import itertools

SAMPLES = 100000

def triangle_num(n):
    return n * (n+1) / 2


def pentagonal_num(n):
    return n * (3 * n -1) / 2


def hexagonal_num(n):
    return n * (2 * n - 1)


if __name__ == '__main__':
    tris = [triangle_num(x) for x in range(2, SAMPLES)]
    pents = [pentagonal_num(x) for x in range(2, SAMPLES)]
    hexs = [hexagonal_num(x) for x in range(2, SAMPLES)]
    triplets = itertools.product(tris, pents, hexs)
    print(set(tris) & set(pents) & set(hexs))