Alfaya Sánchez, David Calvo Pascual, Luis Ángel Martínez de Guinea García, Alejandro Rodrigo Hitos, Javier Srinivasan, Anitha 2025-09-15T13:12:05Z 2025-09-15T13:12:05Z 2025-12-31 0015-0517 https://doi.org/10.1080/00150517.2025.2481607 Artículos en revistas We classify all solution triples with Fibonacci components to the equation a2 +b2 + c2 = 3abc + m, for positive m. We show that for m = 2 they are precisely (1, F(b), F(b + 2)), with even b; for m = 21, there exist exactly two Fibonacci solutions (1, 2, 8) and (2, 2, 13) and for any other m there exists at most one Fibonacci solution, which, in case it exists, is always minimal (i.e. it is a root of a Markoff tree). Moreover, we show that there is an infinite number of values of m admitting exactly one such solution. We classify all solution triples with Fibonacci components to the equation a2 +b2 + c2 = 3abc + m, for positive m. We show that for m = 2 they are precisely (1, F(b), F(b + 2)), with even b; for m = 21, there exist exactly two Fibonacci solutions (1, 2, 8) and (2, 2, 13) and for any other m there exists at most one Fibonacci solution, which, in case it exists, is always minimal (i.e. it is a root of a Markoff tree). Moreover, we show that there is an infinite number of values of m admitting exactly one such solution. en-GB Revista: Fibonacci Quarterly, Periodo: 1, Volumen: online, Número: 3, Página inicial: 517, Página final: 541 Instituto de Investigación Tecnológica (IIT) A classification of Markoff-Fibonacci m-triples info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/openAccess Markoff triples; generalized Markoff equation; Fibonacci solutions Markoff triples; generalized Markoff equation; Fibonacci solutions