2016-06-072016-06-072013-06González Jiménez, E. y Tornero Sánchez, J.M. (2013). Markoff-Rosenberger triples in arithmetic progression. Journal of Symbolic Computation, 53, 53-63.0747-7171http://hdl.handle.net/11441/41959We study the solutions of the Rosenberg–Markoff equation ax2 + by2 + cz2 = dxyz (a generalization of the well–known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x 2 +y 2 +z 2 = dxyz over quadratic fields and the classic Markoff equation x 2 + y 2 + z 2 = 3xyz over an arbitrary number field.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Markoff equationarithmetic progressioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1016/j.jsc.2012.11.003https://idus.us.es/xmlui/handle/11441/41959