Brutkey

Trammell Hudson
@th@social.v.st

This short paper by Lander and Parkin from 1966 almost achieves xkcd's goal of a wordless proof.

COUNTEREXAMPLE TO EULER'S CONJECTURE ON SUMS OF LIKE POWERS BY L. J. LANDER AND T. R. PARKIN Communicated by J. D. Swift, June 27, 1966 A direct search on the CDC 6600 yielded 27^5 + 84^5 + 110^5 + 133^5 = 144^5 as the smallest instance in which four fifth powers sum to a fifth power. This is a counterexample to a conjecture by Euler that at least n nth powers are required to sum to an nth power, n>2.