2^x mod n = 1

2^x mod n = 1

Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 59   Accepted Submission(s) : 16

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

 

Author

MA, Xiao

 

Source

ZOJ Monthly, February 2003

 

#include <stdio.h>
#include <stdlib.h>

int main()
{
    int i,n,x,sign,sum,N;
    while(scanf("%d",&n)!=EOF)
    {
        sign=0;
        if(n%2==0||n==1)
            sign--;
        else
        {
            for(i=1,N=1,sign=0;;i++)
            {
                N=(N*2)%n;
                if(N==1)
                {
                    x=i;
                    sign++;
                    break;
                }
            }

        }
        if(sign==1)
            printf("2^%d mod %d = 1
",x,n);
        else
            printf("2^? mod %d = 1
",n);
    }
}