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arXiv · 1208.4032

On the Markoff Equation

Norbert Riedel
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Abstract

A triple (a, b, c) of positive integers is called a Markoff triple iff it satisfies the Diophantine equation a2+b2+c2=abc . Recasting the Markoff tree, whose vertices are Markoff triples, in the framework of integral upper triangular 3x3 matrices, it will be shown that the largest member of such a triple determines the other two uniquely. This answers a question which has been open for 100 years. The solution of this problem will be obtained in the course of a broader investigation of the Markoff equation by means of 3x3 matrices.

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Norbert Riedel. 2012-08-20. On the Markoff Equation. https://arxiv.org/abs/1208.4032

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