2012/08/20 by Norbert Riedel, Riedel, Norbert
Computer Science · #11D25 #15A36 #Data Visualization and Analytics #FOS: Mathematics #Number Theory (math.NT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1208.4032
openalex publication_date 2012/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.