Source labels openChecked July 26, 2026

Erdős Problem 920

Is it true that, for $k\geq 4$ , $f_k(n) \gg \frac{n^{1-\frac{1}{k-1}}}{(\log n)^{c_k}}$ for some constant $c_k>0$ ?

Combinatorics AMS 5

Mathematical statement

Is it true that, for $k\geq 4$ , $f_k(n) \gg \frac{n^{1-\frac{1}{k-1}}}{(\log n)^{c_k}}$ for some constant $c_k>0$ ?

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_920

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_920 :    answer(sorry) ↔ ∀ k : ℕ, k ≥ 4 → ∃ c > 0,      (fun n ↦ f k n) ≫ (fun n ↦ (n : ℝ) ^ (1 - 1 / ((k : ℝ) - 1)) / (log n) ^ c) := 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/166background erdosproblems.com/920background erdosproblems.com/986background