Source labels openChecked July 26, 2026

Erdős Problem 389

Is it true that for every $n \geq 1$ there is a $k$ such that $n(n + 1) \cdots (n + k - 1) \mid (n + k) \cdots (n + 2k - 1)?$

Number theory AMS 11

Mathematical statement

Is it true that for every $n \geq 1$ there is a $k$ such that

n(n + 1) \cdots (n + k - 1) \mid (n + k) \cdots (n + 2k - 1)?

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_389

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_389 : answer(sorry) ↔    ∀ n ≥ 1, ∃ k ≥ 1, ∏ i ∈ Finset.range k, (n + i) ∣ ∏ i ∈ Finset.range k, (n + k + i) := 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/389background