Erdős problem 741 · problems.science

Let $A\subseteq \mathbb{N}$ be such that $A+A$ has positive density in the literal sense that its natural density exists and is positive. Can one always decompose $A=A_1\sqcup A_2$ such that $A_1+A_1$ and $A_2+A_2$ both have positive density in this sense?

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Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke, Gregory Valiant
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resolved
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