OPENNOTORIOUSnumber theoryadditive basis
Is there $A\subseteq \mathbb{N}$ such that $\lim_{n\to \infty}\frac{1_A\ast 1_A(n)}{\log n}$ exists and is $\neq 0$?
Notes: Erdos believed the answer is negative. Erdos and Sarkozy proved |1_A * 1_A(n) - log n| / sqrt(log n) -> 0 is impossible. Horvath (2007) strengthened this.
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