Erdős problem 939 · problems.science

If $r≥4$ then can the sum of $r-2$ coprime $r$ -powerful numbers ever be itself $r$ -powerful?

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7 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

939.lean

Retained formal statement3 of 7

Euler had conjectured that the sum of $k - 1$ many $k$ -th powers is never a $k$ -th power, but this is false for $k=5$ , as Lander and Parkin [LaPa67] found $27^5+84^5+110^5+133^5=144^5$ .

[LaPa67] Lander, L. J. and Parkin, T. R., "A counterexample to Euler's sum of powers conjecture." Math. Comp. (1967), 101--103.

FormalConjectures/ErdosProblems/939.leanErdos939.erdos_939.variants.euler1 lineExact file

1¬∀ k ≥ 4, ∀ (S : Finset ℕ), S.card = k - 1 → ¬∃ q, ∑ s ∈ S, s ^ k = q ^ k

SolvedStatement only, no proof

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