Irmak, Nurettin2024-12-102024-12-1020241331-0623For n, k >= 2, the k-generalized Fibonacci sequence {F-n((k))}is defined by each term being the sum of the k preceding terms with the initial values 0,0,. . . , 0, 1 (k terms). In this paper, we prove that the system ab + 1 = F-x((k)) ac + 1 = F-y((k)) bc + 1 = F-z((k)) has no solution for 1 <= a < b < c with a <= 10(3) and some positive integers x, y and z.eninfo:eu-repo/semantics/closedAccessDiophantine TriplesK -Generalized Fibonacci NumberArticle2-s2.0-85207474544