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