Source labels openChecked July 26, 2026

Erdős Problem 727: K 2

It is open even for $k = 2$ . Let $k = 2$ . Does $((n+k)!)^2∣(2n)!$ hold for infinitely many n?

Number theory AMS 11

Mathematical statement

It is open even for $k = 2$ . Let $k = 2$ . Does $((n+k)!)^2∣(2n)!$ hold for infinitely many n?

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_727.variants.k_2

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_727.variants.k_2 :    letI k := 2    answer(sorry) ↔ Set.Infinite {n : ℕ | (Nat.factorial (n + k)) ^ 2 ∣ Nat.factorial (2 * n)} := 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/727background