Pseudoprime numbers
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 7954 | Accepted: 3305 |
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-apseudoprimes, 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 anda.
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
<span style="font-size:32px;">#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
using namespace std;
long long a,p;
long long power(long long a,long long p)
{
long long ret=1,temp=p;
while(temp)
{
if(temp&1)
ret=(ret*a)%p;
a=(a*a)%p;
temp>>=1;
}
return ret%p;
}
bool prime(long long m)
{
for(long long i=2;i*i<=m;i++)
if(m%i==0)
return false;
return true;
}
int main()
{
long long a,p;
while(~scanf("%lld %lld",&p,&a))
{
if(a==0&&p==0) return 0;
if(power(a,p)==a%p&&!prime(p))
printf("yes\n");
else
printf("no\n");
}
return 0;
}
</span>