Result: Short Note: Every Large Set of Integers Contains a Three Term Arithmetic Progression

Title:
Short Note: Every Large Set of Integers Contains a Three Term Arithmetic Progression
Authors:
Korvin, Gabor
Publication Year:
2014
Collection:
Mathematics
Subject Terms:
Mathematics - Number Theory, 11B25 Arithmetic progressions, 11B75 Other combinatorial number theory, 11Pxx Additive number theory
Document Type:
Report Working Paper
Access URL:
http://arxiv.org/abs/1404.1557
Accession Number:
edsarx.1404.1557
Database:
arXiv

Further Information

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.