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On one problem of Gowers

I. D. Shkredov
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Abstract

Let A \subseteq [1,..,N]^2 be a set of density at least 1/(log log log N)^c, where c some constant c>0. We prove that A contains a so-called right-angle triangle, i.e. a triple of the form {(k,m), (k+d,m), (k,m+d)}, where d>0.

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I. D. Shkredov. 2004-05-21. On one problem of Gowers. https://arxiv.org/abs/math/0405406

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