The fifth power of 72

72-pow-5.txt

A Python program that proves a = 72 is the smallest solution to
a^5 = b^5 + c^5 + d^5 + e^5 + f^5 where a...f are positive integers.
Prints 72 (19, 43, 46, 47, 67).

import itertools
for base in range(1, 72 + 1):
    for comb in itertools.combinations_with_replacement(range(1, base), 5):
        if sum(b ** 5 for b in comb) == base ** 5:
            print(base, comb)