Short Note: Every Large Set of Integers Contains a Three Term Arithmetic Progression
Number Theory
2014-04-08 v1
Abstract
I show that a trivial modification of a standard proof of the Roth's Theorem on triples in arithmetic progression would lead to the following Theorem: If A is a "large set" that is its elements are monotone increasing integers and the sum of reciprocals of its elements diverges then the sequence contains an arithmetic progression of length three.
Cite
@article{arxiv.1404.1557,
title = {Short Note: Every Large Set of Integers Contains a Three Term Arithmetic Progression},
author = {Gabor Korvin},
journal= {arXiv preprint arXiv:1404.1557},
year = {2014}
}