#include #include #include using namespace std; typedef long long ll; typedef unordered_set usi; ll sieve_size; bitset<10000000> bs; usi primes, carmichael; void sieve(ll upperbound = 65000) { sieve_size=upperbound+1; bs.set(); bs[0]=bs[1]=0; for (ll i=2; i<=sieve_size; i++) if(bs[i]) { for (ll j=i*i; j<=sieve_size; j+=i) bs[j] = 0; primes.insert((int)i); } } long long pwr(long long b, long long e, long long mod) { if (e == 0) return 1%mod; if (e == 1) return b%mod; long long aux = pwr(b, e/2, mod); aux = (aux*aux)%mod; if (e%2) aux = (aux*(b%mod))%mod; return aux; } int main() { sieve(); for (int i = 3; i <= 65000; i++) { if (primes.count(i)) continue; bool ok = true; for (int j = 2; j < i && ok; j++) { ok = pwr(j, i, i) == j; } if (ok) carmichael.insert(i); } int n; while (cin >> n && n) { if (carmichael.count(n)) printf("The number %d is a Carmichael number.\n", n); else printf("%d is normal.\n", n); } return 0; }