Project Euler Problem9

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,

a² + b² = c²

For example, 3² + 4² = 9 + 16 = 25 = 5².

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.

#include <bits/stdc++.h>
using namespace std;

int main()
{
  for(int i=0; i< 1000; i++)
  {
    for(int j=i+1; j<1000; j++)
    {
      for(int k=j+1; k<1000; k++)
      {

         if(i + j + k == 1000 && (i*i + j*j == k*k))
           cout << i*j*k << endl;

      }

    }
  }

}