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Erdős ProblemsNumber theory

Erdős Problem 126

Let f(n)f(n) be maximal such that if A⊆NA\subseteq\mathbb{N} has ∣A∣=n|A| = n then ∏a≠b∈A(a+b)\prod_{a\neq b\in A}(a + b) has at least f(n)f(n) distinct prime factors. Is it true that f(n)log⁡n→∞\frac{f(n)}{\log n} \to\infty?

Number theoryAMS 11

Mathematical statement

Let f(n)f(n) be maximal such that if A⊆NA\subseteq\mathbb{N} has ∣A∣=n|A| = n then ∏a≠b∈A(a+b)\prod_{a\neq b\in A}(a + b) has at least f(n)f(n) distinct prime factors. Is it true that f(n)log⁡n→∞\frac{f(n)}{\log n} \to\infty?

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_126

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_126 : answer(sorry) ↔ ∀ (f : ℕ → ℕ), IsMaximalAddFactorsCard f →    Tendsto (fun n => f n / Real.log n) atTop atTop := 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/126background