On one problem of Gowers
I. D. Shkredov
Abstract
Let A ⊂eq [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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