POJ3641: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
 
[cpp]  
  
[cpp]  
#include  

using namespace std;  
  
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;  
}  
  
long long mod(long long a,long long b,long long m)  
{  
    long long ans = 1;  
    while(b>0)  
    {  
        if(b&1)  
        {  
            ans = ans*a%m;  
            //b--;  
        }  
        b>>=1;  
        a = a*a%m;  
    }  
    return ans;  
}  
  
int main()  
{  
    long long a,p;  
  
    while(cin >> p >> a && (p||a))  
    {  
        long long ans;  
        if(prime(p))  
        cout << "no" << endl;  
        else  
        {  
            ans = mod(a,p,p);  
            if(ans == a)  
            cout << "yes" << endl;  
            else  
            cout << "no" << endl;  
        }  
    }  
  
    return 0;  
}

补充：软件开发 , C++ ,