Some monochromatic patterns in natural numbers
Combinatorics
2026-05-12 v3
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-\v{C}ech compactification of the natural numbers.
Keywords
Cite
@article{arxiv.2411.14066,
title = {Some monochromatic patterns in natural numbers},
author = {Arpita Ghosh and Surojit Ghosh},
journal= {arXiv preprint arXiv:2411.14066},
year = {2026}
}