Monochromatic sums and products

Ben Green; Tom Sanders

doi:10.19086/da.613

Monochromatic sums and products

Number Theory 2018-11-05 v3 Combinatorics

Authors: Ben Green , Tom Sanders

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

Suppose that $\mathbb{F}_p$ is coloured with $r$ colours. Then there is some colour class containing at least $c_r p^2$ quadruples of the form $(x, y , x + y, xy)$ .

Keywords

ramsey theory and colorings exponential sums

Cite

@article{arxiv.1510.08733,
  title  = {Monochromatic sums and products},
  author = {Ben Green and Tom Sanders},
  journal= {arXiv preprint arXiv:1510.08733},
  year   = {2018}
}

Comments

48 pages, accepted for publication in Discrete Analysis. Second version has minor changes arising from the referee report. Third version updated to DAJ format. in Discrete Analysis 2016:5

Related papers

View all related →