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-apseudoprimes for all a.)
Given 2 < p ≤ 1000000000 and 1 < a < p, determine whether or not p is a base-apseudoprime.
Input contains several test cases followed by a line containing "0 0". Each test case consists of a line containing p and a.
For each test case, output "yes" if p is a base-a pseudoprime; otherwise output "no".
3 2 10 3 341 2 341 3 1105 2 1105 3 0 0
no no yes no yes yes
给出a,p,如果(a^p)%p==a则称p为base-a pseudoprimes(注意这里p需为素数),判断p是不是一个base-a pseudoprimes
代码:
#include<iostream>
#include<string>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<iomanip>
#include<queue>
#include<cstring>
#include<map>
using namespace std;
typedef long long ll;
ll p,a;
ll pow_mod(ll n,ll k,ll m) //快速幂求(n^p)%m的值
{
ll res=1;
while(k>0)
{
if(k&1)
res=res*n%m;
n=n*n%m;
k>>=1;
}
return res;
}
bool is_prime(ll x)
{
double tx=sqrt(1.0*x);
ll it=2;
while(it<=tx&&x%it!=0)
it++;
if(it>tx)
return true;
else
return false;
}
int main()
{
while(scanf("%lld%lld",&p,&a)!=EOF)
{
if(p==0&&a==0)
break;
if(is_prime(p)==true)
{
printf("no\n");
continue;
}
ll temp=pow_mod(a,p,p);
if(temp==a)
{
printf("yes\n");
}else{
printf("no\n");
}
}
return 0;
}