Erdős Problem 699
Erdős and Szekeres conjectured that, apart from a finite exceptional set of triples (n, i, j), one can always take p > i in the prime divisor statement.
Mathematical statement
Erdős and Szekeres conjectured that, apart from a finite exceptional set of triples (n, i, j),
one can always take p > i in the prime divisor statement.
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_szekeres_strengthening
theorem erdos_szekeres_strengthening : answer(sorry) ↔ ∃ E : Finset (ℕ × ℕ × ℕ), ∀ n i j : ℕ, 1 ≤ i → i < j → j ≤ n / 2 → (n, i, j) ∉ E → ∃ p : ℕ, p.Prime ∧ i < p ∧ p ∣ Nat.gcd (Nat.choose n i) (Nat.choose n j) := 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