Pseudoprime numbers poj3641

Pseudoprime numbers

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 8682		Accepted: 3645

Description

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 p^th 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 ≤ 1000000000 and 1 < a < p, determine whether or not p is a base-a pseudoprime.

Input

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

Output

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

Sample Input

3 2
10 3
341 2
341 3
1105 2
1105 3
0 0

Sample Output

no
no
yes
no
yes
yes

Source

Waterloo Local Contest, 2007.9.23

题目分析：主要在于素数的判断和快速幂算法

#include <iostream>  
using namespace std;  

int prime(long long a)  
{  
    int i;  
    if(a == 2)  
        return 1;  
    for(i = 2; i*i<=a; i++)  
        if(a%i == 0)  
           return 0;  
    return 1;  
}  

long long mod(long long a,long long b,long long c)  
{  
    long long ans = 1;  
    a=a%c;
    while(b>0)  
    {
        if(b%2==1) ans=(ans*a)%c;
        b=b/2;
        a=(a*a)%c;  
    }
    return ans;  
}    
int main()  
{  
    long long a,p;  
  
    while(cin >> p >> a)  
    {  
        if(p==0 &&    a==0)    break;
        long long ans;  
        if(prime(p))  
        cout << "no" << endl;  
        else  
        {  
            ans = mod(a,p,p);  
            if(ans == a)  
            cout << "yes" << endl;  
            else  
            cout << "no" << endl;  
        }        
    }  
  
    return 0;  
}