README.md

metadata

base_model: deepseek-ai/deepseek-math-7b-base
tags:
  - alignment-handbook
  - generated_from_trainer
  - aimo
widget:
  - example_title: Math problem
    messages:
      - role: user
        content: >-
          For how many values of the constant $k$ will the polynomial
          $x^{2}+kx+36$ have two distinct integer roots?
    output:
      text: >-
        ### Solution: 1. For the polynomial \\( x^2 + kx + 36 \\) to have two
        distinct integer roots, let's denote these roots by \\( r_1 \\) and \\(
        r_2 \\).\n\n2. According to Vieta's formulas, the sum of the roots \\(
        r_1 + r_2 \\) is equal to \\(-k\\), and the product of the roots \\( r_1
        \\cdot r_2 \\) is equal to 36.\n\n3. To find the distinct integer pairs
        \\((r_1, r_2)\\) whose product is 36, we need to determine all pairs of
        integers \\((r_1, r_2)\\) such that \\( r_1 \\cdot r_2 = 36 \\) and \\(
        r_1 \\neq r_2 \\).\n\n4. From the equation \\( r_1 + r_2 = -k \\), for
        each valid pair \\((r_1, r_2)\\), we can compute the corresponding value
        of \\( k \\).\n\n5. Finally, since we need the polynomial to have two
        distinct integer roots, we need to ensure that \\( r_1 \\) and \\( r_2
        \\) are distinct.\n\nLet's start by finding all pairs \\((r_1, r_2)\\)
        such that \\( r_1 \\cdot r_2 = 36 \\). We'll then determine the values
        of \\( k \\) and ensure the roots are distinct.\n```python\nimport
        itertools\n\n# Find all pairs (r1, r2) such that r1 * r2 =
        36\nproduct_36 = 36\nfactor_pairs = []\n\nfor i in range(1, product_36 +
        1):\n if product_36 % i == 0:\n pair = (i, product_36 // i)\n if pair[0]
        != pair[1]: # Ensure distinct pairs\n factor_pairs.append(pair)\n\n#
        Calculate k for each pair and ensure distinct integer
        roots\nvalid_k_values = set()\nfor r1, r2 in factor_pairs:\n if r1 !=
        r2:\n k = -(r1 + r2)\n
        valid_k_values.add(k)\n\nprint((len(valid_k_values),
        sorted(valid_k_values)))\n```\n```output\n(4, [-37, -20, -15,
        -13])\n```\nThe distinct integer values of \\( k \\) that make the
        polynomial \\( x^2 + kx + 36 \\) have two distinct integer roots are
        \\(-37, -20, -15, \\text{and} -13\\).\n\nTherefore, the number of such
        values of \\( k \\) is:\n\n\\[\n\\boxed{4}\n\\]\n
pipeline_tag: text-generation
model-index:
  - name: NuminaMath-7B-TIR-GPTQ
    results: []
license: apache-2.0
language:
  - en

Model Card for NuminaMath 7B TIR GPTQ

NuminaMath is a series of language models that are trained to solve math problems using tool-integrated reasoning (TIR). NuminaMath 7B TIR won the first progress prize of the AI Math Olympiad (AIMO), with a score of 29/50 on the public and private tests sets.

This model is an 8-bit version of AI-MO/NuminaMath-7B-TIR, which we quantized with AutoGPTQ to run fast inference in the Kaggle submissions. Please consult the original model card for more details.