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Erdős problem 741

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Let A⊆NA\subseteq \mathbb{N} be such that A+AA+A has positive density in the literal sense that its natural density exists and is positive. Can one always decompose A=A1⊔A2A=A_1\sqcup A_2 such that A1+A1A_1+A_1 and A2+A2A_2+A_2 both have positive density in this sense?

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  • AI standalone

    Erdős AI contributions wiki · 31 Mar, 2026

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    DeepMind prover agent
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    DeepMind prover agent
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  • argument

    VibeMathed

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