Source labels openChecked July 26, 2026

Erdős Problem 683

There exists $c > 0$ such that $P(n, k) > \min\{n-k+1, k^{1 + c}\}$ for all $0 < k < n$ .}

Number theory AMS 11

Mathematical statement

There exists $c > 0$ such that $P(n, k) > \min\{n-k+1, k^{1 + c}\}$ for all $0 < k < n$ .}

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_683

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_683 : answer(sorry) ↔    (∃ c > (0 : ℝ), ∀ n k : ℕ, 0 < k ∧ k < n → P n k > min (n - k + 1 : ℝ) (k ^ (1 + 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/683background