Pseudoprime numbers
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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
3 210 3341 2341 31105 21105 30 0
Sample Output
nonoyesnoyesyes
不是素数,但满足ap = a (mod p),即ap %p=a,为伪素数,输出 yes,否则输出no.
#include<stdio.h>
__int64 ispri(__int64 num){
for(int i=2;i*i<num;i++)
if(num%i==0)
return 0;
return 1;
}
__int64 quickpow(__int64 a,__int64 b,__int64 c)
{
__int64 tmp=a,res=1;
while(b)
{
if(b&1)
{
res*=tmp;
res%=c;
}
tmp*=tmp;
tmp%=c;
b>>=1;
}
return res;
}
int main()
{
__int64 p,a;
while(~scanf("%I64d %I64d",&p,&a)&&(p||a))
{
if(!ispri(p)&&quickpow(a,p,p)==a%p)
printf("yes\n");
else
printf("no\n");
}
return 0;
}
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