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Erdős problem 789

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Let h(n)h(n) be maximal such that if A⊆ZA\subseteq \mathbb{Z} with ∣A∣=n\lvert A\rvert=n then there is B⊆AB\subseteq A with ∣B∣≥h(n)\lvert B\rvert \geq h(n) such that if a1+⋯+ar=b1+⋯+bsa_1+\cdots+a_r=b_1+\cdots+b_s with ai,bi∈Ba_i,b_i\in B then r=sr=s.

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FormalConjectures/ErdosProblems/

789.lean

Retained formal statement2 of 7

Let h(n)h(n) be maximal such that if A⊆ZA\subseteq \mathbb{Z} with ∣A∣=n\lvert A\rvert=n then there is B⊆AB\subseteq A with ∣B∣≥h(n)\lvert B\rvert \geq h(n) such that if a1+⋯+ar=b1+⋯+bsa_1+\cdots+a_r=b_1+\cdots+b_s with ai,bi∈Ba_i,b_i\in B then r=sr=s.

Is h(n)=Θ((nlog⁡(n)))1/3)h(n) = \Theta((n\log(n)))^{1/3})?

FormalConjectures/ErdosProblems/789.leanErdos789.erdos_789.variants.cube_root_linearithmic1 lineExact file
(fun n => ↑(Erdos789.subsetSumThreshold n)) =Θ[Filter.atTop] fun n => (↑n * Real.log ↑n) ^ (1 / 3)
OpenStatement only, no proof