Triangular, pentagonal, and hexagonal | Project Euler | Problem #45

URL to the problem page: https://projecteuler.net/problem=45

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

Triangle Tₙ=n(n+1)/2     1, 3, 6, 10, 15, ...
Pentagonal Pₙ=n(3n−1)/2     1, 5, 12, 22, 35, ...
Hexagonal Hₙ=n(2n−1)     1, 6, 15, 28, 45, ...

It can be verified that T₂₈₅ = P₁₆₅ = H₁₄₃ = 40755.

Find the next triangle number that is also pentagonal and hexagonal.

#include <iostream>

using namespace std;

int main()

{

    long long i, j, a, result = 0, triangular, pentagonal, hexagonal;

    for (i = 286; result <= 0; i++) {

        triangular = (i * (i + 1)) / 2;

        pentagonal = 0;

        for (j = 166; pentagonal <= triangular; j++) {

            pentagonal = (j * ((3 * j) - 1)) / 2;

            if (pentagonal == triangular) {

                hexagonal = 0;

                for (a = 144; hexagonal <= triangular; a++) {

                    hexagonal = a * ((2 * a) - 1);

                    if (hexagonal == pentagonal) {

                        cout << "First triangle number that is also pentagonal and hexagonal after 40755 is  =  " << triangular << endl;

                        result++;

                        break;

                    }

                }

            }

            if (result > 0) {

                break;

            }

        }

    }

    return 0;

}

CLICK TO SEE THE OUTPUT.