2^x mod n = 1（hd1395）

2^x mod n = 1

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 14214    Accepted Submission(s): 4403

Problem Description

Give a number n, find the minimum x(x>0) that satisfies 2^x mod n = 1.

 

 

Input

One positive integer on each line, the value of n.

 

 

Output

If the minimum x exists, print a line with 2^x mod n = 1.

Print 2^? mod n = 1 otherwise.

You should replace x and n with specific numbers.

 

 

Sample Input

2

5

 

 

Sample Output

2^? mod 2 = 1

2^4 mod 5 = 1

#include <iostream>
using namespace std;
int main()
{
    int n,i,j;
    while(cin>>n)
    {
        int x=2;
        if(n==1||n%2==0)
        {
            cout<<"2^? mod "<<n<<" = 1\n";
            continue;
        }
        for(i=0;;i++)
        {
            if(x==1)
                break;
            else
            {
                x=x*2;
                x=x%n;
            }
        }
        cout<<"2^"<<i+1<<" mod "<<n<<" = 1"<<endl;
    }
}