On the Markoff Equation
Number Theory
2022-08-26 v9
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.
Keywords
Cite
@article{arxiv.1208.4032,
title = {On the Markoff Equation},
author = {Norbert Riedel},
journal= {arXiv preprint arXiv:1208.4032},
year = {2022}
}