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Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

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 Ω(n)=kΩ(n)=k, 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 Ω(n)=kΩ(n)=k, i.e. prime factors counted with multiplicity; this stronger statement would imply the conjectured upper bound for fr(N)f_r(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_535.variants.sunflower_strong

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_535.variants.sunflower_strong {r : } (hr : 3  r) :     c_r > (0 : ),       k : ,  A : Finset ,        AllBigOmega k A         NoConstantPairwiseGcdCoprimeSubsets r A         (A.card : )  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