Erdős problem 749

Let $\epsilon>0$ . Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$ ?

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1 retained statement36c6d0fef71a

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FormalConjectures/ErdosProblems/

749.lean

Retained formal statement1 of 1

Let $\epsilon>0$ . Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$ ?

FormalConjectures/ErdosProblems/749.leanErdos749.erdos_7492 linesExact file

1True ↔2  ∀ ε > 0, ∃ A, 1 - ε ≤ (A + A).lowerDensity ∧ (Nat.cast ∘ AdditiveCombinatorics.sumRep A) =O[Filter.atTop] fun n => 1

OpenStatement only, no proof