A new proof of Sarkozy's theorem
Number Theory
2012-01-17 v3 Classical Analysis and ODEs
Combinatorics
Abstract
It is a striking and elegant fact (proved independently by Furstenberg and Sarkozy) that in any subset of the natural numbers of positive upper density there necessarily exist two distinct elements whose difference is given by a perfect square. In this article we present a new and simple proof of this result by adapting an argument originally developed by Croot and Sisask to give a new proof of Roth's theorem.
Keywords
Cite
@article{arxiv.1107.0243,
title = {A new proof of Sarkozy's theorem},
author = {Neil Lyall},
journal= {arXiv preprint arXiv:1107.0243},
year = {2012}
}
Comments
to appear in the Proc. Amer. Math. Soc