Source labels openChecked July 26, 2026

Erdős Problem 12: Iii

Let $A$ be an infinite set such that there are no distinct $a,b,c \in A$ such that $a \mid (b+c)$ and $b,c > a$ . Is it true that $∑_{n \in A} \frac{1}{n} < \infty$ ?

Number theory AMS 11

Mathematical statement

Let $A$ be an infinite set such that there are no distinct $a,b,c \in A$ such that $a \mid (b+c)$ and $b,c > a$ . Is it true that $∑_{n \in A} \frac{1}{n} < \infty$ ?

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_12.parts.iii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_12.parts.iii :    answer(sorry) ↔ ∀ (A : Set ℕ), IsGood A → Summable (fun (n : A) ↦ (1 / n : ℝ)) := 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/12background