Source labels openChecked July 26, 2026

Erdős Problem 3

If $A \subset \mathbb{N} has$ \sum_{n \in A}\frac 1 n = \infty $, then must$ A$ contain arbitrarily long arithmetic progressions?

Number theory AMS 11

Mathematical statement

If $A \subset \mathbb{N} has$ \sum_{n \in A}\frac 1 n = \infty $, then must$ A$ contain arbitrarily long arithmetic progressions?

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_3

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_3 : answer(sorry) ↔ ∀ A : Set ℕ,    (¬ Summable fun a : A ↦ 1 / (a : ℝ)) →    ∃ᶠ (k : ℕ) in Filter.atTop, ∃ S ⊆ A, S.IsAPOfLength k := 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/3background