The uniqueness of the Markoff numbers

Rosenberger, Gerhard

doi:10.1090/S0025-5718-1976-0396413-1

The uniqueness of the Markoff numbers

Author: Gerhard Rosenberger
Journal: Math. Comp. 30 (1976), 361-365
MSC: Primary 10C30; Secondary 10B10
DOI: https://doi.org/10.1090/S0025-5718-1976-0396413-1
MathSciNet review: 0396413
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Abstract: A Markoff triple is a set of three positive integers satisfying the diophantine equation ${x^2} + {y^2} + {z^2} = 3xyz$. The maximum of the three numbers is called a Markoff number. We show: If there are Markoff triples $({x_1},{y_1},z)$ and $({x_2},{y_2},z)$ with the same Markoff number z, then ${x_1} = {x_2}$ or ${x_1} = {y_2}$.

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