erdos_33

Specification

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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Lean 4 Statement

theorem erdos_33 : ⨅ A : {A : Set ℕ | AdditiveBasisCondition A}, Filter.atTop.limsup (fun N =>
    (A.1.interIcc 1 N).ncard / (√N : EReal)) = answer(sorry)

ID: ErdosProblems__33__erdos_33

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