- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Volume:72 Issue:4
- A Diophantine equation including Fibonacci and Fibonomial coefficients
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