There exists exactly one Pythagorean triplet for which a+b+c=100. Find the product abc.

Special Pythagorean Triplet.cpp

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

// find two numbers who's squares, when added, equal a number whose square root, plus those two numbers equals 1000

int main() {
    cout << []{
        int n = 1000;
        for (int a = 1; a <= n; a++) {
            for (int b = a + 1; b <= n; b++) {
                int c_squared = a * a + b * b;
                double cd = sqrt(c_squared);
                if (cd != (int)cd) {
                    continue;
                }
                int c = cd;
                if (c > b && a + b + c == n) {
                    return a * b * c;
                }
            }
        }
        return 0;
    }();
}