16 بالنسبة للـ 17 عبارة عن نقص 1 مضله 17 إذا صار
+
+45
+00:05:40,900 --> 00:05:47,380
+عندي الآن 11 أُس 104 تطابق نقص 1 مضله 17 أو بمعنى
+
+46
+00:05:47,380 --> 00:05:55,080
+آخر إذا الـ 17 بتقسمالـ 11 أُسمية وأربعة زائد واحد
+
+47
+00:05:55,080 --> 00:06:01,440
+فهو المطلوب في السؤال الأول الآن الشغل مجرد حسابات
+
+48
+00:06:01,440 --> 00:06:07,300
+ولكن تطبيق على Formats Theorem نيجي للسؤال التاني
+
+49
+00:06:07,300 --> 00:06:14,400
+المطلوب نشوف كيف أيضا تطبيق على Formats Theorem
+
+50
+00:06:14,400 --> 00:06:20,280
+نشوف كيف بدنا مبرهن السؤال التاني
+
+51
+00:06:22,570 --> 00:06:30,630
+السؤال التالي يا شباب عندي بقول ماهي الـ 2A إذا
+
+52
+00:06:30,630 --> 00:06:36,370
+كان عندي F الـ greatest common divisor بين الـ A
+
+53
+00:06:36,370 --> 00:06:45,610
+والـ 35 بساوي 1 اثبت انه A تضابر 12 طابق الـ 1
+
+54
+00:06:45,610 --> 00:06:54,640
+modulo 35 انشوف كيف، بدى البرهن اللي هوأسهل عندي
+
+55
+00:06:54,640 --> 00:07:00,600
+الـ 35 العام المشارك اللي على بين الـ A و 35
+
+56
+00:07:00,600 --> 00:07:01,560
+بالساوية
+
+57
+00:07:03,780 --> 00:07:08,360
+أكيد بتساوي سبعة في خمسة اللي هو حللتها الى
+
+58
+00:07:08,360 --> 00:07:13,340
+product of the primes فبصير عيدي الآن مادام العامل
+
+59
+00:07:13,340 --> 00:07:16,200
+المشترك الأعلى بين ال a و الخمسة و تلاتين بساوي
+
+60
+00:07:16,200 --> 00:07:20,260
+واحد اذا أكيد ال greatest common divisor بين ال a
+
+61
+00:07:20,260 --> 00:07:23,800
+و السبعة هو نفسه ال greatest common divisor بين ال
+
+62
+00:07:23,800 --> 00:07:28,400
+a و الخمسة بساوي واحد هذا لإنه ال greatest common
+
+63
+00:07:28,400 --> 00:07:32,340
+divisor بين ال a و الخمسة و تلاتين بساوي واحد طيب
+
+64
+00:07:32,340 --> 00:07:42,250
+جماعةالان بناء على فرمات بتقولي اذا then بقال
+
+65
+00:07:42,250 --> 00:07:49,670
+فرمات theorem بتكون عند ا to the power 6 مطابق
+
+66
+00:07:49,670 --> 00:07:57,030
+الواحد moduloاللي هو سبعة طبعا هو المفهوم انه
+
+67
+00:07:57,030 --> 00:07:59,630
+مادام العالم المشترك الاعلى بين الـA والسبعة بساعة
+
+68
+00:07:59,630 --> 00:08:04,690
+واحد اذا ماكيد السبعة لا تقسم الـA والخمسة لا تقسم
+
+69
+00:08:04,690 --> 00:08:08,830
+الـA اذا ال firmates جاهد زي انه احنا نطبقها في
+
+70
+00:08:08,830 --> 00:08:14,610
+الحالتينفبصير عندي a⁶ تطابق الواحد مدنه جديش مدنه
+
+71
+00:08:14,610 --> 00:08:20,910
+سبعة احنا بدلين a² اذا بصير عندي them and so ومنه
+
+72
+00:08:20,910 --> 00:08:24,970
+a² اللي هي ستة أس اتنين تطابق واحد أس اتنين اللي
+
+73
+00:08:24,970 --> 00:08:29,910
+هي برضه بتطابق الواحد مدنه سبعة هذه النتيجة الأولى
+
+74
+00:08:29,910 --> 00:08:36,510
+similarly وبنفس الأسلوب similarlyعندي by Fermat's
+
+75
+00:08:36,510 --> 00:08:40,210
+theorem أنه نطبق على الـ a الخمسة الخمسة اللي هي
+
+76
+00:08:40,210 --> 00:08:45,030
+تقسم ال a إذا a to the أربعة اللي هي خمسة ناقص
+
+77
+00:08:45,030 --> 00:08:52,940
+واحد تطابق الواحد مدله خمسةومنه ومنه على طول اللي
+
+78
+00:08:52,940 --> 00:08:56,600
+هي a أُس أربعة الكل أُس ثلاثة طبق طبق واحد أُس
+
+79
+00:08:56,600 --> 00:09:02,140
+ثلاثة يعني a أُس اتناشت وطابق الواحد مودولورد خمسة
+
+80
+00:09:02,140 --> 00:09:11,670
+الان عندي واحد وعندي اتنين1 و 2 لإن العامل المشترك
+
+81
+00:09:11,670 --> 00:09:16,190
+الأعلى بين السبعة والخمسة بساوي واحد فبصير عندي
+
+82
+00:09:16,190 --> 00:09:21,530
+اللي هو ال A أس اتناشط وطابق الواحد مدنه حاصل غرب
+
+83
+00:09:21,530 --> 00:09:25,640
+من سبعة في خمسة موجة الدياشر 35من أين جاء
+
+84
+00:09:25,640 --> 00:09:29,820
+المعلومة؟ هذه المعلومة سهلة الان من هنا من الأولى
+
+85
+00:09:29,820 --> 00:09:33,980
+عند السبعة تقسم a أُس 12 ناقص واحد ومن المعلومة
+
+86
+00:09:33,980 --> 00:09:38,700
+الثانية اللي هي الخمسة بتقسم a أُس 12 ناقص واحد
+
+87
+00:09:38,700 --> 00:09:43,330
+السبعةالعوامل هذا المقدار والخمسة من العوامل نفس
+
+88
+00:09:43,330 --> 00:09:46,810
+المقدار والسبعة والخمسة مافيش أصلا بين العوامل
+
+89
+00:09:46,810 --> 00:09:50,130
+يعني مش هيتكرر العامل هان و هان إذا أكيد هذا
+
+90
+00:09:50,130 --> 00:09:53,590
+هيعطيني الخمسة و تلاتين تقسم A أقصى اتناش ناقص
+
+91
+00:09:53,590 --> 00:09:56,830
+واحد اللي هو هو اللي عنه A أقصى اتناش تطابق الواحد
+
+92
+00:09:56,830 --> 00:10:02,290
+مضله اللي هو خمسة و تلاتين واضح ماشي الحل هذا اللي
+
+93
+00:10:02,290 --> 00:10:08,660
+هو السؤال التاني ايه نيدي للسؤال التاني Bالسؤال
+
+94
+00:10:08,660 --> 00:10:12,920
+التاني بيه اللي هو معطيني الـ greatest common
+
+95
+00:10:12,920 --> 00:10:20,660
+divisor بين الـ A و 42 بساوي واحد بيقوللي اثبت
+
+96
+00:10:20,660 --> 00:10:33,360
+then عندي اللي هو A أو ال 6 تطابق الواحد مضمين مضم
+
+97
+00:10:33,360 --> 00:10:34,300
+ال 48
+
+98
+00:10:42,550 --> 00:10:51,630
+موضوله 168 موضوله 168 موضوله 168 موضوله 168 موضوله
+
+99
+00:10:51,630 --> 00:10:55,750
+168 موضوله 168 موضوله 168 موضوله 168 موضوله 168
+
+100
+00:10:55,750 --> 00:11:08,080
+موضوله 168معايا يا شباب 168 بتقسم الـ a6-1 will
+
+101
+00:11:08,080 --> 00:11:16,140
+show that الـ 168 divide a6-1 أو بمعنى آخر زي ما
+
+102
+00:11:16,140 --> 00:11:19,900
+كتبنا في الأول الـ a6 أطابق الواحد modulo من مين
+
+103
+00:11:19,900 --> 00:11:23,260
+modulo 168 solution
+
+104
+00:11:26,960 --> 00:11:32,480
+الان الـ 168 ماعطينا hint اللي هو عبارة عن 1 1 6 8
+
+105
+00:11:32,480 --> 00:11:38,630
+عبارة عن تحليلها تلاتة في سبعة في تمانيةالان
+
+106
+00:11:38,630 --> 00:11:43,590
+الفكرة مشابهة للفكرة اللي فوق عندى اللاحظ انه
+
+107
+00:11:43,590 --> 00:11:48,690
+حللها الى تلت أرقام العامل المشترك الأعلى بين كل
+
+108
+00:11:48,690 --> 00:11:52,210
+اتنين بساوي واحد بين التلاتة والسبعة واحد تلاتة و
+
+109
+00:11:52,210 --> 00:11:55,510
+تمانية واحد و تمانية وسبعة بساوي واحد على أساس ان
+
+110
+00:11:55,510 --> 00:12:02,340
+لو أثبتنالو أثبتنا أن الـ A والـ 6 تطابق الواحد
+
+111
+00:12:02,340 --> 00:12:08,080
+مدله اللي هو ثلاثة ومدله سبعة ومدله تمانية من
+
+112
+00:12:08,080 --> 00:12:13,750
+التلاتة مع بعض حسب ما عملنا في السؤال الأولفبكون
+
+113
+00:12:13,750 --> 00:12:17,310
+اللي هو بما أن العوامل المشترك الأعلى بين هدولة
+
+114
+00:12:17,310 --> 00:12:21,590
+اللي هو بساوي واحد بين كل اتنين فبصير عندي اللي هو
+
+115
+00:12:21,590 --> 00:12:25,330
+A الستة طوابق الواحد مدنه ثلاثة في سبعة في تمانية
+
+116
+00:12:25,330 --> 00:12:29,270
+اللي هو جداش مية تمانية ستين هذه فكرة الحل الان
+
+117
+00:12:29,270 --> 00:12:35,090
+الأولبواسطة فرمات مباشرة زي ايه قبل شوية والثاني
+
+118
+00:12:35,090 --> 00:12:39,390
+بواسطة فرمات مباشرة مبالها دي بدها شغل وشغل بسيط
+
+119
+00:12:39,390 --> 00:12:44,770
+في المعلومة أخدناها قبل هيك حول هذا الأمر دي دي دي
+
+120
+00:12:44,770 --> 00:12:45,250
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+121
+00:12:45,250 --> 00:12:46,290
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+122
+00:12:46,290 --> 00:12:48,010
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+123
+00:12:48,010 --> 00:12:49,190
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+124
+00:12:49,190 --> 00:12:54,910
+دي
+
+125
+00:12:54,910 --> 00:12:58,970
+ديThen لأن العام المشارك الأعلى بين الـ A والـ 6
+
+126
+00:12:58,970 --> 00:13:06,110
+و42 اللي هي 42 عبارة عن 2 في 3 في 7العامل المشترك
+
+127
+00:13:06,110 --> 00:13:11,710
+اللي على بين الـA والـ2 و 41 هو 1 و بين الـA والـ3
+
+128
+00:13:11,710 --> 00:13:16,490
+هو 1 و بين الـA والـ7 هو 1 إذا جهزة عند التلاتة لا
+
+129
+00:13:16,490 --> 00:13:22,310
+تقسم بين الـA إذا فرمت جهزة إذا صار عندي then A
+
+130
+00:13:22,310 --> 00:13:29,230
+أُس 2 تطابق الواحد مودوله اللي هو جداش 3ومنه
+
+131
+00:13:29,230 --> 00:13:33,250
+مباشرة بنرفح هنا القوة تلاتة وهنا القوة تلاتة
+
+132
+00:13:33,250 --> 00:13:38,490
+بيصير عندي and so a أو الستة تطابق الواحد modulo
+
+133
+00:13:38,490 --> 00:13:45,230
+تلاتة هاي أول واحدة واحدة لأن similarly الخمسة أو
+
+134
+00:13:45,230 --> 00:13:54,530
+السبعة لا تقسم ال a إذا أكيد عندي ال a أو الستة
+
+135
+00:13:55,160 --> 00:14:00,780
+تطابق الواحد modulo سبعة ومنه بنفس الطريقة بنرفع
+
+136
+00:14:00,780 --> 00:14:04,820
+التنتين للقوة اتنين فبصير عندي A لا بدون فلس
+
+137
+00:14:04,820 --> 00:14:11,260
+مجاهزة A الستة تطابق الواحد modulo سبعة فبصير عندي
+
+138
+00:14:11,260 --> 00:14:16,040
+التنتين الأولى والثانية جاهزة ضل علينا نجاهز
+
+139
+00:14:16,040 --> 00:14:22,780
+بالنسبة لمين بالنسبة للثمانية طيب عندنا العامل
+
+140
+00:14:22,780 --> 00:14:28,780
+المشترك الأعلىبين الـ a و 42 بساوة واحد إذا أكيد
+
+141
+00:14:28,780 --> 00:14:32,760
+العامل المشترك الأعلى بين ال a و 42 بساوة واحد
+
+142
+00:14:32,760 --> 00:14:39,280
+يعني بمعنى أخر a is an odd number الان a odd
+
+143
+00:14:39,280 --> 00:14:47,940
+number إذا أكيد اللي هو ال a على صورة in the form
+
+144
+00:14:47,940 --> 00:14:57,130
+4k زائد 1 or 4k زائد 3هذا هو الـ A odd number اذا
+
+145
+00:14:57,130 --> 00:15:00,610
+الـ A يمّع على صورة أربعة كيه اربعة كيه زي واحد او
+
+146
+00:15:00,610 --> 00:15:01,550
+اربعة كيه زي تلتة
+
+147
+00:15:25,710 --> 00:15:30,150
+يا اما اربعة K زائد واحد تربيع يا اربعة K زائد
+
+148
+00:15:30,150 --> 00:15:34,830
+تلاتة لكل تربيع وهذه بتساوي ستة عشر K تربيع زائد
+
+149
+00:15:34,830 --> 00:15:40,430
+تمانية K زائد واحد بيساوي ستة عشر K تربيع زائد
+
+150
+00:15:40,430 --> 00:15:44,910
+اللي هو تلاتة فاربعة باطمعش اربعة عشرين K زائد
+
+151
+00:15:44,910 --> 00:15:50,410
+تسعةوهذه نفسها عبارة عن هذه تطابق السفر بالنسبة
+
+152
+00:15:50,410 --> 00:15:52,870
+للتمانية وهذه تطابق السفر للتمانية إذا كانت تطابق
+
+153
+00:15:52,870 --> 00:15:57,150
+الواحد modulo تمانية هذه مصطلحة التمانية اللي
+
+154
+00:15:57,150 --> 00:16:01,250
+بديها أنا الان وهذه تطابق الان هذه برضه مضعفة
+
+155
+00:16:01,250 --> 00:16:04,870
+التمانية وهذه مضعفة التمانية إذا كانت تطابق السفر
+
+156
+00:16:04,870 --> 00:16:08,550
+modulo تمانية والتسعة بتطابق modulo تمانية واحد
+
+157
+00:16:08,550 --> 00:16:14,690
+لأن هي عبارة عن تطابق الواحد modulo تمانيةإذا من
+
+158
+00:16:14,690 --> 00:16:18,830
+عندي سواء كانت اللي هي على صورة أربعة كزات واحد أو
+
+159
+00:16:18,830 --> 00:16:22,450
+أربعة كزات تلاتة اللي هي الـ odd number A أكيد
+
+160
+00:16:22,450 --> 00:16:28,150
+هيطلع عندي A تربية تطابق الواحد modulo من modulo
+
+161
+00:16:28,150 --> 00:16:33,610
+تمانية الآن منها ارفع الجهتين لتلاتة بيصير A أقل
+
+162
+00:16:33,610 --> 00:16:38,590
+ستة تطابق الواحد modulo تمانية هذه صار عندي اللي
+
+163
+00:16:38,590 --> 00:16:43,910
+هي تلاتةلأن بما أنه زي ما قلنا في الأول عامل مشارك
+
+164
+00:16:43,910 --> 00:16:48,510
+الأعلى بين كل اتنين السبعة والتلاتة والسبعة
+
+165
+00:16:48,510 --> 00:16:52,690
+والتمانية والتمانية والتلاتة بساعة واحد وعندي من
+
+166
+00:16:52,690 --> 00:16:57,330
+الحالة الأولى والتانية والتالتة هيكون عندي ال A
+
+167
+00:16:57,330 --> 00:17:04,100
+والستةتطابق الواحد مدن حاصل ضربهم زي السؤال الأولى
+
+168
+00:17:04,100 --> 00:17:07,980
+يعني ثلاثة في سبعة في تمانية اللي هو عبارة عن واحد
+
+169
+00:17:07,980 --> 00:17:12,580
+ستة تمانية أو بمعنى آخر واحد ستة تمانية تقسم الـA
+
+170
+00:17:12,580 --> 00:17:20,620
+والستة ناقص واحد طيب نجي لفرع C آخر فرع عندنا في
+
+171
+00:17:20,620 --> 00:17:29,130
+السؤال التاني برضه الفكرة مشابهة لالسؤال الأول
+
+172
+00:17:29,130 --> 00:17:38,790
+والثاني نشوف إيش بتقول بالظبط عندي السؤال الـ C
+
+173
+00:17:38,790 --> 00:17:45,170
+بقول لي if الـ greatest common divisor بين الـ A و
+
+174
+00:17:45,170 --> 00:17:51,450
+الـ 133 تساوي ال greatest common divisor بين الـ B
+
+175
+00:17:51,450 --> 00:18:01,830
+و الـ 133 يساوي 1then show that الـ 133 تجسم A أُس
+
+176
+00:18:01,830 --> 00:18:10,640
+18 ناقص B أُس 18 solution or proofالآن بعطينا
+
+177
+00:18:10,640 --> 00:18:14,760
+العام المشترك الأعلى بين الـ A و الـ 133 و الـ B و
+
+178
+00:18:14,760 --> 00:18:21,020
+الـ 133 واحد إذن الـ 133 تجسم A أُس 18 نقص B أُس
+
+179
+00:18:21,020 --> 00:18:27,240
+18 الـ A أُس 18 و B أُس 18 بتاعتين مؤشر إنه كإن في
+
+180
+00:18:27,240 --> 00:18:31,740
+شغلعلى الـprime اللي هو تسعة عشر لأنه تسعة عشر
+
+181
+00:18:31,740 --> 00:18:35,860
+فرمة تسعة عشر نقص واحد مين تمانتاش وكأنه يعني
+
+182
+00:18:35,860 --> 00:18:40,300
+احتمال انه يكون الـ133 احد عاملها التسعة عشر اسهل
+
+183
+00:18:40,300 --> 00:18:44,300
+عليها عملية الحسابات لكن هو شراسة ان الـ133 اللي
+
+184
+00:18:44,300 --> 00:18:48,260
+وجدت حللتها هتلاقيها عبارة عن تسعة عشر تسعة عشر في
+
+185
+00:18:48,260 --> 00:18:54,420
+BL في سبعة19x7 إذا جاهزة فيرمات ان نطبق من الـ
+
+186
+00:18:54,420 --> 00:18:57,960
+Fermat theorem الان بناء ان العامل مش شرك الاعلى
+
+187
+00:18:57,960 --> 00:19:04,540
+بين الـA و133 واحد إذا بين الـA و19 والـA و7 واحد
+
+188
+00:19:04,540 --> 00:19:09,520
+وبين الـB و19 والـB و7 برضه مش بساوي واحد إذا الـ
+
+189
+00:19:09,520 --> 00:19:15,680
+Fermat جاهزة إذا by Fermat theorem بكون عندى اللي
+
+190
+00:19:15,680 --> 00:19:18,380
+هو A الـ18
+
+191
+00:19:19,670 --> 00:19:29,490
+تطابق الواحد modulo تسعة عشر ونفس الاشي عندى اللى
+
+192
+00:19:29,490 --> 00:19:35,590
+هو بيقص تمانتاش تطابق الواحد modulo تسعة عشر لنفس
+
+193
+00:19:35,590 --> 00:19:44,530
+الأسباب وعندي بنفس الأسلوبولو جينا للـ7 سيكون عندي
+
+194
+00:19:44,530 --> 00:19:52,690
+A6 تطابق الواحد مودولو A6 تطابق الواحد مودولو 7
+
+195
+00:19:52,690 --> 00:19:56,810
+معايا
+
+196
+00:19:56,810 --> 00:20:03,050
+من المباشرة هذه نرفع القوة تلاتة جهتين فبصير A18
+
+197
+00:20:03,050 --> 00:20:09,590
+تطابق الواحد مودولو 7 والـA18 تطابق الواحد مودولو
+
+198
+00:20:09,590 --> 00:20:21,550
+7الان عندى بنفس الأسلوب السابقمن واحد ومن اتنين
+
+199
+00:20:21,550 --> 00:20:24,410
+لأن العامل المشترك اللي على بين السبعة والتسعة
+
+200
+00:20:24,410 --> 00:20:30,590
+وتعاشر بساوة واحد بطلع ال D A أس تمانتعش تطابق
+
+201
+00:20:30,590 --> 00:20:36,270
+الواحد مو دولة مية و تلاتة و تلاتين وهي سبعة في
+
+202
+00:20:36,270 --> 00:20:42,010
+تسعة عشر واضح اه؟ وال B أس تمانتعش تطابق الواحد مو
+
+203
+00:20:42,010 --> 00:20:46,800
+دولة برضه ده ال D A اش مو دولة تلاتة و تلاتينبنفس
+
+204
+00:20:46,800 --> 00:20:49,740
+الأسلوب لأن العامل مشترك الأعلى بين الـ 7 و 19
+
+205
+00:20:49,740 --> 00:20:56,100
+واحد من التنتير مع بعض إذا الـ A أُس 18 تطابق الـ
+
+206
+00:20:56,100 --> 00:21:07,120
+B أُس 18 Modulo 133 وهذا يعني that is 133 تجسم الـ
+
+207
+00:21:07,120 --> 00:21:14,020
+A أُس 18 ماقص الـ B أُس 18 ندى للسؤال الرابع
+
+208
+00:21:14,020 --> 00:21:22,060
+السؤال الأربعةسؤال أربعة اللي هو a او b ايش بقول
+
+209
+00:21:22,060 --> 00:21:33,980
+السؤال الرابع a a و الميالي derive
+
+210
+00:21:33,980 --> 00:21:38,040
+each of the following congruences a أس واحد و
+
+211
+00:21:38,040 --> 00:21:45,200
+عشرين مطابق ال a موضوله خمس عشر
+
+212
+00:21:48,100 --> 00:21:52,180
+Solution احنا حكينا في الاول عن فرمات Structural و
+
+213
+00:21:52,180 --> 00:21:58,100
+عن Corollary لفرمات الان فرمات بتتعامل مع a تدبط
+
+214
+00:21:58,100 --> 00:22:01,220
+بي minus واحد تطابق الواحد modulo بي لما ال بي لا
+
+215
+00:22:01,220 --> 00:22:05,660
+تقسم ال a ال Corollary بتتعامل مع اي integer a اقص
+
+216
+00:22:05,660 --> 00:22:10,180
+بي تطابق ال a modulo بي
+
+217
+00:22:10,180 --> 00:22:15,880
+الان واضح ان دي بنشتغل على Corollary فرماتالـ 15
+
+218
+00:22:15,880 --> 00:22:21,060
+بنفس الأسلوب السابق تتحلل لخمسة في تلاتة عندي اللي
+
+219
+00:22:21,060 --> 00:22:26,280
+هو الـ A بنسبة .. بناء على corollary لفرمات الـ A
+
+220
+00:22:26,280 --> 00:22:33,640
+أُس خمسة تطابق الـ A Modulo خمسة وأيضا بناء على
+
+221
+00:22:33,640 --> 00:22:38,600
+فرمات ال theorem A أُس تلاتة أو ال corollary
+
+222
+00:22:38,600 --> 00:22:44,280
+لفرمات تطابق ال A Moduloاللي هو تلاتة تذكركم الـ
+
+223
+00:22:44,280 --> 00:22:49,620
+Corollary a to the b تطابق ال a modulo b لكل a
+
+224
+00:22:49,620 --> 00:22:56,700
+element أنزل لأن أضحى الصورة يصير عندي a أُس يرفع
+
+225
+00:22:56,700 --> 00:23:01,700
+للقوة أربعة يصير a أُس عشرين تطابق ال a أُس أربعة
+
+226
+00:23:01,700 --> 00:23:07,680
+modulo خمسة و ال a أُس أربعة لو ضربنا الجهتين في a
+
+227
+00:23:07,680 --> 00:23:14,010
+في جماعة في a أضرب الجهتينفي a فبصير هذه a أس واحد
+
+228
+00:23:14,010 --> 00:23:21,530
+عشرين تطابق ال a أس خمسة modulo خمسة لكن من الأصل
+
+229
+00:23:21,530 --> 00:23:27,350
+ال a أس خمسة تطابق مين تطابق ال a modulo خمسة إذن
+
+230
+00:23:27,350 --> 00:23:32,050
+الآن احنا حصلنا على الجزء الأول اللي هيلزمناه
+
+231
+00:23:32,520 --> 00:23:36,980
+Similar لفي نفس الأسلوب لو جينا نرفع النهاردة
+
+232
+00:23:36,980 --> 00:23:43,140
+نصلها لـ 21 نرفعها للقوة 7 فبصير A أُس 7 في 3 بـ
+
+233
+00:23:43,140 --> 00:23:53,140
+21 تطابق الـ A في A أُس 7 آسف نرفع القوة 7 نرفع
+
+234
+00:23:53,140 --> 00:23:58,080
+الجهتين للقوة 7 واضح؟ فبصير A أُس 7 A أُس 7 اللي
+
+235
+00:23:58,080 --> 00:23:59,620
+هي عبارة عن A أُس 6
+
+236
+00:24:23,030 --> 00:24:26,610
+بصير عندى من الجزء الاول والجزء التاني بما ان
+
+237
+00:24:26,610 --> 00:24:29,490
+العام المشترك الاعلى بين التلاتة والخمسة فكرة
+
+238
+00:24:29,490 --> 00:24:33,440
+متكررةيقولي تلاتة وخمسة بواحد إذا صار عندي A أُس
+
+239
+00:24:33,440 --> 00:24:39,160
+واحد وعشرين وطابق الـ A Modulo خمسة في تلاتة بجديش
+
+240
+00:24:39,160 --> 00:24:44,880
+بخمس عشر وهو المطلوب هذا اللي هو السؤال أربعة A
+
+241
+00:24:44,880 --> 00:24:53,200
+عندي الآن ده نشوف سؤال أربعة B أربعة B عندي B إذا
+
+242
+00:24:53,200 --> 00:24:57,120
+كان السؤال
+
+243
+00:24:57,120 --> 00:25:03,830
+أربعة B يا جماعةبقول ما يلي A السابعة تطابق الـ A
+
+244
+00:25:03,830 --> 00:25:14,050
+موضوع 42 لكل A فكرة مشابهة الـ A 42 ما تاكل فكرة
+
+245
+00:25:14,050 --> 00:25:20,330
+لأ فاش ده يعني الحل سبعة في تلاتة في اتنين مظبوط
+
+246
+00:25:20,330 --> 00:25:26,210
+الأولى مضوع سبعةأكيد by corollary of format
+
+247
+00:25:26,210 --> 00:25:32,030
+solution by corollary of format a7 تطابق ال a
+
+248
+00:25:32,030 --> 00:25:37,150
+modulo 7 هاي أول واحدة التانية a3 تطابق ال a
+
+249
+00:25:37,150 --> 00:25:45,870
+modulo 3 ومنها بدنا نص ان هذه سبعة ال a6تطابق الـ
+
+250
+00:25:45,870 --> 00:25:51,270
+A تربية رفعت الاتنين لأقوى له يواشي اتنين اضرب في
+
+251
+00:25:51,270 --> 00:25:55,530
+A فبصير A أُس سبعة تطابق الـ A تكعيب الـ A تكعيب
+
+252
+00:25:55,530 --> 00:26:00,350
+اشمالها بتطابق الـ A موضلو تلاتة وهذه جهزة
+
+253
+00:26:00,350 --> 00:26:06,950
+Similarly A تربية تطابق الـ A إذا A أُس اضرب
+
+254
+00:26:06,950 --> 00:26:16,060
+الموضلوفاتنيت بيصير A6 مطابق الـ A تكعيب الـ A
+
+255
+00:26:16,060 --> 00:26:23,970
+تكعيب اللي هيأضربه في كمان A فبصير A7 تطابق A7
+
+256
+00:26:23,970 --> 00:26:30,710
+معايا الـ A4 عبارة عن A تربية تربية الـ A تربية
+
+257
+00:26:30,710 --> 00:26:33,950
+بالطابق الـ A فبصير A تربية بالطابق برضه من هنا
+
+258
+00:26:33,950 --> 00:26:40,730
+هترجع الـ A مدل 2 إذا جاهزة للكل A7 طابق الـ A مدل
+
+259
+00:26:40,730 --> 00:26:48,750
+2 مدل 3و مدله 7 اتلقى جمع بعض بما ان العامل مشترك
+
+260
+00:26:48,750 --> 00:26:51,070
+اللي على بين السبعة و التلاتة و اتنين بساعة واحد
+
+261
+00:26:51,070 --> 00:26:54,770
+اذا حيكون عندي a و السبعة تطابق ال a مدله جديش
+
+262
+00:26:54,770 --> 00:27:04,270
+مدله 42 نجي لسؤال اخر يا شباب سؤال اللي هو ستة
+
+263
+00:27:04,270 --> 00:27:10,770
+نشوف سؤال ستة ايش بقول سؤال ستة جزءين الجزء الاول
+
+264
+00:27:10,770 --> 00:27:19,740
+aFind the units digit of تلاتة أسمية تلاتة
+
+265
+00:27:19,740 --> 00:27:25,960
+أسمية
+
+266
+00:27:41,270 --> 00:27:48,950
+تطابق ماذا مدن ومين مدن وعشرة اللي هو المتبقي هي
+
+267
+00:27:48,950 --> 00:27:54,450
+القسمة على عشرة اللي هو خانة الأحد اللي في الرقم
+
+268
+00:27:54,450 --> 00:28:00,410
+اللي عندي الفكرة مشابهة للجبل الآن تلاتة أسمية
+
+269
+00:28:00,410 --> 00:28:03,930
+تطابق مدن وعشرة العشرة بنجسمها لأتنين في مين
+
+270
+00:28:03,930 --> 00:28:10,680
+ونحلها لأتنين في خمسة فالآن بدي أشوف تلاتةby اللي
+
+271
+00:28:10,680 --> 00:28:18,440
+هو Fermat's theorem تلاتة عند التنين لتقسم التلاتة
+
+272
+00:28:18,440 --> 00:28:23,720
+معايا يعني وكأن ال a تلاتة و ال b اتنين إذا
+
+273
+00:28:23,720 --> 00:28:27,920
+التلاتة تطابق تلاتة و أس اتنين ماقص واحد يعني
+
+274
+00:28:27,920 --> 00:28:33,550
+التلاتة تطابق الواحد modulo اتنينومنها على طول
+
+275
+00:28:33,550 --> 00:28:40,530
+ثلاثة أسمية تطابق الواحد مدنه مين مدنه اتنين نيجي
+
+276
+00:28:40,530 --> 00:28:48,810
+لمين؟ للخمسة الخمسة ثلاثة أس أربعة تطابق الواحد
+
+277
+00:28:48,810 --> 00:28:52,370
+مدنه خمسة مدونه ان هذه performance theorem برضه
+
+278
+00:28:52,370 --> 00:28:56,870
+الآن أربعة أرفعها لقوة خمسة عشرين فتصبح ثلاثة
+
+279
+00:28:56,870 --> 00:29:03,050
+أسمية تطابق الواحد مدنه مين مدنه خمسةمن الجهتين
+
+280
+00:29:03,050 --> 00:29:06,250
+لأن العامل مش شابه كدا لبين اتنين وخمسة بساعة واحد
+
+281
+00:29:06,250 --> 00:29:11,570
+فبصير عندي تلاتة أسمية تطابق الواحد مدلوا اتنين
+
+282
+00:29:11,570 --> 00:29:17,730
+وخمسة اللي هو قديش عشرة يعني بكون عندي the units
+
+283
+00:29:17,730 --> 00:29:27,480
+digit of تلاتة أسمية isone هو عبارة عن مين؟ عن
+
+284
+00:29:27,480 --> 00:29:32,160
+اللي هو الواحد الآن هذا اللي هو مين؟ اللي هو عبارة
+
+285
+00:29:32,160 --> 00:29:39,580
+عن السؤال السادس ايه؟ نيجي الآن للسؤال
+
+286
+00:29:41,570 --> 00:29:46,470
+السادس بي لنثبت أنه .. لنثبت مهيالي نشوف ايش
+
+287
+00:29:46,470 --> 00:29:51,730
+السؤال بيقول و نشوف كيف بدنا نحل السؤال prove that
+
+288
+00:29:51,730 --> 00:29:59,450
+for any a element in z a أُس خمسة و ال a have the
+
+289
+00:29:59,450 --> 00:30:07,900
+same unit digitاو units digit نثبت ان ال a أس خمسة
+
+290
+00:30:07,900 --> 00:30:13,660
+و ال a الهن ايه الشمال هن نفس ال units digit يعني
+
+291
+00:30:13,660 --> 00:30:21,700
+بمعنى اخر بدنا نثبت ان a أس خمسة a أس خمسة اللي هو
+
+292
+00:30:21,700 --> 00:30:30,760
+تطابق ال a modulo عشرة تطابق ال a modulo عشرة وهذا
+
+293
+00:30:30,760 --> 00:30:40,470
+الكلام سهلA أُس خمسة A أُس
+
+294
+00:30:40,470 --> 00:30:49,490
+خمسة تطابق الـ A modulo خمسة هذا by corollary of
+
+295
+00:30:49,490 --> 00:30:57,350
+format و الـ A تربيع تطابق الـ A modulo 2 by
+
+296
+00:30:57,350 --> 00:31:03,040
+corollary of formatالآن من هذه بيصير عندي ارفع
+
+297
+00:31:03,040 --> 00:31:07,460
+بيصير a أُس 4 تطابق ال a تربيع اللي هي تطابق ال a
+
+298
+00:31:07,460 --> 00:31:14,020
+modulo 2 واضح اه مضرب في a الجاتين فبيصير a أُس 5
+
+299
+00:31:14,020 --> 00:31:18,740
+تطابق ال a تربيع اللي هي بالطابق أصلا من ال a
+
+300
+00:31:18,740 --> 00:31:24,600
+modulo 2 صار عندي الآن من اللي هو
+
+301
+00:31:27,670 --> 00:31:33,290
+واتنين بيصير عندي A أُس خمسة تطابق الـ A مُدُل
+
+302
+00:31:33,290 --> 00:31:35,930
+وخمسة في اتنين لأن العامل مشترك الأعلى بين الخمسة
+
+303
+00:31:35,930 --> 00:31:40,190
+واثنين بيصيح واحد إذا صار عند ال A أُس خمسة تطابق
+
+304
+00:31:40,190 --> 00:31:43,310
+ال A مُدُل عشرة أو بمعنى أخر ال A أُس خمسة وال A
+
+305
+00:31:43,310 --> 00:31:49,450
+have the same unit digits نجي الآن لسؤال 11 سؤال
+
+306
+00:31:49,450 --> 00:31:54,290
+11 بيقول ما يلي أسرعت ان الفكرة .. الفكرة صارت إيه
+
+307
+00:31:54,290 --> 00:32:05,300
+شمالها؟متشابه اكتر اكتر اكتر اكتر
+
+308
+00:32:05,300 --> 00:32:08,760
+اكتر اكتر اكتر اكتر اكتر اكتر اكتر اكتر اكتر
+
+309
+00:32:27,180 --> 00:32:35,920
+الان لأي البروف البروري البروف لو
+
+310
+00:32:35,920 --> 00:32:40,800
+جينا أخدنا هذه الأساسات كلها واحدة لو جينا أخدنا
+
+311
+00:32:40,800 --> 00:32:48,140
+for any un element in z بركورولري of فرمات يا
+
+312
+00:32:48,140 --> 00:32:57,230
+جماعةن أس بي تطابق الان modulo مين modulo بي هذ بي
+
+313
+00:32:57,230 --> 00:33:03,510
+الكورولري of Fermat طيب الآن بناء على هذه اللي هو
+
+314
+00:33:03,510 --> 00:33:09,790
+الحقيقة بيصير عند then اللي هو واحد أس بي زاد
+
+315
+00:33:09,790 --> 00:33:14,990
+اتنين أس بي لما أصل عند بي ماينس واحد أس بي الأولى
+
+316
+00:33:14,990 --> 00:33:21,110
+تطابق اللي هوتانية تطابق التنين تانية تطابق التنين
+
+317
+00:33:21,110 --> 00:33:21,950
+تانية تطابق التنين تانية تطابق التنين تانية تطابق
+
+318
+00:33:21,950 --> 00:33:24,230
+التنين تانية تطابق التنين تانية تطابق التنين تانية
+
+319
+00:33:24,230 --> 00:33:24,270
+تطابق التنين تانية تطابق التنين تانية تطابق التنين
+
+320
+00:33:24,270 --> 00:33:27,150
+تانية تطابق التنين تانية تطابق التنين تانية تطابق
+
+321
+00:33:27,150 --> 00:33:33,790
+التنين تانية تطابق التنين تانية تطابق التنين تانية
+
+322
+00:33:33,790 --> 00:33:34,550
+تطابق التنين تانية تطابق التنين تانية تطابق التنين
+
+323
+00:33:34,550 --> 00:33:39,770
+تانية تطابق التنين تانية تطابق
+
+324
+00:33:39,770 --> 00:33:46,310
+التنين تانية تطابق التنين تانية تطابق التنين تانية
+
+325
+00:33:46,310 --> 00:33:53,690
+تب في ب ماينوس واحد على اتنين والان ب ماينوس واحد
+
+326
+00:33:53,690 --> 00:34:04,090
+على اتنين عبارة عن عدد لأن ب هو اضبراي فبصير ب نقص
+
+327
+00:34:04,090 --> 00:34:07,070
+واحد even على اتنين بطلع ايش ماله عبارة عن نقص
+
+328
+00:34:07,070 --> 00:34:11,130
+number k إذا ساعت كفي ب عبارة عن ايش من مضاعفات ال
+
+329
+00:34:11,130 --> 00:34:18,670
+ب إذا هذا بطابق الصفر مضلمينمدلو بي لما كانت بي is
+
+330
+00:34:18,670 --> 00:34:23,690
+an odd prime طلع عند هذا المجموع يطابق السفر مدلو
+
+331
+00:34:23,690 --> 00:34:27,350
+بي نشوف سؤال تلاتاشر شباب تلاتاشر بيقول assume
+
+332
+00:34:27,350 --> 00:34:33,870
+that بي و Q are distinct primes بي
+
+333
+00:34:33,870 --> 00:34:40,190
+و Q distinct primes such that بي ماينس واحد بتقسم
+
+334
+00:34:40,190 --> 00:34:48,600
+لكيو ماينس واحدالـ B-1 تجسم
+
+335
+00:34:48,600 --> 00:34:53,220
+الـ Q-1 عامل مشترك اللي على بين اللي هو الـ A و
+
+336
+00:34:53,220 --> 00:34:56,780
+الـ B و الـ Q الـ A و حاصل الضرب الـ B و الـ Q
+
+337
+00:34:56,780 --> 00:35:00,240
+بساعة واحد على أساس أنه يصير فيه حرية الاستخدام في
+
+338
+00:35:00,240 --> 00:35:10,020
+رمات A مع الـ B و A مع الـ Q show that أن A ضمن A
+
+339
+00:35:11,550 --> 00:35:21,410
+to the Q minus واحد تطابق الواحد modulo B في مين B
+
+340
+00:35:21,410 --> 00:35:27,370
+في Q البروف نشوف يا شباب الحل للأمر أكيد المعلومة
+
+341
+00:35:27,370 --> 00:35:34,260
+هذه اللي معطينا إياها فيه إلها قوتها عندي senseب
+
+342
+00:36:05,130 --> 00:36:07,910
+الـ Greatest Common Divisor بين الـ A والـ B في
+
+343
+00:36:07,910 --> 00:36:11,570
+الـ Q بساوة واحد ثم أكيد الـ Greatest Common
+
+344
+00:36:11,570 --> 00:36:14,990
+Divisor بين الـ A والـ B والـ Greatest Common
+
+345
+00:36:14,990 --> 00:36:22,170
+Divisor بين الـ A والـ Q بساوة واحد ومنه هيكون عيد
+
+346
+00:36:22,170 --> 00:36:28,670
+الـ B لتقسم الـ Q وB لتقسم الـ A والـ Q برضه
+
+347
+00:36:28,670 --> 00:36:34,690
+لتقسمين الـ Aالآن هذه اللي هي بتأهل من استخدام الـ
+
+348
+00:36:34,690 --> 00:36:39,850
+Fermat's theorem بالنسبة للـ A للـ B بكون عندي
+
+349
+00:36:39,850 --> 00:36:47,790
+then A to the B minus واحد تطابق الواحد modulo B
+
+350
+00:36:47,790 --> 00:36:55,090
+معايا الان انفع الجهتين للقوة مين؟ للقوة K فبصير
+
+351
+00:36:55,090 --> 00:37:03,880
+عندي andSo a to the b minus 1 الكل أس كي تطابق
+
+352
+00:37:03,880 --> 00:37:11,180
+الواحد أس كي اليمين واحد modulo فيه الان هذه مين
+
+353
+00:37:11,180 --> 00:37:14,740
+هي a to the b minus واحد to the k اللي عبارة عن
+
+354
+00:37:14,740 --> 00:37:20,280
+كيوكو minus واحد لأن and so ال a to the q minus
+
+355
+00:37:20,280 --> 00:37:26,270
+واحد تطابق الواحد modulo ال b هذه أول واحدةهذه
+
+356
+00:37:26,270 --> 00:37:31,110
+نسميها واحد الآن similarly by Fermat's theorem Q
+
+357
+00:37:31,110 --> 00:37:37,170
+لا تقسم الـA then اللي هو الـA to the Q minus واحد
+
+358
+00:37:37,170 --> 00:37:40,910
+تطبيق مباشر على Fermat's theorem تطابق اللي هو
+
+359
+00:37:40,910 --> 00:37:48,630
+الواحد modulo Q الآن الان هي اتنين since ال
+
+360
+00:37:48,630 --> 00:37:53,030
+greatest common divisor بين الـB والـQ بسعر واحد
+
+361
+00:37:53,030 --> 00:38:03,920
+andby one and two we have a to the q minus واحد
+
+362
+00:38:03,920 --> 00:38:14,530
+تطبق الواحد modulo b في q وهو المطلوبفقريباً هذا
+
+363
+00:38:14,530 --> 00:38:19,610
+لمب الأسئلة أو اللي جاب ال .. او الكثير من الأفكار
+
+364
+00:38:19,610 --> 00:38:22,830
+اللي في الأسئلة اللي جاب الـ 13 الان يا شباب بدنا
+
+365
+00:38:22,830 --> 00:38:27,270
+نحل السؤال الأخير في خمسة اتنين اللي هو سؤال أربعة
+
+366
+00:38:27,270 --> 00:38:37,010
+عشر سؤال أربعة عشر بنشوف إيش السؤال بيقول و من ثم
+
+367
+00:38:37,010 --> 00:38:40,830
+بنشوف كيف بدنا نبرهن
+
+368
+00:38:45,640 --> 00:38:49,540
+طيب يا شباب صلى النبي عليه الصلاة والسلام بيقولّي
+
+369
+00:38:49,540 --> 00:38:54,060
+إذا كان بي و Q are distinct primes مختلفات ا prove
+
+370
+00:38:54,060 --> 00:39:04,000
+that بي to the Q minus واحد زاد Q to the بي minus
+
+371
+00:39:04,000 --> 00:39:13,720
+واحد وطابق الواحد موضله برضه مين بفكرة ا prove
+
+372
+00:39:16,100 --> 00:39:20,000
+شوفوا صلى الله عليه الصلاة والسلام عند الـ B و الـ
+
+373
+00:39:20,000 --> 00:39:26,520
+Q هم مختلفين برامج إذا بي لا تقسم الـ Q إذا by
+
+374
+00:39:26,520 --> 00:39:33,160
+Fermat's theorem اللي هو A الـ Q اللي هتلعب له
+
+375
+00:39:33,160 --> 00:39:38,720
+بالـ A بي ماينس واحد وطابق الواحد مو دوله
+
+376
+00:39:44,520 --> 00:39:50,200
+لكن لو أتينا و أخذنا الـ Q أس بي ماينس واحد حط
+
+377
+00:39:50,200 --> 00:39:54,500
+طابق ماذا
+
+378
+00:39:54,500 --> 00:40:05,900
+موضوع الـ Q؟ أكيد حط طابق إيش؟ صفر لأن الـ Q أس بي
+
+379
+00:40:05,900 --> 00:40:11,510
+ماينس واحد من المضاعفات من من المضاعفات الـ Qنجمع
+
+380
+00:40:11,510 --> 00:40:17,750
+المعلومات وعندي أيضًا الـ Q لا تقسم الـ B إذا by
+
+381
+00:40:17,750 --> 00:40:23,850
+Fermat's theorem الـ Q هو عبارة عن الـ prime و الـ
+
+382
+00:40:23,850 --> 00:40:28,510
+B هو الأساس فبصير B to the Q minus واحد تطابق
+
+383
+00:40:28,510 --> 00:40:39,290
+الواحد Modulo مين Modulo هو الـ prime لـ Q وفي
+
+384
+00:40:39,290 --> 00:40:40,350
+نفس الوقت
+
+385
+00:40:42,970 --> 00:40:52,950
+بط عندي الـ B قصة Q مانس واحد تطابق السفر modulo
+
+386
+00:40:52,950 --> 00:40:58,670
+ايش؟ modulo اللي هو B لأنه بتصير اللي هي B قصة Q
+
+387
+00:40:58,670 --> 00:41:04,050
+مانس واحد من مضاعفات مين؟ من مضاعفات الـ B طيب
+
+388
+00:41:04,050 --> 00:41:11,850
+خدوني هذه مخادةهيها ملاش قلبت و أنا قلبت خدوني هذه
+
+389
+00:41:11,850 --> 00:41:19,010
+مع هذه فالتنتين مع بعض together بيصير عندي Q to
+
+390
+00:41:19,010 --> 00:41:24,970
+the B minus واحد زائد B to the Q minus واحد تطابق
+
+391
+00:41:24,970 --> 00:41:31,830
+الواحد هاي الواحد زائد جمعناها السفر هنا والتنتين
+
+392
+00:41:31,830 --> 00:41:40,300
+ايه شمال هنا اللي هو واحدModulo B Similarly عنده
+
+393
+00:41:40,300 --> 00:41:47,980
+خذوا هذه مع هذه بيصير عنده اللي هو ال بي ال Q بي
+
+394
+00:41:47,980 --> 00:41:54,300
+minus واحد عمال في نفس الترتيب زائد ال بي السي Q
+
+395
+00:41:54,300 --> 00:41:59,060
+minus واحد تطابق هذا بالطابق السفر وهذا بالطابق
+
+396
+00:41:59,060 --> 00:42:05,660
+الواحد Modulo Qاللي هي عبارة عن تطابق الواحد
+
+397
+00:42:05,660 --> 00:42:11,060
+modulo q هاي عندى الان واحد وهي عندى اتنين فكرة
+
+398
+00:42:11,060 --> 00:42:14,980
+متكررة صار عندى ال b و ال q العامل مشترك اللي اعلى
+
+399
+00:42:14,980 --> 00:42:18,880
+بينهم بيساو واحد اذا by واحد و اتنين فبصير عندى ال
+
+400
+00:42:18,880 --> 00:42:24,380
+q أس b minus واحد زائد b أس q minus واحد تطابق
+
+401
+00:42:24,380 --> 00:42:31,680
+الواحد modulo b في q حاصل ضرب b في q نكون هيك احنا
+
+402
+00:42:32,900 --> 00:42:38,560
+خلصنا اللي هو الأسئلة على المطلوبة على اللي هي
+
+403
+00:42:38,560 --> 00:42:44,680
+خمسة اتنين اللي هو Fermat's Little Theorem and The
+
+404
+00:42:44,680 --> 00:42:48,340
+Coronary of Fermat's Little Theorem الآن بدنا نبدأ
+
+405
+00:42:48,340 --> 00:42:53,000
+نحكي على خمسة تلاتة أو أسئلة خمسة تلاتة اللي هي
+
+406
+00:42:53,000 --> 00:42:57,160
+بتتعلق بـWilson's theorem بتتعلق بـWilson's
+
+407
+00:42:57,160 --> 00:43:04,750
+theorem خلّينا نشوف اللي هواللي هي أسئلة Wilson's
+
+408
+00:43:04,750 --> 00:43:09,070
+theorem في الأول بس على السريع نقول Wilson's
+
+409
+00:43:09,070 --> 00:43:14,390
+theorem إذا كانت B' بيكون B-1! تطابق ناقص واحد
+
+410
+00:43:14,390 --> 00:43:17,330
+modulo B هذي Wilson's theorem
+
+411
+00:43:21,990 --> 00:43:26,310
+اللي هو برضه هتلزمنا في عنا اللي هو a decoder of
+
+412
+00:43:26,310 --> 00:43:29,250
+congruences X ترجل زائد واحد وطابق السفر مدله B
+
+413
+00:43:29,250 --> 00:43:35,830
+where B is an odd prime لها solution F andol FB
+
+414
+00:43:35,830 --> 00:43:41,550
+على صورة 4K زائد واحدأذن قبل ما نبدأ خلّيني على
+
+415
+00:43:41,550 --> 00:43:49,150
+السريع أذكركم بـWilson's theorem أو بالحل
+
+416
+00:43:49,150 --> 00:43:52,830
+لـquadratic equation x² زاد 1 وطابق صفر modulo b
+
+417
+00:43:52,830 --> 00:43:57,250
+على أساس حنستخدمهم لأن Wilson's theorem زي ما قلنا
+
+418
+00:43:57,250 --> 00:44:03,910
+عند b prime فبكون b minus 1 factorial وطابق نقص 1
+
+419
+00:44:03,910 --> 00:44:10,620
+modulo bأو أيضًا عندي لـQuadratic congruences X
+
+420
+00:44:10,620 --> 00:44:16,540
+ثربية زي واحد تطابق الصفر modulo B has a solution
+
+421
+00:44:16,540 --> 00:44:25,670
+if and only if الـ B تطابق اللي هو الواحدmodulo
+
+422
+00:44:25,670 --> 00:44:31,330
+أربعة أو بلغة ثانية الـ B على صورة أربعة كزائد
+
+423
+00:44:31,330 --> 00:44:38,050
+واحد هذوله اللي هيلزمنا الآن في اللي هو خمسة ثلاثة
+
+424
+00:44:38,050 --> 00:44:43,050
+فنيجي الآن للسؤال الأول لنشوف السؤال الأول إيش
+
+425
+00:44:43,050 --> 00:44:48,970
+بيقول سؤال واحد في خمسة ثلاثة سؤال واحد في خمسة
+
+426
+00:44:48,970 --> 00:44:55,120
+ثلاثة بيقول لي أوجدالمتبقى يجد المتبقى عندما يقسم
+
+427
+00:44:55,120 --> 00:45:00,420
+الـ 15 فيكتوريال إلى 17 المتبقى يجد المتبقى عندما
+
+428
+00:45:00,420 --> 00:45:08,100
+يقسم الـ 15 فيكتوريال إلى 17 المتبقى يجد المتبقى
+
+429
+00:45:08,100 --> 00:45:13,280
+عندما
+
+430
+00:45:13,280 --> 00:45:17,100
+يقسم الـ 15 فيكتوريال إلى 17 المتبقى يجد المتبقى
+
+431
+00:45:17,100 --> 00:45:19,460
+عندما يقسم الـ 15 فيكتوريال إلى 17
+
+432
+00:45:22,090 --> 00:45:28,190
+احنا بنعرف اللي هو by Fermat's theorem اللي هو b-1
+
+433
+00:45:28,190 --> 00:45:35,810
+factorial اللي هو 16 factorial تطابق 16 factorial
+
+434
+00:45:35,810 --> 00:45:42,010
+تطابق الناقص واحد اسف تطابق الناقص واحد modulo
+
+435
+00:45:42,010 --> 00:45:47,270
+اللي هو b ماشي يا شباب 16 factorial تطابق الناقص
+
+436
+00:45:47,270 --> 00:45:52,480
+واحد modulo بيها دي باي ويلسون's theoremطيب الان
+
+437
+00:45:52,480 --> 00:45:59,120
+انا بدي 15 factorial هذه 16 في 15 factorial تطبق
+
+438
+00:45:59,120 --> 00:46:04,500
+ناقص واحد modulo مين modulo مين من جهة أخرى احنا
+
+439
+00:46:04,500 --> 00:46:09,800
+بنعرف modulo B تبع ال V ياش هي 17 معايا شباب 17
+
+440
+00:46:09,800 --> 00:46:14,800
+هذه ال B اللي بتطبق عليها 17الان الـ 6 بالنسبة للـ
+
+441
+00:46:14,800 --> 00:46:19,680
+17 على جهة اللي هي الـ 16 بالنسبة للـ 17 هي ناقص
+
+442
+00:46:19,680 --> 00:46:24,580
+واحد تطابق الناقص واحد مدينه مين؟ مدنه 17 إذا هذه
+
+443
+00:46:24,580 --> 00:46:30,560
+بتطابق الناقص واحد في الخمستاش فيكتوريال لأن ال 16
+
+444
+00:46:30,560 --> 00:46:33,000
+بتطابق الناقص واحد الناقص واحد في الخمستاش
+
+445
+00:46:33,000 --> 00:46:35,320
+فيكتوريال بتطابق ال 16 في الخمستاش واحد فيكتوريال
+
+446
+00:46:35,320 --> 00:46:38,820
+إذا تجسم الجهتين على ناقص واحد فبصير الخمستاش
+
+447
+00:46:38,820 --> 00:46:45,650
+فيكتوريال تطابق الواحدموضنه 17 إذا ال remainder في
+
+448
+00:46:45,650 --> 00:46:51,290
+حالة قسمة الخمست عشر على ال 17 كده بيطلع بيطلع
+
+449
+00:46:51,290 --> 00:46:56,230
+عندي بساوي واحد نجي للسؤال اللي بعده اي سؤال يا
+
+450
+00:46:56,230 --> 00:47:06,960
+شباب نجي اللي هو1a الان 1b find the remainder لما
+
+451
+00:47:06,960 --> 00:47:15,620
+ال 2 في 26 factorial اللي هو is divided by
+
+452
+00:47:15,620 --> 00:47:21,130
+29السينيوشين برضه تطبيق مباشر يا شباب على Fermat's
+
+453
+00:47:21,130 --> 00:47:26,410
+theorem والفكرة تقريبا متكررة عندي اللي هي التسعة
+
+454
+00:47:26,410 --> 00:47:31,010
+وعشرين هو ال prime اللي عندي by Wilson's theorem
+
+455
+00:47:31,010 --> 00:47:37,030
+تمانية وعشرين factorialتطابق الناقص واحد modulo
+
+456
+00:47:37,030 --> 00:47:41,390
+تسعة وعشرين هي Wilson's theorem أنا مين بدي يا
+
+457
+00:47:41,390 --> 00:47:45,270
+شباب؟ ستة وعشرين factorial في مين؟ في اتنين فاللي
+
+458
+00:47:45,270 --> 00:47:49,030
+بتوصلني لستة وعشرين factorial اللي هو اكيد التمنية
+
+459
+00:47:49,030 --> 00:47:51,550
+وعشرين factorial هي تمنية وعشرين factorial عبارة
+
+460
+00:47:51,550 --> 00:47:56,650
+عن اللي عبارة عن ستة وعشرين factorial في سبعة
+
+461
+00:47:56,650 --> 00:48:01,870
+وعشرين في اللي هو تمانية وعشرينمظبوطاً للاقهد اللي
+
+462
+00:48:01,870 --> 00:48:05,030
+هي 28 factorial من اللي فوق قعدت الطابق الناقص
+
+463
+00:48:05,030 --> 00:48:10,290
+واحد module 29 طيب الآن بدأ تصير اللغة سريع
+
+464
+00:48:10,290 --> 00:48:16,390
+نستخدمها ال 28 بالنسبالي 29 ناشر شباب سالب واحد أي
+
+465
+00:48:16,390 --> 00:48:24,350
+سالب واحدالـ 27 بالنسبة للـ 29 الـ 27 تطابق ناقص 2
+
+466
+00:48:24,350 --> 00:48:31,730
+موضله 29 واضح، أه؟ في ناقص 2 في مين؟ في الـ 26
+
+467
+00:48:31,730 --> 00:48:36,370
+فيكتوريا، دلوقتي الأمور عندنا لأن ناقص 1 في ناقص 2
+
+468
+00:48:36,370 --> 00:48:42,610
+تطلع 2 فبصير عبارة عن 2 في 26 فيكتوريا تطابق
+
+469
+00:48:42,610 --> 00:48:48,590
+الناقص 1-1 هو في الواقع جداش بالنسبة لـ 29 يا شباب
+
+470
+00:48:48,590 --> 00:48:57,710
+اللي هو عبارة عن 28 mod 29 إذا المتبقي حين قسمة 2
+
+471
+00:48:57,710 --> 00:49:02,950
+في 26 factorial على 29 مش بساوي اللي هو عبارة عن
+
+472
+00:49:02,950 --> 00:49:12,390
+28 هذا اللي هو سؤال B في السؤال الأول نيدي
+
+473
+00:49:12,390 --> 00:49:26,510
+يا شباب نشوفسؤال 4 نكتب
+
+474
+00:49:26,510 --> 00:49:38,010
+السؤال
+
+475
+00:49:38,840 --> 00:49:44,080
+ونحل السؤال الان يعني برضه تطبيق عمل since theorem
+
+476
+00:49:44,080 --> 00:49:51,560
+ولكن يعني صار فيه تركيب معين سهل برضه لأكثر من ال
+
+477
+00:49:51,560 --> 00:49:58,540
+prime السؤال الأربعة show that
+
+478
+00:49:58,540 --> 00:50:09,130
+اللي هو 18 factorial مطابق الناقص واحدمودلو اربعة
+
+479
+00:50:09,130 --> 00:50:15,080
+تلاتة سبعة solution أو proofالآن يا شباب اللي هو
+
+480
+00:50:15,080 --> 00:50:20,200
+هذه 18 factorial يعني بتعطيني مؤشر ان هو كأنه
+
+481
+00:50:20,200 --> 00:50:23,880
+بنحكي عن اللي هو الـ Brian 19 لأنه الـ Sun بتقول
+
+482
+00:50:23,880 --> 00:50:28,140
+بي ماقص واحد factorial فالآن اللي هي بتعطيني مؤشر
+
+483
+00:50:28,140 --> 00:50:33,520
+ان انا اقسم الـ 437 ع 19 تأكدلي انه انا باقسمها ع
+
+484
+00:50:33,520 --> 00:50:39,140
+ال 19 ولا لأ فعلا لو جيت جسمت هتلاقي ال 400و سبعة
+
+485
+00:50:39,140 --> 00:50:43,640
+و تلاتين بيساوي تسعة عشر في مين في التلاتة و عشرين
+
+486
+00:50:43,640 --> 00:50:48,420
+تسعة عشر في التلاتة و عشرين المفضل الآن الحل الان
+
+487
+00:50:48,420 --> 00:50:58,900
+by Wilson's theorem by Wilson's theorem عندي اللي
+
+488
+00:50:58,900 --> 00:51:05,060
+هو التمنتعش factorial تطابق الناقص واحد mod و mod
+
+489
+00:51:05,060 --> 00:51:13,200
+تسعة عشر هذه جاهزة الآنالان بيولسون فيرم ايضا و
+
+490
+00:51:13,200 --> 00:51:16,540
+لكن الان على الرقم تلاتة عشرين او الـ prime تلاتة
+
+491
+00:51:16,540 --> 00:51:21,240
+عشرين فبصير عنده اتنين عشرين factorial يطابق ناقص
+
+492
+00:51:21,240 --> 00:51:26,240
+واحد modulo جديش يا جماعة modulo تسعة عشر الان
+
+493
+00:51:26,240 --> 00:51:31,970
+اتنين عشرين factorialبدي اجيبها لمين؟ Modulo S في
+
+494
+00:51:31,970 --> 00:51:36,610
+23 بدي اجيبها اشوف ايش بالطابق اللي هو بدي اوصلها
+
+495
+00:51:36,610 --> 00:51:40,390
+للـ18 factorial عارفين ليش؟ احسسوا ان انا اعمل هذه
+
+496
+00:51:40,390 --> 00:51:43,310
+و هذه نفس الاشي و بعدين زي ما عملنا قبل هيك نشوف
+
+497
+00:51:43,310 --> 00:51:46,090
+ايش بقول، بقى الصلاة على النبي عليه الصلاة والسلام
+
+498
+00:51:46,090 --> 00:51:52,370
+هذه بيصير كده؟ 22 في
+
+499
+00:51:52,370 --> 00:52:02,510
+21 في 20 في 19فى 18 فكتوريال تطابق ناقص واحد مدله
+
+500
+00:52:02,510 --> 00:52:07,830
+13 بس قعدت كتابة اللى فوق بالطريقة هذه تطابق من
+
+501
+00:52:07,830 --> 00:52:12,210
+الجهة دىالعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+502
+00:52:12,210 --> 00:52:14,130
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+503
+00:52:14,130 --> 00:52:17,170
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+504
+00:52:17,170 --> 00:52:19,550
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+505
+00:52:19,550 --> 00:52:20,770
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+506
+00:52:20,770 --> 00:52:21,750
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+507
+00:52:21,750 --> 00:52:24,370
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+508
+00:52:24,370 --> 00:52:28,470
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+509
+00:52:28,470 --> 00:52:31,970
+للتلاتة وعشرين بالنسبة للتلاتة وعبتصير الطابق سالب
+
+510
+00:52:31,970 --> 00:52:35,530
+ثلاثة التسعة عشر بالنسبالك تلاتة وعشرين بالطابق
+
+511
+00:52:35,530 --> 00:52:39,390
+اللي هي جداش سالب أربعة في سالب أربعة في اللي
+
+512
+00:52:39,390 --> 00:52:45,270
+بديها تمانتاش factorial صار الآن هذا المقدار بطابق
+
+513
+00:52:45,270 --> 00:52:48,470
+هذا المقدار مضوله تلاتة وعشرين خلّينا نضرب هدول في
+
+514
+00:52:48,470 --> 00:52:52,970
+بعض ناقص ناقص ناقص ناقص يعني كلها زائدأربعة في
+
+515
+00:52:52,970 --> 00:52:55,570
+تلاتة في اتناش في اتنين بابا عشان بيصير اربعة
+
+516
+00:52:55,570 --> 00:53:00,670
+وعشرين في تمانتاش فيكتوريال تطابق ناقص واحد مدل
+
+517
+00:53:00,670 --> 00:53:04,210
+مقدش شباب تلاتة وعشرين الاربع عشرين بالنسبالي
+
+518
+00:53:04,210 --> 00:53:09,810
+تلاتة وعشرين مش بالساعة واحد فبيصير عندي واحد اللي
+
+519
+00:53:09,810 --> 00:53:14,570
+هو مكان الاربع عشرين واحد في تمانتاش بتطلع تمانتاش
+
+520
+00:53:14,570 --> 00:53:19,030
+الفيكتوريال تطابق ناقص واحد مدله تلاتة وعشرين
+
+521
+00:53:19,030 --> 00:53:24,490
+هيصار عندي هذه جاهزةوهذه جاهزة من الأول بنفس
+
+522
+00:53:24,490 --> 00:53:29,090
+الفكرة السابقة المتكررة العامل المشترك لأعلى بين
+
+523
+00:53:29,090 --> 00:53:33,450
+التسعة عشر والتلت عشر وتلت عشرين بساوة واحد وهذا
+
+524
+00:53:33,450 --> 00:53:37,030
+المقدار الطابق الناقص واحد وهذا نفسه الطابق الناقص
+
+525
+00:53:37,030 --> 00:53:41,530
+واحد مضلوا تسعة عشر وتلت عشرين إذن أكيد من واحد
+
+526
+00:53:41,530 --> 00:53:45,710
+واتنين بيطلع تمنتاش فيكتوريالتطابق النقص واحد
+
+527
+00:53:45,710 --> 00:53:49,650
+modulo حصل bargain تسعة عاشر في تلاتة عشرين اللي
+
+528
+00:53:49,650 --> 00:53:58,150
+هو مين اللي عندنا أربعة تلاتة ستة وهو المطلوب نيجي
+
+529
+00:53:58,150 --> 00:54:05,430
+الآن نشوف سؤال ستة بقول ما يلي given a prime
+
+530
+00:54:05,430 --> 00:54:13,430
+number B establish that B minus واحدfactorial
+
+531
+00:54:13,430 --> 00:54:25,430
+تطابق اللي هو P minus واحد modulo اللي هو واحد
+
+532
+00:54:25,430 --> 00:54:32,170
+زائد اتنين زائد تلاتة لما أصل ل P minus واحد زائد
+
+533
+00:54:32,170 --> 00:54:38,610
+تلاتة زائد لما أصل P minus واحد solution خلّينا
+
+534
+00:54:38,610 --> 00:54:46,860
+نحلل السؤالو نشوف ايش اللي بدنا نسويه عندي اللي هو
+
+535
+00:54:46,860 --> 00:54:53,280
+لو طلعنا على اللي هو اللي بدنا نعمله المدره هذا هو
+
+536
+00:54:53,280 --> 00:54:59,200
+المقياسلو طلعنا للمقياس المقياس واحد زائد اتنين
+
+537
+00:54:59,200 --> 00:55:05,560
+زائد تلاتة زائد بي ماينوس واحد مجموعة متتالية حد
+
+538
+00:55:05,560 --> 00:55:12,420
+الاول واحد واساسها واحد فتطلع عنده عبارة عن بي في
+
+539
+00:55:12,420 --> 00:55:18,480
+بي ماينوس واحد على مين على التين وكأنه صارت السؤال
+
+540
+00:55:18,480 --> 00:55:31,680
+تبعنا بدنا نثبتب-1! يطبق الـ B-1 مدلومين مدلو B في
+
+541
+00:55:31,680 --> 00:55:37,880
+B-1 على 2 وكأنه .. طبعا اللي عندى اللي .. اللي ..
+
+542
+00:55:37,880 --> 00:55:40,780
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+543
+00:55:40,780 --> 00:55:40,860
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+544
+00:55:40,860 --> 00:55:40,880
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+545
+00:55:40,880 --> 00:55:40,940
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+546
+00:55:40,940 --> 00:55:41,060
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+547
+00:55:41,060 --> 00:55:41,460
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+548
+00:55:41,460 --> 00:55:41,660
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+549
+00:55:41,660 --> 00:55:52,620
+اللي .. اللي .. اللي .. اللي .. الليعندي اللي هو
+
+550
+00:55:52,620 --> 00:56:01,660
+اكيد اكيد عندي اللي هو من wilson's theorem by
+
+551
+00:56:01,660 --> 00:56:07,940
+wilson's theorem معايا يا شباب بي minus واحد
+
+552
+00:56:07,940 --> 00:56:15,420
+factorial تطابق ناقص واحد مدنونين احنا مدنون بيه
+
+553
+00:56:15,420 --> 00:56:19,540
+بنعرف ولا لا مدنون بيه
+
+554
+00:56:22,490 --> 00:56:28,610
+الان الـ-1 على جهة .. طب احنا بعيدين شوية عن
+
+555
+00:56:28,610 --> 00:56:33,630
+سؤالنا ولا لأ؟ لأ مش بعيدين شوف ليش مش بعيدين الان
+
+556
+00:56:33,630 --> 00:56:38,450
+عندي B-1 تطابق الـ-1 مضل بيه لكن الـ-1 بتطابق مين
+
+557
+00:56:38,450 --> 00:56:46,290
+يا شباب؟ الـB-1 مضل بيه لأن B-1 زاد الـ1 بيصير B
+
+558
+00:56:46,290 --> 00:56:51,800
+بتقسم الـBأذا صار عندى فعل الـ B-1 فكتورة طابق الـ
+
+559
+00:56:51,800 --> 00:56:59,280
+B-1 ميّن modulo B صار الأمر و كأنه بدأنا نصل للي
+
+560
+00:56:59,280 --> 00:57:05,200
+بدناهاعندي بس انا بدي بين بي في بي ماينس واحد على
+
+561
+00:57:05,200 --> 00:57:12,540
+إيش على اللي هي اتنين وكأني هنا وصلت ان ال بي
+
+562
+00:57:12,540 --> 00:57:18,320
+بتجسم ال بي ماينس واحد factorial ناقص ال بي ماينس
+
+563
+00:57:18,320 --> 00:57:28,370
+واحد، مظبوط؟طيب ما هو عند الـ B-1 بتقسم الـ B-1
+
+564
+00:57:28,370 --> 00:57:32,830
+factorial ناقص الـ B-1 هتجيبناها من وين يا جماعة
+
+565
+00:57:32,830 --> 00:57:37,830
+من الـ Nonsense theorem هذه واحد لأن B-1 بتقسم هذا
+
+566
+00:57:37,830 --> 00:57:40,850
+المقدار عارفين ليش؟ أكيد عارفين لأنه لو أخدنا B-1
+
+567
+00:57:40,850 --> 00:57:44,650
+من الجهتين فبصير B-2 factorial ناقص واحد مضربها في
+
+568
+00:57:44,650 --> 00:57:49,890
+الـ B-1 ده الـ B-1 تقسمهاماشي طيب صار عندي الان
+
+569
+00:57:49,890 --> 00:57:56,370
+واحد و اتنين بيعطيني ما يالي لاحظوا ان العامل
+
+570
+00:57:56,370 --> 00:58:00,090
+المشترك الاعلى بين ال b و ال b-1 ايش بساوي بساوي
+
+571
+00:58:00,090 --> 00:58:05,030
+واحد اذا بالفكرة المتكررة اللي حكيناها اذا ال b في
+
+572
+00:58:05,030 --> 00:58:14,070
+ال b-1 تقسم ال b-1 factorial ناقص ال b-1
+
+573
+00:58:16,260 --> 00:58:22,700
+أي سؤال؟ طيب، لكن أنا باعرف من الأصل أن الـ B في
+
+574
+00:58:22,700 --> 00:58:29,180
+الـ B minus 1 على 2 تقسم الـ B في الـ B minus 1
+
+575
+00:58:29,180 --> 00:58:32,820
+أكيد؟
+
+576
+00:58:32,820 --> 00:58:37,340
+ماشي الحال، إذا هذا المقدار بقسم هذا وهذا المقدار
+
+577
+00:58:37,340 --> 00:58:42,180
+نفسه بقسم هذا من التنتين مع بعض، إذا ال .. طبعا
+
+578
+00:58:42,180 --> 00:58:48,380
+هذا انتجر يا شباببقوم العامل هذه إذا الـ B في الـ
+
+579
+00:58:48,380 --> 00:58:58,700
+B-1 على 2 يقسم الـ B-1 factorial ناقص الـ B-1 كمان
+
+580
+00:58:58,700 --> 00:59:03,060
+مرة يا شباب الـ B في الـ B-1 بقسم هذا المقدار قلنا
+
+581
+00:59:03,060 --> 00:59:06,260
+من التنتين اللي فوق لأن العامل مشترك لعيابين هذه
+
+582
+00:59:06,260 --> 00:59:11,670
+وهذه بالساعة واحدةوهذه أنا بعرفها تقسم هذه إذا صار
+
+583
+00:59:11,670 --> 00:59:14,070
+عند بي في بي ماينوس واحد على اتنين بيقسم هذا
+
+584
+00:59:14,070 --> 00:59:19,910
+المقتار وهذا ايش اللي هو هذا هو عبارة عن ال بي
+
+585
+00:59:19,910 --> 00:59:24,590
+ماينوس واحد factorial يطابق ال بي ماينوس واحد
+
+586
+00:59:25,560 --> 00:59:29,760
+موضولة الـ B في الـ B ماينس واحد على اتنين اللي
+
+587
+00:59:29,760 --> 00:59:32,520
+مهمين يا جماعة من اول .. من وسط الدور هو عبارة عن
+
+588
+00:59:32,520 --> 00:59:37,060
+الواحد زي الاتنين زي الـ B ماينس واحد وحصلنا على
+
+589
+00:59:37,060 --> 00:59:43,520
+المطلوب نيجي نشوف السؤال السابع السؤال السابع اش
+
+590
+00:59:43,520 --> 00:59:48,340
+بقول السؤال السابع عند if B is a brine approve
+
+591
+00:59:48,340 --> 00:59:53,120
+that B بي تجسم
+
+592
+00:59:54,610 --> 01:00:07,070
+الـ A to the B زائد الـ B minus واحد factorial في
+
+593
+01:00:07,070 --> 01:00:13,430
+الـ A and الـ B بتجسم الـ A زائد B minus واحد
+
+594
+01:00:13,430 --> 01:00:19,830
+factorial A to the B، مظبوط؟ خلّينا نشوف
+
+595
+01:00:24,100 --> 01:00:29,000
+بنثبت أن هذا المقدار يطابق السفر Modulo B هذا أكيد
+
+596
+01:00:29,000 --> 01:00:33,320
+فيه ويلسون وA to the B فيه ما يسمى Corollary of
+
+597
+01:00:33,320 --> 01:00:40,000
+Format لأن هذا ايش لأي A لأي A مش حاجة عن أي ايش
+
+598
+01:00:40,000 --> 01:00:44,930
+محدد ندى نشوف كيف ايش اللي بقولهالأن بما أنه B'
+
+599
+01:00:45,350 --> 01:00:51,890
+إذا by Wilson's theorem B-1 factorial تطابق السلب
+
+600
+01:00:51,890 --> 01:00:57,730
+واحد مضلومين يا جماعة مضلوا B بدي أحصل على هذه
+
+601
+01:00:57,730 --> 01:01:04,890
+أضرب الجهتين في A فبصير عندي A في B أو B-1
+
+602
+01:01:04,890 --> 01:01:12,740
+factorial في A تطابق ناقص A مضلومين مضلوا Bلكن انا
+
+603
+01:01:12,740 --> 01:01:17,780
+بعرف انه by corollary هذا by Wilson's theory لأن
+
+604
+01:01:17,780 --> 01:01:24,540
+by corollary of Fermat a to the b تطابق ال a
+
+605
+01:01:24,540 --> 01:01:31,420
+modulo b، مظبوط؟ اكيد التنتين مع بعض، التنتين مع
+
+606
+01:01:31,420 --> 01:01:36,140
+بعض بيعطيني اللي هو b minus واحد factorial في ال a
+
+607
+01:01:37,450 --> 01:01:42,670
+بدّل سالب A بضع مين؟ تطابق سالب A to the B لأن A
+
+608
+01:01:42,670 --> 01:01:48,270
+to the B تطابق الـ A Modulo B وهذا ماذا يعني؟ هذا
+
+609
+01:01:48,270 --> 01:01:54,150
+ما يعني Hence الـ B تقسم الـ B minus 1 factorial
+
+610
+01:01:54,150 --> 01:01:59,670
+في الـ A زيد الـ A to the B هذا اللي هو الجزء
+
+611
+01:01:59,670 --> 01:02:05,550
+الأول Similarly بالظبط الجزء الثاني و هتشوف كيف
+
+612
+01:02:05,550 --> 01:02:10,300
+Similarlyالان بدل ما اضرب الجهتين في a اضرب
+
+613
+01:02:10,300 --> 01:02:18,840
+الجهتين في a أُس b فبيحصل عندي a أُس b أو b-1 في a
+
+614
+01:02:18,840 --> 01:02:26,510
+أُس b تطابق ناقص a أُس b modulo a modulo bلكن من
+
+615
+01:02:26,510 --> 01:02:32,190
+فرمات A أُس B تطابق الـ A صح ولا لأ الآن A أُس B
+
+616
+01:02:32,190 --> 01:02:38,410
+تطابق الـ A مضلوا B معايا يا شباب إذا بدي أشيل الـ
+
+617
+01:02:38,410 --> 01:02:42,530
+A أُس B و أحط مكانها من الـ A فبصير اللي فوق B
+
+618
+01:02:42,530 --> 01:02:49,970
+minus 1 factorial A أُس B تطابق مكان الـ A أُس B و
+
+619
+01:02:49,970 --> 01:02:55,890
+أنا إيش بحط الـ A مضلوا Bالان هذا معناته ان بي
+
+620
+01:02:55,890 --> 01:03:01,330
+تقسم بي ماينس واحد فيكتوريا ل A أقص بي زائد مين
+
+621
+01:03:01,330 --> 01:03:07,030
+زائد ايه مالكم ساكتين زائد ايه وكون عندنا حصلنا
+
+622
+01:03:07,030 --> 01:03:12,110
+مين الجزء الثاني من السؤال نيجي الان لسؤال تسعة
+
+623
+01:03:14,360 --> 01:03:20,700
+بقول لي using Wilson's theorem to show that واحد
+
+624
+01:03:20,700 --> 01:03:26,680
+تربية في تلاتة تربية في خمسة تربية في لما أصل عند
+
+625
+01:03:26,680 --> 01:03:34,200
+بي minus اتنين لكل تربية تطابق ناقص واحد قص بي
+
+626
+01:03:34,200 --> 01:03:45,080
+زائد واحد على اتنين modulo اللي هو بي معايااللي هو
+
+627
+01:03:45,080 --> 01:03:52,300
+بي حيث بي is an odd prime بي is an odd a prime
+
+628
+01:03:52,300 --> 01:03:55,480
+approve
+
+629
+01:03:55,480 --> 01:04:01,360
+شوف
+
+630
+01:04:01,360 --> 01:04:09,640
+هذه الملاحظة اللي بنعملها لان عند 2 في 4 في 6 لما
+
+631
+01:04:09,640 --> 01:04:18,810
+أصل لعند اللي هو بي minus 1تطابق الـ B² فبصيرها
+
+632
+01:04:18,810 --> 01:04:23,230
+دقيقة اش انفين بضل اعد اتنين اربعة ستة لما اصل عند
+
+633
+01:04:23,230 --> 01:04:34,450
+الـ B- واحد الان الاتنين الاتنين احنا الـ B- اتنين
+
+634
+01:04:34,450 --> 01:04:39,700
+تطابق اتنين صح؟أو تتطابق ناقص اتنين as if الـ B
+
+635
+01:04:39,700 --> 01:04:44,180
+ناقص ثلاثة أو الـ B minus واحد تتطابق ناقص واحد
+
+636
+01:04:44,180 --> 01:04:46,980
+الـ B minus اتنين تتطابق ناقص اتنين الـ B ناقص
+
+637
+01:04:46,980 --> 01:04:50,600
+ثلاثة تتطابق ناقص ثلاثة الـ B ناقص K in general
+
+638
+01:04:50,600 --> 01:04:56,620
+تتطابق مين ناقص الـ K واضحة هذا مدل المين ومدل الـ
+
+639
+01:04:56,620 --> 01:05:02,300
+B لأن بيضيف هذه بالـ CRB CRB تقسم الـ B إذا هذه
+
+640
+01:05:02,300 --> 01:05:08,670
+التنين هتتطابق المينالـ B ناقص اتنين بس بيبقى عياش
+
+641
+01:05:08,670 --> 01:05:15,890
+بالثاني و بضلي أنزل وهذه بتطابق مين؟ اللي هي ناقص
+
+642
+01:05:15,890 --> 01:05:22,090
+B minus أربعة لما أسأل الأخر واحد الـ B minus واحد
+
+643
+01:05:22,090 --> 01:05:26,050
+الـ B minus K الـ K و K نصارت مين؟ اللي هي B minus
+
+644
+01:05:26,050 --> 01:05:32,430
+واحد فبصير B minus B minus واحد يعني اللي هي تطابق
+
+645
+01:05:32,430 --> 01:05:33,370
+الناقص
+
+646
+01:05:35,590 --> 01:05:39,890
+اللي هو ناقص
+
+647
+01:05:39,890 --> 01:05:47,490
+K تطابق الناقص K اللي هو تطابق مين؟ الناقص واحد P
+
+648
+01:05:47,490 --> 01:05:53,050
+ناقص K اللي هي P ماينس واحد تطابق مين؟ الناقص واحد
+
+649
+01:05:53,050 --> 01:05:58,490
+فاضحة؟ فهذا بيصير مضالة عند مين؟ الناقص واحد اللي
+
+650
+01:05:58,490 --> 01:06:02,150
+جابه ما هتكون مين؟ ناقص ثلاثة و أكتر
+
+651
+01:06:05,910 --> 01:06:08,850
+عارفين ليش ناقص ثلاثة؟ لأنه قبلها دي مباشرة يا
+
+652
+01:06:08,850 --> 01:06:12,330
+شباب مالكم اللي P ناقص ثلاثة و P ناقص ثلاثة الطابق
+
+653
+01:06:12,330 --> 01:06:15,890
+مين؟ ناقص ثلاثة و اللي قبلها P ناقص خمسة الطابق P
+
+654
+01:06:15,890 --> 01:06:20,530
+ناقص خمسة يعني الآن هذي بتصير الطابق عبارة عن ناقص
+
+655
+01:06:20,530 --> 01:06:26,450
+واحد فناقص ثلاثة ناقص خمسة لما أصل ناقص P minus
+
+656
+01:06:26,450 --> 01:06:35,150
+اتنين what's happen؟الآن هذول المحاضر في الواقع
+
+657
+01:06:35,150 --> 01:06:39,950
+هلنين هي عبارة عن شيلك مقصيبك من النواقص عبارة عن
+
+658
+01:06:39,950 --> 01:06:43,390
+الواحد والتنين والتلاتة والاربعة والخمسة والستة
+
+659
+01:06:43,390 --> 01:06:46,190
+وال بي واينس واحد او البي واينس اتنين وبي واينس
+
+660
+01:06:46,190 --> 01:06:50,070
+واحد إذاً عددهم أشمال بي واينس واحد مُص هدولة مُص
+
+661
+01:06:50,070 --> 01:06:54,330
+وهدولة مُص فصار عبارة عن هدولة عددهم اللي هو بي
+
+662
+01:06:54,330 --> 01:06:57,970
+واينس واحد على اتنين هنا كل واحدة فيها ناقص إذاً
+
+663
+01:06:57,970 --> 01:07:01,850
+عبارة عن ناقص واحد قُس بي واينس واحد على مينعلى
+
+664
+01:07:01,850 --> 01:07:05,750
+اتنين مضربة في مين يا شباب في واحد في تلاتة في
+
+665
+01:07:05,750 --> 01:07:14,490
+خمسة في سبعة لما أصل بيه minus اتنين أي سؤال حتى
+
+666
+01:07:14,490 --> 01:07:20,850
+الآن طيب الآن يا شباب اضربولي الجهتين هذه وهذه
+
+667
+01:07:20,850 --> 01:07:25,350
+اضربولي في واحد في تلاتة في خمسة في سبعة في اللي
+
+668
+01:07:25,350 --> 01:07:30,080
+هان فهدولة اضربولي هان في هان فبصير عندىفاهمين؟
+
+669
+01:07:30,080 --> 01:07:34,800
+تضرب الجهتين في مين في هذا المقدار الجهة دي إيش
+
+670
+01:07:34,800 --> 01:07:39,660
+بتصير بتتعبى كامل بتصير عبارة عن واحد في اتنين في
+
+671
+01:07:39,660 --> 01:07:42,400
+تلتة في اربع في خمسة عن بي ماينس واحد يعني بتصير
+
+672
+01:07:42,400 --> 01:07:46,980
+عبارة عن بي ماينس واحد vector إذا ضربت واحد في
+
+673
+01:07:46,980 --> 01:07:52,780
+تلتة في خمسة في بي ماينس اتنينواضربتهم في المقدار
+
+674
+01:07:52,780 --> 01:07:58,980
+هذا 2 في 4 في 6 لما أصل عند بي minus واحد لأن
+
+675
+01:07:58,980 --> 01:08:03,860
+تطابق أو تساوي مساواة حتة ماقص واحد اقص بي minus
+
+676
+01:08:03,860 --> 01:08:10,250
+واحد على 2 فيالمقدار اللي قلنا عنه ضربناها لما
+
+677
+01:08:10,250 --> 01:08:14,670
+نضربهان هذا لما نضربهان بيصير ايش هو هذا عن واحد
+
+678
+01:08:14,670 --> 01:08:18,970
+تربية في تلاتة تربية في خمسة تربية في سبعة تربية
+
+679
+01:08:18,970 --> 01:08:25,450
+لما أصل بيه مانس اتنين لكل تربية مظبوطش يا بابا
+
+680
+01:08:25,450 --> 01:08:30,090
+هذا الآن هو مين في الواقع يا جماعة هذا عبارة عن
+
+681
+01:08:30,090 --> 01:08:35,920
+بيه ناقص واحد factorialصار عند الـ b-1 two
+
+682
+01:08:35,920 --> 01:08:41,340
+factorial هو بساوي ناقص واحد أس بي minus واحد على
+
+683
+01:08:41,340 --> 01:08:48,320
+اتنين في المقدار من واحد خمسة بي ناقص اتنين كلهم
+
+684
+01:08:48,320 --> 01:08:54,640
+تربعة هذا من منصوص theorem هو عبارة عن ناقص واحد
+
+685
+01:08:54,640 --> 01:09:02,900
+إذا صار المقدار هذا بطابق ناقص واحد modulo modulo
+
+686
+01:09:02,900 --> 01:09:10,050
+bودربي هنا في ناقص واحد أس بي ماينس واحد على اتنين
+
+687
+01:09:10,050 --> 01:09:13,990
+و هنا في ناقص واحد أس بي ماينس واحد على اتنين يعني
+
+688
+01:09:13,990 --> 01:09:16,830
+بتضرب الجهتين في هذا النقطة فبصير عندي عبارة عن
+
+689
+01:09:16,830 --> 01:09:21,280
+ناقص واحدنارقص واحد أس بي مانس واحد على اتنين
+
+690
+01:09:21,280 --> 01:09:27,220
+فبصير بي مانس واحد على اتنين زائد واحد تطابق نارقص
+
+691
+01:09:27,220 --> 01:09:31,560
+واحد أس بي مانس واحد على اتنين في اتنين لأنه
+
+692
+01:09:31,560 --> 01:09:37,340
+silent and tail في واحد في تلاتة تربية لما أصل بي
+
+693
+01:09:37,340 --> 01:09:48,140
+مانس اتنين تربية modulo بي هذا مين هوهذا الان هذا
+
+694
+01:09:48,140 --> 01:09:51,640
+اتنين مع اتنين الـ P قُط بي ماينس واحد ايش يا شباب
+
+695
+01:09:51,640 --> 01:09:54,940
+even إذا هذا صار ايش ماله ناقص واحد أس even يعني
+
+696
+01:09:54,940 --> 01:09:59,760
+واحد إذا صار هذا المقدار then اللي هو واحد تربية
+
+697
+01:09:59,760 --> 01:10:04,500
+في تلاتة تربية في بي ماينس اتنين تربية يطابق لإنه
+
+698
+01:10:04,500 --> 01:10:07,820
+صار واحد هذا يطابق هذا المقدار اللي هو ناقص واحد
+
+699
+01:10:07,820 --> 01:10:15,410
+أسB-1 على 2 زائد 1 بيصير عبارة عن B زائد 1 على 2
+
+700
+01:10:15,410 --> 01:10:22,230
+الكل modulo B وهو المطلوب بيجي لسؤال 11 أه اللي
+
+701
+01:10:22,230 --> 01:10:30,550
+شاف برهان اللي هو ال X تربيع زائد 1 وطابق السفر
+
+702
+01:10:30,550 --> 01:10:38,510
+modulo B as a solution if and only if Bاللي هو على
+
+703
+01:10:38,510 --> 01:10:42,830
+صورة 4K زائد واحد اللي هي اللي حكيناها في أول
+
+704
+01:10:42,830 --> 01:10:47,750
+المحاضرة الآن في هذه .. في البرهان بيقولك إيش ال
+
+705
+01:10:47,750 --> 01:10:51,790
+solution للمعادلة .. في البرهان بيقولك إيش ال
+
+706
+01:10:51,790 --> 01:10:56,990
+solution X7 زائد واحد تطابق الصفر modulo B لما B
+
+707
+01:10:56,990 --> 01:11:01,230
+تكون على صورة 4K زائد واحد ال solution كان بالظبط
+
+708
+01:11:01,230 --> 01:11:07,750
+اللي هو عبارة عن B minus 1 factorialعلى او على 2
+
+709
+01:11:07,750 --> 01:11:13,970
+factorial بساوة X هذا اللي هو one solution modulo
+
+710
+01:11:13,970 --> 01:11:19,630
+B هذا اللي هو X تقابل كذا modulo B منين جبت هذا
+
+711
+01:11:19,630 --> 01:11:23,750
+انا من برهان النظرية من برهان النظرية اللي
+
+712
+01:11:23,750 --> 01:11:27,810
+برهننالكم ايه يعني هذا ال solution ل X تقابل 1
+
+713
+01:11:27,810 --> 01:11:31,410
+modulo B انا لما تبقى على سؤال 11 سؤال 11 بيقول لي
+
+714
+01:11:31,410 --> 01:11:35,030
+apply theory الخمسة خمسة to obtain the solution of
+
+715
+01:11:35,030 --> 01:11:42,840
+XX تربية تطابق ناقص واحد مدنه جداشة شباب مدنه تسعة
+
+716
+01:11:42,840 --> 01:11:51,120
+و عشرين مدنه تسعة و عشرين and X كمان واحدة and X
+
+717
+01:11:51,120 --> 01:11:55,840
+تربية تطابق ناقص واحد مدنه سبعة و تلاتين بدنا نحل
+
+718
+01:11:55,840 --> 01:12:00,180
+السؤالين اللي أمامنا أو اللي هو نعمل applications
+
+719
+01:12:00,180 --> 01:12:07,650
+عليهم السؤال الأول هذا solutionمن البرهان النظرية
+
+720
+01:12:07,650 --> 01:12:15,510
+بما أن الـ 29 تطابق الواحد modulo 4 then one
+
+721
+01:12:15,510 --> 01:12:25,230
+solution is Xبتساوي الـ 29 ناقص 1 اللي هو 28 على 2
+
+722
+01:12:25,230 --> 01:12:30,670
+factorial اللي هو عبارة عن جداش 14 factorial 14
+
+723
+01:12:30,670 --> 01:12:33,770
+factorial انا حسبها لو حسبناها اللي جيهاش بتساوي
+
+724
+01:12:33,770 --> 01:12:41,150
+تتعدق12 mod 29 هاي ال solution الأول جملة في
+
+725
+01:12:41,150 --> 01:12:45,010
+البرنام أيضا ال solutions يحدث in pairs واحد من جب
+
+726
+01:12:45,010 --> 01:12:49,010
+و واحد سالبي التاني و إضافة عن X بالطابق نقص 12
+
+727
+01:12:49,010 --> 01:12:55,290
+mod 29 أو بمعنى آخر 17 mod 29 هاي ال solutions
+
+728
+01:12:55,290 --> 01:12:59,460
+اللي همSimilarly لأكثر بيض طبق نقص واحد مدرو سبعة
+
+729
+01:12:59,460 --> 01:13:02,740
+و تلاتين سبعة و تلاتين بصير سبعة و تلاتين نقص واحد
+
+730
+01:13:02,740 --> 01:13:05,100
+على اتنين اللي هي ستة و تلاتين على اتنين اللي هي
+
+731
+01:13:05,100 --> 01:13:09,220
+تمانتاش فيكتوريال مدرو سبعة و تلاتين طيب نيجي
+
+732
+01:13:09,220 --> 01:13:12,740
+للسؤال الأخير السؤال الأتناش نشوف السؤال الأتناش
+
+733
+01:13:12,740 --> 01:13:15,400
+ايش اللي بيقوله السؤال الأتناش
+
+734
+01:13:18,990 --> 01:13:22,410
+أحنا قلنا اكسر بيح زائد واحد تطابق صفر مدنو بيهازا
+
+735
+01:13:22,410 --> 01:13:26,850
+solution if and only if بيهازا solution if and
+
+736
+01:13:26,850 --> 01:13:28,750
+only if بيهازا solution if and only if بيهازا
+
+737
+01:13:28,750 --> 01:13:28,810
+solution if and only if بيهازا solution if and
+
+738
+01:13:28,810 --> 01:13:29,270
+only if بيهازا solution if and only if بيهازا
+
+739
+01:13:29,270 --> 01:13:31,110
+solution if and only if بيهازا solution if and
+
+740
+01:13:31,110 --> 01:13:32,910
+only if بيهازا solution if and only if بيهازا
+
+741
+01:13:32,910 --> 01:13:33,810
+solution if and only if بيهازا solution if and
+
+742
+01:13:33,810 --> 01:13:34,190
+only if بيهازا solution if and only if بيهازا
+
+743
+01:13:34,190 --> 01:13:36,130
+solution if and only if بيهازا solution if and
+
+744
+01:13:36,130 --> 01:13:41,370
+only if بيهازا solution if and only if بيهازا
+
+745
+01:13:41,370 --> 01:13:45,870
+solution if and only if بيهازا solution if and
+
+746
+01:13:45,870 --> 01:13:46,610
+only if بيهازا solution if and only if بيهازا
+
+747
+01:13:46,610 --> 01:13:49,060
+solution if and only if بيهازاB بيساوي 4K زائد
+
+748
+01:13:49,060 --> 01:13:58,620
+تلاتة is prime وA تربيع زائد B تربيع تطابق السفر
+
+749
+01:13:58,620 --> 01:14:03,040
+modulo B then
+
+750
+01:14:03,040 --> 01:14:12,240
+A تطابق الـ B تطابق السفر modulo Bالبروف ايه
+
+751
+01:14:12,240 --> 01:14:17,020
+الاشهدار شوف ايش اللي بتسوي اذكركم في المعلومة ال
+
+752
+01:14:17,020 --> 01:14:20,920
+X تربية زائد واحد ل solution if and only if ال B
+
+753
+01:14:20,920 --> 01:14:24,800
+على سوري 4K زائد واحد يعني اي B مش على سوري 4K
+
+754
+01:14:24,800 --> 01:14:27,400
+زايد واحد ال X تربية تتطبق ناقص واحد فيش ل
+
+755
+01:14:27,400 --> 01:14:32,940
+solution طيب كان هذا اللي .. هذا هتوصلني ل .. ل
+
+756
+01:14:32,940 --> 01:14:39,400
+اللي هو كيف احصل ال 12لأن سؤال 12 بيقول لي إذا
+
+757
+01:14:39,400 --> 01:14:43,500
+كانت B بتسوي 4K زي 3 والـ A تربيع زي B تربيع
+
+758
+01:14:43,500 --> 01:14:47,280
+بالطابق الصفر مضلوا B إثبتني إن الـ A و الـ B
+
+759
+01:14:47,280 --> 01:14:52,260
+متطابقة بطابق الصفر مضلوا مين مضلوا B بدي أفترض لك
+
+760
+01:14:52,260 --> 01:14:56,880
+عكس هذا و أسألك ال contradiction بقول لك suppose
+
+761
+01:14:56,880 --> 01:14:59,560
+that
+
+762
+01:15:00,710 --> 01:15:08,030
+A تطابق الـ B تطابق السفر modulo B does not hold
+
+763
+01:15:08,030 --> 01:15:19,130
+سي A لا تطابق الـ 0 modulo Bأو P لا تطابق الـ Zero
+
+764
+01:15:19,130 --> 01:15:24,290
+مدلوا A ماشي الحال أي ننوم بنفعل نفترض أن الـ A لا
+
+765
+01:15:24,290 --> 01:15:27,590
+تطابق الـ Zero مدلوا B أو الـ B لا تطابق الـ Zero
+
+766
+01:15:27,590 --> 01:15:31,670
+مدلوا B without loss of generality suppose that A
+
+767
+01:15:31,670 --> 01:15:35,090
+لا تطابق الـ Zero مدلوا B أو إنك تفضل تقول suppose
+
+768
+01:15:35,090 --> 01:15:37,810
+that أن A لا تطابق الـ Zero مدلوا B تسبب
+
+769
+01:15:37,810 --> 01:15:40,470
+Contradiction وبعدين تقول Similarly وفعلا
+
+770
+01:15:40,470 --> 01:15:44,390
+Similarly B لا تطابق الـ Zero مدلوا B تسبب
+
+771
+01:15:44,390 --> 01:15:49,670
+Contradictionنشوف ايش اللي بقوله هذا الان انا
+
+772
+01:15:49,670 --> 01:16:00,350
+مفترض ان ال a لا تطابق السفر modulo b الان معناته
+
+773
+01:16:00,350 --> 01:16:04,350
+ان ال a لا تطابق السفر modulo b معناته ال b لا
+
+774
+01:16:04,350 --> 01:16:10,420
+تقسم ال aيعني العامل المشترك الأعلى بين الـP والـA
+
+775
+01:16:10,420 --> 01:16:16,380
+بساوء واحد إذا بناء عليها الـlinear congruences Ax
+
+776
+01:16:16,380 --> 01:16:21,660
+تطابق الواحد model بيه بنظرية سابقة اللي هي نظرية
+
+777
+01:16:21,660 --> 01:16:28,720
+بالظبط نظرية سبعة أربعة سبعة بواسطة أربعة سبعة هذه
+
+778
+01:16:28,720 --> 01:16:29,880
+إليها solution
+
+779
+01:16:32,650 --> 01:16:36,050
+بما أن الـ A والـ B العامل المشترك اللي على بينهم
+
+780
+01:16:36,050 --> 01:16:41,690
+واحد أو الـ B لا تقسم الـ A كبران B إذا الـ A X
+
+781
+01:16:41,690 --> 01:16:46,910
+تطابق الواحد مدلو B has a solution say this
+
+782
+01:16:46,910 --> 01:16:54,870
+solution is X بتساوي C then إذا كان في solution
+
+783
+01:16:54,870 --> 01:16:59,930
+وسميناها C إذا صار عندي A في C تطابق الواحد مدلو
+
+784
+01:17:00,580 --> 01:17:06,540
+مدلوا مين؟ مدلوا بيه الان هو معطيني ان اي تربيع زي
+
+785
+01:17:06,540 --> 01:17:11,040
+بيه تربيه تتعبق السفر مدلوا اياش مدلوا بيه اذا بدي
+
+786
+01:17:11,040 --> 01:17:16,700
+سيري عندى و ضربلي الجهتينقبل ان اضغط على الجهاز
+
+787
+01:17:16,700 --> 01:17:22,540
+الاساسي A تربيع و C تربيع تطابق الواحد مدلو مين
+
+788
+01:17:22,540 --> 01:17:26,340
+مدلو بيه فاهمين ايش ساوي ربعت ايش الجهة التانية و
+
+789
+01:17:26,340 --> 01:17:32,200
+رفعتها القوة ايش اتنين الان بما ان ال A تربيع زاد
+
+790
+01:17:32,200 --> 01:17:35,910
+بيه تربيع الطابق الصفر مدلو بيهوالـ A تربيع C
+
+791
+01:17:35,910 --> 01:17:39,330
+تربيع تطابق الواحد اضرب الجهتين هنا في الـ C تربيع
+
+792
+01:17:39,330 --> 01:17:43,950
+فبصير عندي A تربيع C تربيع زائد B تربيع C تربيع
+
+793
+01:17:43,950 --> 01:17:50,830
+تطابق السفر Modulo مين Modulo B معايا يا شباب طيب
+
+794
+01:17:50,830 --> 01:17:53,490
+الـ A تربيع زي تربيع حداشر بالنسبالي على الـ B
+
+795
+01:17:53,490 --> 01:17:58,730
+واحد هنا اتبتدع فوق اذا صار عندي B تربيع C تربيع
+
+796
+01:17:59,930 --> 01:18:06,870
+زائد واحد تطابق السفر Modulo ايش Modulo B إذا صار
+
+797
+01:18:06,870 --> 01:18:15,930
+عند ال B C لكل تربية تطابق السالب واحد Modulo B من
+
+798
+01:18:15,930 --> 01:18:19,890
+هنا ما قالت الواحد أدها الثانية إيش هذه بتاعي
+
+799
+01:18:19,890 --> 01:18:28,940
+أصلا؟ هذه معناته إنه thisيعني ان X تربيها وتعب
+
+800
+01:18:28,940 --> 01:18:38,260
+ترنافض واحد Modulo بيه مفهوم X بيساوي بي سي which
+
+801
+01:18:38,260 --> 01:18:50,380
+is impossible ليش طيب؟ Because it contradicts
+
+802
+01:18:51,360 --> 01:18:59,280
+اللي هو أقرر Theorem أن الـ B على صورة 4K زائد 3
+
+803
+01:18:59,280 --> 01:19:05,140
+لأن هذه ال solution بس متى لما نكون على صورة B
+
+804
+01:19:05,140 --> 01:19:09,600
+بيبسوة 7K زائد 1 بينما ماعطين الـ B بيبسوة 4K زائد
+
+805
+01:19:09,600 --> 01:19:14,040
+3 إذن وصلتني هنا لـ Contradiction أنه لجينا حلل
+
+806
+01:19:14,040 --> 01:19:17,080
+الـ X التي تتطبق نقص واحد بدل B والـ B اللي هو على
+
+807
+01:19:17,080 --> 01:19:24,120
+صورة 4K زائد 3 فهذا مستحيل إذن الفرضية الأولىأو
+
+808
+01:19:24,120 --> 01:19:28,500
+بمعنى آخر لازم ال a تطابق السفر mod b وsimilarly
+
+809
+01:19:28,500 --> 01:19:32,020
+ال b تطابق ال zero mod b إذا صار عندى لما يكون هذا
+
+810
+01:19:32,020 --> 01:19:38,780
+صحيح لازم نحصل a تطابق ال b تطابق السفر mod b وهيك
+
+811
+01:19:38,780 --> 01:19:43,640
+نكون خلصنا اللى هو مناقشة اللى هو Wilson's theorem
+
+812
+01:19:43,640 --> 01:19:46,040
+واللي هو Fermat's theorem
+
+813
+01:19:49,030 --> 01:19:51,450
+والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/qytPH80aNtM_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/qytPH80aNtM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f31a3169421e9648660eeb78faf13ca1a6f91e56
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/qytPH80aNtM_raw.json
@@ -0,0 +1 @@
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قص 8 حسبته سهل ان شاء الله", "tokens": [6027, 2288, 4587, 2304, 13672, 1829, 1975, 5016, 8315, 2975, 3279, 19, 6055, 9566, 16758, 4587, 2423, 2975, 12174, 9381, 1649, 1072, 13455, 3282, 23758, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 34892, 4587, 2304, 13672, 1829, 1975, 5016, 8315, 2975, 3279, 19, 6055, 9566, 16758, 4587, 2423, 2975, 12174, 9381, 1649, 1072, 13455, 3282, 2423, 7649, 47525, 8315, 8717, 44510, 10721, 8717, 29245, 3215, 2423, 2975, 12174, 9381, 1649, 2423, 2975, 12174, 9381, 1649, 11331, 35457, 47395, 8608, 3224, 1211, 16472, 13412, 16606, 21984], "avg_logprob": -0.28160111288006384, "compression_ratio": 1.9463087248322148, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 219.15, "end": 220.05, "word": "الرقم", "probability": 0.66485595703125}, {"start": 220.05, "end": 220.05, "word": " اللي", "probability": 0.49224853515625}, {"start": 220.05, "end": 220.43, "word": " احنا", "probability": 0.7333984375}, {"start": 220.43, "end": 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للثمانية", "probability": 0.719677734375}, {"start": 859.24, "end": 860.42, "word": " طيب", "probability": 0.7919921875}, {"start": 860.42, "end": 862.36, "word": " عندنا", "probability": 0.52734375}, {"start": 862.36, "end": 862.78, "word": " العامل", "probability": 0.8082682291666666}, {"start": 862.78, "end": 863.28, "word": " المشترك", "probability": 0.862060546875}, {"start": 863.28, "end": 863.8, "word": " الأعلى", "probability": 0.8759765625}], "temperature": 1.0}, {"id": 38, "seek": 89422, "start": 865.1, "end": 894.22, "text": "بين الـ a و 42 بساوة واحد إذا أكيد العامل المشترك الأعلى بين ال a و 42 بساوة واحد يعني بمعنى أخر a is an odd number الان a odd number إذا أكيد اللي هو ال a على صورة in the form 4k زائد 1 or 4k زائد 3", "tokens": [3555, 9957, 2423, 39184, 257, 4032, 14034, 4724, 3794, 995, 2407, 3660, 36764, 24401, 11933, 15730, 5551, 4117, 25708, 18863, 10943, 1211, 9673, 8592, 2655, 31747, 16247, 3615, 23942, 49374, 2423, 257, 4032, 14034, 4724, 3794, 995, 2407, 3660, 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{"start": 881.18, "end": 882.02, "word": " أكيد", "probability": 0.9734700520833334}, {"start": 882.02, "end": 883.48, "word": " اللي", "probability": 0.937255859375}, {"start": 883.48, "end": 883.72, "word": " هو", "probability": 0.98193359375}, {"start": 883.72, "end": 883.9, "word": " ال", "probability": 0.70556640625}, {"start": 883.9, "end": 884.08, "word": " a", "probability": 0.8603515625}, {"start": 884.08, "end": 884.34, "word": " على", "probability": 0.841796875}, {"start": 884.34, "end": 885.36, "word": " صورة", "probability": 0.9664713541666666}, {"start": 885.36, "end": 886.58, "word": " in", "probability": 0.869140625}, {"start": 886.58, "end": 887.32, "word": " the", "probability": 0.90576171875}, {"start": 887.32, "end": 887.94, "word": " form", "probability": 0.94482421875}, {"start": 887.94, "end": 890.2, "word": " 4k", "probability": 0.676513671875}, {"start": 890.2, "end": 890.6, "word": " زائد", "probability": 0.6897786458333334}, {"start": 890.6, "end": 891.18, "word": " 1", "probability": 0.6650390625}, {"start": 891.18, "end": 892.2, "word": " or", "probability": 0.728515625}, {"start": 892.2, "end": 893.46, "word": " 4k", "probability": 0.968505859375}, {"start": 893.46, "end": 894.0, "word": " زائد", "probability": 0.8963216145833334}, {"start": 894.0, "end": 894.22, "word": " 3", "probability": 0.93896484375}], "temperature": 1.0}, {"id": 39, "seek": 90155, "start": 895.17, "end": 901.55, "text": "هذا هو الـ A odd number اذا الـ A يمّع على صورة أربعة كيه اربعة كيه زي واحد او اربعة كيه زي تلتة", "tokens": [3224, 15730, 31439, 2423, 39184, 316, 7401, 1230, 1975, 15730, 2423, 39184, 316, 7251, 2304, 11703, 3615, 15844, 20328, 13063, 3660, 5551, 25513, 27884, 9122, 1829, 3224, 1975, 25513, 27884, 9122, 1829, 3224, 30767, 1829, 36764, 24401, 1975, 2407, 1975, 25513, 27884, 9122, 1829, 3224, 30767, 1829, 6055, 1211, 2655, 3660], "avg_logprob": -0.5264422836212012, "compression_ratio": 1.394736842105263, "no_speech_prob": 0.853515625, "words": 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تربيع يا اربعة K زائد تلاتة لكل تربيع وهذه بتساوي ستة عشر K تربيع زائد تمانية K زائد واحد بيساوي ستة عشر K تربيع زائد اللي هو تلاتة فاربعة باطمعش اربعة عشرين K زائد تسعة", "tokens": [25528, 1975, 15042, 1975, 25513, 27884, 591, 30767, 16373, 3215, 36764, 24401, 6055, 2288, 21292, 3615, 35186, 1975, 25513, 27884, 591, 30767, 16373, 3215, 6055, 1211, 9307, 3660, 5296, 28820, 6055, 2288, 21292, 3615, 37037, 24192, 39894, 3794, 995, 45865, 8608, 2655, 3660, 6225, 46309, 591, 6055, 2288, 21292, 3615, 30767, 16373, 3215, 46811, 7649, 10632, 591, 30767, 16373, 3215, 36764, 24401, 4724, 1829, 3794, 995, 45865, 8608, 2655, 3660, 6225, 46309, 591, 6055, 2288, 21292, 3615, 30767, 16373, 3215, 13672, 1829, 31439, 6055, 1211, 9307, 3660, 6156, 9640, 3555, 27884, 4724, 41193, 2304, 3615, 8592, 1975, 25513, 27884, 6225, 46309, 9957, 591, 30767, 16373, 3215, 6055, 3794, 27884], "avg_logprob": -0.2161931796507402, "compression_ratio": 2.408450704225352, "no_speech_prob": 2.6226043701171875e-06, 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{"start": 1028.8, "end": 1029.36, "word": " أو", "probability": 0.64404296875}, {"start": 1029.36, "end": 1029.74, "word": " بمعنى", "probability": 0.9892578125}, {"start": 1029.74, "end": 1030.08, "word": " آخر", "probability": 0.791015625}, {"start": 1030.08, "end": 1030.52, "word": " واحد", "probability": 0.968017578125}, {"start": 1030.52, "end": 1030.88, "word": " ستة", "probability": 0.97998046875}, {"start": 1030.88, "end": 1031.34, "word": " تمانية", "probability": 0.9931640625}, {"start": 1031.34, "end": 1032.18, "word": " تقسم", "probability": 0.95947265625}, {"start": 1032.18, "end": 1032.58, "word": " الـA", "probability": 0.5975748697916666}, {"start": 1032.58, "end": 1033.42, "word": " والستة", "probability": 0.7903645833333334}, {"start": 1033.42, "end": 1034.26, "word": " ناقص", "probability": 0.88916015625}, {"start": 1034.26, "end": 1035.12, "word": " واحد", "probability": 0.898193359375}, {"start": 1035.12, "end": 1036.72, "word": " طيب", "probability": 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مشابهة", "probability": 0.9517822265625}, {"start": 1044.86, "end": 1045.56, "word": " ل", "probability": 0.48583984375}], "temperature": 1.0}, {"id": 45, "seek": 107577, "start": 1047.23, "end": 1075.77, "text": "السؤال الأول والثاني نشوف إيش بتقول بالظبط عندي السؤال الـ C بقول لي if الـ greatest common divisor بين الـ A و الـ 133 تساوي ال greatest common divisor بين الـ B و الـ 133 يساوي 1", "tokens": [6027, 3794, 33604, 6027, 16247, 12610, 16070, 12984, 7649, 1829, 8717, 8592, 38688, 11933, 1829, 8592, 39894, 39648, 20666, 19913, 3555, 9566, 18871, 16254, 21136, 33604, 6027, 2423, 39184, 383, 4724, 39648, 32239, 498, 2423, 39184, 6636, 2689, 25974, 284, 49374, 2423, 39184, 316, 4032, 2423, 39184, 3705, 18, 6055, 3794, 995, 45865, 2423, 6636, 2689, 25974, 284, 49374, 2423, 39184, 363, 4032, 2423, 39184, 3705, 18, 7251, 3794, 995, 45865, 502], "avg_logprob": -0.2266695156489333, "compression_ratio": 1.7197452229299364, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 1047.23, "end": 1048.39, "word": "السؤال", "probability": 0.9234619140625}, {"start": 1048.39, "end": 1049.13, "word": " الأول", "probability": 0.940185546875}, {"start": 1049.13, "end": 1050.07, "word": " والثاني", "probability": 0.830322265625}, {"start": 1050.07, "end": 1051.91, "word": " نشوف", "probability": 0.7470703125}, {"start": 1051.91, "end": 1053.17, "word": " إيش", "probability": 0.7098795572916666}, {"start": 1053.17, "end": 1053.65, "word": " بتقول", "probability": 0.9755859375}, {"start": 1053.65, "end": 1055.07, "word": " بالظبط", "probability": 0.9832763671875}, {"start": 1055.07, "end": 1055.65, "word": " عندي", "probability": 0.7027587890625}, {"start": 1055.65, "end": 1057.85, "word": " السؤال", "probability": 0.98193359375}, {"start": 1057.85, "end": 1058.43, "word": " الـ", "probability": 0.697509765625}, {"start": 1058.43, "end": 1058.79, "word": " C", "probability": 0.399658203125}, {"start": 1058.79, "end": 1060.13, "word": " بقول", "probability": 0.707763671875}, {"start": 1060.13, "end": 1060.31, "word": " لي", "probability": 0.33447265625}, {"start": 1060.31, "end": 1060.71, "word": " if", "probability": 0.310546875}, {"start": 1060.71, "end": 1061.89, "word": " الـ", "probability": 0.489990234375}, {"start": 1061.89, "end": 1062.23, "word": " greatest", "probability": 0.62841796875}, {"start": 1062.23, "end": 1062.65, "word": " common", "probability": 0.91357421875}, {"start": 1062.65, "end": 1063.55, "word": " divisor", "probability": 0.97705078125}, {"start": 1063.55, "end": 1064.57, "word": " بين", "probability": 0.94140625}, {"start": 1064.57, "end": 1064.81, "word": " الـ", "probability": 0.90576171875}, {"start": 1064.81, "end": 1064.95, "word": " A", "probability": 0.77294921875}, {"start": 1064.95, "end": 1065.17, "word": " و", "probability": 0.6396484375}, {"start": 1065.17, "end": 1065.31, "word": " الـ", "probability": 0.756591796875}, {"start": 1065.31, "end": 1066.79, "word": " 133", "probability": 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0.8892822265625}, {"start": 1075.39, "end": 1075.77, "word": " 1", "probability": 0.6201171875}], "temperature": 1.0}, {"id": 46, "seek": 108734, "start": 1077.05, "end": 1087.35, "text": "then show that الـ 133 تجسم A أُس 18 ناقص B أُس 18 solution or proof", "tokens": [19096, 855, 300, 2423, 39184, 3705, 18, 6055, 7435, 38251, 316, 5551, 10859, 3794, 2443, 8717, 995, 4587, 9381, 363, 5551, 10859, 3794, 2443, 3827, 420, 8177], "avg_logprob": -0.46679687606436865, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 1077.05, "end": 1077.55, "word": "then", "probability": 0.0682373046875}, {"start": 1077.55, "end": 1078.23, "word": " show", "probability": 0.90576171875}, {"start": 1078.23, "end": 1078.77, "word": " that", "probability": 0.91650390625}, {"start": 1078.77, "end": 1079.65, "word": " الـ", "probability": 0.6710205078125}, {"start": 1079.65, "end": 1080.69, "word": " 133", "probability": 0.7293701171875}, {"start": 1080.69, "end": 1081.19, "word": " تجسم", 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الـ 133 و الـ B و الـ 133 واحد إذن الـ 133 تجسم A أُس 18 نقص B أُس 18 الـ A أُس 18 و B أُس 18 بتاعتين مؤشر إنه كإن في شغل", "tokens": [6027, 148, 48506, 45030, 9566, 1829, 8315, 18863, 10943, 9673, 8592, 2655, 31747, 16247, 3615, 23942, 49374, 2423, 39184, 316, 4032, 2423, 39184, 3705, 18, 4032, 2423, 39184, 363, 4032, 2423, 39184, 3705, 18, 36764, 24401, 11933, 8848, 1863, 2423, 39184, 3705, 18, 6055, 7435, 38251, 316, 5551, 10859, 3794, 2443, 8717, 4587, 9381, 363, 5551, 10859, 3794, 2443, 2423, 39184, 316, 5551, 10859, 3794, 2443, 4032, 363, 5551, 10859, 3794, 2443, 39894, 995, 34268, 9957, 3714, 33604, 46309, 36145, 3224, 9122, 28814, 1863, 8978, 13412, 17082, 1211], "avg_logprob": -0.30530197164985573, "compression_ratio": 1.7450980392156863, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1088.32, "end": 1088.88, "word": "الآن", "probability": 0.6173502604166666}, {"start": 1088.88, "end": 1090.64, "word": " بعطينا", "probability": 0.58795166015625}, {"start": 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" B", "probability": 0.50634765625}, {"start": 1100.86, "end": 1101.02, "word": " أُس", "probability": 0.875}, {"start": 1101.02, "end": 1101.46, "word": " 18", "probability": 0.97021484375}, {"start": 1101.46, "end": 1102.28, "word": " الـ", "probability": 0.57342529296875}, {"start": 1102.28, "end": 1102.46, "word": " A", "probability": 0.85791015625}, {"start": 1102.46, "end": 1102.6, "word": " أُس", "probability": 0.9591471354166666}, {"start": 1102.6, "end": 1103.2, "word": " 18", "probability": 0.97265625}, {"start": 1103.2, "end": 1103.74, "word": " و", "probability": 0.8125}, {"start": 1103.74, "end": 1103.92, "word": " B", "probability": 0.6591796875}, {"start": 1103.92, "end": 1104.08, "word": " أُس", "probability": 0.97900390625}, {"start": 1104.08, "end": 1104.5, "word": " 18", "probability": 0.98681640625}, {"start": 1104.5, "end": 1104.98, "word": " بتاعتين", "probability": 0.83306884765625}, {"start": 1104.98, "end": 1105.66, "word": " مؤشر", "probability": 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1303.3, "end": 1304.72, "word": " خمس", "probability": 0.9069010416666666}, {"start": 1304.72, "end": 1305.2, "word": " عشر", "probability": 0.42724609375}], "temperature": 1.0}, {"id": 56, "seek": 133486, "start": 1308.1, "end": 1334.86, "text": "Solution احنا حكينا في الاول عن فرمات Structural و عن Corollary لفرمات الان فرمات بتتعامل مع a تدبط بي minus واحد تطابق الواحد modulo بي لما ال بي لا تقسم ال a ال Corollary بتتعامل مع اي integer a اقص بي تطابق ال a modulo بي الان واضح ان دي بنشتغل على Corollary فرمات", "tokens": [50, 3386, 1975, 5016, 8315, 11331, 4117, 1829, 8315, 8978, 42963, 12610, 18871, 6156, 2288, 2304, 9307, 745, 1757, 1807, 4032, 18871, 3925, 1833, 822, 5296, 5172, 2288, 2304, 9307, 2423, 7649, 6156, 2288, 2304, 9307, 39894, 2655, 3615, 10943, 1211, 20449, 257, 6055, 3215, 3555, 9566, 4724, 1829, 3175, 36764, 24401, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 1072, 13455, 4724, 1829, 5296, 15042, 2423, 4724, 1829, 20193, 6055, 4587, 38251, 2423, 257, 2423, 3925, 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"word": " A", "probability": 0.76708984375}, {"start": 2177.49, "end": 2177.79, "word": " والـ", "probability": 0.93359375}, {"start": 2177.79, "end": 2178.15, "word": " Q", "probability": 0.8271484375}, {"start": 2178.15, "end": 2179.27, "word": " بساوة", "probability": 0.98447265625}, {"start": 2179.27, "end": 2179.61, "word": " واحد", "probability": 0.9912109375}, {"start": 2179.61, "end": 2180.55, "word": " ومنه", "probability": 0.93017578125}, {"start": 2180.55, "end": 2181.83, "word": " هيكون", "probability": 0.6924641927083334}, {"start": 2181.83, "end": 2182.17, "word": " عيد", "probability": 0.7080078125}, {"start": 2182.17, "end": 2182.43, "word": " الـ", "probability": 0.92333984375}, {"start": 2182.43, "end": 2183.17, "word": " B", "probability": 0.73974609375}, {"start": 2183.17, "end": 2184.53, "word": " لتقسم", "probability": 0.76904296875}, {"start": 2184.53, "end": 2184.87, "word": " الـ", "probability": 0.974365234375}, {"start": 2184.87, "end": 2185.09, "word": " Q", "probability": 0.33642578125}, {"start": 2185.09, "end": 2186.35, "word": " وB", "probability": 0.3935546875}, {"start": 2186.35, "end": 2186.85, "word": " لتقسم", "probability": 0.986572265625}, {"start": 2186.85, "end": 2187.07, "word": " الـ", "probability": 0.965576171875}, {"start": 2187.07, "end": 2187.43, "word": " A", "probability": 0.8916015625}, {"start": 2187.43, "end": 2188.17, "word": " والـ", "probability": 0.587890625}, {"start": 2188.17, "end": 2188.39, "word": " Q", "probability": 0.8291015625}, {"start": 2188.39, "end": 2188.67, "word": " برضه", "probability": 0.892578125}, {"start": 2188.67, "end": 2189.83, "word": " لتقسمين", "probability": 0.9712890625}, {"start": 2189.83, "end": 2190.59, "word": " الـ", "probability": 0.9443359375}, {"start": 2190.59, "end": 2190.73, "word": " A", "probability": 0.93896484375}], "temperature": 1.0}, {"id": 90, "seek": 221605, "start": 2191.45, "end": 2216.05, "text": "الآن هذه اللي هي بتأهل من استخدام الـ Fermat's theorem بالنسبة للـ A للـ B بكون عندي then A to the B minus واحد تطابق الواحد modulo B معايا الان انفع الجهتين للقوة مين؟ للقوة K فبصير عندي and", "tokens": [6027, 148, 48506, 29538, 13672, 1829, 39896, 39894, 10721, 3224, 1211, 9154, 44713, 9778, 3215, 10943, 2423, 39184, 43261, 267, 311, 20904, 20666, 1863, 35457, 3660, 24976, 39184, 316, 24976, 39184, 363, 4724, 30544, 18871, 16254, 550, 316, 281, 264, 363, 3175, 36764, 24401, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 1072, 13455, 363, 20449, 995, 25528, 2423, 7649, 16472, 5172, 3615, 25724, 3224, 2655, 9957, 24976, 4587, 2407, 3660, 3714, 9957, 22807, 24976, 4587, 2407, 3660, 591, 6156, 3555, 9381, 13546, 18871, 16254, 293], "avg_logprob": -0.277434601340183, "compression_ratio": 1.4851485148514851, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2191.45, "end": 2191.91, "word": "الآن", "probability": 0.558349609375}, {"start": 2191.91, "end": 2192.71, "word": " هذه", "probability": 0.72802734375}, {"start": 2192.71, "end": 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"end": 2206.97, "word": " modulo", "probability": 0.878173828125}, {"start": 2206.97, "end": 2207.79, "word": " B", "probability": 0.8408203125}, {"start": 2207.79, "end": 2209.11, "word": " معايا", "probability": 0.912109375}, {"start": 2209.11, "end": 2210.85, "word": " الان", "probability": 0.542144775390625}, {"start": 2210.85, "end": 2211.21, "word": " انفع", "probability": 0.8040364583333334}, {"start": 2211.21, "end": 2211.69, "word": " الجهتين", "probability": 0.8260498046875}, {"start": 2211.69, "end": 2212.21, "word": " للقوة", "probability": 0.9683837890625}, {"start": 2212.21, "end": 2212.83, "word": " مين؟", "probability": 0.6216634114583334}, {"start": 2212.83, "end": 2213.61, "word": " للقوة", "probability": 0.9727783203125}, {"start": 2213.61, "end": 2213.97, "word": " K", "probability": 0.8583984375}, {"start": 2213.97, "end": 2215.09, "word": " فبصير", "probability": 0.9193115234375}, {"start": 2215.09, "end": 2215.49, "word": " عندي", "probability": 0.882080078125}, {"start": 2215.49, "end": 2216.05, "word": " and", "probability": 0.88330078125}], "temperature": 1.0}, {"id": 91, "seek": 224521, "start": 2217.06, "end": 2245.22, "text": "So a to the b minus 1 الكل أس كي تطابق الواحد أس كي اليمين واحد modulo فيه الان هذه مين هي a to the b minus واحد to the k اللي عبارة عن كيوكو minus واحد لأن and so ال a to the q minus واحد تطابق الواحد modulo ال b هذه أول واحدة", "tokens": [6455, 257, 281, 264, 272, 3175, 502, 2423, 28820, 5551, 3794, 9122, 1829, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 5551, 3794, 9122, 1829, 2423, 32640, 9957, 36764, 24401, 1072, 13455, 8978, 3224, 2423, 7649, 29538, 3714, 9957, 39896, 257, 281, 264, 272, 3175, 36764, 24401, 281, 264, 350, 13672, 1829, 6225, 3555, 9640, 3660, 18871, 9122, 1829, 2407, 4117, 2407, 3175, 36764, 24401, 5296, 33456, 293, 370, 2423, 257, 281, 264, 9505, 3175, 36764, 24401, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 1072, 13455, 2423, 272, 29538, 5551, 12610, 36764, 24401, 3660], "avg_logprob": 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{"id": 97, "seek": 240994, "start": 2384.52, "end": 2409.94, "text": "لكن لو أتينا و أخذنا الـ Q أس بي ماينس واحد حط طابق ماذا موضوع الـ Q؟ أكيد حط طابق إيش؟ صفر لأن الـ Q أس بي ماينس واحد من المضاعفات من من المضاعفات الـ Q", "tokens": [1211, 19452, 45164, 5551, 31371, 8315, 4032, 5551, 9778, 8848, 8315, 2423, 39184, 1249, 5551, 3794, 4724, 1829, 19446, 9957, 3794, 36764, 24401, 11331, 9566, 23032, 16758, 4587, 3714, 45636, 995, 3714, 2407, 11242, 45367, 2423, 39184, 1249, 22807, 5551, 4117, 25708, 11331, 9566, 23032, 16758, 4587, 11933, 1829, 8592, 22807, 20328, 5172, 2288, 5296, 33456, 2423, 39184, 1249, 5551, 3794, 4724, 1829, 19446, 9957, 3794, 36764, 24401, 9154, 9673, 11242, 45761, 5172, 9307, 9154, 9154, 9673, 11242, 45761, 5172, 9307, 2423, 39184, 1249], "avg_logprob": -0.3159926344366635, "compression_ratio": 1.948905109489051, "no_speech_prob": 0.0, "words": [{"start": 2384.52, "end": 2384.92, "word": "لكن", "probability": 0.548095703125}, {"start": 2384.92, "end": 2385.38, 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theorem الـ Q هو عبارة عن الـ prime و الـ B هو الأساس فبصير B to the Q minus واحد تطابق الواحد Modulo مين Modulo هو الـ prime لـ Q وفي نفس الوقت", "tokens": [1863, 7435, 2304, 3615, 9673, 30241, 20498, 9307, 4032, 3615, 1863, 16254, 36632, 11242, 14111, 995, 2423, 39184, 1249, 20193, 6055, 4587, 38251, 2423, 39184, 363, 11933, 15730, 538, 43261, 267, 311, 20904, 2423, 39184, 1249, 31439, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 5835, 4032, 2423, 39184, 363, 31439, 16247, 3794, 32277, 6156, 3555, 9381, 13546, 363, 281, 264, 1249, 3175, 36764, 24401, 6055, 9566, 16758, 4587, 2423, 14407, 24401, 6583, 13455, 3714, 9957, 6583, 13455, 31439, 2423, 39184, 5835, 5296, 39184, 1249, 4032, 41185, 8717, 36178, 2423, 30543, 2655], "avg_logprob": -0.24541440136406734, "compression_ratio": 1.5120772946859904, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2410.91, "end": 2411.51, "word": "نجمع", "probability": 0.8135986328125}, {"start": 2411.51, "end": 2412.27, "word": " 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Modulo", "probability": 0.68798828125}, {"start": 2433.13, "end": 2433.89, "word": " هو", "probability": 0.79638671875}, {"start": 2433.89, "end": 2434.19, "word": " الـ", "probability": 0.86572265625}, {"start": 2434.19, "end": 2434.49, "word": " prime", "probability": 0.66552734375}, {"start": 2434.49, "end": 2434.73, "word": " لـ", "probability": 0.8701171875}, {"start": 2434.73, "end": 2435.03, "word": " Q", "probability": 0.70068359375}, {"start": 2435.03, "end": 2439.29, "word": " وفي", "probability": 0.869873046875}, {"start": 2439.29, "end": 2439.63, "word": " نفس", "probability": 0.99853515625}, {"start": 2439.63, "end": 2440.35, "word": " الوقت", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 99, "seek": 246598, "start": 2442.97, "end": 2465.99, "text": "بط عندي الـ B قصة Q مانس واحد تطابق السفر modulo ايش؟ modulo اللي هو B لأنه بتصير اللي هي B قصة Q مانس واحد من مضاعفات مين؟ من مضاعفات الـ B طيب خدوني هذه مخادة", "tokens": [3555, 9566, 43242, 1829, 2423, 39184, 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"probability": 0.97265625}, {"start": 2461.27, "end": 2462.29, "word": " مضاعفات", "probability": 0.97470703125}, {"start": 2462.29, "end": 2462.51, "word": " الـ", "probability": 0.950439453125}, {"start": 2462.51, "end": 2462.71, "word": " B", "probability": 0.6630859375}, {"start": 2462.71, "end": 2464.05, "word": " طيب", "probability": 0.8919270833333334}, {"start": 2464.05, "end": 2465.07, "word": " خدوني", "probability": 0.855224609375}, {"start": 2465.07, "end": 2465.37, "word": " هذه", "probability": 0.8623046875}, {"start": 2465.37, "end": 2465.99, "word": " مخادة", "probability": 0.75128173828125}], "temperature": 1.0}, {"id": 100, "seek": 249403, "start": 2466.65, "end": 2494.03, "text": "هيها ملاش قلبت و أنا قلبت خدوني هذه مع هذه فالتنتين مع بعض together بيصير عندي Q to the B minus واحد زائد B to the Q minus واحد تطابق الواحد هاي الواحد زائد جمعناها السفر هنا والتنتين ايه شمال هنا اللي هو واحد", "tokens": [3224, 1829, 11296, 3714, 1211, 33599, 12174, 46152, 2655, 4032, 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اللي هي اتنين وكأني هنا وصلت ان ال بي بتجسم ال بي ماينس واحد factorial ناقص ال بي ماينس واحد، مظبوط؟", "tokens": [3615, 1863, 16254, 4724, 3794, 1975, 8315, 4724, 16254, 49374, 4724, 1829, 8978, 4724, 1829, 19446, 9957, 3794, 36764, 24401, 15844, 11933, 1829, 8592, 15844, 13672, 1829, 39896, 1975, 2655, 1863, 9957, 4032, 4117, 33456, 1829, 34105, 4032, 36520, 2655, 16472, 2423, 4724, 1829, 39894, 7435, 38251, 2423, 4724, 1829, 19446, 9957, 3794, 36764, 24401, 36916, 8717, 995, 4587, 9381, 2423, 4724, 1829, 19446, 9957, 3794, 36764, 24401, 12399, 3714, 19913, 3555, 2407, 9566, 22807], "avg_logprob": -0.3213404628791307, "compression_ratio": 1.7466666666666666, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 3420.8, "end": 3421.34, "word": "عندي", "probability": 0.5843098958333334}, {"start": 3421.34, "end": 3422.4, "word": " بس", "probability": 0.6785888671875}, {"start": 3422.4, "end": 3422.54, "word": " انا", "probability": 0.6728515625}, {"start": 3422.54, "end": 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لاحظوا ان العامل المشترك الاعلى بين ال b و ال b-1 ايش بساوي بساوي واحد اذا بالفكرة المتكررة اللي حكيناها اذا ال b في ال b-1 تقسم ال b-1 factorial ناقص ال b-1", "tokens": [2304, 33599, 1829, 23032, 1829, 3555, 20328, 9640, 18871, 16254, 2423, 7649, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 4724, 40228, 9566, 1829, 22653, 19446, 7251, 6027, 1829, 20193, 5016, 19913, 14407, 16472, 18863, 10943, 1211, 9673, 8592, 2655, 31747, 42963, 3615, 23942, 49374, 2423, 272, 4032, 2423, 272, 12, 16, 1975, 1829, 8592, 4724, 3794, 995, 45865, 4724, 3794, 995, 45865, 36764, 24401, 1975, 15730, 20666, 5172, 4117, 25720, 9673, 2655, 37983, 25720, 13672, 1829, 11331, 4117, 1829, 8315, 11296, 1975, 15730, 2423, 272, 8978, 2423, 272, 12, 16, 6055, 4587, 38251, 2423, 272, 12, 16, 36916, 8717, 995, 4587, 9381, 2423, 272, 12, 16], "avg_logprob": -0.2045852773100416, "compression_ratio": 1.8238341968911918, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 3467.49, "end": 3468.03, "word": "ماشي", 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" السفر", "probability": 0.9796549479166666}, {"start": 4448.08, "end": 4448.98, "word": " modulo", "probability": 0.5865478515625}, {"start": 4448.98, "end": 4449.26, "word": " B", "probability": 0.87841796875}], "temperature": 1.0}, {"id": 181, "seek": 447580, "start": 4451.12, "end": 4475.8, "text": "البروف ايه الاشهدار شوف ايش اللي بتسوي اذكركم في المعلومة ال X تربية زائد واحد ل solution if and only if ال B على سوري 4K زائد واحد يعني اي B مش على سوري 4K زايد واحد ال X تربية تتطبق ناقص واحد فيش ل solution طيب كان هذا اللي .. هذا هتوصلني ل .. ل اللي هو كيف احصل ال 12", "tokens": [6027, 26890, 38688, 1975, 1829, 3224, 2423, 33599, 3224, 3215, 9640, 13412, 38688, 1975, 1829, 8592, 13672, 1829, 39894, 3794, 45865, 1975, 8848, 37983, 24793, 8978, 9673, 30241, 20498, 3660, 2423, 1783, 6055, 25513, 10632, 30767, 16373, 3215, 36764, 24401, 5296, 3827, 498, 293, 787, 498, 2423, 363, 15844, 8608, 13063, 1829, 1017, 42, 30767, 16373, 3215, 36764, 24401, 37495, 22653, 1975, 1829, 363, 37893, 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{"start": 4466.82, "end": 4467.06, "word": " واحد", "probability": 0.98193359375}, {"start": 4467.06, "end": 4467.3, "word": " فيش", "probability": 0.63525390625}, {"start": 4467.3, "end": 4467.4, "word": " ل", "probability": 0.354248046875}, {"start": 4467.4, "end": 4467.98, "word": " solution", "probability": 0.9287109375}, {"start": 4467.98, "end": 4469.34, "word": " طيب", "probability": 0.8719075520833334}, {"start": 4469.34, "end": 4469.74, "word": " كان", "probability": 0.34765625}, {"start": 4469.74, "end": 4469.94, "word": " هذا", "probability": 0.6806640625}, {"start": 4469.94, "end": 4470.08, "word": " اللي", "probability": 0.6221923828125}, {"start": 4470.08, "end": 4470.24, "word": " ..", "probability": 0.435791015625}, {"start": 4470.24, "end": 4470.8, "word": " هذا", "probability": 0.59912109375}, {"start": 4470.8, "end": 4471.46, "word": " هتوصلني", "probability": 0.774658203125}, {"start": 4471.46, "end": 4471.72, "word": " ل", "probability": 0.82568359375}, {"start": 4471.72, "end": 4472.26, "word": " ..", "probability": 0.7744140625}, {"start": 4472.26, "end": 4472.94, "word": " ل", "probability": 0.6083984375}, {"start": 4472.94, "end": 4473.44, "word": " اللي", "probability": 0.78857421875}, {"start": 4473.44, "end": 4473.9, "word": " هو", "probability": 0.99267578125}, {"start": 4473.9, "end": 4475.12, "word": " كيف", "probability": 0.56988525390625}, {"start": 4475.12, "end": 4475.36, "word": " احصل", "probability": 0.66796875}, {"start": 4475.36, "end": 4475.58, "word": " ال", "probability": 0.5625}, {"start": 4475.58, "end": 4475.8, "word": " 12", "probability": 0.6064453125}], "temperature": 1.0}, {"id": 182, "seek": 449956, "start": 4477.98, "end": 4499.56, "text": "لأن سؤال 12 بيقول لي إذا كانت B بتسوي 4K زي 3 والـ A تربيع زي B تربيع بالطابق الصفر مضلوا B إثبتني إن الـ A و الـ B متطابقة بطابق الصفر مضلوا مين مضلوا B بدي أفترض لك عكس هذا و أسألك ال contradiction بقول لك suppose that", "tokens": [1211, 33456, 8608, 33604, 6027, 2272, 4724, 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0.60009765625}, {"start": 4487.0, "end": 4487.16, "word": " الـ", "probability": 0.80517578125}, {"start": 4487.16, "end": 4487.28, "word": " B", "probability": 0.84375}, {"start": 4487.28, "end": 4488.1, "word": " متطابقة", "probability": 0.934814453125}, {"start": 4488.1, "end": 4488.52, "word": " بطابق", "probability": 0.8468017578125}, {"start": 4488.52, "end": 4489.04, "word": " الصفر", "probability": 0.8489583333333334}, {"start": 4489.04, "end": 4489.46, "word": " مضلوا", "probability": 0.9295654296875}, {"start": 4489.46, "end": 4489.82, "word": " مين", "probability": 0.6639404296875}, {"start": 4489.82, "end": 4490.7, "word": " مضلوا", "probability": 0.8756103515625}, {"start": 4490.7, "end": 4490.86, "word": " B", "probability": 0.75927734375}, {"start": 4490.86, "end": 4491.6, "word": " بدي", "probability": 0.5179443359375}, {"start": 4491.6, "end": 4492.0, "word": " أفترض", "probability": 0.8792724609375}, {"start": 4492.0, "end": 4492.26, "word": " لك", "probability": 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الـ 0 modulo B", "tokens": [32, 6055, 9566, 16758, 4587, 2423, 39184, 363, 6055, 9566, 16758, 4587, 21136, 5172, 2288, 1072, 13455, 363, 775, 406, 1797, 8608, 1829, 316, 20193, 6055, 9566, 16758, 4587, 2423, 39184, 1958, 1072, 13455, 363], "avg_logprob": -0.4016927174395985, "compression_ratio": 1.4078947368421053, "no_speech_prob": 0.0, "words": [{"start": 4500.71, "end": 4501.25, "word": "A", "probability": 0.1109619140625}, {"start": 4501.25, "end": 4502.07, "word": " تطابق", "probability": 0.79364013671875}, {"start": 4502.07, "end": 4502.31, "word": " الـ", "probability": 0.8330078125}, {"start": 4502.31, "end": 4502.49, "word": " B", "probability": 0.68310546875}, {"start": 4502.49, "end": 4503.11, "word": " تطابق", "probability": 0.979736328125}, {"start": 4503.11, "end": 4503.63, "word": " السفر", "probability": 0.8352864583333334}, {"start": 4503.63, "end": 4504.23, "word": " modulo", "probability": 0.5498046875}, {"start": 4504.23, "end": 4504.91, "word": " B", "probability": 0.576171875}, {"start": 4504.91, "end": 4505.65, "word": " does", "probability": 0.2435302734375}, {"start": 4505.65, "end": 4506.57, "word": " not", "probability": 0.96240234375}, {"start": 4506.57, "end": 4508.03, "word": " hold", "probability": 0.88525390625}, {"start": 4508.03, "end": 4509.65, "word": " سي", "probability": 0.458251953125}, {"start": 4509.65, "end": 4510.89, "word": " A", "probability": 0.2396240234375}, {"start": 4510.89, "end": 4511.59, "word": " لا", "probability": 0.73876953125}, {"start": 4511.59, "end": 4512.29, "word": " تطابق", "probability": 0.98828125}, {"start": 4512.29, "end": 4512.61, "word": " الـ", "probability": 0.5833740234375}, {"start": 4512.61, "end": 4513.15, "word": " 0", "probability": 0.5439453125}, {"start": 4513.15, "end": 4514.93, "word": " modulo", "probability": 0.855712890625}, {"start": 4514.93, "end": 4515.31, "word": " B", "probability": 0.70703125}], "temperature": 1.0}, {"id": 184, "seek": 454560, "start": 4517.77, "end": 4545.61, "text": "أو P لا تطابق الـ Zero مدلوا A ماشي الحال أي ننوم بنفعل نفترض أن الـ A لا تطابق الـ Zero مدلوا B أو الـ B لا تطابق الـ Zero مدلوا B without loss of generality suppose that A لا تطابق الـ Zero مدلوا B أو إنك تفضل تقول suppose that أن A لا تطابق الـ Zero مدلوا B تسبب Contradiction وبعدين تقول Similarly وفعلا Similarly B لا تطابق الـ Zero مدلوا B تسبب Contradiction", "tokens": [10721, 2407, 430, 20193, 6055, 9566, 16758, 4587, 2423, 39184, 17182, 3714, 3215, 1211, 14407, 316, 3714, 33599, 1829, 21542, 6027, 36632, 8717, 1863, 20498, 44945, 5172, 30241, 8717, 5172, 2655, 43042, 14739, 2423, 39184, 316, 20193, 6055, 9566, 16758, 4587, 2423, 39184, 17182, 3714, 3215, 1211, 14407, 363, 34051, 2423, 39184, 363, 20193, 6055, 9566, 16758, 4587, 2423, 39184, 17182, 3714, 3215, 1211, 14407, 363, 1553, 4470, 295, 1337, 1860, 7297, 300, 316, 20193, 6055, 9566, 16758, 4587, 2423, 39184, 17182, 3714, 3215, 1211, 14407, 363, 34051, 36145, 4117, 6055, 5172, 11242, 1211, 6055, 39648, 7297, 300, 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أصلا؟ هذه معناته إنه this", "tokens": [11622, 16373, 3215, 36764, 24401, 6055, 9566, 16758, 4587, 21136, 5172, 2288, 6583, 13455, 1975, 1829, 8592, 6583, 13455, 363, 11933, 15730, 20328, 9640, 43242, 2423, 363, 383, 5296, 28820, 6055, 2288, 21292, 3660, 6055, 9566, 16758, 4587, 21136, 6027, 3555, 36764, 24401, 6583, 13455, 363, 9154, 34105, 19446, 50239, 2655, 2423, 14407, 24401, 5551, 3215, 11296, 6024, 104, 7649, 10632, 11933, 1829, 8592, 29538, 39894, 45761, 1829, 5551, 9381, 15040, 22807, 29538, 20449, 8315, 47395, 36145, 3224, 341], "avg_logprob": -0.33105468600988386, "compression_ratio": 1.6171428571428572, "no_speech_prob": 8.821487426757812e-06, "words": [{"start": 4679.93, "end": 4680.53, "word": "زائد", "probability": 0.6727701822916666}, {"start": 4680.53, "end": 4681.11, "word": " واحد", "probability": 0.962646484375}, {"start": 4681.11, "end": 4681.83, "word": " تطابق", "probability": 0.9378662109375}, {"start": 4681.83, "end": 4682.41, "word": " السفر", "probability": 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{"start": 4741.76, "end": 4742.36, "word": " بس", "probability": 0.85546875}, {"start": 4742.36, "end": 4742.98, "word": " متى", "probability": 0.75146484375}, {"start": 4742.98, "end": 4743.76, "word": " لما", "probability": 0.89794921875}, {"start": 4743.76, "end": 4744.14, "word": " نكون", "probability": 0.682861328125}, {"start": 4744.14, "end": 4744.46, "word": " على", "probability": 0.95458984375}, {"start": 4744.46, "end": 4744.86, "word": " صورة", "probability": 0.9913736979166666}, {"start": 4744.86, "end": 4745.14, "word": " B", "probability": 0.59521484375}, {"start": 4745.14, "end": 4745.72, "word": " بيبسوة", "probability": 0.5653889973958334}, {"start": 4745.72, "end": 4746.06, "word": " 7K", "probability": 0.756591796875}, {"start": 4746.06, "end": 4746.34, "word": " زائد", "probability": 0.7877604166666666}, {"start": 4746.34, "end": 4746.64, "word": " 1", "probability": 0.96337890625}, {"start": 4746.64, "end": 4747.5, "word": " بينما", "probability": 0.982177734375}, 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0.8702799479166666}, {"start": 4752.52, "end": 4753.24, "word": " أنه", "probability": 0.5369873046875}, {"start": 4753.24, "end": 4753.58, "word": " لجينا", "probability": 0.94580078125}, {"start": 4753.58, "end": 4754.04, "word": " حلل", "probability": 0.7014973958333334}, {"start": 4754.04, "end": 4754.14, "word": " الـ", "probability": 0.870849609375}, {"start": 4754.14, "end": 4754.28, "word": " X", "probability": 0.55224609375}, {"start": 4754.28, "end": 4754.42, "word": " التي", "probability": 0.1636962890625}, {"start": 4754.42, "end": 4754.76, "word": " تتطبق", "probability": 0.621875}, {"start": 4754.76, "end": 4755.12, "word": " نقص", "probability": 0.59130859375}, {"start": 4755.12, "end": 4755.34, "word": " واحد", "probability": 0.7479248046875}, {"start": 4755.34, "end": 4755.56, "word": " بدل", "probability": 0.850830078125}, {"start": 4755.56, "end": 4755.84, "word": " B", "probability": 0.2646484375}, {"start": 4755.84, "end": 4756.48, "word": " والـ", "probability": 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0.96630859375}, {"start": 4760.38, "end": 4760.96, "word": " الأولى", "probability": 0.9930013020833334}], "temperature": 1.0}, {"id": 194, "seek": 478604, "start": 4763.36, "end": 4786.04, "text": "أو بمعنى آخر لازم ال a تطابق السفر mod b وsimilarly ال b تطابق ال zero mod b إذا صار عندى لما يكون هذا صحيح لازم نحصل a تطابق ال b تطابق السفر mod b وهيك نكون خلصنا اللى هو مناقشة اللى هو Wilson's theorem واللي هو Fermat's theorem", "tokens": [10721, 2407, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 5296, 31377, 2304, 2423, 257, 6055, 9566, 16758, 4587, 21136, 5172, 2288, 1072, 272, 4032, 30937, 2202, 356, 2423, 272, 6055, 9566, 16758, 4587, 2423, 4018, 1072, 272, 11933, 15730, 20328, 9640, 43242, 7578, 5296, 15042, 7251, 30544, 23758, 20328, 5016, 1829, 5016, 5296, 31377, 2304, 8717, 5016, 36520, 257, 6055, 9566, 16758, 4587, 2423, 272, 6055, 9566, 16758, 4587, 21136, 5172, 2288, 1072, 272, 37037, 1829, 4117, 8717, 30544, 16490, 1211, 9381, 8315, 13672, 7578, 31439, 3714, 8315, 4587, 8592, 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"end": 4767.26, "word": " b", "probability": 0.213623046875}, {"start": 4767.26, "end": 4768.5, "word": " وsimilarly", "probability": 0.7410888671875}, {"start": 4768.5, "end": 4768.6, "word": " ال", "probability": 0.61328125}, {"start": 4768.6, "end": 4768.76, "word": " b", "probability": 0.91845703125}, {"start": 4768.76, "end": 4769.2, "word": " تطابق", "probability": 0.98486328125}, {"start": 4769.2, "end": 4769.34, "word": " ال", "probability": 0.890625}, {"start": 4769.34, "end": 4769.56, "word": " zero", "probability": 0.377685546875}, {"start": 4769.56, "end": 4769.74, "word": " mod", "probability": 0.99267578125}, {"start": 4769.74, "end": 4770.16, "word": " b", "probability": 0.865234375}, {"start": 4770.16, "end": 4770.7, "word": " إذا", "probability": 0.570068359375}, {"start": 4770.7, "end": 4771.0, "word": " صار", "probability": 0.83642578125}, {"start": 4771.0, "end": 4771.32, "word": " عندى", "probability": 0.637451171875}, {"start": 4771.32, "end": 4771.48, "word": " لما", "probability": 0.80224609375}, {"start": 4771.48, "end": 4771.74, "word": " يكون", "probability": 0.939697265625}, {"start": 4771.74, "end": 4772.02, "word": " هذا", "probability": 0.78662109375}, {"start": 4772.02, "end": 4773.06, "word": " صحيح", "probability": 0.9898681640625}, {"start": 4773.06, "end": 4773.82, "word": " لازم", "probability": 0.9723307291666666}, {"start": 4773.82, "end": 4774.22, "word": " نحصل", "probability": 0.9775390625}, {"start": 4774.22, "end": 4774.52, "word": " a", "probability": 0.5048828125}, {"start": 4774.52, "end": 4774.94, "word": " تطابق", "probability": 0.95751953125}, {"start": 4774.94, "end": 4775.08, "word": " ال", "probability": 0.67431640625}, {"start": 4775.08, "end": 4775.3, "word": " b", "probability": 0.9404296875}, {"start": 4775.3, "end": 4776.28, "word": " تطابق", "probability": 0.984619140625}, {"start": 4776.28, "end": 4776.66, "word": " السفر", "probability": 0.8255208333333334}, {"start": 4776.66, "end": 4776.86, "word": " mod", "probability": 0.98583984375}, {"start": 4776.86, "end": 4777.34, "word": " b", "probability": 0.9169921875}, {"start": 4777.34, "end": 4778.78, "word": " وهيك", "probability": 0.6064453125}, {"start": 4778.78, "end": 4779.1, "word": " نكون", "probability": 0.7880859375}, {"start": 4779.1, "end": 4779.86, "word": " خلصنا", "probability": 0.9786376953125}, {"start": 4779.86, "end": 4780.5, "word": " اللى", "probability": 0.5206298828125}, {"start": 4780.5, "end": 4780.82, "word": " هو", "probability": 0.833984375}, {"start": 4780.82, "end": 4781.88, "word": " مناقشة", "probability": 0.9509765625}, {"start": 4781.88, "end": 4782.46, "word": " اللى", "probability": 0.5751953125}, {"start": 4782.46, "end": 4782.62, "word": " هو", "probability": 0.91064453125}, {"start": 4782.62, "end": 4783.24, "word": " Wilson's", "probability": 0.587890625}, {"start": 4783.24, "end": 4783.64, "word": " theorem", "probability": 0.8642578125}, {"start": 4783.64, "end": 4784.88, "word": " واللي", "probability": 0.251251220703125}, {"start": 4784.88, "end": 4785.0, "word": " هو", "probability": 0.95166015625}, {"start": 4785.0, "end": 4785.58, "word": " Fermat's", "probability": 0.9401041666666666}, {"start": 4785.58, "end": 4786.04, "word": " theorem", "probability": 0.90380859375}], "temperature": 1.0}, {"id": 195, "seek": 479145, "start": 4789.03, "end": 4791.45, "text": "والسلام عليكم ورحمة الله وبركاته", "tokens": [2407, 6027, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.20289522058823528, "compression_ratio": 0.9836065573770492, "no_speech_prob": 0.0, "words": [{"start": 4789.03, "end": 4789.83, "word": "والسلام", "probability": 0.59228515625}, {"start": 4789.83, "end": 4790.23, "word": " عليكم", "probability": 0.958740234375}, {"start": 4790.23, "end": 4790.59, "word": " ورحمة", "probability": 0.966552734375}, {"start": 4790.59, "end": 4790.79, "word": " الله", "probability": 0.96728515625}, {"start": 4790.79, "end": 4791.45, "word": " وبركاته", "probability": 0.98955078125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 4791.4840625, "duration_after_vad": 4648.663124999997}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/qytPH80aNtM_raw.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/qytPH80aNtM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7533e35a052b2163d133ff602531674020c2ff6f
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/qytPH80aNtM_raw.srt
@@ -0,0 +1,3260 @@
+1
+00:00:21,040 --> 00:00:25,860
+بسم الله الرحمن الرحيم المحاضرة رقم 26 مساق نظرية
+
+2
+00:00:25,860 --> 00:00:30,380
+الاعداد طلاب طالبات الجامعة الإسلامية كلية العلوم
+
+3
+00:00:30,380 --> 00:00:35,680
+والتربية قسم رياضيات اليوم ان شاء الله هيكون في
+
+4
+00:00:35,680 --> 00:00:42,800
+عنا مرادعة او مناقشة لأسئلة شبطة الخمسة وهو حول
+
+5
+00:00:42,800 --> 00:00:48,220
+Fermat's theorem وWilson's
+
+6
+00:00:48,220 --> 00:00:55,810
+theoremنبدأ في خمسة اتنين للأسئلة المطلوبة أن
+
+7
+00:00:55,810 --> 00:01:02,170
+السؤال الأول السؤال الأول يقول ما يلي use Fermat
+
+8
+00:01:02,170 --> 00:01:06,990
+theorem Fermat theorem to verify that سبعة عشر
+
+9
+00:01:06,990 --> 00:01:12,970
+divides أحداش أثنية وأربعة زائد واحد نثبت أنه سبعة
+
+10
+00:01:12,970 --> 00:01:15,590
+عشر تقسم لحداش
+
+11
+00:01:21,470 --> 00:01:28,710
+اشان نثبت اللي هو ان السبعتاش تقسم ل 11 أس 104
+
+12
+00:01:28,710 --> 00:01:38,820
+زائد 1بيعني ذلك إنه نثبت إن 11 قسمية وأربعة تطابق
+
+13
+00:01:38,820 --> 00:01:45,520
+الناقص واحد أو بمعنى زائد واحد تطابق السفر modulo
+
+14
+00:01:45,520 --> 00:01:50,780
+17 هذا اللي بدنا نثبته أو بمعنى آخر بدنا نثبت إن
+
+15
+00:01:50,780 --> 00:01:58,370
+11 قسمية وأربعة تطابق الناقص واحد modulo 17الان
+
+16
+00:01:58,370 --> 00:02:03,770
+نذكركم فرماتس فيرم فرماتس فيرم بتقول ماهي ليه لو
+
+17
+00:02:03,770 --> 00:02:11,730
+كان عند بي ال zebrain و بي لا تقسم العدد a أي
+
+18
+00:02:11,730 --> 00:02:16,530
+integer a بي لا تقسم a فبدي يكون عندي a to the b
+
+19
+00:02:16,530 --> 00:02:26,180
+minus واحد تطابق الواحد modulo اللي هوهذه اللي هي
+
+20
+00:02:26,180 --> 00:02:30,120
+Fermat's theorem وفي عندنا الـ Corollary لـ Fermat
+
+21
+00:02:30,120 --> 00:02:35,780
+اللي هي بتقولنا أي element in Z بكون A to the B
+
+22
+00:02:35,780 --> 00:02:42,600
+تطابق الـ A Modulo B هذه اللي هي النتيجتين المهمين
+
+23
+00:02:42,600 --> 00:02:48,880
+المهمتين في اللي هو خمسة اتنين ندى الآن نشوف ايش
+
+24
+00:02:48,880 --> 00:02:58,920
+الفكرة عندي اللي هو By Fermat's theoremSense 17
+
+25
+00:02:58,920 --> 00:03:07,020
+لتقسم الـ 11 then 11 to the P minus واحد اللي هي
+
+26
+00:03:07,020 --> 00:03:18,420
+16 تطابق الواحد modulo 17 اقرب رقم ل ال 104 اللي
+
+27
+00:03:18,420 --> 00:03:26,340
+هو 96 96 كيف نجيبه 11 أُس 16 أُس 6اللي هو عبارة عن
+
+28
+00:03:26,340 --> 00:03:33,720
+96 تطابق الواحد modulo 17 أنا بدي 104 فبنضرب
+
+29
+00:03:33,720 --> 00:03:43,830
+الجهتين في 11 أس 8الرقم اللي احنا 11104 تطابق ال
+
+30
+00:03:43,830 --> 00:03:50,550
+11 قص 8 modulo 17 هذا اللي هو عبارة عن مين الرقم
+
+31
+00:03:50,550 --> 00:03:59,030
+اللي احنا 11104 تطابق ال 11 قص 8 modulo 17 الان
+
+32
+00:03:59,030 --> 00:04:04,670
+بدنا نبدأ نوجد ال 11 قص 8 ال 11 قص 8 حسبته سهل ان
+
+33
+00:04:04,670 --> 00:04:15,090
+شاء اللهالآن 11 تربيع اللي هو عبارة عن 121 121 او
+
+34
+00:04:15,090 --> 00:04:22,910
+ممكن اللي هو أسهلنا ل 11 modulo 17 نشوف ايش بتطابق
+
+35
+00:04:22,910 --> 00:04:30,030
+يمكن أسهلنا كمان لو قلبنا ل 11 تربيع تطابق اللي هو
+
+36
+00:04:30,030 --> 00:04:35,930
+ماقص 6 تربيعلأن الـ 11 تطابق النقطة 6 مدوله 17
+
+37
+00:04:35,930 --> 00:04:42,330
+اللي هو عبارة عن 36 اللي هو بالنسبة للـ 17 36
+
+38
+00:04:42,330 --> 00:04:50,350
+عبارة عن 2 34 17 في 2 و 34 زاد 2 اذا مدله اللي هو
+
+39
+00:04:50,350 --> 00:04:55,230
+17 صار عند ال 11 تربيه اللي هو عبارة عن جداش عن
+
+40
+00:04:55,230 --> 00:05:06,550
+اتنين صار الآن من اي اتنين وهي عند واحدfrom واحد
+
+41
+00:05:06,550 --> 00:05:18,090
+and اتنين بيصير عندي الـ 11 قص 104 تطابق ال 11 قص
+
+42
+00:05:18,090 --> 00:05:25,300
+8 اللي هي 11 قص 2 قص 4الـ 11 أُس 2 كده شفناها
+
+43
+00:05:25,300 --> 00:05:34,000
+بيساوي 2 وهي ساوي 2 أُس 4 2 أُس 4 عبارة عن 16 الـ
+
+44
+00:05:34,000 --> 00:05:40,900
+16 بالنسبة للـ 17 عبارة عن نقص 1 مضله 17 إذا صار
+
+45
+00:05:40,900 --> 00:05:47,380
+عندي الآن 11 أُس 104 تطابق نقص 1 مضله 17 أو بمعنى
+
+46
+00:05:47,380 --> 00:05:55,080
+آخر إذا الـ 17 بتقسمالـ 11 أُسمية وأربعة زائد واحد
+
+47
+00:05:55,080 --> 00:06:01,440
+فهو المطلوب في السؤال الأول الآن الشغل مجرد حسابات
+
+48
+00:06:01,440 --> 00:06:07,300
+ولكن تطبيق على Formats Theorem نيجي للسؤال التاني
+
+49
+00:06:07,300 --> 00:06:14,400
+المطلوب نشوف كيف أيضا تطبيق على Formats Theorem
+
+50
+00:06:14,400 --> 00:06:20,280
+نشوف كيف بدنا مبرهن السؤال التاني
+
+51
+00:06:22,570 --> 00:06:30,630
+السؤال التالي يا شباب عندي بقول ماهي الـ 2A إذا
+
+52
+00:06:30,630 --> 00:06:36,370
+كان عندي F الـ greatest common divisor بين الـ A
+
+53
+00:06:36,370 --> 00:06:45,610
+والـ 35 بساوي 1 اثبت انه A تضابر 12 طابق الـ 1
+
+54
+00:06:45,610 --> 00:06:54,640
+modulo 35 انشوف كيف، بدى البرهن اللي هوأسهل عندي
+
+55
+00:06:54,640 --> 00:07:00,600
+الـ 35 العام المشارك اللي على بين الـ A و 35
+
+56
+00:07:00,600 --> 00:07:01,560
+بالساوية
+
+57
+00:07:03,780 --> 00:07:08,360
+أكيد بتساوي سبعة في خمسة اللي هو حللتها الى
+
+58
+00:07:08,360 --> 00:07:13,340
+product of the primes فبصير عيدي الآن مادام العامل
+
+59
+00:07:13,340 --> 00:07:16,200
+المشترك الأعلى بين ال a و الخمسة و تلاتين بساوي
+
+60
+00:07:16,200 --> 00:07:20,260
+واحد اذا أكيد ال greatest common divisor بين ال a
+
+61
+00:07:20,260 --> 00:07:23,800
+و السبعة هو نفسه ال greatest common divisor بين ال
+
+62
+00:07:23,800 --> 00:07:28,400
+a و الخمسة بساوي واحد هذا لإنه ال greatest common
+
+63
+00:07:28,400 --> 00:07:32,340
+divisor بين ال a و الخمسة و تلاتين بساوي واحد طيب
+
+64
+00:07:32,340 --> 00:07:42,250
+جماعةالان بناء على فرمات بتقولي اذا then بقال
+
+65
+00:07:42,250 --> 00:07:49,670
+فرمات theorem بتكون عند ا to the power 6 مطابق
+
+66
+00:07:49,670 --> 00:07:57,030
+الواحد moduloاللي هو سبعة طبعا هو المفهوم انه
+
+67
+00:07:57,030 --> 00:07:59,630
+مادام العالم المشترك الاعلى بين الـA والسبعة بساعة
+
+68
+00:07:59,630 --> 00:08:04,690
+واحد اذا ماكيد السبعة لا تقسم الـA والخمسة لا تقسم
+
+69
+00:08:04,690 --> 00:08:08,830
+الـA اذا ال firmates جاهد زي انه احنا نطبقها في
+
+70
+00:08:08,830 --> 00:08:14,610
+الحالتينفبصير عندي a⁶ تطابق الواحد مدنه جديش مدنه
+
+71
+00:08:14,610 --> 00:08:20,910
+سبعة احنا بدلين a² اذا بصير عندي them and so ومنه
+
+72
+00:08:20,910 --> 00:08:24,970
+a² اللي هي ستة أس اتنين تطابق واحد أس اتنين اللي
+
+73
+00:08:24,970 --> 00:08:29,910
+هي برضه بتطابق الواحد مدنه سبعة هذه النتيجة الأولى
+
+74
+00:08:29,910 --> 00:08:36,510
+similarly وبنفس الأسلوب similarlyعندي by Fermat's
+
+75
+00:08:36,510 --> 00:08:40,210
+theorem أنه نطبق على الـ a الخمسة الخمسة اللي هي
+
+76
+00:08:40,210 --> 00:08:45,030
+تقسم ال a إذا a to the أربعة اللي هي خمسة ناقص
+
+77
+00:08:45,030 --> 00:08:52,940
+واحد تطابق الواحد مدله خمسةومنه ومنه على طول اللي
+
+78
+00:08:52,940 --> 00:08:56,600
+هي a أُس أربعة الكل أُس ثلاثة طبق طبق واحد أُس
+
+79
+00:08:56,600 --> 00:09:02,140
+ثلاثة يعني a أُس اتناشت وطابق الواحد مودولورد خمسة
+
+80
+00:09:02,140 --> 00:09:11,670
+الان عندي واحد وعندي اتنين1 و 2 لإن العامل المشترك
+
+81
+00:09:11,670 --> 00:09:16,190
+الأعلى بين السبعة والخمسة بساوي واحد فبصير عندي
+
+82
+00:09:16,190 --> 00:09:21,530
+اللي هو ال A أس اتناشط وطابق الواحد مدنه حاصل غرب
+
+83
+00:09:21,530 --> 00:09:25,640
+من سبعة في خمسة موجة الدياشر 35من أين جاء
+
+84
+00:09:25,640 --> 00:09:29,820
+المعلومة؟ هذه المعلومة سهلة الان من هنا من الأولى
+
+85
+00:09:29,820 --> 00:09:33,980
+عند السبعة تقسم a أُس 12 ناقص واحد ومن المعلومة
+
+86
+00:09:33,980 --> 00:09:38,700
+الثانية اللي هي الخمسة بتقسم a أُس 12 ناقص واحد
+
+87
+00:09:38,700 --> 00:09:43,330
+السبعةالعوامل هذا المقدار والخمسة من العوامل نفس
+
+88
+00:09:43,330 --> 00:09:46,810
+المقدار والسبعة والخمسة مافيش أصلا بين العوامل
+
+89
+00:09:46,810 --> 00:09:50,130
+يعني مش هيتكرر العامل هان و هان إذا أكيد هذا
+
+90
+00:09:50,130 --> 00:09:53,590
+هيعطيني الخمسة و تلاتين تقسم A أقصى اتناش ناقص
+
+91
+00:09:53,590 --> 00:09:56,830
+واحد اللي هو هو اللي عنه A أقصى اتناش تطابق الواحد
+
+92
+00:09:56,830 --> 00:10:02,290
+مضله اللي هو خمسة و تلاتين واضح ماشي الحل هذا اللي
+
+93
+00:10:02,290 --> 00:10:08,660
+هو السؤال التاني ايه نيدي للسؤال التاني Bالسؤال
+
+94
+00:10:08,660 --> 00:10:12,920
+التاني بيه اللي هو معطيني الـ greatest common
+
+95
+00:10:12,920 --> 00:10:20,660
+divisor بين الـ A و 42 بساوي واحد بيقوللي اثبت
+
+96
+00:10:20,660 --> 00:10:33,360
+then عندي اللي هو A أو ال 6 تطابق الواحد مضمين مضم
+
+97
+00:10:33,360 --> 00:10:34,300
+ال 48
+
+98
+00:10:42,550 --> 00:10:51,630
+موضوله 168 موضوله 168 موضوله 168 موضوله 168 موضوله
+
+99
+00:10:51,630 --> 00:10:55,750
+168 موضوله 168 موضوله 168 موضوله 168 موضوله 168
+
+100
+00:10:55,750 --> 00:11:08,080
+موضوله 168معايا يا شباب 168 بتقسم الـ a6-1 will
+
+101
+00:11:08,080 --> 00:11:16,140
+show that الـ 168 divide a6-1 أو بمعنى آخر زي ما
+
+102
+00:11:16,140 --> 00:11:19,900
+كتبنا في الأول الـ a6 أطابق الواحد modulo من مين
+
+103
+00:11:19,900 --> 00:11:23,260
+modulo 168 solution
+
+104
+00:11:26,960 --> 00:11:32,480
+الان الـ 168 ماعطينا hint اللي هو عبارة عن 1 1 6 8
+
+105
+00:11:32,480 --> 00:11:38,630
+عبارة عن تحليلها تلاتة في سبعة في تمانيةالان
+
+106
+00:11:38,630 --> 00:11:43,590
+الفكرة مشابهة للفكرة اللي فوق عندى اللاحظ انه
+
+107
+00:11:43,590 --> 00:11:48,690
+حللها الى تلت أرقام العامل المشترك الأعلى بين كل
+
+108
+00:11:48,690 --> 00:11:52,210
+اتنين بساوي واحد بين التلاتة والسبعة واحد تلاتة و
+
+109
+00:11:52,210 --> 00:11:55,510
+تمانية واحد و تمانية وسبعة بساوي واحد على أساس ان
+
+110
+00:11:55,510 --> 00:12:02,340
+لو أثبتنالو أثبتنا أن الـ A والـ 6 تطابق الواحد
+
+111
+00:12:02,340 --> 00:12:08,080
+مدله اللي هو ثلاثة ومدله سبعة ومدله تمانية من
+
+112
+00:12:08,080 --> 00:12:13,750
+التلاتة مع بعض حسب ما عملنا في السؤال الأولفبكون
+
+113
+00:12:13,750 --> 00:12:17,310
+اللي هو بما أن العوامل المشترك الأعلى بين هدولة
+
+114
+00:12:17,310 --> 00:12:21,590
+اللي هو بساوي واحد بين كل اتنين فبصير عندي اللي هو
+
+115
+00:12:21,590 --> 00:12:25,330
+A الستة طوابق الواحد مدنه ثلاثة في سبعة في تمانية
+
+116
+00:12:25,330 --> 00:12:29,270
+اللي هو جداش مية تمانية ستين هذه فكرة الحل الان
+
+117
+00:12:29,270 --> 00:12:35,090
+الأولبواسطة فرمات مباشرة زي ايه قبل شوية والثاني
+
+118
+00:12:35,090 --> 00:12:39,390
+بواسطة فرمات مباشرة مبالها دي بدها شغل وشغل بسيط
+
+119
+00:12:39,390 --> 00:12:44,770
+في المعلومة أخدناها قبل هيك حول هذا الأمر دي دي دي
+
+120
+00:12:44,770 --> 00:12:45,250
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+121
+00:12:45,250 --> 00:12:46,290
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+122
+00:12:46,290 --> 00:12:48,010
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+123
+00:12:48,010 --> 00:12:49,190
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+124
+00:12:49,190 --> 00:12:54,910
+دي
+
+125
+00:12:54,910 --> 00:12:58,970
+ديThen لأن العام المشارك الأعلى بين الـ A والـ 6
+
+126
+00:12:58,970 --> 00:13:06,110
+و42 اللي هي 42 عبارة عن 2 في 3 في 7العامل المشترك
+
+127
+00:13:06,110 --> 00:13:11,710
+اللي على بين الـA والـ2 و 41 هو 1 و بين الـA والـ3
+
+128
+00:13:11,710 --> 00:13:16,490
+هو 1 و بين الـA والـ7 هو 1 إذا جهزة عند التلاتة لا
+
+129
+00:13:16,490 --> 00:13:22,310
+تقسم بين الـA إذا فرمت جهزة إذا صار عندي then A
+
+130
+00:13:22,310 --> 00:13:29,230
+أُس 2 تطابق الواحد مودوله اللي هو جداش 3ومنه
+
+131
+00:13:29,230 --> 00:13:33,250
+مباشرة بنرفح هنا القوة تلاتة وهنا القوة تلاتة
+
+132
+00:13:33,250 --> 00:13:38,490
+بيصير عندي and so a أو الستة تطابق الواحد modulo
+
+133
+00:13:38,490 --> 00:13:45,230
+تلاتة هاي أول واحدة واحدة لأن similarly الخمسة أو
+
+134
+00:13:45,230 --> 00:13:54,530
+السبعة لا تقسم ال a إذا أكيد عندي ال a أو الستة
+
+135
+00:13:55,160 --> 00:14:00,780
+تطابق الواحد modulo سبعة ومنه بنفس الطريقة بنرفع
+
+136
+00:14:00,780 --> 00:14:04,820
+التنتين للقوة اتنين فبصير عندي A لا بدون فلس
+
+137
+00:14:04,820 --> 00:14:11,260
+مجاهزة A الستة تطابق الواحد modulo سبعة فبصير عندي
+
+138
+00:14:11,260 --> 00:14:16,040
+التنتين الأولى والثانية جاهزة ضل علينا نجاهز
+
+139
+00:14:16,040 --> 00:14:22,780
+بالنسبة لمين بالنسبة للثمانية طيب عندنا العامل
+
+140
+00:14:22,780 --> 00:14:28,780
+المشترك الأعلىبين الـ a و 42 بساوة واحد إذا أكيد
+
+141
+00:14:28,780 --> 00:14:32,760
+العامل المشترك الأعلى بين ال a و 42 بساوة واحد
+
+142
+00:14:32,760 --> 00:14:39,280
+يعني بمعنى أخر a is an odd number الان a odd
+
+143
+00:14:39,280 --> 00:14:47,940
+number إذا أكيد اللي هو ال a على صورة in the form
+
+144
+00:14:47,940 --> 00:14:57,130
+4k زائد 1 or 4k زائد 3هذا هو الـ A odd number اذا
+
+145
+00:14:57,130 --> 00:15:00,610
+الـ A يمّع على صورة أربعة كيه اربعة كيه زي واحد او
+
+146
+00:15:00,610 --> 00:15:01,550
+اربعة كيه زي تلتة
+
+147
+00:15:25,710 --> 00:15:30,150
+يا اما اربعة K زائد واحد تربيع يا اربعة K زائد
+
+148
+00:15:30,150 --> 00:15:34,830
+تلاتة لكل تربيع وهذه بتساوي ستة عشر K تربيع زائد
+
+149
+00:15:34,830 --> 00:15:40,430
+تمانية K زائد واحد بيساوي ستة عشر K تربيع زائد
+
+150
+00:15:40,430 --> 00:15:44,910
+اللي هو تلاتة فاربعة باطمعش اربعة عشرين K زائد
+
+151
+00:15:44,910 --> 00:15:50,410
+تسعةوهذه نفسها عبارة عن هذه تطابق السفر بالنسبة
+
+152
+00:15:50,410 --> 00:15:52,870
+للتمانية وهذه تطابق السفر للتمانية إذا كانت تطابق
+
+153
+00:15:52,870 --> 00:15:57,150
+الواحد modulo تمانية هذه مصطلحة التمانية اللي
+
+154
+00:15:57,150 --> 00:16:01,250
+بديها أنا الان وهذه تطابق الان هذه برضه مضعفة
+
+155
+00:16:01,250 --> 00:16:04,870
+التمانية وهذه مضعفة التمانية إذا كانت تطابق السفر
+
+156
+00:16:04,870 --> 00:16:08,550
+modulo تمانية والتسعة بتطابق modulo تمانية واحد
+
+157
+00:16:08,550 --> 00:16:14,690
+لأن هي عبارة عن تطابق الواحد modulo تمانيةإذا من
+
+158
+00:16:14,690 --> 00:16:18,830
+عندي سواء كانت اللي هي على صورة أربعة كزات واحد أو
+
+159
+00:16:18,830 --> 00:16:22,450
+أربعة كزات تلاتة اللي هي الـ odd number A أكيد
+
+160
+00:16:22,450 --> 00:16:28,150
+هيطلع عندي A تربية تطابق الواحد modulo من modulo
+
+161
+00:16:28,150 --> 00:16:33,610
+تمانية الآن منها ارفع الجهتين لتلاتة بيصير A أقل
+
+162
+00:16:33,610 --> 00:16:38,590
+ستة تطابق الواحد modulo تمانية هذه صار عندي اللي
+
+163
+00:16:38,590 --> 00:16:43,910
+هي تلاتةلأن بما أنه زي ما قلنا في الأول عامل مشارك
+
+164
+00:16:43,910 --> 00:16:48,510
+الأعلى بين كل اتنين السبعة والتلاتة والسبعة
+
+165
+00:16:48,510 --> 00:16:52,690
+والتمانية والتمانية والتلاتة بساعة واحد وعندي من
+
+166
+00:16:52,690 --> 00:16:57,330
+الحالة الأولى والتانية والتالتة هيكون عندي ال A
+
+167
+00:16:57,330 --> 00:17:04,100
+والستةتطابق الواحد مدن حاصل ضربهم زي السؤال الأولى
+
+168
+00:17:04,100 --> 00:17:07,980
+يعني ثلاثة في سبعة في تمانية اللي هو عبارة عن واحد
+
+169
+00:17:07,980 --> 00:17:12,580
+ستة تمانية أو بمعنى آخر واحد ستة تمانية تقسم الـA
+
+170
+00:17:12,580 --> 00:17:20,620
+والستة ناقص واحد طيب نجي لفرع C آخر فرع عندنا في
+
+171
+00:17:20,620 --> 00:17:29,130
+السؤال التاني برضه الفكرة مشابهة لالسؤال الأول
+
+172
+00:17:29,130 --> 00:17:38,790
+والثاني نشوف إيش بتقول بالظبط عندي السؤال الـ C
+
+173
+00:17:38,790 --> 00:17:45,170
+بقول لي if الـ greatest common divisor بين الـ A و
+
+174
+00:17:45,170 --> 00:17:51,450
+الـ 133 تساوي ال greatest common divisor بين الـ B
+
+175
+00:17:51,450 --> 00:18:01,830
+و الـ 133 يساوي 1then show that الـ 133 تجسم A أُس
+
+176
+00:18:01,830 --> 00:18:10,640
+18 ناقص B أُس 18 solution or proofالآن بعطينا
+
+177
+00:18:10,640 --> 00:18:14,760
+العام المشترك الأعلى بين الـ A و الـ 133 و الـ B و
+
+178
+00:18:14,760 --> 00:18:21,020
+الـ 133 واحد إذن الـ 133 تجسم A أُس 18 نقص B أُس
+
+179
+00:18:21,020 --> 00:18:27,240
+18 الـ A أُس 18 و B أُس 18 بتاعتين مؤشر إنه كإن في
+
+180
+00:18:27,240 --> 00:18:31,740
+شغلعلى الـprime اللي هو تسعة عشر لأنه تسعة عشر
+
+181
+00:18:31,740 --> 00:18:35,860
+فرمة تسعة عشر نقص واحد مين تمانتاش وكأنه يعني
+
+182
+00:18:35,860 --> 00:18:40,300
+احتمال انه يكون الـ133 احد عاملها التسعة عشر اسهل
+
+183
+00:18:40,300 --> 00:18:44,300
+عليها عملية الحسابات لكن هو شراسة ان الـ133 اللي
+
+184
+00:18:44,300 --> 00:18:48,260
+وجدت حللتها هتلاقيها عبارة عن تسعة عشر تسعة عشر في
+
+185
+00:18:48,260 --> 00:18:54,420
+BL في سبعة19x7 إذا جاهزة فيرمات ان نطبق من الـ
+
+186
+00:18:54,420 --> 00:18:57,960
+Fermat theorem الان بناء ان العامل مش شرك الاعلى
+
+187
+00:18:57,960 --> 00:19:04,540
+بين الـA و133 واحد إذا بين الـA و19 والـA و7 واحد
+
+188
+00:19:04,540 --> 00:19:09,520
+وبين الـB و19 والـB و7 برضه مش بساوي واحد إذا الـ
+
+189
+00:19:09,520 --> 00:19:15,680
+Fermat جاهزة إذا by Fermat theorem بكون عندى اللي
+
+190
+00:19:15,680 --> 00:19:18,380
+هو A الـ18
+
+191
+00:19:19,670 --> 00:19:29,490
+تطابق الواحد modulo تسعة عشر ونفس الاشي عندى اللى
+
+192
+00:19:29,490 --> 00:19:35,590
+هو بيقص تمانتاش تطابق الواحد modulo تسعة عشر لنفس
+
+193
+00:19:35,590 --> 00:19:44,530
+الأسباب وعندي بنفس الأسلوبولو جينا للـ7 سيكون عندي
+
+194
+00:19:44,530 --> 00:19:52,690
+A6 تطابق الواحد مودولو A6 تطابق الواحد مودولو 7
+
+195
+00:19:52,690 --> 00:19:56,810
+معايا
+
+196
+00:19:56,810 --> 00:20:03,050
+من المباشرة هذه نرفع القوة تلاتة جهتين فبصير A18
+
+197
+00:20:03,050 --> 00:20:09,590
+تطابق الواحد مودولو 7 والـA18 تطابق الواحد مودولو
+
+198
+00:20:09,590 --> 00:20:21,550
+7الان عندى بنفس الأسلوب السابقمن واحد ومن اتنين
+
+199
+00:20:21,550 --> 00:20:24,410
+لأن العامل المشترك اللي على بين السبعة والتسعة
+
+200
+00:20:24,410 --> 00:20:30,590
+وتعاشر بساوة واحد بطلع ال D A أس تمانتعش تطابق
+
+201
+00:20:30,590 --> 00:20:36,270
+الواحد مو دولة مية و تلاتة و تلاتين وهي سبعة في
+
+202
+00:20:36,270 --> 00:20:42,010
+تسعة عشر واضح اه؟ وال B أس تمانتعش تطابق الواحد مو
+
+203
+00:20:42,010 --> 00:20:46,800
+دولة برضه ده ال D A اش مو دولة تلاتة و تلاتينبنفس
+
+204
+00:20:46,800 --> 00:20:49,740
+الأسلوب لأن العامل مشترك الأعلى بين الـ 7 و 19
+
+205
+00:20:49,740 --> 00:20:56,100
+واحد من التنتير مع بعض إذا الـ A أُس 18 تطابق الـ
+
+206
+00:20:56,100 --> 00:21:07,120
+B أُس 18 Modulo 133 وهذا يعني that is 133 تجسم الـ
+
+207
+00:21:07,120 --> 00:21:14,020
+A أُس 18 ماقص الـ B أُس 18 ندى للسؤال الرابع
+
+208
+00:21:14,020 --> 00:21:22,060
+السؤال الأربعةسؤال أربعة اللي هو a او b ايش بقول
+
+209
+00:21:22,060 --> 00:21:33,980
+السؤال الرابع a a و الميالي derive
+
+210
+00:21:33,980 --> 00:21:38,040
+each of the following congruences a أس واحد و
+
+211
+00:21:38,040 --> 00:21:45,200
+عشرين مطابق ال a موضوله خمس عشر
+
+212
+00:21:48,100 --> 00:21:52,180
+Solution احنا حكينا في الاول عن فرمات Structural و
+
+213
+00:21:52,180 --> 00:21:58,100
+عن Corollary لفرمات الان فرمات بتتعامل مع a تدبط
+
+214
+00:21:58,100 --> 00:22:01,220
+بي minus واحد تطابق الواحد modulo بي لما ال بي لا
+
+215
+00:22:01,220 --> 00:22:05,660
+تقسم ال a ال Corollary بتتعامل مع اي integer a اقص
+
+216
+00:22:05,660 --> 00:22:10,180
+بي تطابق ال a modulo بي
+
+217
+00:22:10,180 --> 00:22:15,880
+الان واضح ان دي بنشتغل على Corollary فرماتالـ 15
+
+218
+00:22:15,880 --> 00:22:21,060
+بنفس الأسلوب السابق تتحلل لخمسة في تلاتة عندي اللي
+
+219
+00:22:21,060 --> 00:22:26,280
+هو الـ A بنسبة .. بناء على corollary لفرمات الـ A
+
+220
+00:22:26,280 --> 00:22:33,640
+أُس خمسة تطابق الـ A Modulo خمسة وأيضا بناء على
+
+221
+00:22:33,640 --> 00:22:38,600
+فرمات ال theorem A أُس تلاتة أو ال corollary
+
+222
+00:22:38,600 --> 00:22:44,280
+لفرمات تطابق ال A Moduloاللي هو تلاتة تذكركم الـ
+
+223
+00:22:44,280 --> 00:22:49,620
+Corollary a to the b تطابق ال a modulo b لكل a
+
+224
+00:22:49,620 --> 00:22:56,700
+element أنزل لأن أضحى الصورة يصير عندي a أُس يرفع
+
+225
+00:22:56,700 --> 00:23:01,700
+للقوة أربعة يصير a أُس عشرين تطابق ال a أُس أربعة
+
+226
+00:23:01,700 --> 00:23:07,680
+modulo خمسة و ال a أُس أربعة لو ضربنا الجهتين في a
+
+227
+00:23:07,680 --> 00:23:14,010
+في جماعة في a أضرب الجهتينفي a فبصير هذه a أس واحد
+
+228
+00:23:14,010 --> 00:23:21,530
+عشرين تطابق ال a أس خمسة modulo خمسة لكن من الأصل
+
+229
+00:23:21,530 --> 00:23:27,350
+ال a أس خمسة تطابق مين تطابق ال a modulo خمسة إذن
+
+230
+00:23:27,350 --> 00:23:32,050
+الآن احنا حصلنا على الجزء الأول اللي هيلزمناه
+
+231
+00:23:32,520 --> 00:23:36,980
+Similar لفي نفس الأسلوب لو جينا نرفع النهاردة
+
+232
+00:23:36,980 --> 00:23:43,140
+نصلها لـ 21 نرفعها للقوة 7 فبصير A أُس 7 في 3 بـ
+
+233
+00:23:43,140 --> 00:23:53,140
+21 تطابق الـ A في A أُس 7 آسف نرفع القوة 7 نرفع
+
+234
+00:23:53,140 --> 00:23:58,080
+الجهتين للقوة 7 واضح؟ فبصير A أُس 7 A أُس 7 اللي
+
+235
+00:23:58,080 --> 00:23:59,620
+هي عبارة عن A أُس 6
+
+236
+00:24:23,030 --> 00:24:26,610
+بصير عندى من الجزء الاول والجزء التاني بما ان
+
+237
+00:24:26,610 --> 00:24:29,490
+العام المشترك الاعلى بين التلاتة والخمسة فكرة
+
+238
+00:24:29,490 --> 00:24:33,440
+متكررةيقولي تلاتة وخمسة بواحد إذا صار عندي A أُس
+
+239
+00:24:33,440 --> 00:24:39,160
+واحد وعشرين وطابق الـ A Modulo خمسة في تلاتة بجديش
+
+240
+00:24:39,160 --> 00:24:44,880
+بخمس عشر وهو المطلوب هذا اللي هو السؤال أربعة A
+
+241
+00:24:44,880 --> 00:24:53,200
+عندي الآن ده نشوف سؤال أربعة B أربعة B عندي B إذا
+
+242
+00:24:53,200 --> 00:24:57,120
+كان السؤال
+
+243
+00:24:57,120 --> 00:25:03,830
+أربعة B يا جماعةبقول ما يلي A السابعة تطابق الـ A
+
+244
+00:25:03,830 --> 00:25:14,050
+موضوع 42 لكل A فكرة مشابهة الـ A 42 ما تاكل فكرة
+
+245
+00:25:14,050 --> 00:25:20,330
+لأ فاش ده يعني الحل سبعة في تلاتة في اتنين مظبوط
+
+246
+00:25:20,330 --> 00:25:26,210
+الأولى مضوع سبعةأكيد by corollary of format
+
+247
+00:25:26,210 --> 00:25:32,030
+solution by corollary of format a7 تطابق ال a
+
+248
+00:25:32,030 --> 00:25:37,150
+modulo 7 هاي أول واحدة التانية a3 تطابق ال a
+
+249
+00:25:37,150 --> 00:25:45,870
+modulo 3 ومنها بدنا نص ان هذه سبعة ال a6تطابق الـ
+
+250
+00:25:45,870 --> 00:25:51,270
+A تربية رفعت الاتنين لأقوى له يواشي اتنين اضرب في
+
+251
+00:25:51,270 --> 00:25:55,530
+A فبصير A أُس سبعة تطابق الـ A تكعيب الـ A تكعيب
+
+252
+00:25:55,530 --> 00:26:00,350
+اشمالها بتطابق الـ A موضلو تلاتة وهذه جهزة
+
+253
+00:26:00,350 --> 00:26:06,950
+Similarly A تربية تطابق الـ A إذا A أُس اضرب
+
+254
+00:26:06,950 --> 00:26:16,060
+الموضلوفاتنيت بيصير A6 مطابق الـ A تكعيب الـ A
+
+255
+00:26:16,060 --> 00:26:23,970
+تكعيب اللي هيأضربه في كمان A فبصير A7 تطابق A7
+
+256
+00:26:23,970 --> 00:26:30,710
+معايا الـ A4 عبارة عن A تربية تربية الـ A تربية
+
+257
+00:26:30,710 --> 00:26:33,950
+بالطابق الـ A فبصير A تربية بالطابق برضه من هنا
+
+258
+00:26:33,950 --> 00:26:40,730
+هترجع الـ A مدل 2 إذا جاهزة للكل A7 طابق الـ A مدل
+
+259
+00:26:40,730 --> 00:26:48,750
+2 مدل 3و مدله 7 اتلقى جمع بعض بما ان العامل مشترك
+
+260
+00:26:48,750 --> 00:26:51,070
+اللي على بين السبعة و التلاتة و اتنين بساعة واحد
+
+261
+00:26:51,070 --> 00:26:54,770
+اذا حيكون عندي a و السبعة تطابق ال a مدله جديش
+
+262
+00:26:54,770 --> 00:27:04,270
+مدله 42 نجي لسؤال اخر يا شباب سؤال اللي هو ستة
+
+263
+00:27:04,270 --> 00:27:10,770
+نشوف سؤال ستة ايش بقول سؤال ستة جزءين الجزء الاول
+
+264
+00:27:10,770 --> 00:27:19,740
+aFind the units digit of تلاتة أسمية تلاتة
+
+265
+00:27:19,740 --> 00:27:25,960
+أسمية
+
+266
+00:27:41,270 --> 00:27:48,950
+تطابق ماذا مدن ومين مدن وعشرة اللي هو المتبقي هي
+
+267
+00:27:48,950 --> 00:27:54,450
+القسمة على عشرة اللي هو خانة الأحد اللي في الرقم
+
+268
+00:27:54,450 --> 00:28:00,410
+اللي عندي الفكرة مشابهة للجبل الآن تلاتة أسمية
+
+269
+00:28:00,410 --> 00:28:03,930
+تطابق مدن وعشرة العشرة بنجسمها لأتنين في مين
+
+270
+00:28:03,930 --> 00:28:10,680
+ونحلها لأتنين في خمسة فالآن بدي أشوف تلاتةby اللي
+
+271
+00:28:10,680 --> 00:28:18,440
+هو Fermat's theorem تلاتة عند التنين لتقسم التلاتة
+
+272
+00:28:18,440 --> 00:28:23,720
+معايا يعني وكأن ال a تلاتة و ال b اتنين إذا
+
+273
+00:28:23,720 --> 00:28:27,920
+التلاتة تطابق تلاتة و أس اتنين ماقص واحد يعني
+
+274
+00:28:27,920 --> 00:28:33,550
+التلاتة تطابق الواحد modulo اتنينومنها على طول
+
+275
+00:28:33,550 --> 00:28:40,530
+ثلاثة أسمية تطابق الواحد مدنه مين مدنه اتنين نيجي
+
+276
+00:28:40,530 --> 00:28:48,810
+لمين؟ للخمسة الخمسة ثلاثة أس أربعة تطابق الواحد
+
+277
+00:28:48,810 --> 00:28:52,370
+مدنه خمسة مدونه ان هذه performance theorem برضه
+
+278
+00:28:52,370 --> 00:28:56,870
+الآن أربعة أرفعها لقوة خمسة عشرين فتصبح ثلاثة
+
+279
+00:28:56,870 --> 00:29:03,050
+أسمية تطابق الواحد مدنه مين مدنه خمسةمن الجهتين
+
+280
+00:29:03,050 --> 00:29:06,250
+لأن العامل مش شابه كدا لبين اتنين وخمسة بساعة واحد
+
+281
+00:29:06,250 --> 00:29:11,570
+فبصير عندي تلاتة أسمية تطابق الواحد مدلوا اتنين
+
+282
+00:29:11,570 --> 00:29:17,730
+وخمسة اللي هو قديش عشرة يعني بكون عندي the units
+
+283
+00:29:17,730 --> 00:29:27,480
+digit of تلاتة أسمية isone هو عبارة عن مين؟ عن
+
+284
+00:29:27,480 --> 00:29:32,160
+اللي هو الواحد الآن هذا اللي هو مين؟ اللي هو عبارة
+
+285
+00:29:32,160 --> 00:29:39,580
+عن السؤال السادس ايه؟ نيجي الآن للسؤال
+
+286
+00:29:41,570 --> 00:29:46,470
+السادس بي لنثبت أنه .. لنثبت مهيالي نشوف ايش
+
+287
+00:29:46,470 --> 00:29:51,730
+السؤال بيقول و نشوف كيف بدنا نحل السؤال prove that
+
+288
+00:29:51,730 --> 00:29:59,450
+for any a element in z a أُس خمسة و ال a have the
+
+289
+00:29:59,450 --> 00:30:07,900
+same unit digitاو units digit نثبت ان ال a أس خمسة
+
+290
+00:30:07,900 --> 00:30:13,660
+و ال a الهن ايه الشمال هن نفس ال units digit يعني
+
+291
+00:30:13,660 --> 00:30:21,700
+بمعنى اخر بدنا نثبت ان a أس خمسة a أس خمسة اللي هو
+
+292
+00:30:21,700 --> 00:30:30,760
+تطابق ال a modulo عشرة تطابق ال a modulo عشرة وهذا
+
+293
+00:30:30,760 --> 00:30:40,470
+الكلام سهلA أُس خمسة A أُس
+
+294
+00:30:40,470 --> 00:30:49,490
+خمسة تطابق الـ A modulo خمسة هذا by corollary of
+
+295
+00:30:49,490 --> 00:30:57,350
+format و الـ A تربيع تطابق الـ A modulo 2 by
+
+296
+00:30:57,350 --> 00:31:03,040
+corollary of formatالآن من هذه بيصير عندي ارفع
+
+297
+00:31:03,040 --> 00:31:07,460
+بيصير a أُس 4 تطابق ال a تربيع اللي هي تطابق ال a
+
+298
+00:31:07,460 --> 00:31:14,020
+modulo 2 واضح اه مضرب في a الجاتين فبيصير a أُس 5
+
+299
+00:31:14,020 --> 00:31:18,740
+تطابق ال a تربيع اللي هي بالطابق أصلا من ال a
+
+300
+00:31:18,740 --> 00:31:24,600
+modulo 2 صار عندي الآن من اللي هو
+
+301
+00:31:27,670 --> 00:31:33,290
+واتنين بيصير عندي A أُس خمسة تطابق الـ A مُدُل
+
+302
+00:31:33,290 --> 00:31:35,930
+وخمسة في اتنين لأن العامل مشترك الأعلى بين الخمسة
+
+303
+00:31:35,930 --> 00:31:40,190
+واثنين بيصيح واحد إذا صار عند ال A أُس خمسة تطابق
+
+304
+00:31:40,190 --> 00:31:43,310
+ال A مُدُل عشرة أو بمعنى أخر ال A أُس خمسة وال A
+
+305
+00:31:43,310 --> 00:31:49,450
+have the same unit digits نجي الآن لسؤال 11 سؤال
+
+306
+00:31:49,450 --> 00:31:54,290
+11 بيقول ما يلي أسرعت ان الفكرة .. الفكرة صارت إيه
+
+307
+00:31:54,290 --> 00:32:05,300
+شمالها؟متشابه اكتر اكتر اكتر اكتر
+
+308
+00:32:05,300 --> 00:32:08,760
+اكتر اكتر اكتر اكتر اكتر اكتر اكتر اكتر اكتر
+
+309
+00:32:27,180 --> 00:32:35,920
+الان لأي البروف البروري البروف لو
+
+310
+00:32:35,920 --> 00:32:40,800
+جينا أخدنا هذه الأساسات كلها واحدة لو جينا أخدنا
+
+311
+00:32:40,800 --> 00:32:48,140
+for any un element in z بركورولري of فرمات يا
+
+312
+00:32:48,140 --> 00:32:57,230
+جماعةن أس بي تطابق الان modulo مين modulo بي هذ بي
+
+313
+00:32:57,230 --> 00:33:03,510
+الكورولري of Fermat طيب الآن بناء على هذه اللي هو
+
+314
+00:33:03,510 --> 00:33:09,790
+الحقيقة بيصير عند then اللي هو واحد أس بي زاد
+
+315
+00:33:09,790 --> 00:33:14,990
+اتنين أس بي لما أصل عند بي ماينس واحد أس بي الأولى
+
+316
+00:33:14,990 --> 00:33:21,110
+تطابق اللي هوتانية تطابق التنين تانية تطابق التنين
+
+317
+00:33:21,110 --> 00:33:21,950
+تانية تطابق التنين تانية تطابق التنين تانية تطابق
+
+318
+00:33:21,950 --> 00:33:24,230
+التنين تانية تطابق التنين تانية تطابق التنين تانية
+
+319
+00:33:24,230 --> 00:33:24,270
+تطابق التنين تانية تطابق التنين تانية تطابق التنين
+
+320
+00:33:24,270 --> 00:33:27,150
+تانية تطابق التنين تانية تطابق التنين تانية تطابق
+
+321
+00:33:27,150 --> 00:33:33,790
+التنين تانية تطابق التنين تانية تطابق التنين تانية
+
+322
+00:33:33,790 --> 00:33:34,550
+تطابق التنين تانية تطابق التنين تانية تطابق التنين
+
+323
+00:33:34,550 --> 00:33:39,770
+تانية تطابق التنين تانية تطابق
+
+324
+00:33:39,770 --> 00:33:46,310
+التنين تانية تطابق التنين تانية تطابق التنين تانية
+
+325
+00:33:46,310 --> 00:33:53,690
+تب في ب ماينوس واحد على اتنين والان ب ماينوس واحد
+
+326
+00:33:53,690 --> 00:34:04,090
+على اتنين عبارة عن عدد لأن ب هو اضبراي فبصير ب نقص
+
+327
+00:34:04,090 --> 00:34:07,070
+واحد even على اتنين بطلع ايش ماله عبارة عن نقص
+
+328
+00:34:07,070 --> 00:34:11,130
+number k إذا ساعت كفي ب عبارة عن ايش من مضاعفات ال
+
+329
+00:34:11,130 --> 00:34:18,670
+ب إذا هذا بطابق الصفر مضلمينمدلو بي لما كانت بي is
+
+330
+00:34:18,670 --> 00:34:23,690
+an odd prime طلع عند هذا المجموع يطابق السفر مدلو
+
+331
+00:34:23,690 --> 00:34:27,350
+بي نشوف سؤال تلاتاشر شباب تلاتاشر بيقول assume
+
+332
+00:34:27,350 --> 00:34:33,870
+that بي و Q are distinct primes بي
+
+333
+00:34:33,870 --> 00:34:40,190
+و Q distinct primes such that بي ماينس واحد بتقسم
+
+334
+00:34:40,190 --> 00:34:48,600
+لكيو ماينس واحدالـ B-1 تجسم
+
+335
+00:34:48,600 --> 00:34:53,220
+الـ Q-1 عامل مشترك اللي على بين اللي هو الـ A و
+
+336
+00:34:53,220 --> 00:34:56,780
+الـ B و الـ Q الـ A و حاصل الضرب الـ B و الـ Q
+
+337
+00:34:56,780 --> 00:35:00,240
+بساعة واحد على أساس أنه يصير فيه حرية الاستخدام في
+
+338
+00:35:00,240 --> 00:35:10,020
+رمات A مع الـ B و A مع الـ Q show that أن A ضمن A
+
+339
+00:35:11,550 --> 00:35:21,410
+to the Q minus واحد تطابق الواحد modulo B في مين B
+
+340
+00:35:21,410 --> 00:35:27,370
+في Q البروف نشوف يا شباب الحل للأمر أكيد المعلومة
+
+341
+00:35:27,370 --> 00:35:34,260
+هذه اللي معطينا إياها فيه إلها قوتها عندي senseب
+
+342
+00:36:05,130 --> 00:36:07,910
+الـ Greatest Common Divisor بين الـ A والـ B في
+
+343
+00:36:07,910 --> 00:36:11,570
+الـ Q بساوة واحد ثم أكيد الـ Greatest Common
+
+344
+00:36:11,570 --> 00:36:14,990
+Divisor بين الـ A والـ B والـ Greatest Common
+
+345
+00:36:14,990 --> 00:36:22,170
+Divisor بين الـ A والـ Q بساوة واحد ومنه هيكون عيد
+
+346
+00:36:22,170 --> 00:36:28,670
+الـ B لتقسم الـ Q وB لتقسم الـ A والـ Q برضه
+
+347
+00:36:28,670 --> 00:36:34,690
+لتقسمين الـ Aالآن هذه اللي هي بتأهل من استخدام الـ
+
+348
+00:36:34,690 --> 00:36:39,850
+Fermat's theorem بالنسبة للـ A للـ B بكون عندي
+
+349
+00:36:39,850 --> 00:36:47,790
+then A to the B minus واحد تطابق الواحد modulo B
+
+350
+00:36:47,790 --> 00:36:55,090
+معايا الان انفع الجهتين للقوة مين؟ للقوة K فبصير
+
+351
+00:36:55,090 --> 00:37:03,880
+عندي andSo a to the b minus 1 الكل أس كي تطابق
+
+352
+00:37:03,880 --> 00:37:11,180
+الواحد أس كي اليمين واحد modulo فيه الان هذه مين
+
+353
+00:37:11,180 --> 00:37:14,740
+هي a to the b minus واحد to the k اللي عبارة عن
+
+354
+00:37:14,740 --> 00:37:20,280
+كيوكو minus واحد لأن and so ال a to the q minus
+
+355
+00:37:20,280 --> 00:37:26,270
+واحد تطابق الواحد modulo ال b هذه أول واحدةهذه
+
+356
+00:37:26,270 --> 00:37:31,110
+نسميها واحد الآن similarly by Fermat's theorem Q
+
+357
+00:37:31,110 --> 00:37:37,170
+لا تقسم الـA then اللي هو الـA to the Q minus واحد
+
+358
+00:37:37,170 --> 00:37:40,910
+تطبيق مباشر على Fermat's theorem تطابق اللي هو
+
+359
+00:37:40,910 --> 00:37:48,630
+الواحد modulo Q الآن الان هي اتنين since ال
+
+360
+00:37:48,630 --> 00:37:53,030
+greatest common divisor بين الـB والـQ بسعر واحد
+
+361
+00:37:53,030 --> 00:38:03,920
+andby one and two we have a to the q minus واحد
+
+362
+00:38:03,920 --> 00:38:14,530
+تطبق الواحد modulo b في q وهو المطلوبفقريباً هذا
+
+363
+00:38:14,530 --> 00:38:19,610
+لمب الأسئلة أو اللي جاب ال .. او الكثير من الأفكار
+
+364
+00:38:19,610 --> 00:38:22,830
+اللي في الأسئلة اللي جاب الـ 13 الان يا شباب بدنا
+
+365
+00:38:22,830 --> 00:38:27,270
+نحل السؤال الأخير في خمسة اتنين اللي هو سؤال أربعة
+
+366
+00:38:27,270 --> 00:38:37,010
+عشر سؤال أربعة عشر بنشوف إيش السؤال بيقول و من ثم
+
+367
+00:38:37,010 --> 00:38:40,830
+بنشوف كيف بدنا نبرهن
+
+368
+00:38:45,640 --> 00:38:49,540
+طيب يا شباب صلى النبي عليه الصلاة والسلام بيقولّي
+
+369
+00:38:49,540 --> 00:38:54,060
+إذا كان بي و Q are distinct primes مختلفات ا prove
+
+370
+00:38:54,060 --> 00:39:04,000
+that بي to the Q minus واحد زاد Q to the بي minus
+
+371
+00:39:04,000 --> 00:39:13,720
+واحد وطابق الواحد موضله برضه مين بفكرة ا prove
+
+372
+00:39:16,100 --> 00:39:20,000
+شوفوا صلى الله عليه الصلاة والسلام عند الـ B و الـ
+
+373
+00:39:20,000 --> 00:39:26,520
+Q هم مختلفين برامج إذا بي لا تقسم الـ Q إذا by
+
+374
+00:39:26,520 --> 00:39:33,160
+Fermat's theorem اللي هو A الـ Q اللي هتلعب له
+
+375
+00:39:33,160 --> 00:39:38,720
+بالـ A بي ماينس واحد وطابق الواحد مو دوله
+
+376
+00:39:44,520 --> 00:39:50,200
+لكن لو أتينا و أخذنا الـ Q أس بي ماينس واحد حط
+
+377
+00:39:50,200 --> 00:39:54,500
+طابق ماذا
+
+378
+00:39:54,500 --> 00:40:05,900
+موضوع الـ Q؟ أكيد حط طابق إيش؟ صفر لأن الـ Q أس بي
+
+379
+00:40:05,900 --> 00:40:11,510
+ماينس واحد من المضاعفات من من المضاعفات الـ Qنجمع
+
+380
+00:40:11,510 --> 00:40:17,750
+المعلومات وعندي أيضًا الـ Q لا تقسم الـ B إذا by
+
+381
+00:40:17,750 --> 00:40:23,850
+Fermat's theorem الـ Q هو عبارة عن الـ prime و الـ
+
+382
+00:40:23,850 --> 00:40:28,510
+B هو الأساس فبصير B to the Q minus واحد تطابق
+
+383
+00:40:28,510 --> 00:40:39,290
+الواحد Modulo مين Modulo هو الـ prime لـ Q وفي
+
+384
+00:40:39,290 --> 00:40:40,350
+نفس الوقت
+
+385
+00:40:42,970 --> 00:40:52,950
+بط عندي الـ B قصة Q مانس واحد تطابق السفر modulo
+
+386
+00:40:52,950 --> 00:40:58,670
+ايش؟ modulo اللي هو B لأنه بتصير اللي هي B قصة Q
+
+387
+00:40:58,670 --> 00:41:04,050
+مانس واحد من مضاعفات مين؟ من مضاعفات الـ B طيب
+
+388
+00:41:04,050 --> 00:41:11,850
+خدوني هذه مخادةهيها ملاش قلبت و أنا قلبت خدوني هذه
+
+389
+00:41:11,850 --> 00:41:19,010
+مع هذه فالتنتين مع بعض together بيصير عندي Q to
+
+390
+00:41:19,010 --> 00:41:24,970
+the B minus واحد زائد B to the Q minus واحد تطابق
+
+391
+00:41:24,970 --> 00:41:31,830
+الواحد هاي الواحد زائد جمعناها السفر هنا والتنتين
+
+392
+00:41:31,830 --> 00:41:40,300
+ايه شمال هنا اللي هو واحدModulo B Similarly عنده
+
+393
+00:41:40,300 --> 00:41:47,980
+خذوا هذه مع هذه بيصير عنده اللي هو ال بي ال Q بي
+
+394
+00:41:47,980 --> 00:41:54,300
+minus واحد عمال في نفس الترتيب زائد ال بي السي Q
+
+395
+00:41:54,300 --> 00:41:59,060
+minus واحد تطابق هذا بالطابق السفر وهذا بالطابق
+
+396
+00:41:59,060 --> 00:42:05,660
+الواحد Modulo Qاللي هي عبارة عن تطابق الواحد
+
+397
+00:42:05,660 --> 00:42:11,060
+modulo q هاي عندى الان واحد وهي عندى اتنين فكرة
+
+398
+00:42:11,060 --> 00:42:14,980
+متكررة صار عندى ال b و ال q العامل مشترك اللي اعلى
+
+399
+00:42:14,980 --> 00:42:18,880
+بينهم بيساو واحد اذا by واحد و اتنين فبصير عندى ال
+
+400
+00:42:18,880 --> 00:42:24,380
+q أس b minus واحد زائد b أس q minus واحد تطابق
+
+401
+00:42:24,380 --> 00:42:31,680
+الواحد modulo b في q حاصل ضرب b في q نكون هيك احنا
+
+402
+00:42:32,900 --> 00:42:38,560
+خلصنا اللي هو الأسئلة على المطلوبة على اللي هي
+
+403
+00:42:38,560 --> 00:42:44,680
+خمسة اتنين اللي هو Fermat's Little Theorem and The
+
+404
+00:42:44,680 --> 00:42:48,340
+Coronary of Fermat's Little Theorem الآن بدنا نبدأ
+
+405
+00:42:48,340 --> 00:42:53,000
+نحكي على خمسة تلاتة أو أسئلة خمسة تلاتة اللي هي
+
+406
+00:42:53,000 --> 00:42:57,160
+بتتعلق بـWilson's theorem بتتعلق بـWilson's
+
+407
+00:42:57,160 --> 00:43:04,750
+theorem خلّينا نشوف اللي هواللي هي أسئلة Wilson's
+
+408
+00:43:04,750 --> 00:43:09,070
+theorem في الأول بس على السريع نقول Wilson's
+
+409
+00:43:09,070 --> 00:43:14,390
+theorem إذا كانت B' بيكون B-1! تطابق ناقص واحد
+
+410
+00:43:14,390 --> 00:43:17,330
+modulo B هذي Wilson's theorem
+
+411
+00:43:21,990 --> 00:43:26,310
+اللي هو برضه هتلزمنا في عنا اللي هو a decoder of
+
+412
+00:43:26,310 --> 00:43:29,250
+congruences X ترجل زائد واحد وطابق السفر مدله B
+
+413
+00:43:29,250 --> 00:43:35,830
+where B is an odd prime لها solution F andol FB
+
+414
+00:43:35,830 --> 00:43:41,550
+على صورة 4K زائد واحدأذن قبل ما نبدأ خلّيني على
+
+415
+00:43:41,550 --> 00:43:49,150
+السريع أذكركم بـWilson's theorem أو بالحل
+
+416
+00:43:49,150 --> 00:43:52,830
+لـquadratic equation x² زاد 1 وطابق صفر modulo b
+
+417
+00:43:52,830 --> 00:43:57,250
+على أساس حنستخدمهم لأن Wilson's theorem زي ما قلنا
+
+418
+00:43:57,250 --> 00:44:03,910
+عند b prime فبكون b minus 1 factorial وطابق نقص 1
+
+419
+00:44:03,910 --> 00:44:10,620
+modulo bأو أيضًا عندي لـQuadratic congruences X
+
+420
+00:44:10,620 --> 00:44:16,540
+ثربية زي واحد تطابق الصفر modulo B has a solution
+
+421
+00:44:16,540 --> 00:44:25,670
+if and only if الـ B تطابق اللي هو الواحدmodulo
+
+422
+00:44:25,670 --> 00:44:31,330
+أربعة أو بلغة ثانية الـ B على صورة أربعة كزائد
+
+423
+00:44:31,330 --> 00:44:38,050
+واحد هذوله اللي هيلزمنا الآن في اللي هو خمسة ثلاثة
+
+424
+00:44:38,050 --> 00:44:43,050
+فنيجي الآن للسؤال الأول لنشوف السؤال الأول إيش
+
+425
+00:44:43,050 --> 00:44:48,970
+بيقول سؤال واحد في خمسة ثلاثة سؤال واحد في خمسة
+
+426
+00:44:48,970 --> 00:44:55,120
+ثلاثة بيقول لي أوجدالمتبقى يجد المتبقى عندما يقسم
+
+427
+00:44:55,120 --> 00:45:00,420
+الـ 15 فيكتوريال إلى 17 المتبقى يجد المتبقى عندما
+
+428
+00:45:00,420 --> 00:45:08,100
+يقسم الـ 15 فيكتوريال إلى 17 المتبقى يجد المتبقى
+
+429
+00:45:08,100 --> 00:45:13,280
+عندما
+
+430
+00:45:13,280 --> 00:45:17,100
+يقسم الـ 15 فيكتوريال إلى 17 المتبقى يجد المتبقى
+
+431
+00:45:17,100 --> 00:45:19,460
+عندما يقسم الـ 15 فيكتوريال إلى 17
+
+432
+00:45:22,090 --> 00:45:28,190
+احنا بنعرف اللي هو by Fermat's theorem اللي هو b-1
+
+433
+00:45:28,190 --> 00:45:35,810
+factorial اللي هو 16 factorial تطابق 16 factorial
+
+434
+00:45:35,810 --> 00:45:42,010
+تطابق الناقص واحد اسف تطابق الناقص واحد modulo
+
+435
+00:45:42,010 --> 00:45:47,270
+اللي هو b ماشي يا شباب 16 factorial تطابق الناقص
+
+436
+00:45:47,270 --> 00:45:52,480
+واحد modulo بيها دي باي ويلسون's theoremطيب الان
+
+437
+00:45:52,480 --> 00:45:59,120
+انا بدي 15 factorial هذه 16 في 15 factorial تطبق
+
+438
+00:45:59,120 --> 00:46:04,500
+ناقص واحد modulo مين modulo مين من جهة أخرى احنا
+
+439
+00:46:04,500 --> 00:46:09,800
+بنعرف modulo B تبع ال V ياش هي 17 معايا شباب 17
+
+440
+00:46:09,800 --> 00:46:14,800
+هذه ال B اللي بتطبق عليها 17الان الـ 6 بالنسبة للـ
+
+441
+00:46:14,800 --> 00:46:19,680
+17 على جهة اللي هي الـ 16 بالنسبة للـ 17 هي ناقص
+
+442
+00:46:19,680 --> 00:46:24,580
+واحد تطابق الناقص واحد مدينه مين؟ مدنه 17 إذا هذه
+
+443
+00:46:24,580 --> 00:46:30,560
+بتطابق الناقص واحد في الخمستاش فيكتوريال لأن ال 16
+
+444
+00:46:30,560 --> 00:46:33,000
+بتطابق الناقص واحد الناقص واحد في الخمستاش
+
+445
+00:46:33,000 --> 00:46:35,320
+فيكتوريال بتطابق ال 16 في الخمستاش واحد فيكتوريال
+
+446
+00:46:35,320 --> 00:46:38,820
+إذا تجسم الجهتين على ناقص واحد فبصير الخمستاش
+
+447
+00:46:38,820 --> 00:46:45,650
+فيكتوريال تطابق الواحدموضنه 17 إذا ال remainder في
+
+448
+00:46:45,650 --> 00:46:51,290
+حالة قسمة الخمست عشر على ال 17 كده بيطلع بيطلع
+
+449
+00:46:51,290 --> 00:46:56,230
+عندي بساوي واحد نجي للسؤال اللي بعده اي سؤال يا
+
+450
+00:46:56,230 --> 00:47:06,960
+شباب نجي اللي هو1a الان 1b find the remainder لما
+
+451
+00:47:06,960 --> 00:47:15,620
+ال 2 في 26 factorial اللي هو is divided by
+
+452
+00:47:15,620 --> 00:47:21,130
+29السينيوشين برضه تطبيق مباشر يا شباب على Fermat's
+
+453
+00:47:21,130 --> 00:47:26,410
+theorem والفكرة تقريبا متكررة عندي اللي هي التسعة
+
+454
+00:47:26,410 --> 00:47:31,010
+وعشرين هو ال prime اللي عندي by Wilson's theorem
+
+455
+00:47:31,010 --> 00:47:37,030
+تمانية وعشرين factorialتطابق الناقص واحد modulo
+
+456
+00:47:37,030 --> 00:47:41,390
+تسعة وعشرين هي Wilson's theorem أنا مين بدي يا
+
+457
+00:47:41,390 --> 00:47:45,270
+شباب؟ ستة وعشرين factorial في مين؟ في اتنين فاللي
+
+458
+00:47:45,270 --> 00:47:49,030
+بتوصلني لستة وعشرين factorial اللي هو اكيد التمنية
+
+459
+00:47:49,030 --> 00:47:51,550
+وعشرين factorial هي تمنية وعشرين factorial عبارة
+
+460
+00:47:51,550 --> 00:47:56,650
+عن اللي عبارة عن ستة وعشرين factorial في سبعة
+
+461
+00:47:56,650 --> 00:48:01,870
+وعشرين في اللي هو تمانية وعشرينمظبوطاً للاقهد اللي
+
+462
+00:48:01,870 --> 00:48:05,030
+هي 28 factorial من اللي فوق قعدت الطابق الناقص
+
+463
+00:48:05,030 --> 00:48:10,290
+واحد module 29 طيب الآن بدأ تصير اللغة سريع
+
+464
+00:48:10,290 --> 00:48:16,390
+نستخدمها ال 28 بالنسبالي 29 ناشر شباب سالب واحد أي
+
+465
+00:48:16,390 --> 00:48:24,350
+سالب واحدالـ 27 بالنسبة للـ 29 الـ 27 تطابق ناقص 2
+
+466
+00:48:24,350 --> 00:48:31,730
+موضله 29 واضح، أه؟ في ناقص 2 في مين؟ في الـ 26
+
+467
+00:48:31,730 --> 00:48:36,370
+فيكتوريا، دلوقتي الأمور عندنا لأن ناقص 1 في ناقص 2
+
+468
+00:48:36,370 --> 00:48:42,610
+تطلع 2 فبصير عبارة عن 2 في 26 فيكتوريا تطابق
+
+469
+00:48:42,610 --> 00:48:48,590
+الناقص 1-1 هو في الواقع جداش بالنسبة لـ 29 يا شباب
+
+470
+00:48:48,590 --> 00:48:57,710
+اللي هو عبارة عن 28 mod 29 إذا المتبقي حين قسمة 2
+
+471
+00:48:57,710 --> 00:49:02,950
+في 26 factorial على 29 مش بساوي اللي هو عبارة عن
+
+472
+00:49:02,950 --> 00:49:12,390
+28 هذا اللي هو سؤال B في السؤال الأول نيدي
+
+473
+00:49:12,390 --> 00:49:26,510
+يا شباب نشوفسؤال 4 نكتب
+
+474
+00:49:26,510 --> 00:49:38,010
+السؤال
+
+475
+00:49:38,840 --> 00:49:44,080
+ونحل السؤال الان يعني برضه تطبيق عمل since theorem
+
+476
+00:49:44,080 --> 00:49:51,560
+ولكن يعني صار فيه تركيب معين سهل برضه لأكثر من ال
+
+477
+00:49:51,560 --> 00:49:58,540
+prime السؤال الأربعة show that
+
+478
+00:49:58,540 --> 00:50:09,130
+اللي هو 18 factorial مطابق الناقص واحدمودلو اربعة
+
+479
+00:50:09,130 --> 00:50:15,080
+تلاتة سبعة solution أو proofالآن يا شباب اللي هو
+
+480
+00:50:15,080 --> 00:50:20,200
+هذه 18 factorial يعني بتعطيني مؤشر ان هو كأنه
+
+481
+00:50:20,200 --> 00:50:23,880
+بنحكي عن اللي هو الـ Brian 19 لأنه الـ Sun بتقول
+
+482
+00:50:23,880 --> 00:50:28,140
+بي ماقص واحد factorial فالآن اللي هي بتعطيني مؤشر
+
+483
+00:50:28,140 --> 00:50:33,520
+ان انا اقسم الـ 437 ع 19 تأكدلي انه انا باقسمها ع
+
+484
+00:50:33,520 --> 00:50:39,140
+ال 19 ولا لأ فعلا لو جيت جسمت هتلاقي ال 400و سبعة
+
+485
+00:50:39,140 --> 00:50:43,640
+و تلاتين بيساوي تسعة عشر في مين في التلاتة و عشرين
+
+486
+00:50:43,640 --> 00:50:48,420
+تسعة عشر في التلاتة و عشرين المفضل الآن الحل الان
+
+487
+00:50:48,420 --> 00:50:58,900
+by Wilson's theorem by Wilson's theorem عندي اللي
+
+488
+00:50:58,900 --> 00:51:05,060
+هو التمنتعش factorial تطابق الناقص واحد mod و mod
+
+489
+00:51:05,060 --> 00:51:13,200
+تسعة عشر هذه جاهزة الآنالان بيولسون فيرم ايضا و
+
+490
+00:51:13,200 --> 00:51:16,540
+لكن الان على الرقم تلاتة عشرين او الـ prime تلاتة
+
+491
+00:51:16,540 --> 00:51:21,240
+عشرين فبصير عنده اتنين عشرين factorial يطابق ناقص
+
+492
+00:51:21,240 --> 00:51:26,240
+واحد modulo جديش يا جماعة modulo تسعة عشر الان
+
+493
+00:51:26,240 --> 00:51:31,970
+اتنين عشرين factorialبدي اجيبها لمين؟ Modulo S في
+
+494
+00:51:31,970 --> 00:51:36,610
+23 بدي اجيبها اشوف ايش بالطابق اللي هو بدي اوصلها
+
+495
+00:51:36,610 --> 00:51:40,390
+للـ18 factorial عارفين ليش؟ احسسوا ان انا اعمل هذه
+
+496
+00:51:40,390 --> 00:51:43,310
+و هذه نفس الاشي و بعدين زي ما عملنا قبل هيك نشوف
+
+497
+00:51:43,310 --> 00:51:46,090
+ايش بقول، بقى الصلاة على النبي عليه الصلاة والسلام
+
+498
+00:51:46,090 --> 00:51:52,370
+هذه بيصير كده؟ 22 في
+
+499
+00:51:52,370 --> 00:52:02,510
+21 في 20 في 19فى 18 فكتوريال تطابق ناقص واحد مدله
+
+500
+00:52:02,510 --> 00:52:07,830
+13 بس قعدت كتابة اللى فوق بالطريقة هذه تطابق من
+
+501
+00:52:07,830 --> 00:52:12,210
+الجهة دىالعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+502
+00:52:12,210 --> 00:52:14,130
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+503
+00:52:14,130 --> 00:52:17,170
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+504
+00:52:17,170 --> 00:52:19,550
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+505
+00:52:19,550 --> 00:52:20,770
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+506
+00:52:20,770 --> 00:52:21,750
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+507
+00:52:21,750 --> 00:52:24,370
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+508
+00:52:24,370 --> 00:52:28,470
+للتلاتة وعشرين بالنسبة للتلاتة وعشرين بالنسبة
+
+509
+00:52:28,470 --> 00:52:31,970
+للتلاتة وعشرين بالنسبة للتلاتة وعبتصير الطابق سالب
+
+510
+00:52:31,970 --> 00:52:35,530
+ثلاثة التسعة عشر بالنسبالك تلاتة وعشرين بالطابق
+
+511
+00:52:35,530 --> 00:52:39,390
+اللي هي جداش سالب أربعة في سالب أربعة في اللي
+
+512
+00:52:39,390 --> 00:52:45,270
+بديها تمانتاش factorial صار الآن هذا المقدار بطابق
+
+513
+00:52:45,270 --> 00:52:48,470
+هذا المقدار مضوله تلاتة وعشرين خلّينا نضرب هدول في
+
+514
+00:52:48,470 --> 00:52:52,970
+بعض ناقص ناقص ناقص ناقص يعني كلها زائدأربعة في
+
+515
+00:52:52,970 --> 00:52:55,570
+تلاتة في اتناش في اتنين بابا عشان بيصير اربعة
+
+516
+00:52:55,570 --> 00:53:00,670
+وعشرين في تمانتاش فيكتوريال تطابق ناقص واحد مدل
+
+517
+00:53:00,670 --> 00:53:04,210
+مقدش شباب تلاتة وعشرين الاربع عشرين بالنسبالي
+
+518
+00:53:04,210 --> 00:53:09,810
+تلاتة وعشرين مش بالساعة واحد فبيصير عندي واحد اللي
+
+519
+00:53:09,810 --> 00:53:14,570
+هو مكان الاربع عشرين واحد في تمانتاش بتطلع تمانتاش
+
+520
+00:53:14,570 --> 00:53:19,030
+الفيكتوريال تطابق ناقص واحد مدله تلاتة وعشرين
+
+521
+00:53:19,030 --> 00:53:24,490
+هيصار عندي هذه جاهزةوهذه جاهزة من الأول بنفس
+
+522
+00:53:24,490 --> 00:53:29,090
+الفكرة السابقة المتكررة العامل المشترك لأعلى بين
+
+523
+00:53:29,090 --> 00:53:33,450
+التسعة عشر والتلت عشر وتلت عشرين بساوة واحد وهذا
+
+524
+00:53:33,450 --> 00:53:37,030
+المقدار الطابق الناقص واحد وهذا نفسه الطابق الناقص
+
+525
+00:53:37,030 --> 00:53:41,530
+واحد مضلوا تسعة عشر وتلت عشرين إذن أكيد من واحد
+
+526
+00:53:41,530 --> 00:53:45,710
+واتنين بيطلع تمنتاش فيكتوريالتطابق النقص واحد
+
+527
+00:53:45,710 --> 00:53:49,650
+modulo حصل bargain تسعة عاشر في تلاتة عشرين اللي
+
+528
+00:53:49,650 --> 00:53:58,150
+هو مين اللي عندنا أربعة تلاتة ستة وهو المطلوب نيجي
+
+529
+00:53:58,150 --> 00:54:05,430
+الآن نشوف سؤال ستة بقول ما يلي given a prime
+
+530
+00:54:05,430 --> 00:54:13,430
+number B establish that B minus واحدfactorial
+
+531
+00:54:13,430 --> 00:54:25,430
+تطابق اللي هو P minus واحد modulo اللي هو واحد
+
+532
+00:54:25,430 --> 00:54:32,170
+زائد اتنين زائد تلاتة لما أصل ل P minus واحد زائد
+
+533
+00:54:32,170 --> 00:54:38,610
+تلاتة زائد لما أصل P minus واحد solution خلّينا
+
+534
+00:54:38,610 --> 00:54:46,860
+نحلل السؤالو نشوف ايش اللي بدنا نسويه عندي اللي هو
+
+535
+00:54:46,860 --> 00:54:53,280
+لو طلعنا على اللي هو اللي بدنا نعمله المدره هذا هو
+
+536
+00:54:53,280 --> 00:54:59,200
+المقياسلو طلعنا للمقياس المقياس واحد زائد اتنين
+
+537
+00:54:59,200 --> 00:55:05,560
+زائد تلاتة زائد بي ماينوس واحد مجموعة متتالية حد
+
+538
+00:55:05,560 --> 00:55:12,420
+الاول واحد واساسها واحد فتطلع عنده عبارة عن بي في
+
+539
+00:55:12,420 --> 00:55:18,480
+بي ماينوس واحد على مين على التين وكأنه صارت السؤال
+
+540
+00:55:18,480 --> 00:55:31,680
+تبعنا بدنا نثبتب-1! يطبق الـ B-1 مدلومين مدلو B في
+
+541
+00:55:31,680 --> 00:55:37,880
+B-1 على 2 وكأنه .. طبعا اللي عندى اللي .. اللي ..
+
+542
+00:55:37,880 --> 00:55:40,780
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+543
+00:55:40,780 --> 00:55:40,860
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+544
+00:55:40,860 --> 00:55:40,880
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+545
+00:55:40,880 --> 00:55:40,940
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+546
+00:55:40,940 --> 00:55:41,060
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+547
+00:55:41,060 --> 00:55:41,460
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+548
+00:55:41,460 --> 00:55:41,460
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+549
+00:55:41,460 --> 00:55:41,660
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+550
+00:55:41,660 --> 00:55:41,660
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+551
+00:55:41,660 --> 00:55:52,620
+اللي .. اللي .. اللي .. اللي .. الليعندي اللي هو
+
+552
+00:55:52,620 --> 00:56:01,660
+اكيد اكيد عندي اللي هو من wilson's theorem by
+
+553
+00:56:01,660 --> 00:56:07,940
+wilson's theorem معايا يا شباب بي minus واحد
+
+554
+00:56:07,940 --> 00:56:15,420
+factorial تطابق ناقص واحد مدنونين احنا مدنون بيه
+
+555
+00:56:15,420 --> 00:56:19,540
+بنعرف ولا لا مدنون بيه
+
+556
+00:56:22,490 --> 00:56:28,610
+الان الـ-1 على جهة .. طب احنا بعيدين شوية عن
+
+557
+00:56:28,610 --> 00:56:33,630
+سؤالنا ولا لأ؟ لأ مش بعيدين شوف ليش مش بعيدين الان
+
+558
+00:56:33,630 --> 00:56:38,450
+عندي B-1 تطابق الـ-1 مضل بيه لكن الـ-1 بتطابق مين
+
+559
+00:56:38,450 --> 00:56:46,290
+يا شباب؟ الـB-1 مضل بيه لأن B-1 زاد الـ1 بيصير B
+
+560
+00:56:46,290 --> 00:56:51,800
+بتقسم الـBأذا صار عندى فعل الـ B-1 فكتورة طابق الـ
+
+561
+00:56:51,800 --> 00:56:59,280
+B-1 ميّن modulo B صار الأمر و كأنه بدأنا نصل للي
+
+562
+00:56:59,280 --> 00:57:05,200
+بدناهاعندي بس انا بدي بين بي في بي ماينس واحد على
+
+563
+00:57:05,200 --> 00:57:12,540
+إيش على اللي هي اتنين وكأني هنا وصلت ان ال بي
+
+564
+00:57:12,540 --> 00:57:18,320
+بتجسم ال بي ماينس واحد factorial ناقص ال بي ماينس
+
+565
+00:57:18,320 --> 00:57:28,370
+واحد، مظبوط؟طيب ما هو عند الـ B-1 بتقسم الـ B-1
+
+566
+00:57:28,370 --> 00:57:32,830
+factorial ناقص الـ B-1 هتجيبناها من وين يا جماعة
+
+567
+00:57:32,830 --> 00:57:37,830
+من الـ Nonsense theorem هذه واحد لأن B-1 بتقسم هذا
+
+568
+00:57:37,830 --> 00:57:40,850
+المقدار عارفين ليش؟ أكيد عارفين لأنه لو أخدنا B-1
+
+569
+00:57:40,850 --> 00:57:44,650
+من الجهتين فبصير B-2 factorial ناقص واحد مضربها في
+
+570
+00:57:44,650 --> 00:57:49,890
+الـ B-1 ده الـ B-1 تقسمهاماشي طيب صار عندي الان
+
+571
+00:57:49,890 --> 00:57:56,370
+واحد و اتنين بيعطيني ما يالي لاحظوا ان العامل
+
+572
+00:57:56,370 --> 00:58:00,090
+المشترك الاعلى بين ال b و ال b-1 ايش بساوي بساوي
+
+573
+00:58:00,090 --> 00:58:05,030
+واحد اذا بالفكرة المتكررة اللي حكيناها اذا ال b في
+
+574
+00:58:05,030 --> 00:58:14,070
+ال b-1 تقسم ال b-1 factorial ناقص ال b-1
+
+575
+00:58:16,260 --> 00:58:22,700
+أي سؤال؟ طيب، لكن أنا باعرف من الأصل أن الـ B في
+
+576
+00:58:22,700 --> 00:58:29,180
+الـ B minus 1 على 2 تقسم الـ B في الـ B minus 1
+
+577
+00:58:29,180 --> 00:58:32,820
+أكيد؟
+
+578
+00:58:32,820 --> 00:58:37,340
+ماشي الحال، إذا هذا المقدار بقسم هذا وهذا المقدار
+
+579
+00:58:37,340 --> 00:58:42,180
+نفسه بقسم هذا من التنتين مع بعض، إذا ال .. طبعا
+
+580
+00:58:42,180 --> 00:58:48,380
+هذا انتجر يا شباببقوم العامل هذه إذا الـ B في الـ
+
+581
+00:58:48,380 --> 00:58:58,700
+B-1 على 2 يقسم الـ B-1 factorial ناقص الـ B-1 كمان
+
+582
+00:58:58,700 --> 00:59:03,060
+مرة يا شباب الـ B في الـ B-1 بقسم هذا المقدار قلنا
+
+583
+00:59:03,060 --> 00:59:06,260
+من التنتين اللي فوق لأن العامل مشترك لعيابين هذه
+
+584
+00:59:06,260 --> 00:59:11,670
+وهذه بالساعة واحدةوهذه أنا بعرفها تقسم هذه إذا صار
+
+585
+00:59:11,670 --> 00:59:14,070
+عند بي في بي ماينوس واحد على اتنين بيقسم هذا
+
+586
+00:59:14,070 --> 00:59:19,910
+المقتار وهذا ايش اللي هو هذا هو عبارة عن ال بي
+
+587
+00:59:19,910 --> 00:59:24,590
+ماينوس واحد factorial يطابق ال بي ماينوس واحد
+
+588
+00:59:25,560 --> 00:59:29,760
+موضولة الـ B في الـ B ماينس واحد على اتنين اللي
+
+589
+00:59:29,760 --> 00:59:32,520
+مهمين يا جماعة من اول .. من وسط الدور هو عبارة عن
+
+590
+00:59:32,520 --> 00:59:37,060
+الواحد زي الاتنين زي الـ B ماينس واحد وحصلنا على
+
+591
+00:59:37,060 --> 00:59:43,520
+المطلوب نيجي نشوف السؤال السابع السؤال السابع اش
+
+592
+00:59:43,520 --> 00:59:48,340
+بقول السؤال السابع عند if B is a brine approve
+
+593
+00:59:48,340 --> 00:59:53,120
+that B بي تجسم
+
+594
+00:59:54,610 --> 01:00:07,070
+الـ A to the B زائد الـ B minus واحد factorial في
+
+595
+01:00:07,070 --> 01:00:13,430
+الـ A and الـ B بتجسم الـ A زائد B minus واحد
+
+596
+01:00:13,430 --> 01:00:19,830
+factorial A to the B، مظبوط؟ خلّينا نشوف
+
+597
+01:00:24,100 --> 01:00:29,000
+بنثبت أن هذا المقدار يطابق السفر Modulo B هذا أكيد
+
+598
+01:00:29,000 --> 01:00:33,320
+فيه ويلسون وA to the B فيه ما يسمى Corollary of
+
+599
+01:00:33,320 --> 01:00:40,000
+Format لأن هذا ايش لأي A لأي A مش حاجة عن أي ايش
+
+600
+01:00:40,000 --> 01:00:44,930
+محدد ندى نشوف كيف ايش اللي بقولهالأن بما أنه B'
+
+601
+01:00:45,350 --> 01:00:51,890
+إذا by Wilson's theorem B-1 factorial تطابق السلب
+
+602
+01:00:51,890 --> 01:00:57,730
+واحد مضلومين يا جماعة مضلوا B بدي أحصل على هذه
+
+603
+01:00:57,730 --> 01:01:04,890
+أضرب الجهتين في A فبصير عندي A في B أو B-1
+
+604
+01:01:04,890 --> 01:01:12,740
+factorial في A تطابق ناقص A مضلومين مضلوا Bلكن انا
+
+605
+01:01:12,740 --> 01:01:17,780
+بعرف انه by corollary هذا by Wilson's theory لأن
+
+606
+01:01:17,780 --> 01:01:24,540
+by corollary of Fermat a to the b تطابق ال a
+
+607
+01:01:24,540 --> 01:01:31,420
+modulo b، مظبوط؟ اكيد التنتين مع بعض، التنتين مع
+
+608
+01:01:31,420 --> 01:01:36,140
+بعض بيعطيني اللي هو b minus واحد factorial في ال a
+
+609
+01:01:37,450 --> 01:01:42,670
+بدّل سالب A بضع مين؟ تطابق سالب A to the B لأن A
+
+610
+01:01:42,670 --> 01:01:48,270
+to the B تطابق الـ A Modulo B وهذا ماذا يعني؟ هذا
+
+611
+01:01:48,270 --> 01:01:54,150
+ما يعني Hence الـ B تقسم الـ B minus 1 factorial
+
+612
+01:01:54,150 --> 01:01:59,670
+في الـ A زيد الـ A to the B هذا اللي هو الجزء
+
+613
+01:01:59,670 --> 01:02:05,550
+الأول Similarly بالظبط الجزء الثاني و هتشوف كيف
+
+614
+01:02:05,550 --> 01:02:10,300
+Similarlyالان بدل ما اضرب الجهتين في a اضرب
+
+615
+01:02:10,300 --> 01:02:18,840
+الجهتين في a أُس b فبيحصل عندي a أُس b أو b-1 في a
+
+616
+01:02:18,840 --> 01:02:26,510
+أُس b تطابق ناقص a أُس b modulo a modulo bلكن من
+
+617
+01:02:26,510 --> 01:02:32,190
+فرمات A أُس B تطابق الـ A صح ولا لأ الآن A أُس B
+
+618
+01:02:32,190 --> 01:02:38,410
+تطابق الـ A مضلوا B معايا يا شباب إذا بدي أشيل الـ
+
+619
+01:02:38,410 --> 01:02:42,530
+A أُس B و أحط مكانها من الـ A فبصير اللي فوق B
+
+620
+01:02:42,530 --> 01:02:49,970
+minus 1 factorial A أُس B تطابق مكان الـ A أُس B و
+
+621
+01:02:49,970 --> 01:02:55,890
+أنا إيش بحط الـ A مضلوا Bالان هذا معناته ان بي
+
+622
+01:02:55,890 --> 01:03:01,330
+تقسم بي ماينس واحد فيكتوريا ل A أقص بي زائد مين
+
+623
+01:03:01,330 --> 01:03:07,030
+زائد ايه مالكم ساكتين زائد ايه وكون عندنا حصلنا
+
+624
+01:03:07,030 --> 01:03:12,110
+مين الجزء الثاني من السؤال نيجي الان لسؤال تسعة
+
+625
+01:03:14,360 --> 01:03:20,700
+بقول لي using Wilson's theorem to show that واحد
+
+626
+01:03:20,700 --> 01:03:26,680
+تربية في تلاتة تربية في خمسة تربية في لما أصل عند
+
+627
+01:03:26,680 --> 01:03:34,200
+بي minus اتنين لكل تربية تطابق ناقص واحد قص بي
+
+628
+01:03:34,200 --> 01:03:45,080
+زائد واحد على اتنين modulo اللي هو بي معايااللي هو
+
+629
+01:03:45,080 --> 01:03:52,300
+بي حيث بي is an odd prime بي is an odd a prime
+
+630
+01:03:52,300 --> 01:03:55,480
+approve
+
+631
+01:03:55,480 --> 01:04:01,360
+شوف
+
+632
+01:04:01,360 --> 01:04:09,640
+هذه الملاحظة اللي بنعملها لان عند 2 في 4 في 6 لما
+
+633
+01:04:09,640 --> 01:04:18,810
+أصل لعند اللي هو بي minus 1تطابق الـ B² فبصيرها
+
+634
+01:04:18,810 --> 01:04:23,230
+دقيقة اش انفين بضل اعد اتنين اربعة ستة لما اصل عند
+
+635
+01:04:23,230 --> 01:04:34,450
+الـ B- واحد الان الاتنين الاتنين احنا الـ B- اتنين
+
+636
+01:04:34,450 --> 01:04:39,700
+تطابق اتنين صح؟أو تتطابق ناقص اتنين as if الـ B
+
+637
+01:04:39,700 --> 01:04:44,180
+ناقص ثلاثة أو الـ B minus واحد تتطابق ناقص واحد
+
+638
+01:04:44,180 --> 01:04:46,980
+الـ B minus اتنين تتطابق ناقص اتنين الـ B ناقص
+
+639
+01:04:46,980 --> 01:04:50,600
+ثلاثة تتطابق ناقص ثلاثة الـ B ناقص K in general
+
+640
+01:04:50,600 --> 01:04:56,620
+تتطابق مين ناقص الـ K واضحة هذا مدل المين ومدل الـ
+
+641
+01:04:56,620 --> 01:05:02,300
+B لأن بيضيف هذه بالـ CRB CRB تقسم الـ B إذا هذه
+
+642
+01:05:02,300 --> 01:05:08,670
+التنين هتتطابق المينالـ B ناقص اتنين بس بيبقى عياش
+
+643
+01:05:08,670 --> 01:05:15,890
+بالثاني و بضلي أنزل وهذه بتطابق مين؟ اللي هي ناقص
+
+644
+01:05:15,890 --> 01:05:22,090
+B minus أربعة لما أسأل الأخر واحد الـ B minus واحد
+
+645
+01:05:22,090 --> 01:05:26,050
+الـ B minus K الـ K و K نصارت مين؟ اللي هي B minus
+
+646
+01:05:26,050 --> 01:05:32,430
+واحد فبصير B minus B minus واحد يعني اللي هي تطابق
+
+647
+01:05:32,430 --> 01:05:33,370
+الناقص
+
+648
+01:05:35,590 --> 01:05:39,890
+اللي هو ناقص
+
+649
+01:05:39,890 --> 01:05:47,490
+K تطابق الناقص K اللي هو تطابق مين؟ الناقص واحد P
+
+650
+01:05:47,490 --> 01:05:53,050
+ناقص K اللي هي P ماينس واحد تطابق مين؟ الناقص واحد
+
+651
+01:05:53,050 --> 01:05:58,490
+فاضحة؟ فهذا بيصير مضالة عند مين؟ الناقص واحد اللي
+
+652
+01:05:58,490 --> 01:06:02,150
+جابه ما هتكون مين؟ ناقص ثلاثة و أكتر
+
+653
+01:06:05,910 --> 01:06:08,850
+عارفين ليش ناقص ثلاثة؟ لأنه قبلها دي مباشرة يا
+
+654
+01:06:08,850 --> 01:06:12,330
+شباب مالكم اللي P ناقص ثلاثة و P ناقص ثلاثة الطابق
+
+655
+01:06:12,330 --> 01:06:15,890
+مين؟ ناقص ثلاثة و اللي قبلها P ناقص خمسة الطابق P
+
+656
+01:06:15,890 --> 01:06:20,530
+ناقص خمسة يعني الآن هذي بتصير الطابق عبارة عن ناقص
+
+657
+01:06:20,530 --> 01:06:26,450
+واحد فناقص ثلاثة ناقص خمسة لما أصل ناقص P minus
+
+658
+01:06:26,450 --> 01:06:35,150
+اتنين what's happen؟الآن هذول المحاضر في الواقع
+
+659
+01:06:35,150 --> 01:06:39,950
+هلنين هي عبارة عن شيلك مقصيبك من النواقص عبارة عن
+
+660
+01:06:39,950 --> 01:06:43,390
+الواحد والتنين والتلاتة والاربعة والخمسة والستة
+
+661
+01:06:43,390 --> 01:06:46,190
+وال بي واينس واحد او البي واينس اتنين وبي واينس
+
+662
+01:06:46,190 --> 01:06:50,070
+واحد إذاً عددهم أشمال بي واينس واحد مُص هدولة مُص
+
+663
+01:06:50,070 --> 01:06:54,330
+وهدولة مُص فصار عبارة عن هدولة عددهم اللي هو بي
+
+664
+01:06:54,330 --> 01:06:57,970
+واينس واحد على اتنين هنا كل واحدة فيها ناقص إذاً
+
+665
+01:06:57,970 --> 01:07:01,850
+عبارة عن ناقص واحد قُس بي واينس واحد على مينعلى
+
+666
+01:07:01,850 --> 01:07:05,750
+اتنين مضربة في مين يا شباب في واحد في تلاتة في
+
+667
+01:07:05,750 --> 01:07:14,490
+خمسة في سبعة لما أصل بيه minus اتنين أي سؤال حتى
+
+668
+01:07:14,490 --> 01:07:20,850
+الآن طيب الآن يا شباب اضربولي الجهتين هذه وهذه
+
+669
+01:07:20,850 --> 01:07:25,350
+اضربولي في واحد في تلاتة في خمسة في سبعة في اللي
+
+670
+01:07:25,350 --> 01:07:30,080
+هان فهدولة اضربولي هان في هان فبصير عندىفاهمين؟
+
+671
+01:07:30,080 --> 01:07:34,800
+تضرب الجهتين في مين في هذا المقدار الجهة دي إيش
+
+672
+01:07:34,800 --> 01:07:39,660
+بتصير بتتعبى كامل بتصير عبارة عن واحد في اتنين في
+
+673
+01:07:39,660 --> 01:07:42,400
+تلتة في اربع في خمسة عن بي ماينس واحد يعني بتصير
+
+674
+01:07:42,400 --> 01:07:46,980
+عبارة عن بي ماينس واحد vector إذا ضربت واحد في
+
+675
+01:07:46,980 --> 01:07:52,780
+تلتة في خمسة في بي ماينس اتنينواضربتهم في المقدار
+
+676
+01:07:52,780 --> 01:07:58,980
+هذا 2 في 4 في 6 لما أصل عند بي minus واحد لأن
+
+677
+01:07:58,980 --> 01:08:03,860
+تطابق أو تساوي مساواة حتة ماقص واحد اقص بي minus
+
+678
+01:08:03,860 --> 01:08:10,250
+واحد على 2 فيالمقدار اللي قلنا عنه ضربناها لما
+
+679
+01:08:10,250 --> 01:08:14,670
+نضربهان هذا لما نضربهان بيصير ايش هو هذا عن واحد
+
+680
+01:08:14,670 --> 01:08:18,970
+تربية في تلاتة تربية في خمسة تربية في سبعة تربية
+
+681
+01:08:18,970 --> 01:08:25,450
+لما أصل بيه مانس اتنين لكل تربية مظبوطش يا بابا
+
+682
+01:08:25,450 --> 01:08:30,090
+هذا الآن هو مين في الواقع يا جماعة هذا عبارة عن
+
+683
+01:08:30,090 --> 01:08:35,920
+بيه ناقص واحد factorialصار عند الـ b-1 two
+
+684
+01:08:35,920 --> 01:08:41,340
+factorial هو بساوي ناقص واحد أس بي minus واحد على
+
+685
+01:08:41,340 --> 01:08:48,320
+اتنين في المقدار من واحد خمسة بي ناقص اتنين كلهم
+
+686
+01:08:48,320 --> 01:08:54,640
+تربعة هذا من منصوص theorem هو عبارة عن ناقص واحد
+
+687
+01:08:54,640 --> 01:09:02,900
+إذا صار المقدار هذا بطابق ناقص واحد modulo modulo
+
+688
+01:09:02,900 --> 01:09:10,050
+bودربي هنا في ناقص واحد أس بي ماينس واحد على اتنين
+
+689
+01:09:10,050 --> 01:09:13,990
+و هنا في ناقص واحد أس بي ماينس واحد على اتنين يعني
+
+690
+01:09:13,990 --> 01:09:16,830
+بتضرب الجهتين في هذا النقطة فبصير عندي عبارة عن
+
+691
+01:09:16,830 --> 01:09:21,280
+ناقص واحدنارقص واحد أس بي مانس واحد على اتنين
+
+692
+01:09:21,280 --> 01:09:27,220
+فبصير بي مانس واحد على اتنين زائد واحد تطابق نارقص
+
+693
+01:09:27,220 --> 01:09:31,560
+واحد أس بي مانس واحد على اتنين في اتنين لأنه
+
+694
+01:09:31,560 --> 01:09:37,340
+silent and tail في واحد في تلاتة تربية لما أصل بي
+
+695
+01:09:37,340 --> 01:09:48,140
+مانس اتنين تربية modulo بي هذا مين هوهذا الان هذا
+
+696
+01:09:48,140 --> 01:09:51,640
+اتنين مع اتنين الـ P قُط بي ماينس واحد ايش يا شباب
+
+697
+01:09:51,640 --> 01:09:54,940
+even إذا هذا صار ايش ماله ناقص واحد أس even يعني
+
+698
+01:09:54,940 --> 01:09:59,760
+واحد إذا صار هذا المقدار then اللي هو واحد تربية
+
+699
+01:09:59,760 --> 01:10:04,500
+في تلاتة تربية في بي ماينس اتنين تربية يطابق لإنه
+
+700
+01:10:04,500 --> 01:10:07,820
+صار واحد هذا يطابق هذا المقدار اللي هو ناقص واحد
+
+701
+01:10:07,820 --> 01:10:15,410
+أسB-1 على 2 زائد 1 بيصير عبارة عن B زائد 1 على 2
+
+702
+01:10:15,410 --> 01:10:22,230
+الكل modulo B وهو المطلوب بيجي لسؤال 11 أه اللي
+
+703
+01:10:22,230 --> 01:10:30,550
+شاف برهان اللي هو ال X تربيع زائد 1 وطابق السفر
+
+704
+01:10:30,550 --> 01:10:38,510
+modulo B as a solution if and only if Bاللي هو على
+
+705
+01:10:38,510 --> 01:10:42,830
+صورة 4K زائد واحد اللي هي اللي حكيناها في أول
+
+706
+01:10:42,830 --> 01:10:47,750
+المحاضرة الآن في هذه .. في البرهان بيقولك إيش ال
+
+707
+01:10:47,750 --> 01:10:51,790
+solution للمعادلة .. في البرهان بيقولك إيش ال
+
+708
+01:10:51,790 --> 01:10:56,990
+solution X7 زائد واحد تطابق الصفر modulo B لما B
+
+709
+01:10:56,990 --> 01:11:01,230
+تكون على صورة 4K زائد واحد ال solution كان بالظبط
+
+710
+01:11:01,230 --> 01:11:07,750
+اللي هو عبارة عن B minus 1 factorialعلى او على 2
+
+711
+01:11:07,750 --> 01:11:13,970
+factorial بساوة X هذا اللي هو one solution modulo
+
+712
+01:11:13,970 --> 01:11:19,630
+B هذا اللي هو X تقابل كذا modulo B منين جبت هذا
+
+713
+01:11:19,630 --> 01:11:23,750
+انا من برهان النظرية من برهان النظرية اللي
+
+714
+01:11:23,750 --> 01:11:27,810
+برهننالكم ايه يعني هذا ال solution ل X تقابل 1
+
+715
+01:11:27,810 --> 01:11:31,410
+modulo B انا لما تبقى على سؤال 11 سؤال 11 بيقول لي
+
+716
+01:11:31,410 --> 01:11:35,030
+apply theory الخمسة خمسة to obtain the solution of
+
+717
+01:11:35,030 --> 01:11:42,840
+XX تربية تطابق ناقص واحد مدنه جداشة شباب مدنه تسعة
+
+718
+01:11:42,840 --> 01:11:51,120
+و عشرين مدنه تسعة و عشرين and X كمان واحدة and X
+
+719
+01:11:51,120 --> 01:11:55,840
+تربية تطابق ناقص واحد مدنه سبعة و تلاتين بدنا نحل
+
+720
+01:11:55,840 --> 01:12:00,180
+السؤالين اللي أمامنا أو اللي هو نعمل applications
+
+721
+01:12:00,180 --> 01:12:07,650
+عليهم السؤال الأول هذا solutionمن البرهان النظرية
+
+722
+01:12:07,650 --> 01:12:15,510
+بما أن الـ 29 تطابق الواحد modulo 4 then one
+
+723
+01:12:15,510 --> 01:12:25,230
+solution is Xبتساوي الـ 29 ناقص 1 اللي هو 28 على 2
+
+724
+01:12:25,230 --> 01:12:30,670
+factorial اللي هو عبارة عن جداش 14 factorial 14
+
+725
+01:12:30,670 --> 01:12:33,770
+factorial انا حسبها لو حسبناها اللي جيهاش بتساوي
+
+726
+01:12:33,770 --> 01:12:41,150
+تتعدق12 mod 29 هاي ال solution الأول جملة في
+
+727
+01:12:41,150 --> 01:12:45,010
+البرنام أيضا ال solutions يحدث in pairs واحد من جب
+
+728
+01:12:45,010 --> 01:12:49,010
+و واحد سالبي التاني و إضافة عن X بالطابق نقص 12
+
+729
+01:12:49,010 --> 01:12:55,290
+mod 29 أو بمعنى آخر 17 mod 29 هاي ال solutions
+
+730
+01:12:55,290 --> 01:12:59,460
+اللي همSimilarly لأكثر بيض طبق نقص واحد مدرو سبعة
+
+731
+01:12:59,460 --> 01:13:02,740
+و تلاتين سبعة و تلاتين بصير سبعة و تلاتين نقص واحد
+
+732
+01:13:02,740 --> 01:13:05,100
+على اتنين اللي هي ستة و تلاتين على اتنين اللي هي
+
+733
+01:13:05,100 --> 01:13:09,220
+تمانتاش فيكتوريال مدرو سبعة و تلاتين طيب نيجي
+
+734
+01:13:09,220 --> 01:13:12,740
+للسؤال الأخير السؤال الأتناش نشوف السؤال الأتناش
+
+735
+01:13:12,740 --> 01:13:15,400
+ايش اللي بيقوله السؤال الأتناش
+
+736
+01:13:18,990 --> 01:13:22,410
+أحنا قلنا اكسر بيح زائد واحد تطابق صفر مدنو بيهازا
+
+737
+01:13:22,410 --> 01:13:26,850
+solution if and only if بيهازا solution if and
+
+738
+01:13:26,850 --> 01:13:28,750
+only if بيهازا solution if and only if بيهازا
+
+739
+01:13:28,750 --> 01:13:28,810
+solution if and only if بيهازا solution if and
+
+740
+01:13:28,810 --> 01:13:29,270
+only if بيهازا solution if and only if بيهازا
+
+741
+01:13:29,270 --> 01:13:31,110
+solution if and only if بيهازا solution if and
+
+742
+01:13:31,110 --> 01:13:32,910
+only if بيهازا solution if and only if بيهازا
+
+743
+01:13:32,910 --> 01:13:33,810
+solution if and only if بيهازا solution if and
+
+744
+01:13:33,810 --> 01:13:34,190
+only if بيهازا solution if and only if بيهازا
+
+745
+01:13:34,190 --> 01:13:36,130
+solution if and only if بيهازا solution if and
+
+746
+01:13:36,130 --> 01:13:41,370
+only if بيهازا solution if and only if بيهازا
+
+747
+01:13:41,370 --> 01:13:45,870
+solution if and only if بيهازا solution if and
+
+748
+01:13:45,870 --> 01:13:46,610
+only if بيهازا solution if and only if بيهازا
+
+749
+01:13:46,610 --> 01:13:49,060
+solution if and only if بيهازاB بيساوي 4K زائد
+
+750
+01:13:49,060 --> 01:13:58,620
+تلاتة is prime وA تربيع زائد B تربيع تطابق السفر
+
+751
+01:13:58,620 --> 01:14:03,040
+modulo B then
+
+752
+01:14:03,040 --> 01:14:12,240
+A تطابق الـ B تطابق السفر modulo Bالبروف ايه
+
+753
+01:14:12,240 --> 01:14:17,020
+الاشهدار شوف ايش اللي بتسوي اذكركم في المعلومة ال
+
+754
+01:14:17,020 --> 01:14:20,920
+X تربية زائد واحد ل solution if and only if ال B
+
+755
+01:14:20,920 --> 01:14:24,800
+على سوري 4K زائد واحد يعني اي B مش على سوري 4K
+
+756
+01:14:24,800 --> 01:14:27,400
+زايد واحد ال X تربية تتطبق ناقص واحد فيش ل
+
+757
+01:14:27,400 --> 01:14:32,940
+solution طيب كان هذا اللي .. هذا هتوصلني ل .. ل
+
+758
+01:14:32,940 --> 01:14:39,400
+اللي هو كيف احصل ال 12لأن سؤال 12 بيقول لي إذا
+
+759
+01:14:39,400 --> 01:14:43,500
+كانت B بتسوي 4K زي 3 والـ A تربيع زي B تربيع
+
+760
+01:14:43,500 --> 01:14:47,280
+بالطابق الصفر مضلوا B إثبتني إن الـ A و الـ B
+
+761
+01:14:47,280 --> 01:14:52,260
+متطابقة بطابق الصفر مضلوا مين مضلوا B بدي أفترض لك
+
+762
+01:14:52,260 --> 01:14:56,880
+عكس هذا و أسألك ال contradiction بقول لك suppose
+
+763
+01:14:56,880 --> 01:14:59,560
+that
+
+764
+01:15:00,710 --> 01:15:08,030
+A تطابق الـ B تطابق السفر modulo B does not hold
+
+765
+01:15:08,030 --> 01:15:19,130
+سي A لا تطابق الـ 0 modulo Bأو P لا تطابق الـ Zero
+
+766
+01:15:19,130 --> 01:15:24,290
+مدلوا A ماشي الحال أي ننوم بنفعل نفترض أن الـ A لا
+
+767
+01:15:24,290 --> 01:15:27,590
+تطابق الـ Zero مدلوا B أو الـ B لا تطابق الـ Zero
+
+768
+01:15:27,590 --> 01:15:31,670
+مدلوا B without loss of generality suppose that A
+
+769
+01:15:31,670 --> 01:15:35,090
+لا تطابق الـ Zero مدلوا B أو إنك تفضل تقول suppose
+
+770
+01:15:35,090 --> 01:15:37,810
+that أن A لا تطابق الـ Zero مدلوا B تسبب
+
+771
+01:15:37,810 --> 01:15:40,470
+Contradiction وبعدين تقول Similarly وفعلا
+
+772
+01:15:40,470 --> 01:15:44,390
+Similarly B لا تطابق الـ Zero مدلوا B تسبب
+
+773
+01:15:44,390 --> 01:15:49,670
+Contradictionنشوف ايش اللي بقوله هذا الان انا
+
+774
+01:15:49,670 --> 01:16:00,350
+مفترض ان ال a لا تطابق السفر modulo b الان معناته
+
+775
+01:16:00,350 --> 01:16:04,350
+ان ال a لا تطابق السفر modulo b معناته ال b لا
+
+776
+01:16:04,350 --> 01:16:10,420
+تقسم ال aيعني العامل المشترك الأعلى بين الـP والـA
+
+777
+01:16:10,420 --> 01:16:16,380
+بساوء واحد إذا بناء عليها الـlinear congruences Ax
+
+778
+01:16:16,380 --> 01:16:21,660
+تطابق الواحد model بيه بنظرية سابقة اللي هي نظرية
+
+779
+01:16:21,660 --> 01:16:28,720
+بالظبط نظرية سبعة أربعة سبعة بواسطة أربعة سبعة هذه
+
+780
+01:16:28,720 --> 01:16:29,880
+إليها solution
+
+781
+01:16:32,650 --> 01:16:36,050
+بما أن الـ A والـ B العامل المشترك اللي على بينهم
+
+782
+01:16:36,050 --> 01:16:41,690
+واحد أو الـ B لا تقسم الـ A كبران B إذا الـ A X
+
+783
+01:16:41,690 --> 01:16:46,910
+تطابق الواحد مدلو B has a solution say this
+
+784
+01:16:46,910 --> 01:16:54,870
+solution is X بتساوي C then إذا كان في solution
+
+785
+01:16:54,870 --> 01:16:59,930
+وسميناها C إذا صار عندي A في C تطابق الواحد مدلو
+
+786
+01:17:00,580 --> 01:17:06,540
+مدلوا مين؟ مدلوا بيه الان هو معطيني ان اي تربيع زي
+
+787
+01:17:06,540 --> 01:17:11,040
+بيه تربيه تتعبق السفر مدلوا اياش مدلوا بيه اذا بدي
+
+788
+01:17:11,040 --> 01:17:16,700
+سيري عندى و ضربلي الجهتينقبل ان اضغط على الجهاز
+
+789
+01:17:16,700 --> 01:17:22,540
+الاساسي A تربيع و C تربيع تطابق الواحد مدلو مين
+
+790
+01:17:22,540 --> 01:17:26,340
+مدلو بيه فاهمين ايش ساوي ربعت ايش الجهة التانية و
+
+791
+01:17:26,340 --> 01:17:32,200
+رفعتها القوة ايش اتنين الان بما ان ال A تربيع زاد
+
+792
+01:17:32,200 --> 01:17:35,910
+بيه تربيع الطابق الصفر مدلو بيهوالـ A تربيع C
+
+793
+01:17:35,910 --> 01:17:39,330
+تربيع تطابق الواحد اضرب الجهتين هنا في الـ C تربيع
+
+794
+01:17:39,330 --> 01:17:43,950
+فبصير عندي A تربيع C تربيع زائد B تربيع C تربيع
+
+795
+01:17:43,950 --> 01:17:50,830
+تطابق السفر Modulo مين Modulo B معايا يا شباب طيب
+
+796
+01:17:50,830 --> 01:17:53,490
+الـ A تربيع زي تربيع حداشر بالنسبالي على الـ B
+
+797
+01:17:53,490 --> 01:17:58,730
+واحد هنا اتبتدع فوق اذا صار عندي B تربيع C تربيع
+
+798
+01:17:59,930 --> 01:18:06,870
+زائد واحد تطابق السفر Modulo ايش Modulo B إذا صار
+
+799
+01:18:06,870 --> 01:18:15,930
+عند ال B C لكل تربية تطابق السالب واحد Modulo B من
+
+800
+01:18:15,930 --> 01:18:19,890
+هنا ما قالت الواحد أدها الثانية إيش هذه بتاعي
+
+801
+01:18:19,890 --> 01:18:28,940
+أصلا؟ هذه معناته إنه thisيعني ان X تربيها وتعب
+
+802
+01:18:28,940 --> 01:18:38,260
+ترنافض واحد Modulo بيه مفهوم X بيساوي بي سي which
+
+803
+01:18:38,260 --> 01:18:50,380
+is impossible ليش طيب؟ Because it contradicts
+
+804
+01:18:51,360 --> 01:18:59,280
+اللي هو أقرر Theorem أن الـ B على صورة 4K زائد 3
+
+805
+01:18:59,280 --> 01:19:05,140
+لأن هذه ال solution بس متى لما نكون على صورة B
+
+806
+01:19:05,140 --> 01:19:09,600
+بيبسوة 7K زائد 1 بينما ماعطين الـ B بيبسوة 4K زائد
+
+807
+01:19:09,600 --> 01:19:14,040
+3 إذن وصلتني هنا لـ Contradiction أنه لجينا حلل
+
+808
+01:19:14,040 --> 01:19:17,080
+الـ X التي تتطبق نقص واحد بدل B والـ B اللي هو على
+
+809
+01:19:17,080 --> 01:19:24,120
+صورة 4K زائد 3 فهذا مستحيل إذن الفرضية الأولىأو
+
+810
+01:19:24,120 --> 01:19:28,500
+بمعنى آخر لازم ال a تطابق السفر mod b وsimilarly
+
+811
+01:19:28,500 --> 01:19:32,020
+ال b تطابق ال zero mod b إذا صار عندى لما يكون هذا
+
+812
+01:19:32,020 --> 01:19:38,780
+صحيح لازم نحصل a تطابق ال b تطابق السفر mod b وهيك
+
+813
+01:19:38,780 --> 01:19:43,640
+نكون خلصنا اللى هو مناقشة اللى هو Wilson's theorem
+
+814
+01:19:43,640 --> 01:19:46,040
+واللي هو Fermat's theorem
+
+815
+01:19:49,030 --> 01:19:51,450
+والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/tX1wPJj5Rh0.srt b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/tX1wPJj5Rh0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f637427fbfec6cbe82f44aeb65eb2c6e04258404
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/tX1wPJj5Rh0.srt
@@ -0,0 +1,1815 @@
+1
+00:00:19,440 --> 00:00:26,980
+بسم الله الرحمن الرحيم المحاضرة اليوم هي عبارة عن
+
+2
+00:00:26,980 --> 00:00:32,300
+الـ Brines and Their Distribution اللي هو الشطر 
+
+3
+00:00:32,300 --> 00:00:37,260
+الثالث في مساق نظرية الأعداد لقسم الرياضيات
+
+4
+00:00:37,260 --> 00:00:44,140
+بالجامعة الإسلامية الـ section الأول هنتحدث عن The
+
+5
+00:00:44,140 --> 00:00:47,040
+Fundamental Theorem of Arithmetic أو النظرية
+
+6
+00:00:47,040 --> 00:00:52,600
+الأساسية للحساب قبل الحديث عن النظرية الأساسية
+
+7
+00:00:52,600 --> 00:00:57,700
+للحساب لابد أن هناك أن نعرف  ماذا بدنا نعرف الآن شو
+
+8
+00:00:57,700 --> 00:01:02,370
+نقصد بالـ prime number أو العدد الأولي حديثنا
+
+9
+00:01:02,370 --> 00:01:10,910
+هيكون عن الأعداد الموجبة والأعداد السالبة بنفس
+
+10
+00:01:10,910 --> 00:01:14,930
+الأسلوب زي بالظبط ما حكينا عن الـ Common divisors
+
+11
+00:01:14,930 --> 00:01:18,750
+الموجبة وتركنا الحديث عن السالبة لأن اللي بيدرس 
+
+12
+00:01:18,750 --> 00:01:26,070
+الموجبة بتغني عن من؟ عن السالبة إلى حد بعيد فهنعرف
+
+13
+00:01:26,070 --> 00:01:33,240
+اللي هو أن B أكبر من 1 العدد بي أكبر من واحد الـ 
+
+14
+00:01:33,240 --> 00:01:39,160
+integer بنسميه prime أو عدد أولي إذا كان عاملين بس
+
+15
+00:01:39,160 --> 00:01:46,960
+مختلفين العدد نفسه و وإيش والواحد إذا بي is called
+
+16
+00:01:46,960 --> 00:01:52,600
+a prime number if its only divisors are one and بي
+
+17
+00:01:52,600 --> 00:01:58,710
+ماشي العالم العدد اللي بيكونش أولي بنسميه Composite 
+
+18
+00:01:58,710 --> 00:02:08,370
+العدد
+
+19
+00:02:08,370 --> 00:02:12,290
+اللي بنسميه Composite اللي هو اللي مش prime number
+
+20
+00:02:12,790 --> 00:02:17,270
+إلى أن أمثلة الـ 2 أكيد عدد أول زي ما أنتم عارفين
+
+21
+00:02:17,270 --> 00:02:21,090
+لأنه قواسمه اللي هو واحد واتنين التلاتة قواسمه بس
+
+22
+00:02:21,090 --> 00:02:25,070
+اللي هو واحد وتلاتة الخمسة السبعة إلى آخره كلنا دول
+
+23
+00:02:25,070 --> 00:02:30,150
+أعداد أولية بينما على سبيل المثال زي ما أنتم
+
+24
+00:02:30,150 --> 00:02:36,230
+عارفين الـ 6 والـ 9 والـ 15 كلها أعداد غير أولية اللي
+
+25
+00:02:36,230 --> 00:02:42,590
+هي بنسميها Composite Numbers طيب لأنه فيه divisors
+
+26
+00:02:42,590 --> 00:02:49,830
+لها غير نفسها و غير الواحد طيب لإن نطلع لفوق نيجي
+
+27
+00:02:49,830 --> 00:02:57,210
+لأن لأول لأول خاصية لأول خاصية اللي هي عبر نظرية
+
+28
+00:02:57,210 --> 00:03:03,910
+ثلاثة واحد إذا كان B is prime and B بيقسم الـ A B
+
+29
+00:03:03,910 --> 00:03:09,330
+then B بيقسم الـ A or B بيقسم الـ B B prime يعني B 
+
+30
+00:03:09,330 --> 00:03:15,090
+كتلة واحدة لأن هذه الكتلة أو هذا الرقم بيقسم الـ A
+
+31
+00:03:15,090 --> 00:03:19,750
+في B إذاً هذه الكتلة مستحيلة تكون موزعة جزء من هنا
+
+32
+00:03:19,750 --> 00:03:26,430
+وجزء من هنا إذاً يا بتقسم A يا بتقسم B واضح؟ يعني
+
+33
+00:03:26,430 --> 00:03:32,770
+ممكن تقسم التنتين لأنها تكون B عند معناه أن تقسم
+
+34
+00:03:32,770 --> 00:03:36,830
+التنتين في نفس الوقت لأ إحنا بنحكي عن B بتقسم A في
+
+35
+00:03:36,830 --> 00:03:43,850
+B تؤدي إلى يا B بتقسم A يا B بتقسم B ومدام Or إذا 
+
+36
+00:03:43,850 --> 00:03:49,910
+إحنا Inclusive Or فبتكون صحيحة إذا كانت برضه
+
+37
+00:03:49,910 --> 00:03:53,970
+بتقسم التنتين يعني مثلا على سبيل المثال عند
+
+38
+00:03:53,970 --> 00:04:02,700
+التنتين بتقسم الأربعة في الستة على سبيل المثال هذه
+
+39
+00:04:02,700 --> 00:04:08,060
+الاثنين برايه إذا لازم يا بتقسم الأربعة يا بتقسم إيش
+
+40
+00:04:08,060 --> 00:04:12,760
+فهذه الحالة قسمت الاثنين يعني مثلا اثنين مثال آخر
+
+41
+00:04:12,760 --> 00:04:18,160
+ثلاثة في اثنين هذا بيعطيني اثنين بيقسم الثلاثة or
+
+42
+00:04:18,160 --> 00:04:22,840
+اثنين بتقسم مين اثنين هي قسمت فعليا مين وضحت
+
+43
+00:04:22,840 --> 00:04:26,720
+الجملة دي لها Orange ما لا صحيحة إذا بتقسم واحد
+
+44
+00:04:26,720 --> 00:04:34,840
+منهم أو اثنين سوي لكن لكن الآن اللي بتحكيه 
+
+45
+00:04:34,840 --> 00:04:40,960
+النظرية إنه لازم تقسم واحد منه على الأقل هذا
+
+46
+00:04:40,960 --> 00:04:45,180
+الكلام ليس شرطًا أن يكون صحيحًا في حالة الـPH
+
+47
+00:04:45,180 --> 00:04:50,700
+مالها العدد هذا ليس الـ prime يعني لو كان الـ C 
+
+48
+00:04:50,700 --> 00:04:56,840
+بيقسم الـ A في الـ B و هذا ليس الـ prime ليس شرطًا
+
+49
+00:04:56,840 --> 00:05:00,920
+أن الـ C تقسم الـ A أو الـ B بيقسم الـ C بيقسم الـ
+
+50
+00:05:00,920 --> 00:05:04,880
+B بعطيك مثال هي عندك على سبيل المثال الـ trivial
+
+51
+00:05:04,880 --> 00:05:09,800
+case ستة بتقسم اثنين في مين في ثلاثة
+
+52
+00:05:13,270 --> 00:05:19,450
+6 لا تقسم الـ 2 وفي نفس الوقت 6 لا تقسم الـ 3 لا هي
+
+53
+00:05:19,450 --> 00:05:23,330
+عامل مع عامل الـ 2 ولا عامل مع عامل الـ 3 إذا لما
+
+54
+00:05:23,330 --> 00:05:27,410
+يكون هذا مش الـ Prime ليس شرطًا النظرية هي الشمال
+
+55
+00:05:27,410 --> 00:05:28,890
+هي تكون صحيحة
+
+56
+00:05:41,190 --> 00:05:46,150
+عشان تنفي نظرية بكفي أنك تجيب counterexample إيش
+
+57
+00:05:46,150 --> 00:05:52,890
+واحد فهذه مش حالة خاصة هذا counterexample على أن
+
+58
+00:05:52,890 --> 00:05:57,390
+النظرية أشمالها ليست صحيحة فيش غير أمثلة؟ لا في
+
+59
+00:05:57,390 --> 00:06:03,330
+غير أمثلة بنلاقي أمثلة غير المثال إنه عندك الـ C
+
+60
+00:06:03,330 --> 00:06:07,270
+بتقسم الـ AB عندك
+
+61
+00:06:07,270 --> 00:06:09,030
+6
+
+62
+00:06:10,610 --> 00:06:16,330
+خلّينا نقول بتقسم اللي هو أربعة في ثلاثة مظبوط
+
+63
+00:06:16,330 --> 00:06:21,990
+كثير بتلاقي خلّيها ثمانية خلّيها ستة عشان اللي 
+
+64
+00:06:21,990 --> 00:06:25,810
+بدّك إياها بس شيل منها إياها ثلاثة ماتخليش ثلاثة
+
+65
+00:06:25,810 --> 00:06:31,610
+فاهم عليها وهذه خلّيها خمسة عشر كل إن أنفلة على إنه
+
+66
+00:06:31,610 --> 00:06:37,970
+ليس شرطا إنه الستة بتقسم الثمانية and
+
+67
+00:06:42,890 --> 00:06:50,150
+6 لا تقسم الـ 15 معايا
+
+68
+00:06:50,150 --> 00:06:56,470
+لأن عند 6 لا تقسم الـ 15 بط 6 لا تقسم الـ 8 أن 6 لا 
+
+69
+00:06:56,470 --> 00:07:01,890
+تقسم الـ 15 امتلاك كثير طيب صلى الله عليه الصلاة
+
+70
+00:07:01,890 --> 00:07:06,050
+والسلام بدنا ميجي نبرهن أن لو قيلت بي برايم بي
+
+71
+00:07:06,050 --> 00:07:09,890
+بتقسم الـ a بي معناه بي بتقسم الـ a أو بي بتقسم الـ
+
+72
+00:07:09,890 --> 00:07:10,070
+b
+
+73
+00:07:18,230 --> 00:07:24,230
+ب تجسم ال a في b بيعطيني ب تجسم ال a بيعطيني ب 
+
+74
+00:07:24,230 --> 00:07:30,070
+تجسم ال a بيعطيني ب تجسم ال b بيعطيني بيعطيني ب
+
+75
+00:07:30,070 --> 00:07:33,090
+تجسم ال a بيعطيني بيعطيني بيعطيني بيعطيني بيعطيني
+
+76
+00:07:33,090 --> 00:07:33,690
+بيعطيني بيعطيني بيعطيني بيعطيني بيعطيني بيعطيني
+
+77
+00:07:33,690 --> 00:07:36,770
+بيعطيني بيعطيني بيعطيني
+
+78
+00:07:36,770 --> 00:07:37,090
+بيع
+
+79
+00:07:40,770 --> 00:07:47,250
+بتقسم الـ A في B و B لا تقسم مين يعني بدي أفترض أن
+
+80
+00:07:47,250 --> 00:07:51,250
+المعطيات موجودة و بدي أفترض أن بي لا تقسم ال A و
+
+81
+00:07:51,250 --> 00:07:57,490
+أثبت لك أنه لازم تقسم مين ال B طيب مدام بي لا تقسم
+
+82
+00:07:57,490 --> 00:08:03,450
+ال A وعوامل الـ B هي الواحد يا الـ B وB مش من عوامل
+
+83
+00:08:03,450 --> 00:08:07,470
+الـ A إذاً بس العامل المشترك بين الـ A و الـ A هو
+
+84
+00:08:07,470 --> 00:08:11,730
+مين؟ الواحد إذاً صار عند them the greatest common
+
+85
+00:08:11,730 --> 00:08:16,810
+divisor بين الـ B و الـ A بساوي واحد وأخذنا نظرية
+
+86
+00:08:16,810 --> 00:08:21,290
+قبل بهيك إنه لو كان العامل المشترك الأعلى بين الـ
+
+87
+00:08:21,290 --> 00:08:26,150
+B و الـ A بساوي واحد إذاً الـ B بتقسم مين؟ الـ B
+
+88
+00:08:26,150 --> 00:08:35,920
+إذاً then B بتقسم الـ B بنظرية سابقة وهو المطلوب أي
+
+89
+00:08:35,920 --> 00:08:48,220
+سؤال أي استفسار طيب اطلع للفور عندي
+
+90
+00:08:48,220 --> 00:08:54,940
+if B is a prime and B بتقسم ال A1 في ال A2 في ال
+
+91
+00:08:54,940 --> 00:09:00,830
+AN إذا الـ B بتقسم الـ A كـ for some K ك بين الواحد
+
+92
+00:09:00,830 --> 00:09:09,390
+وبين الان هذه هي my induction معايا عندي النظرية 
+
+93
+00:09:09,390 --> 00:09:14,830
+بالظبط اللي بتقوله أو الـ corollary بتقول ما يليه
+
+94
+00:09:14,830 --> 00:09:20,870
+إذا كان عندي B prime B
+
+95
+00:09:20,870 --> 00:09:24,950
+is a prime وكان 
+
+96
+00:09:24,950 --> 00:09:35,860
+B بتقسم الـ A1 في الـ A2 لعند الـ AN هذا بيؤدي إلى
+
+97
+00:09:35,860 --> 00:09:44,400
+B بيقسم الـ AK for some K أكبر ويساوي 1 أصغر
+
+98
+00:09:44,400 --> 00:09:50,460
+ويساوي 100 أصغر ويساوي N الآن الـ Value Induction 
+
+99
+00:09:50,460 --> 00:09:54,880
+وانتم عارفين بنفترض .. بنثبت أولًا شيء صحيحة
+
+100
+00:09:54,880 --> 00:09:58,040
+الجملة لحد طبعا في حالة الواحد هنا trivial case
+
+101
+00:09:58,040 --> 00:10:01,300
+أنه B بتقسم الـ A واحد تؤدي إلى B بتقسم الـ A واحد
+
+102
+00:10:01,300 --> 00:10:06,140
+trivial case حتى الاثنين لو كانت B تقسم A واحد في
+
+103
+00:10:06,140 --> 00:10:12,380
+A اثنين اللي هو هي النظرية اللي قبل بشوية إذا اللي 
+
+104
+00:10:12,380 --> 00:10:17,950
+.. اللي ضال عليها أن أثبت اللي هو أحد أمرين اللي هو
+
+105
+00:10:17,950 --> 00:10:24,450
+induction hypothesis إما بنفرض إنه صحيحة عند M 
+
+106
+00:10:24,450 --> 00:10:31,830
+بتساوي K وبنثبت ل K زائد واحد أو بنفترض صحتها لكل
+
+107
+00:10:31,830 --> 00:10:37,850
+أن أصغر أو يساوي K و بنثبت صحتها عند K زائد واحد
+
+108
+00:10:37,850 --> 00:10:44,030
+اللي هو الاثنين اللي هو الأسلوبين في الـ induction 
+
+109
+00:10:44,030 --> 00:10:50,190
+صحيحات وبنبرهنين اللي هو بطريقة الـ induction واضح
+
+110
+00:10:51,310 --> 00:10:55,570
+الآن ننجنا نظريتنا زي ما قلنا في حالة الان بيساوي
+
+111
+00:10:55,570 --> 00:10:58,730
+واحد اللي هو الـ conclusion اللي هي يا شي the
+
+112
+00:10:58,730 --> 00:11:01,970
+trivial الآن في حالة الان اثنين اللي هي مين 
+
+113
+00:11:01,970 --> 00:11:07,670
+النظرية اللي عندنا الآن إذا بدي أفترض الآن صحة 
+
+114
+00:11:07,670 --> 00:11:12,050
+النظرية بدي أفترض أن بي بتقسم a واحد اثنين عند مين
+
+115
+00:11:12,050 --> 00:11:22,090
+عند a and معايا اه إذا الآن بدي أثبت صحتها عند الـ 
+
+116
+00:11:22,090 --> 00:11:28,910
+N N زائد واحد أو أن أثبت أفرض صحتها عند N ناقص
+
+117
+00:11:28,910 --> 00:11:33,150
+واحد أو أقل من الـ N و أثبت لك صحتها عند الـ N
+
+118
+00:11:33,150 --> 00:11:37,010
+فهو الـ N اللي ماخذه بيثبت إن لو كانت B بيكسب أي 
+
+119
+00:11:37,010 --> 00:11:42,190
+واحد أي اثنين عند A N ويثبت إن B بتقسم واحدة منهم
+
+120
+00:11:42,190 --> 00:11:48,030
+يعني بيثبت صحتها عند مين؟ عند الـ N عند مين؟ عند
+
+121
+00:11:48,030 --> 00:11:52,030
+الـ N عندك B بتقسم .. وفرض .. فرض صحتها لمين؟
+
+122
+00:11:52,030 --> 00:11:58,310
+لأجل من N يعني من N ناقص واحد ونازل فرض صحة اللي
+
+123
+00:11:58,310 --> 00:12:05,010
+هو النظرية لأن B بتقسم من هذولا إذا عند هذول بتقسم 
+
+124
+00:12:05,010 --> 00:12:11,490
+إنه مجموعتين A واحد لعند A N ناقص واحد في A N 
+
+125
+00:12:11,490 --> 00:12:17,590
+مظبوط؟ الآن هدول و كم صار حاصل غير رقمين بيقسم
+
+126
+00:12:17,590 --> 00:12:21,590
+الرقم الأول في الرقم الثاني إذا من النظرية اللي
+
+127
+00:12:21,590 --> 00:12:25,630
+قبل بشوية بيقسم واحد منهم إذا كانت بيه تقسمه
+
+128
+00:12:25,630 --> 00:12:31,050
+نهيان بكنا خلصنا إذا كانت بيه تقسمه هذا بنستخدم الـ 
+
+129
+00:12:31,050 --> 00:12:34,670
+induction hypothesis اللي فرض ما صحة النظرية عند
+
+130
+00:12:34,670 --> 00:12:39,050
+أداء المنقم بإننا نستنتج إن بيه بتقسم نين؟ واحد من
+
+131
+00:12:39,050 --> 00:12:43,080
+هذول في كل الأحوال الجانبية تقسمين لوا واحد منها
+
+132
+00:12:43,080 --> 00:12:48,260
+الأقل كمان مرة الآن بدي أفترض صحة النظرية 
+
+133
+00:12:50,750 --> 00:12:56,490
+صحيحة النظرية لأ لأ لأ a واحد لعند a ان ناقص واحد
+
+134
+00:12:56,490 --> 00:12:59,730
+ده الاشي اللي اجال من مين من ان و برج الله صحتها 
+
+135
+00:12:59,730 --> 00:13:04,190
+لعند مين لعند a يعني يعني بدي أثبت لك أن هذا يؤدي
+
+136
+00:13:04,190 --> 00:13:10,890
+إلى بي بتقسم a ك for some k أكبر يساوي واحد و أصغر
+
+137
+00:13:10,890 --> 00:13:19,650
+يساوي مين n الآن هذا إيش بتسوي فيه مظبوط الآن بي
+
+138
+00:13:19,650 --> 00:13:25,990
+بتقسم a واحد لعند a ناقص واحد وفي مين؟ فيه يعني
+
+139
+00:13:25,990 --> 00:13:30,530
+إذا من النظرية اللي جابلتي شوية هيكون بي بتقسم هذه 
+
+140
+00:13:30,530 --> 00:13:35,510
+و بي بتقسم هذه إذا قسمت هذه خلصنا إذا قسمت هذه 
+
+141
+00:13:35,510 --> 00:13:40,950
+معناه تصارت بي بتقسم الـ a واحد لعند الـ a ناقص واحد لأن
+
+142
+00:13:40,950 --> 00:13:45,200
+هذه أجالي من n وأنا مفترض صحيتها بأجالي من n إذا 
+
+143
+00:13:45,200 --> 00:13:51,720
+أكيد بيبتكسب union واحدة من هنا إذا صارت بي بتكسب 
+
+144
+00:13:51,720 --> 00:13:57,440
+الـ AK for some K بين واحد و بين N ناقص واحد اللي هي K
+
+145
+00:13:57,440 --> 00:14:05,760
+بين N أو بين الواحد بين الواحد و بين N ناقص واحد
+
+146
+00:14:05,760 --> 00:14:09,160
+أكيد موجودة بين الواحد و الـ N وحالة الـ N لحالة
+
+147
+00:14:09,160 --> 00:14:12,960
+أخدناها كانت هذه لو طلعت هي أي سؤال
+
+148
+00:14:17,020 --> 00:14:25,560
+أي سؤال؟ طيب اطلع للبعد نيجي ناخد Corollary لنظرية
+
+149
+00:14:25,560 --> 00:14:30,780
+الـ
+
+150
+00:14:30,780 --> 00:14:41,880
+Corollary هي كما يلي لو الآن عندي الـ B والـ Q1 والـ
+
+151
+00:14:41,880 --> 00:14:52,400
+الـ Q2 والـ QN كلها كتلة واحدة كتلة
+
+152
+00:14:52,400 --> 00:14:55,980
+واحدة كتلة واحدة كتلة واحدة كتلة واحدة كتلة واحدة
+
+153
+00:14:55,980 --> 00:14:57,280
+كتلة واحدة كتلة واحدة كتلة واحدة كتلة واحدة كتلة
+
+154
+00:14:57,280 --> 00:14:57,580
+واحدة كتلة واحدة كتلة واحدة كتلة واحدة كتلة واحدة
+
+155
+00:14:57,580 --> 00:14:58,620
+واحدة كترة واحدة كترة واحدة كترة واحدة كترة واحدة
+
+156
+00:14:58,620 --> 00:15:01,620
+كترة واحدة كترة واحدة كترة واحدة كترة واحدة كترة
+
+157
+00:15:01,620 --> 00:15:04,820
+واحدة كترة واحدة كترة واحدة كترة واحدة كترة واحدة
+
+158
+00:15:04,820 --> 00:15:09,490
+كترة واحدة كترة واحدة كترة واحدة كترة واحدة الـ B
+
+159
+00:15:09,490 --> 00:15:14,990
+هذي منين؟ واحدة منهم لن تتجزى لأن الـ B لا تتجزى
+
+160
+00:15:14,990 --> 00:15:18,030
+لكي تقول لي جيزوفي هتف الـ Q واحد وجيزوفي الـ Q
+
+161
+00:15:18,030 --> 00:15:23,850
+اتنين لأ الـ B هتكون واحدة من هذول اللي عندي واضح
+
+162
+00:15:25,760 --> 00:15:31,040
+if b و q1 اللي عندك un are all primes and b
+
+163
+00:15:31,040 --> 00:15:36,540
+divides q1, q2, qn then b بيساوي qk for some k بين
+
+164
+00:15:36,540 --> 00:15:40,800
+الواحد و بين مين و بين الان خلّيني نشوف كيف نشوف
+
+165
+00:15:40,800 --> 00:15:46,260
+كيف انبرهنها كيف
+
+166
+00:15:46,260 --> 00:15:50,120
+انبرهن الـ corollary اللي عندي
+
+167
+00:15:53,350 --> 00:16:01,490
+كتلة واحدة بتجسم Q واحد لعند Q and و هذولا كل
+
+168
+00:16:01,490 --> 00:16:06,850
+واحدة فيهم كتلة واحدة إذا B هتجسم إيش؟ B هتكون
+
+169
+00:16:06,850 --> 00:16:11,250
+واحدة منهم معايا؟ الآن شوفوا صلي على النبي عليه
+
+170
+00:16:11,250 --> 00:16:20,790
+الصلاة والسلام هذا بيعطيني بيساوي QK for some K
+
+171
+00:16:20,790 --> 00:16:29,280
+بين الواحد و بين الان الآن since الـ B بتقسم Q واحد
+
+172
+00:16:29,280 --> 00:16:36,840
+لعندي Q and then by theorem اللي قبل بشوية أو by
+
+173
+00:16:36,840 --> 00:16:40,780
+corollary حتى الـ
+
+174
+00:16:40,780 --> 00:16:46,040
+B هتقسم QK for some K
+
+175
+00:16:50,190 --> 00:16:58,310
+الآن بي أحد عوامل البرايم Q كي بي مش الواحد لأنه
+
+176
+00:16:58,310 --> 00:17:04,150
+برايم إذا إذا أكيد ال بي ككتلة واحدة هو ال بي
+
+177
+00:17:04,150 --> 00:17:08,390
+بيجسم من عامل من عوامل الـ Q طب الـ Q أصلا نفسها
+
+178
+00:17:08,390 --> 00:17:11,670
+عاملها هي والواحد مدام بي مش الواحد إذا بي من
+
+179
+00:17:11,670 --> 00:17:19,660
+هتكون الـ Q إذا بي بيساوي الـ Q كمان مرة كمان مرة يا
+
+180
+00:17:19,660 --> 00:17:29,280
+محمد؟ بقول إن بي مش الواحد و بي هي كتلة واحدة فاش 
+
+181
+00:17:29,280 --> 00:17:34,780
+عوامل فيها لغير حالها هي نفسها عامل من عوامل الـQK
+
+182
+00:17:34,780 --> 00:17:40,320
+والـQK فاش فيها عامل إلا هي والـQK هي والواحد
+
+183
+00:17:40,320 --> 00:17:45,520
+طب البي مش الواحد إذا البي هتكون مين هي؟ الـQK إذا
+
+184
+00:17:45,520 --> 00:17:51,150
+انصرت البي إيش بتساوي؟ الـQK أي سؤال؟ كنت بتسأل ليش
+
+185
+00:17:51,150 --> 00:17:56,670
+الواحد بالظبط عدد الأولي؟ هو احنا .. شوف عليّ احنا
+
+186
+00:17:56,670 --> 00:18:02,510
+المعرفين العدد الأولي هو العدد ال .. العدد ..
+
+187
+00:18:02,510 --> 00:18:07,690
+العدد ال .. ال .. المودب طبعا و السالب بنفع نعمل
+
+188
+00:18:07,690 --> 00:18:10,610
+.. في تجاهة السالب خلّيني أحكي عن المودب هو العدد
+
+189
+00:18:10,610 --> 00:18:16,690
+اللي دي له عاملان مختلفان .. مختلفان عاملان
+
+190
+00:18:16,690 --> 00:18:20,160
+مختلفان أكبر من سفر
+
+191
+00:18:23,000 --> 00:18:28,420
+اللي هو واحد ومين والعدد نفسه. طب ليش احنا عملنا
+
+192
+00:18:28,420 --> 00:18:33,960
+تعريفنا استثناءً لإن بعد .. بعد شوية حين .. لما
+
+193
+00:18:33,960 --> 00:18:38,000
+نعمل الـ Chemical Form أو نعمل اللي هو .. نحكي عن
+
+194
+00:18:38,000 --> 00:18:42,280
+فنضام تلثيوم وVerithmetic حيصير اللي هو أي عدد في
+
+195
+00:18:42,280 --> 00:18:48,960
+الدنيا .. أي عدد في الدنيا عنده لو أنا بدي أجزه إلى
+
+196
+00:18:48,960 --> 00:18:52,560
+أجزاء الأولية، لو قلنا مثلا، هل جيت الـ16؟ أو
+
+197
+00:18:52,560 --> 00:18:56,800
+خلّيني أقول الـ6، مثال بسيط، الـ6 اللي هو عبارة عن
+
+198
+00:18:56,800 --> 00:19:02,140
+2×100، إذا جزّقناه إلى إيش؟ العوامل الأولية، لو
+
+199
+00:19:02,140 --> 00:19:06,640
+بدنا نعتبر العام 1 عدد أولي، أه، كمان يعني بالإضافة
+
+200
+00:19:06,640 --> 00:19:09,320
+لأنه هي تعرفنا انبنى عليهك لكن تعرفنا انبنى عليهك
+
+201
+00:19:09,320 --> 00:19:12,340
+لسبب، لإنه عارفين إيه اللي بيحصل في المستقبل؟ إنه
+
+202
+00:19:12,340 --> 00:19:16,600
+بيحصل في واحد، في واحد، في واحد، في واحد، جد ما
+
+203
+00:19:16,600 --> 00:19:21,140
+بده، فبيصير عندي اللي هو الـRepresentation للستة
+
+204
+00:19:21,140 --> 00:19:24,540
+as a product of brands، النظرية البعد شوية has
+
+205
+00:19:24,540 --> 00:19:29,530
+infinite number of representations يعني بروح بكون
+
+206
+00:19:29,530 --> 00:19:33,410
+شيلت إشي مهم جداً من الـ Representation اللي هو
+
+207
+00:19:33,410 --> 00:19:36,450
+الـ uniqueness of the representation of the number
+
+208
+00:19:36,450 --> 00:19:41,270
+واضح؟ و هتلاقي بعملي مشاكل أخرى في أماكن أخرى وفيش
+
+209
+00:19:41,270 --> 00:19:47,770
+سبب واضح أن يخلونيا كمان أن أدخله من ضمن الأعداد
+
+210
+00:19:47,770 --> 00:19:52,700
+الأولية و أشيل كلمة الـ distinct واضح فعشان يك احنا
+
+211
+00:19:52,700 --> 00:19:57,520
+يا بنعرف العدد الأول انه بي أكبر من واحد ولا هو
+
+212
+00:19:57,520 --> 00:20:02,780
+عاملان ونسكت أكيد هيكون الـ distinct او انه نقول
+
+213
+00:20:02,780 --> 00:20:08,380
+الـ B positive ولا هو عاملان مختلفان فبكون في هذا
+
+214
+00:20:08,380 --> 00:20:15,280
+الحديث استثنين من الواحد واضح ها طيب اطلع لفوق
+
+215
+00:20:15,280 --> 00:20:21,200
+نيجي الآن لـ Fundamental Theorem of Arithmetic
+
+216
+00:20:21,200 --> 00:20:25,060
+Fundamental Theorem of Arithmetic هتلاقي الـ
+
+217
+00:20:25,060 --> 00:20:29,060
+Representation اللي بنبنيه على الـ Fundamental
+
+218
+00:20:29,060 --> 00:20:35,780
+Theorem of Arithmetic كثير له فائدة سواء في الحلول
+
+219
+00:20:35,780 --> 00:20:40,680
+للأسئلة أو حتى في الـ Applications لتطبيقه على
+
+220
+00:20:40,680 --> 00:20:45,840
+نظريات أخرى لإثباتها بنشوف كيف .. إيش بتقول
+
+221
+00:20:45,840 --> 00:20:49,170
+Fundamental Theorem of Arithmetic؟ Every positive
+
+222
+00:20:49,170 --> 00:20:56,150
+integer N أكبر من 1 أي N إيش ماله أكبر من واحد Can
+
+223
+00:20:56,150 --> 00:21:01,050
+be expressed as a product of EIH يعني بنحلل العدد
+
+224
+00:21:01,050 --> 00:21:05,310
+إلى أوامله الأولية وبنكتبه على صورة Product of EIH
+
+225
+00:21:05,310 --> 00:21:11,220
+و Over Primes This representation is unique apart
+
+226
+00:21:11,220 --> 00:21:22,140
+from the order in which the factors occur. المقصود
+
+227
+00:21:22,140 --> 00:21:27,300
+فيه كتالة الآن يعني زي مثلًا اللي قبل شوية ستة
+
+228
+00:21:27,300 --> 00:21:30,580
+بساوة اتنين في مين في تلاتة، هاي عامله الأولي، هاي
+
+229
+00:21:30,580 --> 00:21:35,220
+اللي هو حصل الـ product of إيش؟ of primes، هذا إحنا
+
+230
+00:21:35,220 --> 00:21:40,120
+بنقول عنه representation unique بعيدًا عن الـ
+
+231
+00:21:40,120 --> 00:21:44,040
+order، يعني إيش؟ يعني مابتدينش واحد يقول تلاتة في
+
+232
+00:21:44,040 --> 00:21:47,640
+اتنين representation تاني، لأ، هذا المقصود فيه
+
+233
+00:21:47,640 --> 00:21:52,510
+اللي هو apart from the order in which the factors
+
+234
+00:21:52,510 --> 00:21:59,410
+occurs بعيدا عن الترتيب اللي هو الـ factors اللي
+
+235
+00:21:59,410 --> 00:22:06,490
+أنا بطلح الـ primes اللي بحللها من العدد هذا اللي هي
+
+236
+00:22:06,490 --> 00:22:07,850
+النظرية
+
+237
+00:22:14,410 --> 00:22:20,250
+صليت عن النبي عليه الصلاة والسلام تعالى نشوف مع
+
+238
+00:22:20,250 --> 00:22:30,590
+بعض كيف نبرهن أو نفهم برهان أي نظرية عندي إن أكبر
+
+239
+00:22:30,590 --> 00:22:34,970
+من واحد بدأ
+
+240
+00:22:34,970 --> 00:22:41,470
+أثبت إن هذا الان بقدر احلله لعوامله الأولية تشوف
+
+241
+00:22:41,470 --> 00:22:53,760
+كيف عندي حالتين يا N براين يا N composite أو ازدادت
+
+242
+00:22:53,760 --> 00:22:58,240
+براين إذا N براين خلصنا كتبنا الـ N بتساوي إيش الـ
+
+243
+00:22:58,240 --> 00:23:05,900
+N نفسها إذا كانت N composite معناته فيها عوامل غير
+
+244
+00:23:05,900 --> 00:23:12,380
+الواحد وغير الـ N يعني في عوامل للـ N دي أو أكتر من
+
+245
+00:23:12,380 --> 00:23:19,300
+D بين الواحد وبين مين لا هي الواحد ولا هي إيش الان
+
+246
+00:23:19,300 --> 00:23:24,040
+ماشي الحالة إذا صورة العوامل هذه بين الواحد وبين
+
+247
+00:23:24,040 --> 00:23:28,960
+الان عبارة عن مجموعة من الغير خالية لأنه فرضت انه
+
+248
+00:23:28,960 --> 00:23:33,520
+composite غير خالية من الأعداد الموجبة إذا by well
+
+249
+00:23:33,520 --> 00:23:38,300
+ordering principle it has a least element ناشي
+
+250
+00:23:38,300 --> 00:23:42,100
+الحال سمين الـ least element في هذولة الـ divisors
+
+251
+00:23:42,100 --> 00:23:47,570
+اسمه ايه إيش؟ B1 مثلا معايا سميني يا اسمه يا إيش بي
+
+252
+00:23:47,570 --> 00:23:51,130
+وان عدد لسه اه أنا لسه ما أثبتش إنه براين بس بده عنه
+
+253
+00:23:51,130 --> 00:23:57,690
+براين إيش ماله فسميته بي وان إذا صارت الان عند الان
+
+254
+00:23:57,690 --> 00:24:05,590
+تبعته كتبت على صورة بي وان في أنوان الـ B1 اتفجن
+
+255
+00:24:05,590 --> 00:24:12,390
+أشماله واحد من الـ divisors اللي منين للـ N لأن هو
+
+256
+00:24:12,390 --> 00:24:15,490
+الـ least divisor في هذه الحالة إذا صارت الـ N
+
+257
+00:24:15,490 --> 00:24:19,670
+بتساوي B1 في 100 في N قطعا عندي على جهة خلّيني
+
+258
+00:24:19,670 --> 00:24:29,290
+أعمل الـ X واحد وفي عندي N والـ N أكبر من 100 أكيد
+
+259
+00:24:29,290 --> 00:24:32,910
+الان بقى بقى بي واحد في مين فان واحد و بي واحد مش
+
+260
+00:24:32,910 --> 00:24:36,510
+هو الواحد لأن الـ advisor أكبر من بيه من الواحد إذا
+
+261
+00:24:36,510 --> 00:24:40,350
+أكيد الان بي واحد فان واحد والان واحد أشماله
+
+262
+00:24:40,350 --> 00:24:48,850
+أصغر من مين من الان معايا يا جماعة الان الادعاء
+
+263
+00:24:48,850 --> 00:24:56,660
+أنه عند بي واحد لازم يكون إيش Ibrahim مظبوط ليش
+
+264
+00:24:56,660 --> 00:25:00,640
+لأنه لو ما كانش بي واحد Ibrahim بي واحد Ibrahim
+
+265
+00:25:00,640 --> 00:25:05,600
+معناه تقوله عامل معاه لو كان الواحد بي واحد مش
+
+266
+00:25:05,600 --> 00:25:09,700
+Ibrahim معناه تقولها عامل إنه ما كان عامل اسمه ايه
+
+267
+00:25:09,700 --> 00:25:13,660
+بيكسب الـ بي واحد وعند الـ بي واحد هو من عامل مين
+
+268
+00:25:13,660 --> 00:25:20,160
+الامر إذاً فان الـ A أشماله بيجسم الـ N والـ A
+
+269
+00:25:20,160 --> 00:25:24,480
+أصغر من مين؟ من الـ B1 ومن عوامل الـ N إذا
+
+270
+00:25:24,480 --> 00:25:28,100
+Contradiction لأن الـ B1 احنا قد ماه The least
+
+271
+00:25:28,100 --> 00:25:34,560
+element أو The least divisor كم مرة؟ أه يا محمد؟
+
+272
+00:25:34,560 --> 00:25:45,050
+زي اللي حسب أنك فهم؟ طيب جميل إذا في سؤال بعيد أه
+
+273
+00:25:45,050 --> 00:25:49,050
+طيب الان إيش اللي عملناه لإن هذا الخطوة خلاص عليها
+
+274
+00:25:49,050 --> 00:25:54,350
+نركب البرهان الانصارة N كان بي written as B1 في N1
+
+275
+00:25:54,350 --> 00:25:59,870
+B1 مين الـ prime الان اللي عملته مع N بعمل مع مين
+
+276
+00:25:59,870 --> 00:26:06,330
+مع N1 يعني الان لو كان N1 prime بكون خلصنا معانا يا
+
+277
+00:26:06,330 --> 00:26:11,430
+محمد؟ إذا كان الواحد مش الـ prime برضه بعمل نفسي
+
+278
+00:26:11,430 --> 00:26:16,010
+ليشي؟ فيه عوامل وهذا العوامل بين الواحد وبين
+
+279
+00:26:16,010 --> 00:26:20,250
+الان واحد إذا باخد من بين برضه الـ least element
+
+280
+00:26:20,250 --> 00:26:26,470
+إذا برضه بحصل على كمان أن اتنين وهكذا الآن أنا 
+
+281
+00:26:26,470 --> 00:26:30,450
+بضعف إنه هينتهي، هتمتهي الأمور يعني حال في الآخر
+
+282
+00:26:30,450 --> 00:26:36,150
+حصل ليش نهاية ليش؟ لأنه أصلاً الـ .. ال .. ال .. ال
+
+283
+00:26:36,150 --> 00:26:40,010
+.. الفرق بين N واحد واحد عبارة عن finite number
+
+284
+00:26:40,010 --> 00:26:44,650
+يعني هيكون عندي finite number of steps بكون خلصت
+
+285
+00:26:44,650 --> 00:26:51,250
+من كتابة الـ N على صورة B1، B2، لعند مثلا B، K،
+
+286
+00:26:51,250 --> 00:27:00,040
+وكل الأشمال هم الـ primes واضح؟ أي سؤال؟أي استفسار
+
+287
+00:27:00,040 --> 00:27:03,460
+طيب صلى على النبي عليه الصلاة والسلام هذا كله
+
+288
+00:27:03,460 --> 00:27:07,600
+تأهله كله لبن جميل every positive integer أن أكبر
+
+289
+00:27:07,600 --> 00:27:11,680
+من واحد can be expressed as a product of the
+
+290
+00:27:11,680 --> 00:27:17,880
+primes ضال أثبتاش ان this product is unique آسف
+
+291
+00:27:17,880 --> 00:27:21,920
+this representation is unique يعني عندي بس one
+
+292
+00:27:21,920 --> 00:27:27,220
+representation خلينا نشوف إذا إيش هنقول الآن نفترض
+
+293
+00:27:27,220 --> 00:27:33,580
+في two representations نفترض أن N can be written
+
+294
+00:27:33,580 --> 00:27:41,280
+as P1 P2 لعند PR مثلا و .. و .. و .. اللي هي P1
+
+295
+00:27:41,280 --> 00:27:46,180
+لعند PR are primes و برضه قدرنا نكتبها على صورة Q1
+
+296
+00:27:46,180 --> 00:27:55,120
+Q2 لعند QS و برضه أشمالهم are primes بتثبت لك إن
+
+297
+00:27:55,120 --> 00:28:01,620
+الـ B1 واحدة من هدول والـ B2 واحدة من هدول والـ Qr
+
+298
+00:28:01,620 --> 00:28:08,400
+واحدة من هدول وهدولة في الآخر اللي هو عددهم من
+
+299
+00:28:08,400 --> 00:28:12,560
+واحد لعند R هو نفسه من واحد لعند S يعني هيكون إيه
+
+300
+00:28:12,560 --> 00:28:16,040
+الشمال وR إيه بتساوي؟ بتساوي S حتى لو مختلف إيه
+
+301
+00:28:16,040 --> 00:28:24,420
+الترتيب فهيكون عندي الـالـ B1 بتساوي واحدة من هدول
+
+302
+00:28:24,420 --> 00:28:28,640
+وبنشيلها الـ B2 واحدة من هدول وبنشيلها الـ B3
+
+303
+00:28:28,640 --> 00:28:33,680
+واحدة من هدول وبنشيلها لما نخلص الـ PR بيكون خلصنا
+
+304
+00:28:33,680 --> 00:28:36,500
+عالمياً على كل الـ primes اللي هنا يعني كل واحد
+
+305
+00:28:36,500 --> 00:28:42,400
+قلوا بس واحدة على جبالهم فاضح أه؟ طيب خليني أشوف
+
+306
+00:28:42,400 --> 00:28:42,700
+كيف
+
+307
+00:28:46,310 --> 00:28:48,030
+شوف وصلنا على النبي عليه الصلاة والسلام إن شاء
+
+308
+00:28:48,030 --> 00:28:51,670
+الله الله أمره مش صعب هذا بساوي هذا صح ولا لأ؟
+
+309
+00:28:51,670 --> 00:29:01,230
+معناه أن الـB1 هيجسم مين؟ Q1، Q2، لعند Q، S صح
+
+310
+00:29:01,230 --> 00:29:08,030
+ولا لأ؟ أكيد، مدام هيجسمه، إذا صار عند الـB1، واحد
+
+311
+00:29:08,030 --> 00:29:13,570
+من هدول معايا، إذا الـB1 بساوي
+
+312
+00:29:15,160 --> 00:29:23,300
+QK for some K أكبر بيشوف واحد و أزرع بيشوف مين و
+
+313
+00:29:23,300 --> 00:29:30,940
+طبعا اطلع لفوق اطلع
+
+314
+00:29:30,940 --> 00:29:37,200
+لفوق كمان كمان خلصنا من هنا انزل
+
+315
+00:29:37,200 --> 00:29:41,020
+فرضنا
+
+316
+00:29:41,020 --> 00:29:46,430
+ان بي واحد و بي اتنين عند PRو Q1 و Q2 لعين مين؟
+
+317
+00:29:46,430 --> 00:29:50,430
+لعين QS وفرض لك without loss of generality أن R
+
+318
+00:29:50,430 --> 00:29:56,050
+أصغر سوى مين؟ S نريد أن نصل إلى R أيش هي؟ بتساوى S
+
+319
+00:29:56,050 --> 00:29:59,210
+طبعا نحن نقول نفرض R أصغر بـ S أصغر سوى R نفس
+
+320
+00:29:59,210 --> 00:30:03,730
+الأشياء R أصغر سوى S أو S أصغر سوى R نفرضها ونصل
+
+321
+00:30:03,730 --> 00:30:07,430
+إلى R أصغر سوى S يعني عدد هنا نفس العدد هنا لأن
+
+322
+00:30:07,430 --> 00:30:11,430
+نفس أصلا ال representations بس ممكن يكون أشمالهم
+
+323
+00:30:11,430 --> 00:30:18,300
+ترتيبهم مختلفةالآن صار عندى بي واحد ايش بيساوي الـ
+
+324
+00:30:18,300 --> 00:30:23,620
+Q K فوق some K عندى اذا بي واحد اكيد هيكون اكبر
+
+325
+00:30:23,620 --> 00:30:30,560
+بيساوي ايش الـ Q واحد معايا مش عارف مشي مش عارف
+
+326
+00:30:30,560 --> 00:30:36,660
+ايه الـ Q اللي رتبناه بيدي ارتبه مضحكت ولا مضحكت
+
+327
+00:30:36,660 --> 00:30:42,800
+احنا لما اثبتنا وجوده كيف اثبتنا وجوده قولنا N
+
+328
+00:30:42,800 --> 00:30:49,450
+بتساويB1 في n واحد بي واحد ايش مالها كانت اصغر
+
+329
+00:30:49,450 --> 00:30:57,310
+divisor لمين للن ماشي الحال و بدينا نغتب طيب الان
+
+330
+00:30:57,310 --> 00:31:02,870
+عندي ال بي واحد تكسب لكيو واحد ال كيو اتنين لعند
+
+331
+00:31:02,870 --> 00:31:11,330
+مين لكيو اس الان بي واحد بيساوي كيو كيهلأن هو
+
+332
+00:31:11,330 --> 00:31:18,090
+بتدعي بناء عليه بي واحد أكبر يساوي كيو واحد أيوا
+
+333
+00:31:18,090 --> 00:31:25,690
+يا جماعة بي واحد أكبر يساوي مين؟ كيو واحد ليش؟
+
+334
+00:31:25,690 --> 00:31:32,330
+بي واحد أكبر يساوي كيو واحد عندك الكيو لكيو واحد
+
+335
+00:31:32,330 --> 00:31:38,250
+إيش علاقة بالكيو كيه؟ الكيو كيه درطبة
+
+336
+00:31:40,680 --> 00:31:44,340
+خلّيني أبدأ بالكمية الصغيرة مش مشكلة أكبر أو ساوى
+
+337
+00:31:44,340 --> 00:31:49,940
+مين الـ Q1 بيصير P1 أكبر أو ساوى مين الـ Q1
+
+338
+00:31:49,940 --> 00:31:55,600
+Similarly عشان سهل بس على .. خلّيني أقول رتبت عشان
+
+339
+00:31:55,600 --> 00:32:01,560
+اللي هو سهل البرهان Similarly إيش بدي أستخدم Q1
+
+340
+00:32:01,560 --> 00:32:16,240
+أيوة يا جماعة Q1 تجسم P1 P2لعين PR مظبوط او لا هذا
+
+341
+00:32:16,240 --> 00:32:22,580
+بيساوي هذا مظبوط هيك اذا كي واحد بيجسم هذا اذا كي
+
+342
+00:32:22,580 --> 00:32:30,330
+واحدبساوة بك او بم for صمم بين الواحد اللي عند ال
+
+343
+00:32:30,330 --> 00:32:35,510
+R مظبوط ومنه زي ما عملناه بالظبط اللي هو عندك U
+
+344
+00:32:35,510 --> 00:32:40,250
+واحد أكبر يساوي بي واحد together ال Q واحد ده ايش
+
+345
+00:32:40,250 --> 00:32:48,230
+بيساوي بي واحد الان شيلت هذا وشيلت هذا بكرر الآن
+
+346
+00:32:48,230 --> 00:32:54,280
+من الاتنين والتلاتة الاخرينالآن عندي .. عندي
+
+347
+00:32:54,280 --> 00:33:02,220
+باختصار الـ R أصغر و أصغر S الان لو كان الـ S ماقص
+
+348
+00:33:02,220 --> 00:33:07,940
+R أكبر strictly من 0 أكبر strictly من 0 معناته أنه
+
+349
+00:33:08,870 --> 00:33:12,510
+أنا أخدت من هنا صار عندها بي واحد بي اتنين بي ار
+
+350
+00:33:12,510 --> 00:33:18,610
+اللي هي اللي هي الكيوز اللي بقابلها وزاد عنها إش
+
+351
+00:33:18,610 --> 00:33:22,650
+هان إذا صار اللي بقابلها إش مالين غير متساويين
+
+352
+00:33:22,650 --> 00:33:26,090
+وهذا contradiction إذا غصب عن اللي لازم اللي هو
+
+353
+00:33:26,090 --> 00:33:31,110
+الار راقص والأس نقصارش هتطلع بساوة سفر وهذا بثبت
+
+354
+00:33:31,110 --> 00:33:34,210
+أن ال representation إش ماله is unique
+
+355
+00:33:42,640 --> 00:33:47,760
+يقولنا as unique apart from order عشان هيك زبطت
+
+356
+00:33:47,760 --> 00:33:56,600
+الأمور عندي في المنطقة هذه أي سؤال طيب
+
+357
+00:33:56,600 --> 00:34:06,740
+الآن ماخد
+
+358
+00:34:06,740 --> 00:34:10,300
+الآن اللي هو مثال 360 و اعمل لك ال representation
+
+359
+00:34:10,300 --> 00:34:17,600
+لهالـ Representation 2×2×2×3×3×5
+
+360
+00:34:17,600 --> 00:34:26,240
+طبعا الآن الشكل اللي أمامنا شوية يعني لو
+
+361
+00:34:26,240 --> 00:34:30,940
+كان .. لو كان الرقم كبير بصير الصفحة يمكن ما تكفيش
+
+362
+00:34:30,940 --> 00:34:35,020
+فالآن بدنا نحاول نحكي بلغة
+
+363
+00:34:37,700 --> 00:34:45,400
+تكون كلنا نحكي بنفس اللغة اللغة
+
+364
+00:34:45,400 --> 00:34:52,080
+اللي بنحكي فيها خليك
+
+365
+00:34:52,080 --> 00:34:57,700
+.. لأ بدنا نرجع للنظرية النظرية .. للنظرية الان
+
+366
+00:34:57,700 --> 00:35:02,320
+بدنا نبنع النظرية انه اي positive integer N بنقدر
+
+367
+00:35:02,320 --> 00:35:06,320
+نكتبه على صورة product of primesوقلنا في الأخر
+
+368
+00:35:06,320 --> 00:35:10,740
+جملة apart from order in which factors the factors
+
+369
+00:35:10,740 --> 00:35:15,600
+occur يعني بمعنى آخر بدنا نتفجلنا نتفج مع بعض على
+
+370
+00:35:15,600 --> 00:35:19,860
+order معين ونمشي عليه عشان هكذا بدنا نيجي لحاجة
+
+371
+00:35:19,860 --> 00:35:22,860
+اسمها ال canonical form عشان لما أكتب ال
+
+372
+00:35:22,860 --> 00:35:25,020
+representation أنا لو تكتب انت ال representation
+
+373
+00:35:25,020 --> 00:35:28,940
+يكون ال representations اللي إيه شماله كلها زي بعض
+
+374
+00:35:28,940 --> 00:35:34,100
+فهنيجي اطلع لفوق الـ A نيجي لاللي هو ال canonical
+
+375
+00:35:34,100 --> 00:35:39,730
+form عندي اللي هي الـ Corollary بتوضح إنه إيش اللي
+
+376
+00:35:39,730 --> 00:35:45,190
+بدنايا خلّيك واقف هنا لأن بتقولّك إنه أنا positive
+
+377
+00:35:45,190 --> 00:35:47,690
+integer أنا أكبر من واحد كان بي written uniquely
+
+378
+00:35:47,690 --> 00:35:53,470
+in canonical form نشوف إيش ال canonical form لأن
+
+379
+00:35:53,470 --> 00:35:56,830
+أن بتساوى بي واحد كي واحد بي اتنين كي اتنين لعند بي
+
+380
+00:35:56,830 --> 00:36:06,770
+ار كي ار for اللي هي عندي I بيساوي 1 و2 لعند الـR
+
+381
+00:36:06,770 --> 00:36:11,650
+وEach Ki is a positive integer and each Bi is a
+
+382
+00:36:11,650 --> 00:36:18,610
+prime with B1 بيساوي 1 و2 لعند الـR وEach Ki is a
+
+383
+00:36:18,610 --> 00:36:21,050
+بيساوي 1 و2 لعند الـR وEach Ki is a positive
+
+384
+00:36:21,050 --> 00:36:21,610
+integer and each Bi is a prime with B1 بيساوي 1 و2
+
+385
+00:36:21,610 --> 00:36:22,010
+لعند الـR وEach Ki is a positive integer and each
+
+386
+00:36:22,010 --> 00:36:23,310
+Bi is a prime with B1 بيساوي 1 و2 لعند الـR وEach
+
+387
+00:36:23,310 --> 00:36:23,490
+Ki is a positive integer and each Bi is a prime
+
+388
+00:36:23,490 --> 00:36:27,290
+with B1 بيساوي 1 و2 لعند الـR وEach Ki is a
+
+389
+00:36:27,290 --> 00:36:30,450
+بيساوي 1 و2 لعند الـR وEach Ki is a positive
+
+390
+00:36:30,450 --> 00:36:35,160
+integer and each Bi is a prime with B1 بيساوي 1 الـ
+
+391
+00:36:35,160 --> 00:36:45,260
+360 اللي جابل بشوية اللي كتبناها اكمل هي 2×2×3
+
+392
+00:36:46,470 --> 00:36:49,910
+في خمسة لو تركناها إلينا كل واحد هيكتبها بشكل لأ
+
+393
+00:36:49,910 --> 00:36:52,870
+خلينا نكتب زي بعض إنها نبدأنا من الصغير ل prime
+
+394
+00:36:52,870 --> 00:36:57,590
+ونرفعه للأسل اللي هو التكرار تلاتة في تلاتة تردية
+
+395
+00:36:57,590 --> 00:37:03,550
+في خمسة فهذا بنسميها ال canonical form لها وهذا
+
+396
+00:37:03,550 --> 00:37:08,010
+اللي هو is unique اللي هو ال representation is
+
+397
+00:37:08,010 --> 00:37:12,050
+unique أتماداً عن اللي حكيناه قبل بشوية وعلى اللي
+
+398
+00:37:12,050 --> 00:37:20,660
+اتعرفنا عليه وأعطاك أمثلة، هاي المثال 4725 بساوي 3
+
+399
+00:37:20,660 --> 00:37:24,520
+تكعيب في 5 تربيع في 11 في 7، لو الآن قلنا لكم كل
+
+400
+00:37:24,520 --> 00:37:28,720
+كومة كتبوها في كانون كالفور، هتكتبوها زي بعض، الآن
+
+401
+00:37:28,720 --> 00:37:37,970
+17460 هيها و هيكذا، اخلع لفوق لأن هذه في Theorems
+
+402
+00:37:37,970 --> 00:37:42,530
+Theorem اللي هو الجذر التنين is a rational number
+
+403
+00:37:42,530 --> 00:37:46,370
+أسف، is an irrational number هذا ممكن يتكرر معاكم
+
+404
+00:37:46,370 --> 00:37:49,170
+في المبادئ وبتكرر معاكم في التحليل وبتكرر معاكم
+
+405
+00:37:49,170 --> 00:37:55,470
+هنا لأن هنا يعني ممكن قرماله شوية مختلف لكن نفس
+
+406
+00:37:55,470 --> 00:38:01,690
+الروح تبدأ نثبت إنه جذر التنين is irrational
+
+407
+00:38:03,860 --> 00:38:09,020
+يعني هو هنا عبارة عن كتطبيق على نظرية الأعداد أما
+
+408
+00:38:09,020 --> 00:38:12,660
+هو احنا كل حديثنا في الـ .. في الـ .. في الـcourse
+
+409
+00:38:12,660 --> 00:38:19,080
+كل حديثنا تحت سقف الـZ بل معظم حديثنا تحت سقف اللي
+
+410
+00:38:19,080 --> 00:38:23,160
+هو الـnatural numbers اه لكن احنا ده ده خليني
+
+411
+00:38:23,160 --> 00:38:27,240
+اقوله كتطبيق للي اللي بنحكي جذر التنين is a
+
+412
+00:38:27,240 --> 00:38:33,750
+rational number بتفترض أن جذر التنين rational اه
+
+413
+00:38:33,750 --> 00:38:39,050
+إذا جذر التنين أكيد كلكم بعرف هنكتب على صورة A
+
+414
+00:38:39,050 --> 00:38:48,150
+على B ماشي الحال معايا اه و ال B اكيد أشماله أكبر
+
+415
+00:38:48,150 --> 00:38:53,710
+من واحد لانه لو كانت واحد معناته ال A بيساوي جذر
+
+416
+00:38:53,710 --> 00:38:57,410
+التنين مافيش انتجار A بيساوي إيش جذر التنين فاهمين
+
+417
+00:38:57,410 --> 00:39:04,080
+عليها طيب إذا الان ربّقلي الجهتين بيصير A بيساوي 2
+
+418
+00:39:04,080 --> 00:39:10,880
+B تربيع اي تربيع؟ معايا B تربيع اي تربيع
+
+419
+00:39:10,880 --> 00:39:16,500
+بيساوي 2 في B تربيع؟ معايا الان بدي افترضلك من
+
+420
+00:39:16,500 --> 00:39:20,380
+رأس الدور انا حور ال grade from the divisors بين ال 
+
+421
+00:39:20,380 --> 00:39:24,240
+a و الـ b ايش بيساوي؟ بيساوي 1 اختصرت لو في ايش
+
+422
+00:39:24,240 --> 00:39:31,980
+اختصرت ورميته وهذا طبعا بقدر أعمله الآن حصلّك
+
+423
+00:39:31,980 --> 00:39:34,680
+لطلاق، وده أقول لك هذا الكلام أصلا مبنى على خطأ
+
+424
+00:39:34,680 --> 00:39:39,020
+لأنه أنت فرضت أن هذا عبارة عن Rational Number صارت
+
+425
+00:39:39,020 --> 00:39:47,220
+عندي الـ B بتجسم مين؟ الـ A تربيع، والـ B أكبر من 
+
+426
+00:39:47,220 --> 00:39:55,680
+1، إذن صار في Prime هنا اللي هو في اللعاب
+
+427
+00:39:55,680 --> 00:39:59,800
+المشترك بين الـ Greatest Common Divisor بين حتى
+
+428
+00:39:59,800 --> 00:40:06,940
+بالهدف بين الـ B و الـ A هصير أكبر من واحد
+
+429
+00:40:06,940 --> 00:40:15,600
+contradiction كمان مرة عند
+
+430
+00:40:15,600 --> 00:40:20,210
+الـ B تربيع بتقسم الـ A تربيع و الـ B بتقسم الـ B 
+
+431
+00:40:20,210 --> 00:40:25,130
+تربيع إذا الـ B بتقسم مين مظبوط يا عم جاد الـ B
+
+432
+00:40:25,130 --> 00:40:30,090
+تربيع تقسم الـ A تربيع و الـ B بتقسم الـ B تربيع إذا
+
+433
+00:40:30,090 --> 00:40:33,410
+الـ B بتقسم الـ A تربيع إذا صار العالم المشترك
+
+434
+00:40:33,410 --> 00:40:36,650
+العليا بين الـ B و الـ A أكيد أكبر من مين؟ من واحد
+
+435
+00:40:36,650 --> 00:40:41,290
+طبعا هو أحكي هنا شيء مشابه يعني
+
+436
+00:40:46,990 --> 00:40:51,050
+بنستخدم الـ bfg ده عيلها على طول منها فاهمين واضح
+
+437
+00:40:51,050 --> 00:40:57,530
+أه؟ أي سؤال؟ بيكون اليوم اللي هو اتحدثنا عن الـ
+
+438
+00:40:57,530 --> 00:41:02,150
+fundamental theorem of arithmetic و أثبتنا أنه أي 
+
+439
+00:41:02,150 --> 00:41:07,910
+representation أو representation لأي positive
+
+440
+00:41:07,910 --> 00:41:12,830
+integer N أكبر من واحد can be uniquely written as
+
+441
+00:41:12,830 --> 00:41:18,440
+a product of prime apart from the order ومن ثم
+
+442
+00:41:18,440 --> 00:41:23,340
+لنوحد الحديث سويا ويكون فيه عندنا كلنا اللي هو
+
+443
+00:41:23,340 --> 00:41:27,830
+representation زي بعض اللي هو اتفجنا على صورة للـ
+
+444
+00:41:27,830 --> 00:41:30,630
+Representation اللي سمناها الـ Canonical Form أننا
+
+445
+00:41:30,630 --> 00:41:36,430
+نرتب هذه الأعداد B1,B2,B3 لعند Br تساعدي واللي 
+
+446
+00:41:36,430 --> 00:41:41,270
+بتكرر نرفعه لأس ونكتبه على صورة B1,Alpha 1,B2
+
+447
+00:41:41,270 --> 00:41:46,330
+,Alpha 2 لعند Br,Alpha R هذا الـ Representation
+
+448
+00:41:46,330 --> 00:41:50,880
+اللي هو الـ Canonical Form is unique  واخدنا
+
+449
+00:41:50,880 --> 00:41:54,440
+application على اللي هو نظرية الأعداد اللي هو نجدر
+
+450
+00:41:54,440 --> 00:41:58,260
+اتنين is a rational number بكون هيك انتهينا من
+
+451
+00:41:58,260 --> 00:42:04,680
+المحاضرة السادسة في هذا الـ .. في هذه المادة وان 
+
+452
+00:42:04,680 --> 00:42:08,520
+شاء الله المرة القادمة هنحكي عن some properties of 
+
+453
+00:42:08,520 --> 00:42:12,620
+primes أو أنه هنعمل discussion ان شاء الله على 
+
+454
+00:42:12,620 --> 00:42:15,520
+chapter اتنين وشكرا لكم 
diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/tX1wPJj5Rh0_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/tX1wPJj5Rh0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..43824fefe4dc7c18595a3d83569779a3e5209c2e
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/tX1wPJj5Rh0_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4142, "start": 19.44, "end": 41.42, "text": "بسم الله الرحمن الرحيم المحاضرة اليوم هي عبارة عن الـ Brines and Their Distribution اللي هو الشبطر الثالث في مساق نظرية الأعداد لقسم الرياضيات بالجامعة الإسلامية ال section الأول", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 5016, 46958, 25720, 45595, 20498, 39896, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 1603, 1652, 293, 6710, 9840, 30783, 13672, 1829, 31439, 25124, 3555, 9566, 2288, 6024, 104, 6027, 12984, 8978, 47524, 995, 4587, 8717, 19913, 2288, 10632, 16247, 22488, 18513, 5296, 4587, 38251, 2423, 16572, 46958, 1829, 9307, 20666, 7435, 10943, 27884, 33688, 3794, 37440, 10632, 2423, 3541, 16247, 12610], "avg_logprob": -0.15473090236385664, "compression_ratio": 1.5945945945945945, "no_speech_prob": 4.351139068603516e-06, "words": [{"start": 19.44, "end": 19.82, "word": "بسم", "probability": 0.87353515625}, {"start": 19.82, "end": 20.04, "word": " الله", "probability": 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"seek": 53508, "start": 509.12, "end": 535.08, "text": "B بتجسم الـ B بنظرية سابقة وهو المطلوب أي سؤال اي استفسار طيب اطلع للفور عندي if B is a prime and B بتجسم ال A1 في ال A2 في ال AN", "tokens": [33, 39894, 7435, 38251, 2423, 39184, 363, 44945, 19913, 2288, 10632, 8608, 16758, 28671, 37037, 2407, 9673, 9566, 1211, 37746, 36632, 8608, 33604, 6027, 1975, 1829, 44713, 36178, 9640, 23032, 1829, 3555, 1975, 9566, 1211, 3615, 24976, 5172, 13063, 18871, 16254, 498, 363, 307, 257, 5835, 293, 363, 39894, 7435, 38251, 2423, 316, 16, 8978, 2423, 316, 17, 8978, 2423, 5252], "avg_logprob": -0.2633568524352966, "compression_ratio": 1.3783783783783783, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 509.12, "end": 509.64, "word": "B", "probability": 0.2279052734375}, {"start": 509.64, "end": 510.68, "word": " بتجسم", "probability": 0.5912272135416666}, {"start": 510.68, "end": 510.98, "word": " الـ", "probability": 0.873046875}, {"start": 510.98, "end": 511.24, "word": " B", "probability": 0.420654296875}, {"start": 511.24, "end": 512.52, "word": " بنظرية", "probability": 0.878173828125}, {"start": 512.52, "end": 513.24, "word": " سابقة", "probability": 0.98046875}, {"start": 513.24, "end": 514.36, "word": " وهو", "probability": 0.6148681640625}, {"start": 514.36, "end": 514.86, "word": " المطلوب", "probability": 0.98828125}, {"start": 514.86, "end": 515.92, "word": " أي", "probability": 0.54541015625}, {"start": 515.92, "end": 516.44, "word": " سؤال", "probability": 0.9889322916666666}, {"start": 516.44, "end": 518.26, "word": " اي", "probability": 0.58526611328125}, {"start": 518.26, "end": 519.18, "word": " استفسار", "probability": 0.95068359375}, {"start": 519.18, "end": 521.26, "word": " طيب", "probability": 0.8572591145833334}, {"start": 521.26, "end": 522.02, "word": " اطلع", "probability": 0.89599609375}, {"start": 522.02, "end": 522.48, "word": " للفور", "probability": 0.7163899739583334}, {"start": 522.48, "end": 528.22, "word": " عندي", "probability": 0.772705078125}, {"start": 528.22, "end": 530.12, "word": " if", "probability": 0.66650390625}, {"start": 530.12, "end": 530.36, "word": " B", "probability": 0.82177734375}, {"start": 530.36, "end": 530.56, "word": " is", "probability": 0.9521484375}, {"start": 530.56, "end": 530.7, "word": " a", "probability": 0.73583984375}, {"start": 530.7, "end": 531.08, "word": " prime", "probability": 0.85107421875}, {"start": 531.08, "end": 532.78, "word": " and", "probability": 0.89697265625}, {"start": 532.78, "end": 532.98, "word": " B", "probability": 0.76611328125}, {"start": 532.98, "end": 533.44, "word": " بتجسم", "probability": 0.8798828125}, {"start": 533.44, "end": 533.58, "word": " ال", "probability": 0.89453125}, {"start": 533.58, "end": 533.98, "word": " A1", "probability": 0.4234619140625}, {"start": 533.98, "end": 534.2, "word": " في", "probability": 0.6318359375}, {"start": 534.2, "end": 534.3, "word": " ال", "probability": 0.875}, {"start": 534.3, "end": 534.56, 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"end": 1404.38, "text": "أو أكتر من D بين الواحد وبين مين لا هي الواحد ولا هي إيش الان ماشي الحالة إذا صورة العوامل هذه بين الواحد وبين الان", "tokens": [10721, 2407, 5551, 4117, 2655, 2288, 9154, 413, 49374, 2423, 14407, 24401, 46599, 9957, 3714, 9957, 20193, 39896, 2423, 14407, 24401, 49429, 39896, 11933, 1829, 8592, 2423, 7649, 3714, 33599, 1829, 21542, 6027, 3660, 11933, 15730, 20328, 13063, 3660, 18863, 2407, 10943, 1211, 29538, 49374, 2423, 14407, 24401, 46599, 9957, 2423, 7649], "avg_logprob": -0.18352005279289102, "compression_ratio": 1.8141592920353982, "no_speech_prob": 7.450580596923828e-06, "words": [{"start": 1391.6, "end": 1391.9, "word": "أو", "probability": 0.89990234375}, {"start": 1391.9, "end": 1392.2, "word": " أكتر", "probability": 0.93212890625}, {"start": 1392.2, "end": 1392.38, "word": " من", "probability": 0.9912109375}, {"start": 1392.38, "end": 1392.66, "word": " D", "probability": 0.57177734375}, {"start": 1392.66, "end": 1393.5, "word": " بين", 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this representation is unique يعني عندي بس one representation خلينا نشوف", "tokens": [10721, 1829, 44713, 36178, 9640, 23032, 1829, 3555, 20328, 23942, 15844, 28239, 21292, 47356, 31767, 15040, 3660, 16070, 3794, 37440, 23758, 28242, 3224, 6055, 10721, 3224, 43761, 28242, 3224, 5296, 3555, 1863, 10874, 2304, 26895, 633, 3353, 24922, 14739, 5551, 4117, 26890, 9154, 36764, 24401, 393, 312, 12675, 382, 257, 1674, 295, 264, 738, 2967, 48812, 6027, 5551, 12984, 3555, 2655, 33599, 16472, 341, 1674, 307, 3845, 19753, 3794, 5172, 341, 10290, 307, 3845, 37495, 22653, 18871, 16254, 4724, 3794, 472, 10290, 16490, 1211, 9957, 995, 8717, 8592, 38688], "avg_logprob": -0.2539930502573649, "compression_ratio": 1.542857142857143, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 1618.92, "end": 1619.26, "word": "أي", "probability": 0.880615234375}, {"start": 1619.26, "end": 1620.04, "word": " استفسار", "probability": 0.953125}, {"start": 1620.04, "end": 1620.92, "word": " طيب", 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واحدة", "probability": 0.98681640625}, {"start": 1679.14, "end": 1679.24, "word": " من", "probability": 0.99658203125}, {"start": 1679.24, "end": 1679.82, "word": " هدول", "probability": 0.99169921875}, {"start": 1679.82, "end": 1681.06, "word": " والـ", "probability": 0.8212890625}, {"start": 1681.06, "end": 1681.62, "word": " QR", "probability": 0.591552734375}, {"start": 1681.62, "end": 1681.98, "word": " واحدة", "probability": 0.9954427083333334}, {"start": 1681.98, "end": 1682.12, "word": " من", "probability": 0.99755859375}, {"start": 1682.12, "end": 1683.38, "word": " هدول", "probability": 0.99169921875}, {"start": 1683.38, "end": 1684.92, "word": " وهدولة", "probability": 0.83935546875}, {"start": 1684.92, "end": 1685.02, "word": " في", "probability": 0.9638671875}, {"start": 1685.02, "end": 1685.7, "word": " الآخر", "probability": 0.9807942708333334}, {"start": 1685.7, "end": 1686.84, "word": " اللي", "probability": 0.962890625}, {"start": 1686.84, "end": 1687.18, "word": " 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"word": " كبير", "probability": 0.9952799479166666}, {"start": 2068.26, "end": 2069.44, "word": " بصير", "probability": 0.7734375}, {"start": 2069.44, "end": 2069.82, "word": " الصفحة", "probability": 0.953125}, {"start": 2069.82, "end": 2070.04, "word": " يمكن", "probability": 0.6805419921875}, {"start": 2070.04, "end": 2070.2, "word": " ما", "probability": 0.640625}, {"start": 2070.2, "end": 2070.94, "word": " تكفيش", "probability": 0.9046630859375}, {"start": 2070.94, "end": 2072.62, "word": " فالآن", "probability": 0.8765869140625}, {"start": 2072.62, "end": 2072.94, "word": " بدنا", "probability": 0.923583984375}, {"start": 2072.94, "end": 2073.56, "word": " نحاول", "probability": 0.9967041015625}, {"start": 2073.56, "end": 2074.46, "word": " نحكي", "probability": 0.9840087890625}, {"start": 2074.46, "end": 2075.02, "word": " بلغة", "probability": 0.97705078125}], "temperature": 1.0}, {"id": 83, "seek": 210466, "start": 2077.7, "end": 2104.66, "text": "تكون كلنا نحكي بنفس اللغة اللغة اللي بنحكي فيها خليك .. لأ بدنا نرجع للنظرية النظرية .. للنظرية الان بدنا نبنع النظرية انه اي positive integer N بنقدر نكتبه على صورة product of primes", "tokens": [2655, 30544, 28242, 8315, 8717, 5016, 4117, 1829, 44945, 36178, 13672, 17082, 3660, 13672, 17082, 3660, 13672, 1829, 44945, 5016, 4117, 1829, 8978, 11296, 16490, 20292, 4117, 4386, 5296, 10721, 47525, 8315, 8717, 47341, 3615, 24976, 1863, 19913, 2288, 10632, 28239, 19913, 2288, 10632, 4386, 24976, 1863, 19913, 2288, 10632, 2423, 7649, 47525, 8315, 8717, 3555, 1863, 3615, 28239, 19913, 2288, 10632, 16472, 3224, 1975, 1829, 3353, 24922, 426, 44945, 28543, 2288, 8717, 4117, 2655, 3555, 3224, 15844, 20328, 13063, 3660, 1674, 295, 2886, 279], "avg_logprob": -0.278706384259601, "compression_ratio": 1.6836158192090396, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2077.7, "end": 2078.64, "word": "تكون", "probability": 0.6533203125}, {"start": 2078.64, "end": 2079.58, "word": " كلنا", "probability": 0.52056884765625}, {"start": 2079.58, "end": 2080.0, "word": " نحكي", "probability": 0.9156494140625}, {"start": 2080.0, "end": 2080.32, "word": " بنفس", "probability": 0.931640625}, {"start": 2080.32, "end": 2080.78, "word": " اللغة", "probability": 0.9925130208333334}, {"start": 2080.78, "end": 2085.4, "word": " اللغة", "probability": 0.8701171875}, {"start": 2085.4, "end": 2085.56, "word": " اللي", "probability": 0.89501953125}, {"start": 2085.56, "end": 2086.06, "word": " بنحكي", "probability": 0.83624267578125}, {"start": 2086.06, "end": 2087.88, "word": " فيها", "probability": 0.95166015625}, {"start": 2087.88, "end": 2092.08, "word": " خليك", "probability": 0.5834147135416666}, {"start": 2092.08, "end": 2092.16, "word": " ..", "probability": 0.2607421875}, {"start": 2092.16, "end": 2092.26, "word": " لأ", "probability": 0.8056640625}, {"start": 2092.26, "end": 2092.5, "word": " بدنا", "probability": 0.6492919921875}, {"start": 2092.5, "end": 2092.68, "word": " نرجع", "probability": 0.8639322916666666}, {"start": 2092.68, "end": 2093.36, "word": " للنظرية", "probability": 0.96025390625}, {"start": 2093.36, "end": 2095.16, "word": " النظرية", "probability": 0.9327392578125}, {"start": 2095.16, "end": 2095.28, "word": " ..", "probability": 0.371826171875}, {"start": 2095.28, "end": 2096.34, "word": " للنظرية", "probability": 0.9359375}, {"start": 2096.34, "end": 2097.7, "word": " الان", "probability": 0.567626953125}, {"start": 2097.7, "end": 2098.48, "word": " بدنا", "probability": 0.8779296875}, {"start": 2098.48, "end": 2098.74, "word": " نبنع", "probability": 0.7435302734375}, {"start": 2098.74, "end": 2099.22, "word": " النظرية", "probability": 0.971923828125}, {"start": 2099.22, "end": 2099.9, "word": " انه", "probability": 0.5057373046875}, {"start": 2099.9, "end": 2100.76, "word": " اي", "probability": 0.813232421875}, {"start": 2100.76, "end": 2101.06, "word": " positive", "probability": 0.857421875}, {"start": 2101.06, "end": 2101.46, "word": " integer", "probability": 0.87744140625}, {"start": 2101.46, "end": 2101.78, "word": " N", "probability": 0.364501953125}, {"start": 2101.78, "end": 2102.32, "word": " بنقدر", "probability": 0.7609049479166666}, {"start": 2102.32, "end": 2102.74, "word": " نكتبه", "probability": 0.96533203125}, {"start": 2102.74, "end": 2102.9, "word": " على", "probability": 0.86572265625}, {"start": 2102.9, "end": 2103.18, "word": " صورة", "probability": 0.8697916666666666}, {"start": 2103.18, "end": 2103.52, "word": " product", "probability": 0.82470703125}, {"start": 2103.52, "end": 2104.1, "word": " of", "probability": 0.9169921875}, {"start": 2104.1, "end": 2104.66, "word": " primes", "probability": 0.54150390625}], "temperature": 1.0}, {"id": 84, "seek": 213500, "start": 2105.54, "end": 2135.0, "text": "وقلنا في الأخر جملة apart from order in which factors the factors occur يعني بمعنى آخر بدنا نتفجلنا نتفج مع بعض على order معين ونمشي عليه عشان هكذا بدنا نيجي لحاجة اسمها ال canonical form عشان لما أكتب ال representation أنا لو تكتب انت ال representation يكون ال representations اللي إيه شماله كلها زي بعض فهنيجي اطلع لفوق الـ A نيجي لاللي هو ال canonical form", "tokens": [2407, 4587, 1211, 8315, 8978, 16247, 34740, 10874, 2304, 37977, 4936, 490, 1668, 294, 597, 6771, 264, 6771, 5160, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 47525, 8315, 8717, 2655, 5172, 7435, 1211, 8315, 8717, 2655, 5172, 7435, 20449, 45030, 11242, 15844, 1668, 20449, 9957, 4032, 1863, 2304, 8592, 1829, 47356, 6225, 8592, 7649, 8032, 4117, 15730, 47525, 8315, 8717, 1829, 7435, 1829, 5296, 5016, 26108, 3660, 24525, 2304, 11296, 2423, 46491, 1254, 6225, 8592, 7649, 5296, 15042, 5551, 4117, 2655, 3555, 2423, 10290, 41850, 45164, 6055, 4117, 2655, 3555, 16472, 2655, 2423, 10290, 7251, 30544, 2423, 33358, 13672, 1829, 11933, 1829, 3224, 13412, 2304, 6027, 3224, 28242, 11296, 30767, 1829, 45030, 11242, 6156, 3224, 1863, 1829, 7435, 1829, 1975, 9566, 1211, 3615, 5296, 5172, 30543, 2423, 39184, 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" representation", "probability": 0.953125}, {"start": 2125.02, "end": 2125.38, "word": " يكون", "probability": 0.770263671875}, {"start": 2125.38, "end": 2125.86, "word": " ال", "probability": 0.8876953125}, {"start": 2125.86, "end": 2126.54, "word": " representations", "probability": 0.94970703125}, {"start": 2126.54, "end": 2126.9, "word": " اللي", "probability": 0.58746337890625}, {"start": 2126.9, "end": 2127.16, "word": " إيه", "probability": 0.6688639322916666}, {"start": 2127.16, "end": 2127.7, "word": " شماله", "probability": 0.9117431640625}, {"start": 2127.7, "end": 2128.44, "word": " كلها", "probability": 0.607177734375}, {"start": 2128.44, "end": 2128.64, "word": " زي", "probability": 0.984130859375}, {"start": 2128.64, "end": 2128.94, "word": " بعض", "probability": 0.995361328125}, {"start": 2128.94, "end": 2130.58, "word": " فهنيجي", "probability": 0.815673828125}, {"start": 2130.58, "end": 2130.86, "word": " اطلع", "probability": 0.85113525390625}, {"start": 2130.86, "end": 2131.18, "word": " لفوق", "probability": 0.7132161458333334}, {"start": 2131.18, "end": 2131.38, "word": " الـ", "probability": 0.286376953125}, {"start": 2131.38, "end": 2131.48, "word": " A", "probability": 0.412109375}, {"start": 2131.48, "end": 2132.34, "word": " نيجي", "probability": 0.936767578125}, {"start": 2132.34, "end": 2133.08, "word": " لاللي", "probability": 0.633544921875}, {"start": 2133.08, "end": 2133.46, "word": " هو", "probability": 0.98583984375}, {"start": 2133.46, "end": 2133.72, "word": " ال", "probability": 0.85400390625}, {"start": 2133.72, "end": 2134.1, "word": " canonical", "probability": 0.9765625}, {"start": 2134.1, "end": 2135.0, "word": " form", "probability": 0.931640625}], "temperature": 1.0}, {"id": 85, "seek": 216329, "start": 2136.07, "end": 2163.29, "text": "عندي اللي هي الـ Corollary بتوضح إنه إيش اللي بدنايا خلّيك واقف هنا لأن بتقولّك إنه أنا positive integer أنا أكبر من واحد كان بي written uniquely in canonical form نشوف إيش ال canonical form لأن أن بتسوأ بي واحد كي واحد بي اتنين كي اتنين لعند بي ار كي ار four اللي هي عندي", "tokens": [3615, 1863, 16254, 13672, 1829, 39896, 2423, 39184, 3925, 1833, 822, 39894, 2407, 11242, 5016, 36145, 3224, 11933, 1829, 8592, 13672, 1829, 47525, 8315, 25528, 16490, 1211, 11703, 1829, 4117, 36764, 4587, 5172, 34105, 5296, 33456, 39894, 39648, 11703, 4117, 36145, 3224, 41850, 3353, 24922, 41850, 5551, 4117, 26890, 9154, 36764, 24401, 25961, 4724, 1829, 3720, 31474, 294, 46491, 1254, 8717, 8592, 38688, 11933, 1829, 8592, 2423, 46491, 1254, 5296, 33456, 14739, 39894, 3794, 2407, 10721, 4724, 1829, 36764, 24401, 9122, 1829, 36764, 24401, 4724, 1829, 1975, 2655, 1863, 9957, 9122, 1829, 1975, 2655, 1863, 9957, 5296, 3615, 41260, 4724, 1829, 1975, 2288, 9122, 1829, 1975, 2288, 1451, 13672, 1829, 39896, 43242, 1829], "avg_logprob": -0.31332237913943173, "compression_ratio": 1.7905982905982907, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2136.07, "end": 2136.61, "word": 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جذر التنين is a rational number بتفترض أن جذر التنين rational", "tokens": [40228, 22653, 31439, 34105, 6225, 3555, 9640, 3660, 18871, 9122, 2655, 9566, 21292, 4587, 15844, 8717, 19913, 2288, 10632, 16247, 22488, 18513, 5551, 15042, 31439, 5551, 5016, 8315, 28242, 11331, 16254, 12984, 8315, 8978, 2423, 39184, 4386, 8978, 2423, 39184, 4386, 8978, 2423, 31913, 28242, 11331, 16254, 12984, 8315, 6055, 33753, 8608, 4587, 5172, 2423, 39184, 57, 4724, 1211, 20449, 19913, 2304, 11331, 16254, 12984, 8315, 6055, 33753, 8608, 4587, 5172, 13672, 1829, 31439, 2423, 39184, 16296, 3547, 5551, 3224, 44381, 5551, 5016, 8315, 11778, 3224, 11778, 3224, 16490, 1211, 9957, 1829, 5551, 39648, 3224, 9122, 2655, 9566, 21292, 4587, 5296, 20292, 13672, 1829, 44945, 5016, 4117, 1829, 10874, 8848, 2288, 16712, 1863, 9957, 307, 257, 15090, 1230, 39894, 5172, 2655, 43042, 14739, 10874, 8848, 2288, 16712, 1863, 9957, 15090], "avg_logprob": -0.16149808659808326, "compression_ratio": 1.9456066945606694, 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"probability": 0.9404296875}, {"start": 2498.31, "end": 2498.61, "word": " صورة", "probability": 0.98291015625}, {"start": 2498.61, "end": 2499.51, "word": " B1", "probability": 0.8701171875}, {"start": 2499.51, "end": 2500.27, "word": ",Alpha", "probability": 0.4932454427083333}, {"start": 2500.27, "end": 2500.55, "word": " 1", "probability": 0.818359375}, {"start": 2500.55, "end": 2501.27, "word": ",B2", "probability": 0.9256184895833334}, {"start": 2501.27, "end": 2501.63, "word": ",Alpha", "probability": 0.9622395833333334}, {"start": 2501.63, "end": 2501.83, "word": " 2", "probability": 0.9580078125}, {"start": 2501.83, "end": 2502.25, "word": " لعند", "probability": 0.9601236979166666}, {"start": 2502.25, "end": 2503.43, "word": " Br", "probability": 0.9033203125}, {"start": 2503.43, "end": 2504.55, "word": ",Alpha", "probability": 0.78662109375}, {"start": 2504.55, "end": 2504.87, "word": " R", "probability": 0.8681640625}, {"start": 2504.87, "end": 2505.37, "word": " هذا", 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في هذا ال .. في هذه المادة وان شاء الله المرة القادمة هنحكي عن some properties of primes او انه هنعمل discussion ان شاء الله على chapter اتنين وشكرا لكم", "tokens": [2407, 47283, 3215, 8315, 3861, 15844, 13672, 1829, 31439, 8717, 19913, 2288, 10632, 16247, 22488, 18513, 13672, 1829, 31439, 8717, 7435, 3215, 2288, 1975, 2655, 1863, 9957, 307, 257, 15090, 1230, 4724, 30544, 39896, 4117, 16472, 47395, 1829, 8315, 9154, 9673, 5016, 46958, 25720, 21136, 18513, 3794, 3660, 8978, 23758, 2423, 4386, 8978, 29538, 9673, 18513, 3660, 4032, 7649, 13412, 16606, 21984, 9673, 25720, 25062, 18513, 46007, 8032, 1863, 5016, 4117, 1829, 18871, 512, 7221, 295, 582, 1532, 1975, 2407, 16472, 3224, 8032, 1863, 25957, 1211, 5017, 16472, 13412, 16606, 21984, 15844, 7187, 1975, 2655, 1863, 9957, 4032, 8592, 4117, 23557, 5296, 24793], "avg_logprob": -0.1826923075490273, "compression_ratio": 1.7091633466135459, "no_speech_prob": 4.351139068603516e-06, "words": [{"start": 2509.88, "end": 2510.88, "word": "واخدنا", 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diff --git a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/v7sgo3kFh8Y_raw.json b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/v7sgo3kFh8Y_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e661c265fcf17dada60229102e35f0178c1b61cd
--- /dev/null
+++ b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/v7sgo3kFh8Y_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3904, "start": 19.42, "end": 39.04, "text": "بسم الله الرحمن الرحيم اليوم إن شاء الله المحاضرة الثانية في مساق نظرية الأعداد قسم الرياضيات بالجامعة الإسلامية غزر اتحدثنا المرة الماضية عن القوابلية القسمة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 36145, 13412, 16606, 21984, 9673, 5016, 46958, 25720, 6024, 104, 7649, 10632, 8978, 47524, 995, 4587, 8717, 19913, 2288, 10632, 16247, 22488, 18513, 12174, 38251, 2423, 16572, 46958, 1829, 9307, 20666, 7435, 10943, 27884, 33688, 3794, 37440, 10632, 32771, 11622, 2288, 1975, 2655, 24401, 12984, 8315, 9673, 25720, 9673, 46958, 10632, 18871, 25062, 2407, 16758, 1211, 10632, 25062, 38251, 3660], "avg_logprob": -0.11664496703694265, "compression_ratio": 1.8598726114649682, "no_speech_prob": 2.562999725341797e-06, "words": [{"start": 19.42, "end": 19.86, "word": "بسم", "probability": 0.83154296875}, {"start": 19.86, "end": 20.08, "word": " الله", "probability": 0.96240234375}, {"start": 20.08, "end": 20.48, "word": " الرحمن", "probability": 0.9759114583333334}, {"start": 20.48, "end": 20.94, "word": " الرحيم", "probability": 0.99560546875}, {"start": 20.94, "end": 22.98, "word": " اليوم", "probability": 0.941650390625}, {"start": 22.98, "end": 23.12, "word": " إن", "probability": 0.65869140625}, {"start": 23.12, "end": 23.26, "word": " شاء", "probability": 0.985595703125}, {"start": 23.26, "end": 23.38, "word": " الله", "probability": 0.9736328125}, {"start": 23.38, "end": 23.96, "word": " المحاضرة", "probability": 0.9813232421875}, {"start": 23.96, "end": 25.42, "word": " الثانية", "probability": 0.943603515625}, {"start": 25.42, "end": 26.24, "word": " في", "probability": 0.93408203125}, {"start": 26.24, "end": 26.66, "word": " مساق", "probability": 0.9104817708333334}, {"start": 26.66, "end": 27.28, "word": " نظرية", "probability": 0.9376220703125}, {"start": 27.28, "end": 28.2, "word": " الأعداد", "probability": 0.95556640625}, {"start": 28.2, "end": 29.02, "word": " قسم", "probability": 0.927490234375}, {"start": 29.02, "end": 29.6, "word": " الرياضيات", "probability": 0.9369140625}, {"start": 29.6, "end": 30.26, "word": " بالجامعة", "probability": 0.90771484375}, {"start": 30.26, "end": 31.08, "word": " الإسلامية", "probability": 0.9805908203125}, {"start": 31.08, "end": 31.56, "word": " غزر", "probability": 0.8592122395833334}, {"start": 31.56, "end": 34.7, "word": " اتحدثنا", "probability": 0.91181640625}, {"start": 34.7, "end": 34.98, "word": " المرة", "probability": 0.954345703125}, {"start": 34.98, "end": 35.72, "word": " الماضية", "probability": 0.7578125}, {"start": 35.72, "end": 36.9, "word": " عن", "probability": 0.98828125}, {"start": 36.9, "end": 38.2, "word": " القوابلية", "probability": 0.621533203125}, {"start": 38.2, "end": 39.04, "word": " القسمة", "probability": 0.9825846354166666}], "temperature": 1.0}, {"id": 2, "seek": 6396, "start": 40.08, "end": 63.96, "text": "أو عن خوارزمية القسمة حاجة سميناها الـdivision algorithm ايش اللي حكيناه حكينا انه لو كان عندنا الـA والـB عبارة عن integers عداد صحيحة وكان عند الـB أكبر من سفر قلنا بنقدر نلاقي there exist unique integers R", "tokens": [10721, 2407, 18871, 16490, 2407, 9640, 11622, 2304, 10632, 25062, 38251, 3660, 11331, 26108, 3660, 8608, 2304, 1829, 8315, 11296, 2423, 39184, 67, 592, 1991, 9284, 1975, 1829, 8592, 13672, 1829, 11331, 4117, 1829, 8315, 3224, 11331, 4117, 1829, 8315, 16472, 3224, 45164, 25961, 43242, 8315, 2423, 39184, 32, 16070, 39184, 33, 6225, 3555, 9640, 3660, 18871, 41674, 6225, 3215, 18513, 20328, 5016, 1829, 5016, 3660, 4032, 41361, 43242, 2423, 39184, 33, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 12174, 1211, 8315, 4724, 1863, 28543, 2288, 8717, 15040, 38436, 456, 2514, 3845, 41674, 497], "avg_logprob": -0.2187500015685433, "compression_ratio": 1.5797101449275361, "no_speech_prob": 1.9073486328125e-06, "words": [{"start": 40.08, "end": 40.82, "word": "أو", "probability": 0.802734375}, {"start": 40.82, "end": 41.24, "word": " عن", "probability": 0.95849609375}, {"start": 41.24, "end": 42.3, "word": " خوارزمية", "probability": 0.91015625}, {"start": 42.3, "end": 42.94, "word": " القسمة", "probability": 0.9869791666666666}, {"start": 42.94, "end": 43.36, "word": " حاجة", "probability": 0.8919270833333334}, {"start": 43.36, "end": 43.82, "word": " سميناها", "probability": 0.77353515625}, {"start": 43.82, "end": 44.44, "word": " الـdivision", "probability": 0.6125}, {"start": 44.44, "end": 45.66, "word": " algorithm", "probability": 0.94580078125}, {"start": 45.66, "end": 46.12, "word": " ايش", "probability": 0.6842447916666666}, {"start": 46.12, "end": 46.26, "word": " اللي", "probability": 0.937255859375}, {"start": 46.26, "end": 47.26, "word": " حكيناه", "probability": 0.92373046875}, {"start": 47.26, "end": 47.86, "word": " حكينا", "probability": 0.86627197265625}, {"start": 47.86, "end": 48.1, "word": " انه", "probability": 0.665283203125}, {"start": 48.1, "end": 48.2, "word": " لو", "probability": 0.96923828125}, {"start": 48.2, "end": 48.44, "word": " كان", "probability": 0.99658203125}, {"start": 48.44, "end": 48.96, "word": " عندنا", "probability": 0.94287109375}, {"start": 48.96, "end": 49.64, "word": " الـA", "probability": 0.70849609375}, {"start": 49.64, "end": 51.18, "word": " والـB", "probability": 0.7980143229166666}, {"start": 51.18, "end": 51.88, "word": " عبارة", "probability": 0.993896484375}, {"start": 51.88, "end": 52.1, "word": " عن", "probability": 0.994140625}, {"start": 52.1, "end": 52.58, "word": " integers", "probability": 0.88037109375}, {"start": 52.58, "end": 53.72, "word": " عداد", "probability": 0.76611328125}, {"start": 53.72, "end": 54.58, "word": " صحيحة", "probability": 0.98037109375}, {"start": 54.58, "end": 55.26, "word": " وكان", "probability": 0.91650390625}, {"start": 55.26, "end": 55.58, "word": " عند", "probability": 0.8916015625}, {"start": 55.58, "end": 56.0, "word": " الـB", "probability": 0.9358723958333334}, {"start": 56.0, "end": 56.46, "word": " أكبر", "probability": 0.9051106770833334}, {"start": 56.46, "end": 56.66, "word": " من", "probability": 0.9970703125}, {"start": 56.66, "end": 57.08, "word": " سفر", "probability": 0.697021484375}, {"start": 57.08, "end": 58.36, "word": " قلنا", "probability": 0.5725911458333334}, {"start": 58.36, "end": 58.96, "word": " بنقدر", "probability": 0.7205810546875}, {"start": 58.96, "end": 59.58, "word": " نلاقي", "probability": 0.9541015625}, {"start": 59.58, "end": 60.58, "word": " there", "probability": 0.5966796875}, {"start": 60.58, "end": 61.12, "word": " exist", "probability": 0.77734375}, {"start": 61.12, "end": 61.78, "word": " unique", "probability": 0.81201171875}, {"start": 61.78, "end": 62.64, "word": " integers", "probability": 0.962890625}, {"start": 62.64, "end": 63.96, "word": " R", "probability": 0.666015625}], "temperature": 1.0}, {"id": 3, "seek": 8098, "start": 64.66, "end": 80.98, "text": "هو متبقى القسمة و الـ Q هي ناتج القسمة such that الـ A بتساوي الـ B في Q زائد R حيث R أكبر أو يساوي سفر وأصغر من مين من B", "tokens": [3224, 2407, 44650, 3555, 4587, 7578, 25062, 38251, 3660, 4032, 2423, 39184, 1249, 39896, 8717, 9307, 7435, 25062, 38251, 3660, 1270, 300, 2423, 39184, 316, 39894, 3794, 995, 45865, 2423, 39184, 363, 8978, 1249, 30767, 16373, 3215, 497, 11331, 1829, 12984, 497, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 8608, 5172, 2288, 36725, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 363], "avg_logprob": -0.17658729449151053, "compression_ratio": 1.4071428571428573, "no_speech_prob": 3.039836883544922e-06, "words": [{"start": 64.66, "end": 65.0, "word": "هو", "probability": 0.8388671875}, {"start": 65.0, "end": 65.66, "word": " متبقى", "probability": 0.7698974609375}, {"start": 65.66, "end": 66.44, "word": " القسمة", "probability": 0.9820963541666666}, {"start": 66.44, "end": 67.06, "word": " و", "probability": 0.673828125}, {"start": 67.06, "end": 67.32, "word": " الـ", "probability": 0.586181640625}, {"start": 67.32, "end": 67.72, "word": " Q", "probability": 0.492919921875}, {"start": 67.72, "end": 68.6, "word": " هي", "probability": 0.955078125}, {"start": 68.6, "end": 69.08, "word": " ناتج", "probability": 0.98974609375}, {"start": 69.08, "end": 70.36, "word": " القسمة", "probability": 0.98095703125}, {"start": 70.36, "end": 70.8, "word": " such", "probability": 0.6884765625}, {"start": 70.8, "end": 71.6, "word": " that", "probability": 0.951171875}, {"start": 71.6, "end": 72.3, "word": " الـ", "probability": 0.748291015625}, {"start": 72.3, "end": 72.72, "word": " A", "probability": 0.7958984375}, {"start": 72.72, "end": 73.92, "word": " بتساوي", "probability": 0.659912109375}, {"start": 73.92, "end": 74.06, "word": " الـ", "probability": 0.869384765625}, {"start": 74.06, "end": 74.28, "word": " B", "probability": 0.7373046875}, {"start": 74.28, "end": 74.44, "word": " في", "probability": 0.72021484375}, {"start": 74.44, "end": 74.9, "word": " Q", "probability": 0.841796875}, {"start": 74.9, "end": 75.94, "word": " زائد", "probability": 0.7124837239583334}, {"start": 75.94, "end": 76.2, "word": " R", "probability": 0.96728515625}, {"start": 76.2, "end": 76.58, "word": " حيث", "probability": 0.9864908854166666}, {"start": 76.58, "end": 77.02, "word": " R", "probability": 0.66650390625}, {"start": 77.02, "end": 77.56, "word": " أكبر", "probability": 0.9658203125}, {"start": 77.56, "end": 77.76, "word": " أو", "probability": 0.9267578125}, {"start": 77.76, "end": 78.12, "word": " يساوي", "probability": 0.9781494140625}, {"start": 78.12, "end": 78.6, "word": " سفر", "probability": 0.8201497395833334}, {"start": 78.6, "end": 79.66, "word": " وأصغر", "probability": 0.923095703125}, {"start": 79.66, "end": 79.86, "word": " من", "probability": 0.99658203125}, {"start": 79.86, "end": 80.28, "word": " مين", "probability": 0.853515625}, {"start": 80.28, "end": 80.78, "word": " من", "probability": 0.61962890625}, {"start": 80.78, "end": 80.98, "word": " B", "probability": 0.9111328125}], "temperature": 1.0}, {"id": 4, "seek": 9527, "start": 81.71, "end": 95.27, "text": "هذا اللي اتحدثناه المرة الماضية وبرهمنا النظرية ان لو كان في عندي a two integers a وb والمقسوم عليه b أكبر من 0 بقدر ألاقي اللي هو ناتج قسم واحد", "tokens": [3224, 15730, 13672, 1829, 1975, 2655, 24401, 12984, 8315, 3224, 9673, 25720, 9673, 46958, 10632, 4032, 26890, 3224, 2304, 8315, 28239, 19913, 2288, 10632, 16472, 45164, 25961, 8978, 43242, 1829, 257, 732, 41674, 257, 4032, 65, 4032, 45340, 4587, 3794, 20498, 47356, 272, 5551, 4117, 26890, 9154, 1958, 4724, 28543, 2288, 5551, 15040, 38436, 13672, 1829, 31439, 8717, 9307, 7435, 12174, 38251, 36764, 24401], "avg_logprob": -0.16622596153846153, "compression_ratio": 1.49079754601227, "no_speech_prob": 1.5497207641601562e-06, "words": [{"start": 81.71, "end": 82.05, "word": "هذا", "probability": 0.92626953125}, {"start": 82.05, "end": 82.15, "word": " اللي", "probability": 0.83544921875}, {"start": 82.15, "end": 82.91, "word": " اتحدثناه", "probability": 0.8557535807291666}, {"start": 82.91, "end": 83.19, "word": " المرة", "probability": 0.95654296875}, {"start": 83.19, "end": 83.75, "word": " الماضية", "probability": 0.9939778645833334}, {"start": 83.75, "end": 84.53, "word": " وبرهمنا", "probability": 0.82001953125}, {"start": 84.53, "end": 85.33, "word": " النظرية", "probability": 0.9644775390625}, {"start": 85.33, "end": 86.05, "word": " ان", "probability": 0.50244140625}, {"start": 86.05, "end": 86.25, "word": " لو", "probability": 0.79833984375}, {"start": 86.25, "end": 86.51, "word": " كان", "probability": 0.982421875}, {"start": 86.51, "end": 86.65, "word": " في", "probability": 0.8544921875}, {"start": 86.65, "end": 87.25, "word": " عندي", "probability": 0.63671875}, {"start": 87.25, "end": 87.51, "word": " a", "probability": 0.491455078125}, {"start": 87.51, "end": 87.71, "word": " two", "probability": 0.64697265625}, {"start": 87.71, "end": 88.13, "word": " integers", "probability": 0.9501953125}, {"start": 88.13, "end": 88.47, "word": " a", "probability": 0.83544921875}, {"start": 88.47, "end": 88.81, "word": " وb", "probability": 0.680419921875}, {"start": 88.81, "end": 90.31, "word": " والمقسوم", "probability": 0.81240234375}, {"start": 90.31, "end": 90.65, "word": " عليه", "probability": 0.953125}, {"start": 90.65, "end": 90.89, "word": " b", "probability": 0.77392578125}, {"start": 90.89, "end": 91.27, "word": " أكبر", "probability": 0.9166666666666666}, {"start": 91.27, "end": 91.45, "word": " من", "probability": 0.99365234375}, {"start": 91.45, "end": 91.79, "word": " 0", "probability": 0.47265625}, {"start": 91.79, "end": 93.05, "word": " بقدر", "probability": 0.9441731770833334}, {"start": 93.05, "end": 93.55, "word": " ألاقي", "probability": 0.8318684895833334}, {"start": 93.55, "end": 93.79, "word": " اللي", "probability": 0.9150390625}, {"start": 93.79, "end": 93.93, "word": " هو", "probability": 0.97265625}, {"start": 93.93, "end": 94.33, "word": " ناتج", "probability": 0.9820963541666666}, {"start": 94.33, "end": 94.65, "word": " قسم", "probability": 0.97412109375}, {"start": 94.65, "end": 95.27, "word": " واحد", "probability": 0.93408203125}], "temperature": 1.0}, {"id": 5, "seek": 11193, "start": 96.05, "end": 111.93, "text": "هو متبقى قسم واحد يحقق ما يلي ان ايه بتسوى BQ زاد R حيث R أكبر يسوى صفر وأصغر من مين أصغر من B عاملنا هذا الكلام قولنا في Corollary لهذه النظرية", "tokens": [3224, 2407, 44650, 3555, 4587, 7578, 12174, 38251, 36764, 24401, 7251, 5016, 4587, 4587, 19446, 7251, 20292, 16472, 1975, 1829, 3224, 39894, 3794, 2407, 7578, 363, 48, 30767, 18513, 497, 11331, 1829, 12984, 497, 5551, 4117, 26890, 7251, 3794, 2407, 7578, 20328, 5172, 2288, 36725, 9381, 17082, 2288, 9154, 3714, 9957, 5551, 9381, 17082, 2288, 9154, 363, 6225, 10943, 1211, 8315, 23758, 2423, 28820, 10943, 12174, 12610, 8315, 8978, 3925, 1833, 822, 46740, 24192, 28239, 19913, 2288, 10632], "avg_logprob": -0.2507911445219306, "compression_ratio": 1.463855421686747, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 96.05, "end": 96.45, "word": "هو", "probability": 0.539794921875}, {"start": 96.45, "end": 97.07, "word": " متبقى", "probability": 0.8553466796875}, {"start": 97.07, "end": 97.31, "word": " قسم", "probability": 0.978515625}, {"start": 97.31, "end": 97.91, "word": " واحد", "probability": 0.94189453125}, {"start": 97.91, "end": 98.89, "word": " يحقق", "probability": 0.9658203125}, {"start": 98.89, "end": 99.07, "word": " ما", "probability": 0.90283203125}, {"start": 99.07, "end": 99.43, "word": " يلي", "probability": 0.9208984375}, {"start": 99.43, "end": 100.17, "word": " ان", "probability": 0.51416015625}, {"start": 100.17, "end": 100.47, "word": " ايه", "probability": 0.7246907552083334}, {"start": 100.47, "end": 100.89, "word": " بتسوى", "probability": 0.61370849609375}, {"start": 100.89, "end": 101.37, "word": " BQ", "probability": 0.485107421875}, {"start": 101.37, "end": 101.83, "word": " زاد", "probability": 0.62744140625}, {"start": 101.83, "end": 102.05, "word": " R", "probability": 0.83154296875}, {"start": 102.05, "end": 102.35, "word": " حيث", "probability": 0.95654296875}, {"start": 102.35, "end": 102.59, "word": " R", "probability": 0.5908203125}, {"start": 102.59, "end": 102.87, "word": " أكبر", "probability": 0.9513346354166666}, {"start": 102.87, "end": 103.11, "word": " يسوى", "probability": 0.8111572265625}, {"start": 103.11, "end": 103.41, "word": " صفر", "probability": 0.7810872395833334}, {"start": 103.41, "end": 103.79, "word": " وأصغر", "probability": 0.888916015625}, {"start": 103.79, "end": 103.95, "word": " من", "probability": 0.98681640625}, {"start": 103.95, "end": 104.33, "word": " مين", "probability": 0.747802734375}, {"start": 104.33, "end": 105.41, "word": " أصغر", "probability": 0.8731689453125}, {"start": 105.41, "end": 105.71, "word": " من", "probability": 0.98681640625}, {"start": 105.71, "end": 105.93, "word": " B", "probability": 0.69580078125}, {"start": 105.93, "end": 107.43, "word": " عاملنا", "probability": 0.74365234375}, {"start": 107.43, "end": 107.67, "word": " هذا", "probability": 0.95654296875}, {"start": 107.67, "end": 108.17, "word": " الكلام", "probability": 0.97119140625}, {"start": 108.17, "end": 108.79, "word": " قولنا", "probability": 0.7239583333333334}, {"start": 108.79, "end": 109.13, "word": " في", "probability": 0.87060546875}, {"start": 109.13, "end": 109.91, "word": " Corollary", "probability": 0.6797078450520834}, {"start": 109.91, "end": 111.15, "word": " لهذه", "probability": 0.8896484375}, {"start": 111.15, "end": 111.93, "word": " النظرية", "probability": 0.976318359375}], "temperature": 1.0}, {"id": 6, "seek": 13904, "start": 112.64, "end": 139.04, "text": "قلنا لو in general كان عندي a انتجر و b انتجر بس بيه أشماله لا يساوي سفر يعني شملنا الموجب والسالب من الأعداد الصحيحة و بدنا نجسم عليها برضه النظرية تطبق وتصبح بالشكل التالي ان there exist أيضا unique integers R وQ بحيث", "tokens": [4587, 1211, 8315, 45164, 294, 2674, 25961, 43242, 1829, 257, 16472, 2655, 7435, 2288, 4032, 272, 16472, 2655, 7435, 2288, 4724, 3794, 4724, 1829, 3224, 5551, 8592, 2304, 6027, 3224, 20193, 7251, 3794, 995, 45865, 8608, 5172, 2288, 37495, 22653, 13412, 2304, 1211, 8315, 9673, 29245, 3555, 16070, 3794, 6027, 3555, 9154, 16247, 22488, 18513, 31767, 5016, 1829, 5016, 3660, 4032, 47525, 8315, 8717, 7435, 38251, 25894, 11296, 4724, 43042, 3224, 28239, 19913, 2288, 10632, 6055, 9566, 3555, 4587, 34683, 9381, 49628, 20666, 8592, 28820, 16712, 6027, 1829, 16472, 456, 2514, 36632, 11242, 995, 3845, 41674, 497, 4032, 48, 4724, 5016, 1829, 12984], "avg_logprob": -0.21559495851397514, "compression_ratio": 1.5407725321888412, "no_speech_prob": 2.9206275939941406e-06, "words": [{"start": 112.64, "end": 113.16, "word": "قلنا", "probability": 0.5707194010416666}, {"start": 113.16, "end": 113.58, "word": " لو", "probability": 0.70947265625}, {"start": 113.58, "end": 113.88, "word": " in", 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{"start": 120.02, "end": 120.42, "word": " يساوي", "probability": 0.67742919921875}, {"start": 120.42, "end": 120.74, "word": " سفر", "probability": 0.859375}, {"start": 120.74, "end": 121.02, "word": " يعني", "probability": 0.868896484375}, {"start": 121.02, "end": 121.64, "word": " شملنا", "probability": 0.8787841796875}, {"start": 121.64, "end": 122.26, "word": " الموجب", "probability": 0.9519856770833334}, {"start": 122.26, "end": 122.94, "word": " والسالب", "probability": 0.9114990234375}, {"start": 122.94, "end": 123.12, "word": " من", "probability": 0.9833984375}, {"start": 123.12, "end": 123.64, "word": " الأعداد", "probability": 0.94677734375}, {"start": 123.64, "end": 124.28, "word": " الصحيحة", "probability": 0.980859375}, {"start": 124.28, "end": 124.6, "word": " و", "probability": 0.7451171875}, {"start": 124.6, "end": 124.88, "word": " بدنا", "probability": 0.769775390625}, {"start": 124.88, "end": 125.16, "word": " نجسم", "probability": 0.75390625}, {"start": 125.16, "end": 125.8, "word": " عليها", "probability": 0.9921875}, {"start": 125.8, "end": 126.6, "word": " برضه", "probability": 0.9376627604166666}, {"start": 126.6, "end": 127.36, "word": " النظرية", "probability": 0.9700927734375}, {"start": 127.36, "end": 128.48, "word": " تطبق", "probability": 0.86767578125}, {"start": 128.48, "end": 129.32, "word": " وتصبح", "probability": 0.8517252604166666}, {"start": 129.32, "end": 130.02, "word": " بالشكل", "probability": 0.9733072916666666}, {"start": 130.02, "end": 130.74, "word": " التالي", "probability": 0.9871419270833334}, {"start": 130.74, "end": 131.48, "word": " ان", "probability": 0.568359375}, {"start": 131.48, "end": 131.76, "word": " there", "probability": 0.64013671875}, {"start": 131.76, "end": 132.44, "word": " exist", "probability": 0.8212890625}, {"start": 132.44, "end": 133.28, "word": " أيضا", "probability": 0.8317057291666666}, {"start": 133.28, "end": 133.74, "word": " unique", "probability": 0.8740234375}, {"start": 133.74, "end": 134.52, "word": " integers", "probability": 0.95654296875}, {"start": 134.52, "end": 135.46, "word": " R", "probability": 0.4892578125}, {"start": 135.46, "end": 137.16, "word": " وQ", "probability": 0.7353515625}, {"start": 137.16, "end": 139.04, "word": " بحيث", "probability": 0.8824462890625}], "temperature": 1.0}, {"id": 7, "seek": 16528, "start": 139.52, "end": 165.28, "text": "أن A بيساوي B في Q زائد R حيث الـ R أكبر أو ساوي سفر و أصغر في هذه الحالمين من الـ absolute value للـ B هذا اللي اتحدثنا المرة الماضية الآن بناء على الـ division algorithm هذا بيساعدنا في حلول كثير من الأسئلة", "tokens": [33456, 316, 4724, 1829, 3794, 995, 45865, 363, 8978, 1249, 30767, 16373, 3215, 497, 11331, 1829, 12984, 2423, 39184, 497, 5551, 4117, 26890, 34051, 8608, 995, 45865, 8608, 5172, 2288, 4032, 5551, 9381, 17082, 2288, 8978, 29538, 21542, 45340, 9957, 9154, 2423, 39184, 8236, 2158, 24976, 39184, 363, 23758, 13672, 1829, 1975, 2655, 24401, 12984, 8315, 9673, 25720, 9673, 46958, 10632, 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"probability": 0.9794921875}, {"start": 145.58, "end": 146.64, "word": " الـ", "probability": 0.880615234375}, {"start": 146.64, "end": 146.86, "word": " R", "probability": 0.490234375}, {"start": 146.86, "end": 147.3, "word": " أكبر", "probability": 0.970703125}, {"start": 147.3, "end": 147.44, "word": " أو", "probability": 0.96728515625}, {"start": 147.44, "end": 147.68, "word": " ساوي", "probability": 0.8098958333333334}, {"start": 147.68, "end": 148.1, "word": " سفر", "probability": 0.7132975260416666}, {"start": 148.1, "end": 148.38, "word": " و", "probability": 0.6552734375}, {"start": 148.38, "end": 148.6, "word": " أصغر", "probability": 0.8199462890625}, {"start": 148.6, "end": 148.72, "word": " في", "probability": 0.85595703125}, {"start": 148.72, "end": 148.84, "word": " هذه", "probability": 0.90625}, {"start": 148.84, "end": 149.6, "word": " الحالمين", "probability": 0.780517578125}, {"start": 149.6, "end": 150.14, "word": " من", "probability": 0.96630859375}, {"start": 150.14, "end": 150.22, "word": " الـ", "probability": 0.81787109375}, {"start": 150.22, "end": 150.54, "word": " absolute", "probability": 0.4248046875}, {"start": 150.54, "end": 151.26, "word": " value", "probability": 0.99072265625}, {"start": 151.26, "end": 151.88, "word": " للـ", "probability": 0.86328125}, {"start": 151.88, "end": 152.06, "word": " B", "probability": 0.796875}, {"start": 152.06, "end": 152.98, "word": " هذا", "probability": 0.81689453125}, {"start": 152.98, "end": 153.12, "word": " اللي", "probability": 0.9189453125}, {"start": 153.12, "end": 153.68, "word": " اتحدثنا", "probability": 0.9345703125}, {"start": 153.68, "end": 154.26, "word": " المرة", "probability": 0.97216796875}, {"start": 154.26, "end": 155.12, "word": " الماضية", "probability": 0.9959309895833334}, {"start": 155.12, "end": 156.3, "word": " الآن", "probability": 0.776123046875}, {"start": 156.3, "end": 157.08, "word": " بناء", "probability": 0.87939453125}, {"start": 157.08, "end": 157.4, "word": " على", "probability": 0.67724609375}, {"start": 157.4, "end": 157.8, "word": " الـ", "probability": 0.7197265625}, {"start": 157.8, "end": 158.1, "word": " division", "probability": 0.5732421875}, {"start": 158.1, "end": 158.82, "word": " algorithm", "probability": 0.94873046875}, {"start": 158.82, "end": 159.98, "word": " هذا", "probability": 0.53125}, {"start": 159.98, "end": 161.3, "word": " بيساعدنا", "probability": 0.9055989583333334}, {"start": 161.3, "end": 162.52, "word": " في", "probability": 0.8349609375}, {"start": 162.52, "end": 163.8, "word": " حلول", "probability": 0.92578125}, {"start": 163.8, "end": 164.44, "word": " كثير", "probability": 0.9397786458333334}, {"start": 164.44, "end": 164.66, "word": " من", "probability": 0.99169921875}, {"start": 164.66, "end": 165.28, "word": " الأسئلة", "probability": 0.989013671875}], "temperature": 1.0}, {"id": 8, "seek": 18214, "start": 166.08, "end": 182.14, "text": "المطروحة في هذا الـ section أو هذا الشبتر وأخذنا بعض التطبيقات عليها واليوم بدنا اللي هو ناخد تطبيقات أخرى للمسائل اللي طلبنا منكم تحلوها المرة الماضية الآن", "tokens": [45340, 9566, 32887, 5016, 3660, 8978, 23758, 2423, 39184, 3541, 34051, 23758, 25124, 3555, 2655, 2288, 36725, 9778, 8848, 8315, 45030, 11242, 16712, 9566, 21292, 4587, 9307, 25894, 11296, 16070, 1829, 20498, 47525, 8315, 13672, 1829, 31439, 8717, 47283, 3215, 6055, 9566, 21292, 4587, 9307, 5551, 34740, 7578, 5296, 19528, 3794, 16373, 1211, 13672, 1829, 23032, 46152, 8315, 9154, 24793, 6055, 5016, 1211, 2407, 11296, 9673, 25720, 9673, 46958, 10632, 6024, 48506], "avg_logprob": -0.14929366438356165, "compression_ratio": 1.6411764705882352, "no_speech_prob": 5.125999450683594e-05, "words": [{"start": 166.08, "end": 167.02, "word": "المطروحة", "probability": 0.88154296875}, {"start": 167.02, "end": 167.18, "word": " في", "probability": 0.94580078125}, {"start": 167.18, "end": 167.62, "word": " هذا", "probability": 0.86181640625}, {"start": 167.62, "end": 168.04, "word": " الـ", "probability": 0.714111328125}, {"start": 168.04, "end": 168.52, "word": " section", "probability": 0.375732421875}, {"start": 168.52, "end": 168.82, "word": " أو", "probability": 0.91162109375}, {"start": 168.82, "end": 169.14, "word": " هذا", "probability": 0.94140625}, {"start": 169.14, "end": 169.74, "word": " الشبتر", "probability": 0.7484130859375}, {"start": 169.74, "end": 171.76, "word": " وأخذنا", "probability": 0.755126953125}, {"start": 171.76, "end": 172.02, "word": " بعض", "probability": 0.984619140625}, {"start": 172.02, "end": 172.72, "word": " التطبيقات", "probability": 0.983203125}, {"start": 172.72, "end": 173.06, "word": " عليها", "probability": 0.96923828125}, {"start": 173.06, "end": 173.58, "word": " واليوم", "probability": 0.8230794270833334}, {"start": 173.58, "end": 174.04, "word": " بدنا", "probability": 0.84033203125}, {"start": 174.04, "end": 174.28, "word": " اللي", "probability": 0.68603515625}, {"start": 174.28, "end": 174.5, "word": " هو", "probability": 0.97412109375}, {"start": 174.5, "end": 174.9, "word": " ناخد", "probability": 0.9910481770833334}, {"start": 174.9, "end": 175.54, "word": " تطبيقات", "probability": 0.98642578125}, {"start": 175.54, "end": 176.16, "word": " أخرى", "probability": 0.9697265625}, {"start": 176.16, "end": 177.52, "word": " للمسائل", "probability": 0.912109375}, {"start": 177.52, "end": 177.68, "word": " اللي", "probability": 0.943359375}, {"start": 177.68, "end": 178.08, "word": " طلبنا", "probability": 0.9912109375}, {"start": 178.08, "end": 178.32, "word": " منكم", "probability": 0.869873046875}, {"start": 178.32, "end": 178.96, "word": " تحلوها", "probability": 0.858056640625}, {"start": 178.96, "end": 179.62, "word": " المرة", "probability": 0.967529296875}, {"start": 179.62, "end": 180.54, "word": " الماضية", "probability": 0.99169921875}, {"start": 180.54, "end": 182.14, "word": " الآن", "probability": 0.6973876953125}], "temperature": 1.0}, {"id": 9, "seek": 21287, "start": 183.83, "end": 212.87, "text": "نشوف كيف يتم تطبيق هذه النظرية من خلال المسائل اللي سنحلها اليوم أول شغلة السؤال الأول show that any integer of the form 6k 1 5 is also of the form 3j 2 but not conversely ما هي اللي بدوها؟ اللي بدوها ما هي ليه؟", "tokens": [1863, 8592, 38688, 9122, 33911, 7251, 39237, 6055, 9566, 21292, 4587, 29538, 28239, 19913, 2288, 10632, 9154, 16490, 1211, 6027, 9673, 3794, 16373, 1211, 13672, 1829, 8608, 1863, 5016, 1211, 11296, 45595, 20498, 5551, 12610, 13412, 17082, 37977, 21136, 33604, 6027, 16247, 12610, 855, 300, 604, 24922, 295, 264, 1254, 1386, 74, 502, 1025, 307, 611, 295, 264, 1254, 805, 73, 568, 457, 406, 2615, 736, 19446, 39896, 13672, 1829, 47525, 2407, 11296, 22807, 13672, 1829, 47525, 2407, 11296, 19446, 39896, 32239, 3224, 22807], "avg_logprob": -0.3465073417214786, "compression_ratio": 1.5048076923076923, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 183.83, "end": 184.35, "word": "نشوف", "probability": 0.63330078125}, {"start": 184.35, "end": 184.73, "word": " كيف", "probability": 0.9619140625}, {"start": 184.73, "end": 185.39, "word": " يتم", "probability": 0.640625}, {"start": 185.39, "end": 185.83, "word": " تطبيق", "probability": 0.9732666015625}, {"start": 185.83, "end": 186.07, "word": " هذه", "probability": 0.85888671875}, {"start": 186.07, "end": 186.73, "word": " النظرية", "probability": 0.938720703125}, {"start": 186.73, "end": 187.81, "word": " من", "probability": 0.293212890625}, {"start": 187.81, "end": 188.83, "word": " خلال", "probability": 0.9763997395833334}, {"start": 188.83, "end": 189.51, "word": " المسائل", "probability": 0.8353271484375}, {"start": 189.51, "end": 189.73, "word": " اللي", "probability": 0.5650634765625}, {"start": 189.73, "end": 192.17, "word": " سنحلها", "probability": 0.83193359375}, {"start": 192.17, "end": 192.67, "word": " اليوم", "probability": 0.960693359375}, {"start": 192.67, "end": 193.67, "word": " أول", "probability": 0.82177734375}, {"start": 193.67, "end": 194.15, "word": " شغلة", "probability": 0.6796875}, {"start": 194.15, "end": 195.23, "word": " السؤال", "probability": 0.7642415364583334}, {"start": 195.23, "end": 195.65, "word": " الأول", "probability": 0.975830078125}, {"start": 195.65, "end": 196.29, "word": " show", "probability": 0.29296875}, {"start": 196.29, "end": 196.67, "word": " that", "probability": 0.92822265625}, {"start": 196.67, "end": 196.97, "word": " any", "probability": 0.8310546875}, {"start": 196.97, "end": 197.57, "word": " integer", "probability": 0.85888671875}, {"start": 197.57, "end": 198.69, "word": " of", "probability": 0.927734375}, {"start": 198.69, "end": 198.89, "word": " the", "probability": 0.8896484375}, {"start": 198.89, "end": 199.23, "word": " form", "probability": 0.91650390625}, {"start": 199.23, "end": 200.53, "word": " 6k", "probability": 0.5076904296875}, {"start": 200.53, "end": 200.97, "word": " 1", "probability": 0.01006317138671875}, {"start": 200.97, "end": 201.63, "word": " 5", "probability": 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{"start": 1905.09, "end": 1905.47, "word": " أدرس", "probability": 0.9842529296875}, {"start": 1905.47, "end": 1905.81, "word": " مين", "probability": 0.93798828125}, {"start": 1905.81, "end": 1906.45, "word": " الموجب", "probability": 0.8253580729166666}, {"start": 1906.45, "end": 1907.01, "word": " والثاني", "probability": 0.8758544921875}, {"start": 1907.01, "end": 1907.29, "word": " ميرور", "probability": 0.7223307291666666}, {"start": 1907.29, "end": 1907.55, "word": " له", "probability": 0.359130859375}, {"start": 1907.55, "end": 1909.07, "word": " فعشان", "probability": 0.86962890625}, {"start": 1909.07, "end": 1909.31, "word": " هيك", "probability": 0.913330078125}, {"start": 1909.31, "end": 1909.69, "word": " احنا", "probability": 0.87890625}], "temperature": 1.0}, {"id": 75, "seek": 193685, "start": 1910.55, "end": 1936.85, "text": "هندرس اللي هي القواسم الموجبة بعد ذلك القواسم الموجبة و هننطلق لل greatest common divisor اللي هو العامل المشترك الأعلى ماشي وال least common multiple المضاعف المشترك البسيط كل هذا هنحكي فيه في مين في القواسم المشترك الموجبة معايا؟ طيب", "tokens": [3224, 41260, 2288, 3794, 13672, 1829, 39896, 25062, 14407, 38251, 9673, 29245, 49401, 39182, 29910, 23275, 25062, 14407, 38251, 9673, 29245, 49401, 4032, 8032, 1863, 1863, 9566, 1211, 4587, 24976, 6636, 2689, 25974, 284, 13672, 1829, 31439, 18863, 10943, 1211, 9673, 8592, 2655, 31747, 16247, 3615, 23942, 3714, 33599, 1829, 16070, 1935, 2689, 3866, 9673, 11242, 45761, 5172, 9673, 8592, 2655, 31747, 29739, 3794, 1829, 9566, 28242, 23758, 8032, 1863, 5016, 4117, 1829, 8978, 3224, 8978, 3714, 9957, 8978, 25062, 14407, 38251, 9673, 8592, 2655, 31747, 9673, 29245, 49401, 20449, 995, 25528, 22807, 23032, 1829, 3555], "avg_logprob": -0.13619523687460988, "compression_ratio": 1.8888888888888888, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1910.55, "end": 1911.25, "word": "هندرس", "probability": 0.79443359375}, {"start": 1911.25, "end": 1911.53, "word": " اللي", 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1919.83, "word": " common", "probability": 0.91455078125}, {"start": 1919.83, "end": 1920.61, "word": " divisor", "probability": 0.9609375}, {"start": 1920.61, "end": 1921.23, "word": " اللي", "probability": 0.958251953125}, {"start": 1921.23, "end": 1921.39, "word": " هو", "probability": 0.9873046875}, {"start": 1921.39, "end": 1921.89, "word": " العامل", "probability": 0.98291015625}, {"start": 1921.89, "end": 1922.51, "word": " المشترك", "probability": 0.9923095703125}, {"start": 1922.51, "end": 1923.33, "word": " الأعلى", "probability": 0.9329427083333334}, {"start": 1923.33, "end": 1924.23, "word": " ماشي", "probability": 0.8670247395833334}, {"start": 1924.23, "end": 1925.15, "word": " وال", "probability": 0.316650390625}, {"start": 1925.15, "end": 1925.67, "word": " least", "probability": 0.94384765625}, {"start": 1925.67, "end": 1926.03, "word": " common", "probability": 0.92578125}, {"start": 1926.03, "end": 1926.59, "word": " multiple", "probability": 0.88720703125}, {"start": 1926.59, "end": 1927.59, "word": " المضاعف", "probability": 0.959716796875}, {"start": 1927.59, "end": 1928.17, "word": " المشترك", "probability": 0.98486328125}, {"start": 1928.17, "end": 1929.43, "word": " البسيط", "probability": 0.9930419921875}, {"start": 1929.43, "end": 1930.03, "word": " كل", "probability": 0.701171875}, {"start": 1930.03, "end": 1930.27, "word": " هذا", "probability": 0.412841796875}, {"start": 1930.27, "end": 1930.77, "word": " هنحكي", "probability": 0.95712890625}, {"start": 1930.77, "end": 1931.03, "word": " فيه", "probability": 0.9873046875}, {"start": 1931.03, "end": 1931.17, "word": " في", "probability": 0.90234375}, {"start": 1931.17, "end": 1931.57, "word": " مين", "probability": 0.79150390625}, {"start": 1931.57, "end": 1932.33, "word": " في", "probability": 0.60302734375}, {"start": 1932.33, "end": 1933.09, "word": " القواسم", "probability": 0.9384765625}, {"start": 1933.09, "end": 1933.81, "word": " المشترك", "probability": 0.994384765625}, {"start": 1933.81, "end": 1934.55, "word": " الموجبة", "probability": 0.970703125}, {"start": 1934.55, "end": 1936.53, "word": " معايا؟", "probability": 0.8470458984375}, {"start": 1936.53, "end": 1936.85, "word": " طيب", "probability": 0.94482421875}], "temperature": 1.0}, {"id": 76, "seek": 195344, "start": 1938.4, "end": 1953.44, "text": "الان ناخد بعض الخواص اللي هي قواسم الأعداد ناخد النظرية الأولى اللى عندنا النظرية تتحدث بما يلي", "tokens": [6027, 7649, 8717, 47283, 3215, 45030, 11242, 33962, 14407, 9381, 13672, 1829, 39896, 12174, 14407, 38251, 16247, 22488, 18513, 8717, 47283, 3215, 28239, 19913, 2288, 10632, 16247, 12610, 7578, 13672, 7578, 43242, 8315, 28239, 19913, 2288, 10632, 6055, 2655, 24401, 12984, 4724, 15042, 7251, 20292], "avg_logprob": -0.28209917571233667, "compression_ratio": 1.6111111111111112, "no_speech_prob": 0.0, "words": [{"start": 1938.4, "end": 1939.0, "word": "الان", "probability": 0.3614501953125}, {"start": 1939.0, "end": 1939.48, "word": " ناخد", "probability": 0.7823893229166666}, {"start": 1939.48, "end": 1939.9, "word": " بعض", "probability": 0.9267578125}, {"start": 1939.9, "end": 1940.78, "word": " الخواص", "probability": 0.577392578125}, {"start": 1940.78, "end": 1941.9, "word": " اللي", "probability": 0.60498046875}, {"start": 1941.9, "end": 1942.5, "word": " هي", "probability": 0.8037109375}, {"start": 1942.5, "end": 1943.92, "word": " قواسم", "probability": 0.7317708333333334}, {"start": 1943.92, "end": 1944.5, "word": " الأعداد", "probability": 0.90234375}, {"start": 1944.5, "end": 1945.74, "word": " ناخد", "probability": 0.68701171875}, {"start": 1945.74, "end": 1946.7, "word": " النظرية", "probability": 0.884765625}, {"start": 1946.7, "end": 1947.66, "word": " الأولى", "probability": 0.97900390625}, {"start": 1947.66, "end": 1947.86, "word": " اللى", "probability": 0.6964111328125}, {"start": 1947.86, "end": 1948.5, "word": " عندنا", "probability": 0.772216796875}, {"start": 1948.5, "end": 1950.34, "word": " النظرية", "probability": 0.93115234375}, {"start": 1950.34, "end": 1951.7, "word": " تتحدث", "probability": 0.9395751953125}, {"start": 1951.7, "end": 1952.92, "word": " بما", "probability": 0.9375}, {"start": 1952.92, "end": 1953.44, "word": " يلي", "probability": 0.896728515625}], "temperature": 1.0}, {"id": 77, "seek": 197415, "start": 1960.87, "end": 1974.15, "text": "for any integers a,b and c the following holds لأن لأي integers a,b,c عندي الـ a عامل من عوامل السفر", "tokens": [2994, 604, 41674, 257, 11, 65, 293, 269, 264, 3480, 9190, 5296, 33456, 5296, 10721, 1829, 41674, 257, 11, 65, 11, 66, 43242, 1829, 2423, 39184, 257, 6225, 10943, 1211, 9154, 6225, 2407, 10943, 1211, 21136, 5172, 2288], "avg_logprob": -0.27443910103577834, "compression_ratio": 1.1944444444444444, "no_speech_prob": 0.0, "words": [{"start": 1960.87, "end": 1961.19, "word": "for", "probability": 0.191162109375}, {"start": 1961.19, "end": 1961.51, "word": " any", "probability": 0.8837890625}, {"start": 1961.51, "end": 1962.23, "word": " integers", "probability": 0.91357421875}, {"start": 1962.23, "end": 1963.15, "word": " a", "probability": 0.763671875}, {"start": 1963.15, "end": 1963.47, "word": ",b", "probability": 0.629638671875}, {"start": 1963.47, "end": 1963.79, "word": " and", "probability": 0.450927734375}, {"start": 1963.79, "end": 1964.19, "word": " c", "probability": 0.97021484375}, {"start": 1964.19, "end": 1964.69, "word": " the", "probability": 0.54833984375}, {"start": 1964.69, "end": 1965.25, "word": " following", "probability": 0.85302734375}, {"start": 1965.25, "end": 1965.83, "word": " holds", "probability": 0.892578125}, {"start": 1965.83, "end": 1966.75, "word": " لأن", "probability": 0.669921875}, {"start": 1966.75, "end": 1967.01, "word": " لأي", "probability": 0.758544921875}, {"start": 1967.01, "end": 1967.45, "word": " integers", "probability": 0.79248046875}, {"start": 1967.45, "end": 1967.77, "word": " a", "probability": 0.9150390625}, {"start": 1967.77, "end": 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