Problem 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
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题意:给出 p 和 a,若 a^p 对 p 取余且 p 不是素数,则输出 yes,否则输出 no
思路:大整数快速幂求模,加素数判断
Source Program
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<string>
#include<cstdlib>
#include<queue>
#include<set>
#include<map>
#include<stack>
#include<ctime>
#include<vector>
#define INF 0x3f3f3f3f
#define PI acos(-1.0)
#define N 1000005
#define MOD 1e9+7
#define E 1e-6
#define LL long long
using namespace std;
LL Pow_Mod(LL a, LL b, LL m)
{
LL res=1;
while(b)
{
if(b&1)
res=(res*a)%m;
a=(a*a)%m;
b>>=1;
}
return res;
}
bool prime(LL n)
{
if(n==2)
return true;
for(LL i=2;i*i<=n;i++)
if(n%i==0)
return false;
return true;
}
int main()
{
LL p,a;
while(scanf("%lld%lld",&p,&a)!=EOF&&(p+a))
{
if( !prime(p) && Pow_Mod(a,p,p)==a )
printf("yes\n");
else
printf("no\n");
}
return 0;
}