学步园

题意：判断一个数是否是基于a的伪素数。只有当p是合数且a^p = a ( mod p ) 时，才输出yes。

题解：Miller_Rabin素数测试。

#include<cstdio>
#include<ctime>
#include<cstdlib>
using namespace std;
#define lint __int64

lint modular_exponent ( lint a, lint b, lint n )
{
    lint ret = 1;
    for ( ; b; b >>= 1, a = a*a%n )
        if ( b & 1 )
            ret = ret * a % n;
    return ret;
}

int miller_rabin ( int n, int time = 20 )
{
    if ( n==1 || (n!=2&&!(n%2)) || (n!=3&&!(n%3)) || (n!=5&&!(n%5)) || (n!=7&&!(n%7)) )
        return 0;
    while ( time-- )
    {
        lint m = modular_exponent ( rand()%(n-1) + 1, n-1, n );
        if ( m != 1 ) return 0;
    }
    return 1;
}

int main()
{
    lint p, a;
    while ( 1 )
    {
        scanf("%I64d%I64d",&p,&a);
        if ( a == 0 && p == 0 ) break;
        if ( modular_exponent(a,p,p) == a && !miller_rabin(p) )
            printf("yes\n");
        else printf("no\n");
    }
    return 0;
}