Erdős problem 1108 · problems.science

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

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FormalConjectures/ErdosProblems/

1108.lean

Retained formal statement1 of 2

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

FormalConjectures/ErdosProblems/1108.leanErdos1108.erdos_1108.parts.i1 lineExact file

1True ↔ ∀ k ≥ 2, {a | a ∈ Erdos1108.FactorialSums ∧ ∃ m, m ^ k = a}.Finite

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