Project Euler 9 - Pythagorean Triplet

/*
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a^2 + b^2 = c^2
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product a*b*c.
*/

#include <iostream>
#include <stdlib.h>
#include <math.h>
#define LIMIT 1000

using namespace std;

// Auxiliary Functions
bool isPythagorianTriplete(int a, int b, int c){
    if(c == sqrt(a*a + b*b)){
        return true;
    }
    return false;
}

int main()
{
    int a, b, c;
    for(int i=0; i<LIMIT; i++){
        for(int j=0; j<LIMIT; j++){
            for(int k=0; k<LIMIT; k++){
                if(isPythagorianTriplete(i, j, k) == true && i < j && j < k && i+j+k == 1000){
                    a = i;
                    b = j;
                    c = k;
                }
            }
        }
    }
    cout << "These numbers are: " << a << ", " << b << " and " << c << ", so " << a << " * " << b << " * " << c << " = " << a * b * c << endl;
    return 0;
}