#!/usr/bin/env python
#
from math import log10


def main():
    for x, y, z, num_nodes in sorted(list(get_matches(90, 90)), key=lambda val: val[3]):
        if num_nodes < 1000000:
            print(f"{x}**{y} == {y}**{z} == {num_nodes}")


def get_matches(max_x: int, max_y: int):
    for x in range(2, max_x):
        for y in range(2, max_y):
            diff, y_exp = check(x, y)
            if diff == 0:
                yield (x, y, y_exp, x**y)


def check(x: int, y: int):
    num_nodes = x**y
    # y**z = x**y
    # zlogy = ylogx
    # z = ylogx/logy

    # flipped:
    exp_for_y = y * log10(x) / log10(y)
    # Round the exp for y to be a plain integer
    exp_for_y = round(exp_for_y)
    flipped_num_nodes = y**exp_for_y

    # compare the num nodes after rounding to find a good fit with integers.
    diff = abs(num_nodes - flipped_num_nodes)

    return diff, exp_for_y


if __name__ == "__main__":
    main()