erdos_1108.k_th_powers

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?

theorem erdos_1108.k_th_powers : answer(sorry) ↔ ∀ k ≥ 2,
    Set.Finite { a | a ∈ FactorialSums ∧ ∃ m : ℕ, m ^ k = a }

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