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arXiv · 2511.09365

Bounds for monochromatic solutions to $\{x+y,xy\}$

Ben Green·Mehtaab Sawhney
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Abstract

Let $r$ be a sufficiently large positive integer, and let $N \ge \exp\exp(r^{50})$. Then any $r$-colouring of $[N]$ contains a monochromatic copy of $\{x+y,xy\}$ with $x > y > 2$.

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Ben Green, Mehtaab Sawhney. 2025-11-19. Bounds for monochromatic solutions to $\{x+y,xy\}$. https://arxiv.org/abs/2511.09365

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