# Monochromatic sums and products

@article{Green2016MonochromaticSA,
title={Monochromatic sums and products},
author={Ben Green and Tom Sanders},
journal={arXiv: Number Theory},
year={2016},
pages={613}
}
• Published 29 October 2015
• Mathematics
• arXiv: Number Theory
Monochromatic sums and products, Discrete Analysis 2016:5, 48pp. An old and still unsolved problem in Ramsey theory asks whether if the positive integers are coloured with finitely many colours, then there are positive integers $x$ and $y$ such that $x, y, x+y$ and $xy$ all have the same colour. In fact, it is not even known whether it is always possible to find $x$ and $y$ such that $x+y$ and $xy$ have the same colour. This paper is about the corresponding question when $\mathbb{N}$ is…

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