Irmak, NurettinLuca, Florian2025-07-102025-07-1020250031-53031588-2829https://doi.org/10.1007/s10998-025-00657-xhttps://hdl.handle.net/20.500.13091/10149Let k >= 2 be a fixed integer. The k-generalized Lucas sequence {Ln(k)}n >= 0 starts with the positive integer initial values k, 1, 3, ..., 2k-1-1, and each term afterward is the sum of the k consecutive preceding elements. In this paper, we find all solutions of the equation Ln(k)=(2a-1)(2b-1) in integers n >= 2,k >= 2, b >= a >= 0\.eninfo:eu-repo/semantics/closedAccessK-Generalized Lucas SequenceBaker MethodArticle10.1007/s10998-025-00657-x2-s2.0-105007627619