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}
}
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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