UVA 10006 Carmichael Numbers

#include <map>
#include <set>
#include <list>
#include <cmath>
#include<cctype>
#include <ctime>
#include <deque>
#include <stack>
#include <queue>
#include <cstdio>
#include <string>
#include <vector>
#include<climits>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#define LL long long
#define PI 3.1415926535897932626
using namespace std;
int gcd(int a, int b) {return a % b == 0 ? b : gcd(b, a % b);}
bool prime[66000];
LL N;
void init()
{
    for (int i=0;i<66000;i++) prime[i]=true;
    prime[0]=prime[1]=false;
    for (int i=2;i*i<66000;i++)
        if (prime[i])
        for (int j=i+i;j<66000;j+=i)
         prime[j]=false;
}
LL pow_mod(LL a,LL b,LL m)
{
    LL ans=1;
    a%=m;
    while (b)
    {
        if (b&1) ans=(ans*a)%m;
        a=(a*a)%m;
        b>>=1;
    }
    return ans;
}
int main()
{
    init();
    while (scanf("%lld",&N)!=EOF)
    {
        if (N==0) break;
        if (prime[N]) {printf("%lld is normal.\n",N);continue;}
        bool flag=false;
        for (LL i=2;i<N;i++)
            if (pow_mod(i,N,N)!=i)
        {
            flag=true;
            break;
        }
        if (flag) printf("%lld is normal.\n",N);
        else printf("The number %lld is a Carmichael number.\n",N);
    }
    return 0;
}