poj - 3641 题解

题意：检验一个数是否是质数，且满足a^p = a (mod p)

题解：快速幂，质数检验

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<algorithm>
 4 #include<cmath>
 5 using namespace std;
 6 long long power(long long a,long long b,long long c)
 7 {
 8     long long res,t;
 9     res=1;
10     t=a%c;
11     while(b)
12     {
13         if(b&1)
14         {
15             res*=t;
16             res%=c;
17         }
18         t*=t;
19         t%=c;
20         b>>=1;
21     }
22     return res;
23 }
24 bool is_prime(int x)
25 {
26     bool res=true;
27     for(int i=2;i<=sqrt(x);i++)
28     {
29         if(x%i==0)
30         {
31             res=false;
32         }
33     }
34     return res;
35 }
36 int main()
37 {
38     long long p,a;
39     while(true)
40     {
41         cin>>p>>a;
42         if(p==0&&a==0)
43         {
44             break;
45         }
46         if(is_prime(p))
47         {
48             cout<<"no\n";
49             continue;
50         }
51         if(power(a,p,p)==a)
52         {
53             cout<<"yes\n";
54         }
55         else
56         {
57             cout<<"no\n";
58         }
59     }
60     return 0;
61 }