English

On one problem of Gowers

Number Theory 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0405406,
  title  = {On one problem of Gowers},
  author = {I. D. Shkredov},
  journal= {arXiv preprint arXiv:math/0405406},
  year   = {2007}
}

Comments

39 pages, 1 figure

R2 v1 2026-07-22T17:05:43.974Z