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Questions on the subject additive combinatorics, also known as arithmetic combinatorics, such as questions on: additive bases, sum sets, inverse sum set theorems, sets with small doubling, Sidon sets, Szemerédi's theorem and its ramifications, Gowers uniformity norms, etc. Often combined with the top-level tags nt.number-theory or co.combinatorics. Some additional tags are available for further specialization, including the tags sumsets and sidon-sets.
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Homogeneous arithmetic progressions in difference sets
It's a bit late, but let me point out that there is a wonderfully short and elementary argument of Croot, Ruzsa and Schoen that gives a homogeneous arithmetic progression of length about $\log n$ in $ …