Erdős Problem 142: Lower
Show that , where the largest possible size of a subset of that does not contain any non-trivial -term arithmetic progression.
Mathematical statement
Show that , where the largest possible size of a subset of that does not contain any non-trivial -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.lower
theorem erdos_142.variants.lower (k : ℕ) (hk : 1 < k) : (fun N => (r k N : ℝ)) =o[atTop] (fun N : ℕ => N / (N : ℝ).log) := 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