POJ 3641 pseudoprime Numbers

Pseudoprime numbers

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 7000		Accepted: 2855

Description

Fermat ' s theorem states that for any prime numberPand for any integera> 1,AP=a  (Mod&NBSP; p ). That is, if we raise&NBSP; a   To The&NBSP; p th power and Divide by&NBSP; p , the remainder is &NBSP; a . Some (but not very many) Non-prime values Of&NBSP; p , known as base- a< Span class= "Apple-converted-space" >&NBSP; pseudoprimes, with this property for Some&NBSP; a . (and some, known as Carmichael Numbers, is base- a  pseudoprimes for All&NBSP; 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, the 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

Source

Waterloo Local Contest, 2007.9.23

1#include <cstdio>2#include <cmath>3#include <cstring>4#include <iostream>5 using namespacestd;6 #defineMax 10000000007typedefLong Longll;8 BOOLIsPrime (intN) {//Judging the prime number, the problem max is too large, not suitable for the table method9     if(n==0|| n==1){Ten         return false; One     } A     if(n==2){ -         return true; -     } the     if(n%2==0) -         return false; -     intI=3, HALF=SQRT (n1.0); -      for(; i<=half;i+=2){ +         if(n%i==0){ -             return false; +         } A     } at     return true; - } -ll work (ll A,ll b,ll k) {//a^b mod k quick Power template -     if(a==0){ -         return 0; -     } in     if(b==0){ -         return 1; to     } +ll x=a%k,ans=1; -      for(;b>0; b/=2){ the         if(b%2){ *Ans= (ans*x)%k;//This must be the last to arrive . $         }Panax Notoginsengx=x*x%K; -     } the     returnans; + } A intMain () the { +     intP,a; -      while(cin>>p>>a&&p&&a) { $          //Cout<<isprime (p) <<endl; $          if(!isprime (p) && (Work (a,p,p) ==a%p)) {//pay attention to prime number judgment -cout<<"Yes"<<Endl; -          }         the          Else{ -cout<<"No"<<Endl;Wuyi          } the     } -     return 0; Wu}

POJ 3641 pseudoprime Numbers