Branches of markoff m-triples with two k-ibonacci components

Abstract

We study infinite paths of Markoff m-triples, that is, solutions to the generalised Markoff equationx2 + y2 + z2 = 3xyz + m,with m > 0, with at least two k-Fibonacci components. First, we obtain a complete classification of Markoff m-triples whose last two entries are k-Fibonacci numbers and that are not roots of any Markoff trees. [...]

We study infinite paths of Markoff m-triples, that is, solutions to the generalised Markoff equationx2 + y2 + z2 = 3xyz + m,with m > 0, with at least two k-Fibonacci components. First, we obtain a complete classification of Markoff m-triples whose last two entries are k-Fibonacci numbers and that are not roots of any Markoff trees. [...]