A Diophantine equation including Fibonacci and Fibonomial coefficients

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

References

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