A386541 Lander and Parkin's 1966 counterexample to Euler's sum of powers conjecture: integers a, b, c, d and e, all > 1, such that a^k + b^k + c^k + d^k = e^k, with k = 5.

27, 84, 110, 133, 144

Offset

1,1

Comments

This is the first counterexample (found in 1966) to Euler's sum of powers conjecture. The conjecture, stated in 1769, claims that at least k k-th powers are needed to sum to a k-th power, for k >= 2. See the Wikipedia article for more information.

Links

Table of n, a(n) for n=1..5.

L. J. Lander and T. R. Parkin, Counterexample to Euler’s conjecture on sums of like powers, Bulletin of the American Mathematical Society 72 (1966), p. 1079.

Michael Penn, The sum that fooled Euler, YouTube video, 2026.

Wikipedia, Euler's sum of powers conjecture.

Formula

27^5 + 84^5 + 110^5 + 133^5 = 144^5.

Crossrefs

Cf. A061988, A347773.

Sequence in context: A043182 A039359 A043962 * A035074 A036925 A281090

Adjacent sequences: A386538 A386539 A386540 * A386542 A386543 A386544

Keyword

nonn,full,fini

Author

Paolo Xausa, Jul 25 2025

Status

approved