Irmak, NurettinSiar, ZaferKeskin, Refik2024-11-072024-11-0720191310-51322367-8275https://doi.org/10.7546/nntdm.2019.25.4.96-101https://hdl.handle.net/11480/15920In this paper, we solve the equations L-k = F-n + F-m + F-r,F- F-k = F-n + F-m + F-r, L-k = E-n + L-m + L-r, F-k = E-n + L-m + F-L, for 0 < r <= m <= n and a natural number k. It is shown that only the equation F-k = L-n+ L-m + L-r has a finite number of solutions. The others have infinitely many solutions.eninfo:eu-repo/semantics/openAccessFibonacci numberLucas numberRecurrencesArticle2549610110.7546/nntdm.2019.25.4.96-101WOS:000502371600011N/A