Pseudoprime numbers
Time Limit: 1000MS | | Memory Limit: 65536K |
Total Submissions: 12461 | | Accepted: 5367 |
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
Source
Waterloo Local Contest, 2007.9.23
算法分析:
题意:
输入p,a,如果p是素数输出no,如果p不是素数,判断a^p%p==a是否成立,如果成立输出yes,否则输出no
实现:
题目不难,题意难理解而已,素数判定(不达表)+快速幂取模
代码实现:
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<cmath>
#include<iostream>
#include<sstream>
#include<iterator>
#include<algorithm>
#include<string>
#include<vector>
#include<set>
#include<map>
#include<stack>
#include<deque>
#include<queue>
#include<list>
using namespace std;
typedef long long ll;
ll quick_qow(ll a,ll b,ll k)
{
long long res=1;
while(b>0)
{
if(b%2) res=(res*a)%k;
a=(a*a)%k;
b/=2;
}
return res;
}
int isPrime(int n)
{ //返回1表示判断为质数,0为非质数,在此没有进行输入异常检测
float n_sqrt;
if(n==2 || n==3) return 1;
if(n%6!=1 && n%6!=5) return 0;
n_sqrt=floor(sqrt((float)n));
for(int i=5;i<=n_sqrt;i+=6)
{
if(n%(i)==0 | n%(i+2)==0) return 0;
}
return 1;
}
int main()
{
int p,a;
while(scanf("%d%d",&p,&a)!=EOF&&(p!=0&&a!=0))
{
if(isPrime(p)==1 ) {cout<<"no"<<endl;continue;}
if(quick_qow(a,p,p)==a) cout<<"yes"<<endl;
else cout<<"no"<<endl;
}
}
标签:return,int,ll,long,base,POJ,numbers,Pseudoprime,include From: https://blog.51cto.com/u_14932227/6041963