【POJ 3641】Pseudoprime numbers

Pseudoprime numbers

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-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

#include<stdio.h>#include<string.h>long long quickcmp(long long i,long long j,long long k){    long long sum=1,base=i;    while(j)    {        if(j&1)        {            sum=sum*base%k;        }        base=(base%k*base%k)%k;        j>>=1;    }    return sum;}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;}int main(){    long long p,a;    while(scanf("%lld%lld",&p,&a)!=EOF&&(a||p))    {        if(prime(p))        printf("no\n");        else        {            if(quickcmp(a,p,p)==a)            printf("yes\n");            else             printf("no\n");         }     }    return 0;}