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Erdős problem 1108

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For each k≥2k \geq 2, does the set A={∑n∈Sn!:S⊂N finite}A = \left\{ \sum_{n\in S}n! : S\subset \mathbb{N}\text{ finite}\right\} of all finite sums of distinct factorials contain only finitely many kk-th powers?

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FormalConjectures/ErdosProblems/

1108.lean

Retained formal statement2 of 2

Does the set A={∑n∈Sn!:S⊂N finite}A = \left\{ \sum_{n\in S}n! : S\subset \mathbb{N}\text{ finite}\right\} of all finite sums of distinct factorials contain only finitely many powerful numbers?

FormalConjectures/ErdosProblems/1108.leanErdos1108.erdos_1108.parts.ii1 lineExact file
True ↔ {a | a ∈ Erdos1108.FactorialSums ∧ Erdos1108.IsPowerful a}.Finite
OpenStatement only, no proof