A Note on a Question of Erdös and Graham

  • Authors:

  • J. Solymosi

  • Affiliations:

  • Department of Mathematics, University of California in San Diego, 9500 Gilman Drive, La Jolla CA 92093-0112, USA (e-mail: solymosi@math.ucsd.edu)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2004

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Abstract

We give a quantitative proof that, for sufficiently large $N$, every subset of $[N]^2$ of size at least $\delta N^2$ contains a square, i.e., four points with coordinates $\{(a,b),(a+d,b),(a,b+d),(a+d,b+d)\}$.