Arithmetic Progressions in Sets with Small Sumsets

  • Authors:
  • József Solymosi

  • Affiliations:
  • Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2 (e-mail: solymosi@math.ubc.ca)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2006

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Abstract

We present an elementary proof that if $A$ is a finite set of numbers, and the sumset $A+_GA$ is small, $|A+_GA|\leq c|A|$, along a dense graph $G$, then $A$ contains $k$-term arithmetic progressions.