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arXiv · 2603.03115

Monochromatic sums and quotients in $\mathbb N$

Mauro Di Nasso·Lorenzo Luperi Baglini·Rosario Mennuni·Mariaclara Ragosta·Alessandro Vegnuti
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Abstract

We prove partition regularity of the configuration $x,y,x+y,y/x$ in a strong infinitary form that extends Hindman's Theorem. We study the related issue of partition regularity of configurations involving products of a degree one polynomial in $x$ with one in $y$, reducing the general problem to a handful of special cases.

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Mauro Di Nasso, Lorenzo Luperi Baglini, Rosario Mennuni, Mariaclara Ragosta, Alessandro Vegnuti. 2026-03-03. Monochromatic sums and quotients in $\mathbb N$. https://arxiv.org/abs/2603.03115

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