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

int main(int argc, char *argv[]){
  int i;
  int expo = atoi(argv[1]);
  int mod = (1<<expo)-1;
  int lucas, lucnew;
  
  printf("checking exponent %d\n", expo);

  lucas = 4;
  for(i=2;i<expo;i++){
    lucnew = (int)(pow(lucas,2)-2) % mod;
    printf("S(%d) = (%d^2 - 2) mod %d = %d\n", i, lucas, mod, lucnew);
    lucas = lucnew;
  }
}