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Erdős problem 12

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Let A⊂NA \subset \mathbb{N} be infinite with no distinct a,b,c∈Aa, b, c \in A such that a∣(b+c)a \mid (b + c) with b,c>ab, c > a. Can ∣A∩[1,N]∣/N|A \cap [1, N]|/\sqrt{N} have positive lower limit? Must every such AA fall below N1−cN^{1-c} infinitely often?

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10 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

12.lean

Retained formal statement6 of 9

Erdős and Sárközy proved that such an AA must have density 0. [ErSa70] Erdős, P. and Sárközi, A., On the divisibility properties of sequences of integers. Proc. London Math. Soc. (3) (1970), 97-101

FormalConjectures/ErdosProblems/12.leanErdos12.erdos_12.variants.erdos_sarkozy_density_01 lineExact file
∀ (A : Set ℕ), Erdos12.IsGood A → A.HasDensity 0
SolvedStatement only, no proof