hdu13952^x mod n = 1<数论>

链接:http://acm.hdu.edu.cn/showproblem.php?pid=1395

思路: 由题意得N=2^x(x>=1)为偶数, 所以当 n 也为偶数时  N%n必为偶数, 故不存在;

当n为奇数时,利用同余定理求;

#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <cmath>
using namespace std;

int main( )
{
    int N;
    while( scanf( "%d", &N )!= EOF ){
        if( N==1 || !(N&1) )
            printf( "2^? mod %d = 1\n", N );
        else{
            int t=2, ans=1;
            while( t != 1 ){
                t <<= 1;
                t%=N;
                ans++;
            } 
            printf( "2^%d mod %d = 1\n",ans, N );
            
        }
    }
    return 0;
}