 Small difference set forces a three-term arithmetic progression (source code)

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= Small difference set forces a three-term arithmetic progression

For every $C$ there is $N(C)$ such that a set $A\subseteq\mathbb Z$ with $|A|\geq N(C)$ and $|A-A|\leq C|A|$ contains a nontrivial three-term <arithmetic progression>. The <Freiman-Ruzsa theorem> places $A$ densely in a bounded-rank coset progression, where the <Szemerédi theorem in a bounded-rank coset progression> applies.

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