Source labels openChecked July 26, 2026

Erdős Problem 1108: I

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?

Number theory AMS 11

Mathematical statement

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?

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_1108.parts.i

Canonical source

Complete statement target, proof intentionally absentLean 4

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

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/1108background