Counterexample to Euler’s conjecture on sums of like powers

Abstract

A direct search on the CDC 6600 yielded 27 5 + 84 5 + HO 5 + 133 6 -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 [l] that at least n nth powers are required to sum to an nth power, n>2.