OPENNOTORIOUSnumber theoryadditive basis
If $A\subseteq \mathbb{N}$ is such that $A+A$ contains all but finitely many integers then $\limsup 1_A\ast 1_A(n)=\infty$.
Notes: Conjectured by Erdos and Turan. A stronger variant asks whether limsup 1_A * 1_A(n) / log n > 0. Related to problems 40 and 1145.
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