Erdős Problem 931: Additional Condition
Erdős thought perhaps if the two products have the same factors then . It is an open question whether this is true when allowing a finite number of counterexamples.
Mathematical statement
Erdős thought perhaps if the two products have the same factors then . It is an open question whether this is true when allowing a finite number of counterexamples.
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
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Pinned Lean formulation 1
erdos_931.variants.additional_condition
theorem erdos_931.variants.additional_condition : answer(sorry) ↔ ∀ᵉ (k₁ : ℕ) (k₂ ≥ 3), k₂ ≤ k₁ → {(n₁, n₂) | n₁ + k₁ ≤ n₂ ∧ n₂ ≤ 2 * (n₁ + k₁) ∧ (∏ 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