A Diophantine equation including Fibonacci and Fibonomial coefficients

Year 2023, Volume: 72 Issue: 4, 992 - 999, 29.12.2023

Nurettin Irmak

https://doi.org/10.31801/cfsuasmas.1247415

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

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