Markov's equation is not partition regular

Markov's equation x^2 + y^2 + z^2 = 3xyz is a widely studied topic in number theory, and the structure of its solutions has profound connections with mathematical fields such as combinatorics, hyperbolic geometry, approximation theory, and cluster algebras. In this paper, we prove that Markov's equation is not partition regular, which also confirms a necessary condition for the Uniqueness Conjecture.

Publication Details

Journal
ArXiv.org
Published
2025-10-11
Primary Topic
Advanced Electron Microscopy Techniques and Applications
Type
article
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article

Markov's equation is not partition regular

ArXiv.org
Advanced Electron Microscopy Techniques and Applications
article

Markov's equation is not partition regular

article en

Abstract

Markov's equation x^2 + y^2 + z^2 = 3xyz is a widely studied topic in number theory, and the structure of its solutions has profound connections with mathematical fields such as combinatorics, hyperbolic geometry, approximation theory, and cluster algebras. In this paper, we prove that Markov's equation is not partition regular, which also confirms a necessary condition for the Uniqueness Conjecture.

ArXiv.org
Openalex Percentile: Top 49%
Advanced Electron Microscopy Techniques and Applications
Open Access PDFOpenAlex
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Markov's equation is not partition regular · ArXiv.org (2025) | TGRS Research Map | TGRS