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;
}
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