Monochromatic sums and products

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 $(x,y,x+y,xy)$.

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

References in corpus (2)

• A Szemeredi-type regularity lemma in abelian groups, with applications
• On monochromatic solutions of some nonlinear equations in Z/pZ

Cited by in corpus (5)

• On Rado conditions for nonlinear Diophantine equations
• Bootstrapping partition regularity of linear systems
• Monochromatic products and sums in the rationals
• Partition regularity of Pythagorean pairs
• Revisiting sums and products in countable and finite fields