k-term Arithmetic Progressions in Sumsets

2004/01/20 by Ernie Croot, Croot, Ernie
Mathematics · #11P70 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11P70

paper · pdf · doi:10.48550/arxiv.math/0401262

arxiv created 2004/01/20 · arxiv updated 2009/12/01

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.

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