https://www.youtube.com/watch?v=Gh8h8MJFFdI

results.txt

1^2 = 1(1+1)/2 = 1
6^2 = 8(8+1)/2 = 36
35^2 = 49(49+1)/2 = 1225
204^2 = 288(288+1)/2 = 41616
1189^2 = 1681(1681+1)/2 = 1413721
6930^2 = 9800(9800+1)/2 = 48024900
40391^2 = 57121(57121+1)/2 = 1631432881

square_triangles.py

import sys
import multiprocessing
from itertools import combinations_with_replacement

def cube_triangle(number1, number2):
    cube = number1 ** 2
    triangle = (number2 * (number2 + 1))/2
    if cube == triangle:
        print "{0}^2 = {1}({1}+1)/2 = {2}".format(number1, number2, cube)
        sys.stdout.flush()

numbers = xrange(1, 10**7)

if __name__ == '__main__':
    for number1, number2 in combinations_with_replacement(numbers, 2):
        d = multiprocessing.Process(name='cubtri', target=cube_triangle, args=(number1, number2))
        d.daemon = True
        d.start()