erdos_39

Is there an infinite Sidon set $A\subset \mathbb{N}$ such that $\lvert A\cap \{1\ldots,N\}\rvert \gg_\epsilon N^{1/2-\epsilon}$ for all $\varepsilon > 0$?

theorem erdos_39 : answer(sorry) ↔ ∃ (A : Set ℕ), A.Infinite ∧ IsSidon A ∧
    ∀ᵉ  (ε  > (0 : ℝ)),
    (· ^ (1 / 2 - ε) : ℕ → ℝ) =O[atTop] fun N => (((Set.Icc 1 N) ∩ A).ncard : ℝ)

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