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arXiv · 2411.14066

Some monochromatic patterns in natural numbers

Arpita Ghosh·Surojit Ghosh
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Abstract

The set of sums of two squares plays a significant role in elementary number theory. In this article, we establish the existence of several rich monochromatic configurations in the natural numbers by exploiting algebraic structures induced by the set of sums of two squares. The proofs rely largely on the algebraic properties arising from the induced structures on the Stone-Čech compactification of the natural numbers.

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Arpita Ghosh, Surojit Ghosh. 2026-05-11. Some monochromatic patterns in natural numbers. https://arxiv.org/abs/2411.14066

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