C :

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

int main()
{
	int n;
	scanf("%d", &n);
	int nTwo;
	int j;
	int *a = (int *)malloc(n*sizeof(int));
	int *x = (int *)malloc(n*sizeof(int));
	int i;
	for(i = 0; i < n; i++)
	{
		scanf("%d", &a[i]);
	}
	for(i = 0; i < n; i++)
	{
		if(a[i] == 1)
		{
			x[i] = 1;
			continue;
		}
		if(!(a[i]%2))
		{
			x[i] = 0;
			continue;
		}
		for(j = 2; j < 99999; j++)
		{
			nTwo = pow(2, j);
			if(nTwo % a[i] == 1)
			{
				x[i] = j;
				break;
			}
		}
	}
	for(i = 0; i < n; i++)
	{
		if(!x[i])
		{
			printf("2^? mod %d = 1\n", a[i]);
		}
		else
		{
			printf("2^%d mod %d = 1\n", x[i], a[i]);
		}
	}
	return 0;
}