Erdős problem 33 · problems.science

Let A ⊆ ℕ be a set such that every integer can be written as n^2 + a for some a in A and n ≥ 0. What is the smallest possible value of lim sup n → ∞ |A ∩ {1, …, N}| / N^(1/2)?

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3 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

33.lean

Retained formal statement2 of 3

Erdos observed that this value is finite and > 1.

FormalConjectures/ErdosProblems/33.leanErdos33.erdos_33.variants.one_mem_lowerBounds1 lineExact file

1∃ A, Erdos33.AdditiveBasisCondition A ∧ 1 < Filter.limsup (fun N => ↑(A ∩ Set.Icc 1 N).ncard / √↑N) Filter.atTop

SolvedStatement only, no proof

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