Source labels openChecked July 26, 2026

Erdős Problem 142: Three

Prove an asymptotic formula for $r_3(N)$ , the largest possible size of a subset of $\{1, \dots, N\}$ that does not contain any non-trivial $3$ -term arithmetic progression.

Number theory AMS 11

Mathematical statement

Prove an asymptotic formula for $r_3(N)$ , the largest possible size of a subset of $\{1, \dots, N\}$ that does not contain any non-trivial $3$ -term arithmetic progression.

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_142.variants.three

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_142.variants.three : (fun N => (r 3 N : ℝ)) =Θ[atTop] (answer(sorry) : 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/142background