On monochromatic solutions to x−y=z2

Author: 

Sanders, T

Publication Date: 

22 July 2020

Journal: 

Acta Mathematica Hungarica

Last Updated: 

2021-10-11T20:54:10.117+01:00

Issue: 

2

Volume: 

161

DOI: 

10.1007/s10474-020-01079-6

page: 

550-556

abstract: 

For k∈N, write S(k) for the largest natural number such that there is a k-colouring of {1,…,S(k)} with no monochromatic solution to x−y=z2. That S(k) exists is a result of Bergelson, and a simple example shows that S(k)≥22k−1. The purpose of this note is to show that S(k)≤222O(k) .

Symplectic id: 

1106272

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article