C :

#include<stdio.h>

int main()
{
	int n,x,i,s;
	while(scanf("%d",&n)!=EOF)
	{
		if(n%2==0||n==1)
			printf("2^? mod %d = 1\n",n);
		else
		{
			for(s=i=2;;i++)
			{
				s*=2;
				if(s%n==1)
				{
					printf("2^%d mod %d = 1\n",i,n);
					break;
				}
				s%=n;
			}
		}
	}
	return 0;
}

C++ :

#include<stdio.h>

int main()
{
	int n,x,i,s;
	while(scanf("%d",&n)!=EOF)
	{
		if(n%2==0||n==1)
			printf("2^? mod %d = 1\n",n);
		else
		{
			for(s=i=2;;i++)
			{
				s*=2;
				if(s%n==1)
				{
					printf("2^%d mod %d = 1\n",i,n);
					break;
				}
				s%=n;
			}
		}
	}
	return 0;
}

Java :

import java.util.Scanner;
public class Main{
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        while(in.hasNextInt()){
            int n = in.nextInt();
            int b = Integer.MAX_VALUE;
            if(n==1||n%2==0){
                System.out.println("2^? mod "+n+" = 1");
                continue;
            }
            else{
                for(int i=1;i<b;i++){
                    if(Math.pow(2,i)%n==1){
                        System.out.println("2^"+i+" mod "+n+" = 1");break;
                    }
                }
            }
        }
    }
}