FormalConjectures.ErdosProblems.«66»

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import FormalConjecturesUtil

Erdős Problem 66

Reference: erdosproblems.com/66



namespace Erdos66


open Filter AdditiveCombinatorics

open scoped Topology

Is there and $A \subset \mathbb{N}$ is such that $$\lim_{n\to \infty}\frac{1_A\ast 1_A(n)}{\log n}$$ exists and is $\ne 0$?

@[category research open, AMS 11]
theorem declaration uses 'sorry'erdos_66 : answer(sorry) ↔ ∃ (A : Set ℕ) (c : ℝ), c ≠ 0 ∧
    Tendsto (fun n ↦ (sumRep A n : ℝ) / Real.log n) atTop (𝓝 c) := by⊢ True ↔ ∃ A c, c ≠ 0 ∧ Tendsto (fun n => ↑(sumRep A n) / Real.log ↑n) atTop (𝓝 c)
  sorryAll goals completed! 🐙


-- TODO(firsching): add the theorems/conjectures for the comments on the page

end Erdos66