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Erdős ProblemsNumber theory

Erdős Problem 727

Let k≥2k ≥ 2. Does ((n+k)!)2∣(2n)!((n+k)!)^2∣(2n)! hold for infinitely many nn?

Number theoryAMS 11

Mathematical statement

Let k≥2k ≥ 2. Does ((n+k)!)2∣(2n)!((n+k)!)^2∣(2n)! hold for infinitely many nn?

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

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_727 : answer(sorry) ↔ ∀ k ≥ 2,    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 sourceformalizationerdosproblems.com/727background