Euler Brick Problem

#include <iostream>
#include <stdlib.h>
#include <math.h>
#include <vector>
#include <algorithm>
#define LIMIT 500

using namespace std;

// Auxiliary Functions
double hypot(int a, int b){
    return sqrt(a*a + b*b);
}

bool isInteger(double d){
    if(d == int(d)){
        return true;
    }
    return false;
}

// MAIN FUNCTION
int main()
{
    cout << "LIMIT = " << LIMIT << ", for a, b and c" << endl << endl;
    cout << "Time for 250^3 executions is about 2.1 seconds." << endl;
    cout << "Time for 500^3 executions is about 16.8 seconds." << endl;
    cout << "Time for 750^3 executions is about 52 seconds." << endl;
    cout << "Time for 1000^3 executions is about 125 seconds." << endl << endl;
    vector <int> triades = vector <int> ();
    int counter = 0;
    for(int a=1; a<LIMIT; a++){
        for(int b=1; b<LIMIT; b++){
            for(int c=1; c<LIMIT; c++){
                double hypot1 = hypot(a, b);
                double hypot2 = hypot(a, c);
                double hypot3 = hypot(b, c);
                if(isInteger(hypot1) == true && isInteger(hypot2) == true && isInteger(hypot3) == true && (hypot1 < hypot2) && (hypot2 < hypot3)){
                    counter++;
                    triades.push_back(a);
                    triades.push_back(b);
                    triades.push_back(c);
                    cout << "**** Solution " << counter << " ****" << endl;
                    cout << "(" << a << ", " << b << ", " << c << "), because: " << endl;
                    cout << "x = sqrt(" << a << "^2 + " << b << "^2 = " << hypot1 << endl;
                    cout << "y = sqrt(" << a << "^2 + " << c << "^2 = " << hypot2 << endl;
                    cout << "z = sqrt(" << b << "^2 + " << c << "^2 = " << hypot3 << endl << endl;
                }
            }   // END OF FOR-LOOP-3
        }   // END OF FOR-LOOP-2
    }   // END OF FOR-LOOP-1
    return 0;
}