k-term Arithmetic Progressions in Sumsets
Number Theory
2007-05-23 v1
Abstract
In this paper we give a very elementary proof that if A and B are subsets of {1,2,...,N}, each having at least 5N^{1 - (4(k-1))^{-1}} elements, then the sumset A+B has a k-term arithmetic progression.
Cite
@article{arxiv.math/0401262,
title = {k-term Arithmetic Progressions in Sumsets},
author = {Ernie Croot},
journal= {arXiv preprint arXiv:math/0401262},
year = {2007}
}