Counterexample to Euler’s conjecture on sums of like powers

1966/01/01 by L. J. Lander, T. R. Parkin · 1 voice · 3 citations
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Mathematical Inequalities and Applications

paper · pdf · doi:10.1090/s0002-9904-1966-11654-3

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.

Cited by

• How to generate random lambda terms?
• A variety of Euler's conjecture
• Euler's sum of powers conjecture [wikipedia]

Discussions

• Instead of looking at what I would have said, we can look at what people said when this one-line counterexample to a famous conjecture by Euler was found in 1966: “meh”. [“Counterexample to Euler's C [bsky, 19 points, 2 comments]

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