Erdős Problem #656

Let $A\subset \mathbb{N}$ be a set with positive upper density. Must there exist an infinite set $B$ and integer $t$ such that\[B+B+t\subseteq A?\]

#656: [Er75b]

number theory | additive combinatorics

Erdős [Er75b] posed this as a candidate for a density version of Hindman's theorem (see [172]).

This is true, and was proved by Kra, Moreira, Richter, and Robertson [KMRR24].

See also [109].

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