nick.cpp

#include <iostream>
#include <iomanip>
#include <ctime>

int main()
{
    const auto pentagonal_function = [](double n) -> double { return (n * ((3 * n) - 1)) / 2; };
    const auto hexagonal_function = [](double n) -> double { return n * ((2 * n) - 1); };

    double pent_index = 0;
    double hex_index  = 0;
    unsigned int solution_count = 0;

    std::clock_t start = std::clock();

    std::cout << std::fixed << std::setprecision(0);

    while(true)
    {
        const auto pent_number = pentagonal_function(pent_index);
        const auto hex_number  = hexagonal_function(hex_index);

        if (pent_number < hex_number) ++pent_index;
        else if (pent_number > hex_number) ++hex_index;
        else if (pent_number == hex_number)
        {
            ++solution_count;

            std::cout << "Solution #" << solution_count << " found in " << (std::clock() - start) / (double) CLOCKS_PER_SEC << "s" << ":\n--> Triangular N: " << hex_index * 2 << "\n--> Pentagonal N: " << pent_index << "\n--> Hexagonal N: " << hex_index << "\n";

            ++pent_index;
        }
    }
}