POJ3641 Pseudoprime numbers 【快速幂】

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Pseudoprime numbers
Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 6644 Accepted: 2696

Description

Fermat's theorem states that for any prime number p and for any integer a > 1, ap = 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-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

3 210 3341 2341 31105 21105 30 0

Sample Output

nonoyesnoyesyes

Source

Waterloo Local Contest, 2007.9.23

#include <stdio.h>#include <string.h>#include <math.h>typedef long long LL;bool isPrime(int n) {    if(n < 2) return false;    int t = sqrt((double)n);    for(int i = 2; i <= t; ++i)        if(n % i == 0) return false;    return true;}LL mod_power(LL x, LL n, LL mod) {    LL ret = 1;    for( ; n > 0; n >>= 1) {        if(n & 1) ret = ret * x % mod;        x = x * x % mod;    }    return ret;}int main() {    LL p, a;    while(scanf("%lld%lld", &p, &a), p | a) {        if(isPrime(p)) printf("no\n");        else printf(mod_power(a, p, p) == a ? "yes\n" : "no\n");    }    return 0;}


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