#include <iostream>
#include <cassert>
#include <cstdlib>
#include "Mod.cpp"


int main()
{
//Exrcise 11.5.1 Section 11.5.6
   Mod<13> n11(11);
   Mod<13> n9(9);
   Mod<13> n5(5);
   Mod<13> n8(8);
   assert((n11+n9).value() == 7);
   assert((n9-n11).value() == 11);

   assert( (n5*n8).value() == 1 );
   // no division yet for assert( (n5/n8).value() = 5 );
   Mod<13> s(5);
   // 5^8 is square(square(square(5)))
   s=s*s; //5^2
   s=s*s; //5^4
   s=s*s; //5^8
   assert( s.value() == 1 );
   //or
   assert( n5.square().square().square().value() == 1 );
   //or
   assert( n5.pow(n8).value() == 1);
   
   std::cout << "----\n" << (n8.pow(n5)).value() <<std::endl;
   std::cout << "----\n";

// Exercise 11.5.2 Section 11.5.6
   Mod<561>x(7);  //test number
   const int N=10; // highest power

   Mod<561>p[N+1]; // table of powers of x mod 561: p[i] = x^(i+1)
   p[0]=Mod<561>(x);
   Mod<561>y(x);
   for(int i=1;i<N+1;i++)
   {
       y = y*y;
       p[i] = y;
       std::cout << i << " " << y.value() <<std::endl;
   }
   // calculate x^560 where 560 = binary("100011000")
   std::cout << "----\n" << (p[4]*p[5]*p[9]).value() <<std::endl;

   return 0;
}