Kilic, EmrahAkkus, IlkerOmur, Nese2025-01-212025-01-2120221735-44632008-9473https://doi.org/10.52547/ijmsi.17.1.11https://hdl.handle.net/20.500.12587/24523In this paper we find all solutions of four kinds of the Dio-phantine equations x(2) +/- V(t)xy - y(2) +/- x = 0 and x(2) +/- V(t)xy - y(2) +/- y = 0, for an odd number t, and, x(2) +/- V(t)xy + y(2) - x = 0 and x(2) +/- V(t)xy +/- y(2) - y = 0, for an even number t, where V-n is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh.eninfo:eu-repo/semantics/openAccessLinear recurrences; Generalized Fibonacci and Lucas sequences; Diophantine equations; Continued fractionsArticle171112610.52547/ijmsi.17.1.112-s2.0-85129991481Q3WOS:000798350900002N/A