Markoff Equation and Nilpotent Matrices

Details Markoff Equation and Nilpotent Matrices Markoff Equation and Nilpotent Matrices

2007-09-10

arxiv.org/abs/0709.1499v6

Mathematics

Number Theory

21 pages, minor changes (added "Remark d)" following the proof of Proposition 3.1, and removed the the final "gamma1" term on

Scientific paper

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 intergral 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 almost 100 years.

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