Product of arbitrary Fibonacci numbers with distance 1 to Fibonomial coefficient

Authors : Nurettin IRMAK

Pages : 825-828

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we solve completely the Diophantine equation \begin{gather} F_{n_{1}}F_{n_{2}}\ldots F_{n_{k}}\pm 1={m\brack t}_{F} \end{gather} for $t=1$ and $t=2$ where $2$ < $n_{1}$ < $n_{2}$ < $\ldots$ < $n_{k}$ positive integers and ${m\brack t}_{F}$ is the Fibonomial coefficient.
Keywords : Diophantine equation, Fibonomial coefficient, Fibonacci number