Erdős Problem 535: Sunflower Strong
Erdős [Er73] records that Abbott pointed out the ordinary sunflower conjecture does not seem to suffice here. The stronger auxiliary conjecture uses , i.e. prime factors counted with multiplicity; this stronger statement would imply the conjectured ...
Mathematical statement
Erdős [Er73] records that Abbott pointed out the ordinary sunflower conjecture does not seem to suffice here. The stronger auxiliary conjecture uses , i.e. prime factors counted with multiplicity; this stronger statement would imply the conjectured upper bound for .
Statement source: Erdős Problems statement material
Statement terms: Source-specific
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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_535.variants.sunflower_strong
theorem erdos_535.variants.sunflower_strong {r : ℕ} (hr : 3 ≤ r) : ∃ c_r > (0 : ℝ), ∀ k : ℕ, ∀ A : Finset ℕ, AllBigOmega k A → NoConstantPairwiseGcdCoprimeSubsets r A → (A.card : ℝ) ≤ c_r ^ k := 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