A Diophantine equation including Fibonacci and Fibonomial coefficients

Authors : Nurettin Irmak

Pages : 992-999

Doi:10.31801/cfsuasmas.1247415

View : 65 | Download : 139

Publication Date : 2023-12-29

Article Type : Research Paper

Abstract :In this paper, we solve the equation \\begin{equation*} \\sum_{k=0}^{m} {{2m+1}\\brack{k}}_{F}\\pm F_{t}=F_{n}, \\end{equation*} under weak assumptions. Here, $F_n$ is $n^{th}$ Fibonacci number and ${{.}\\brack {.}}_{F}$ denotes Fibonomial coefficient.
Keywords : Fibonomial coefficient, Fibonacci number, Diophantine equation