Pseudoprime numbers

Pseudoprime numbers

Time Limit: 1000MS Memory limit: 65536K

题目描述

 

Fermat's theorem states that for any prime number p and for any integer a > 1, a^p == a (mod p). That is, if we raise a to the pth power and divide by p, the remainder is a. Some (but not very many) non-prime values of p, known as base-a pseudoprimes, have this property for some a. (And some, known as Carmichael Numbers, are base-a pseudoprimes for all a.)
Given 2 < p ≤ 1,000,000,000 and 1 < a < p, determine whether or not p is a base-a pseudoprime.

输入

 

Input contains several test cases followed by a line containing "0 0". Each test case consists of a line containing p and a.

输出

 

For each test case, output "yes" if p is a base-a pseudoprime; otherwise output "no". 

示例输入

3 2
341 2
0 0

示例输出

no
yes

 

#include<stdio.h>
#include<math.h>
long exp_mod(long a,long n,long m)
{
    long k;
    if(n==0)
        return 1%m;
    if(n==1)
        return a%m;
    k=exp_mod(a,n/2,m);
    k=k*k%m;
    if(n%2==1)
        k=k*a%m;
    return k;
}
int main()
{
    int a,i,flag;
    long p,t,g;
    while(~scanf("%ld %ld",&p,&a)&&(p!=0&&a!=0))
    {
        t=p;flag=0;
        for(i=2;i<=sqrt(t);i++)
            if(t%i==0)
            {
                flag=1;
                break;
            }
            g=exp_mod(a,p,p);
            if(flag==1&&a==g)
                printf("yes\n");
            else
                printf("no\n");
    }
    return 0;
}