Source labels openChecked July 26, 2026

Erdős Problem 931

Let $k_1 \geq k_2 \geq 3$ . Are there only finitely many $n_2\geq n_1 + k_1$ such that $\prod_{1\leq i\leq k_1}(n_1 + i)\ \text{and}\ \prod_{1\leq j\leq k_2} (n_2 + j)$ have the same prime factors?

Number theory AMS 11

Mathematical statement

Let $k_1 \geq k_2 \geq 3$ . Are there only finitely many $n_2\geq n_1 + k_1$ such that

\prod_{1\leq i\leq k_1}(n_1 + i)\ \text{and}\ \prod_{1\leq j\leq k_2} (n_2 + j)

have the same prime factors?

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_931

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_931 : answer(sorry) ↔ ∀ᵉ (k₁ : ℕ) (k₂ ≥ 3), k₂ ≤ k₁ →    { (n₁, n₂) | n₁ + k₁ ≤ n₂ ∧      (∏ i ∈ Finset.Icc 1 k₁, (n₁ + i)).primeFactors =      (∏ j ∈ Finset.Icc 1 k₂, (n₂ + j)).primeFactors }.Finite := 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/931background