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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2023 / Volume: 72 Issue: 4

A Diophantine equation including Fibonacci and Fibonomial coefficients

Nurettin Irmak(KONYA TECHNICAL UNIVERSITY)0000-0003-0409-4342
Pages
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Publication Date
2023-12-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Here, $F_n$ is $n^{th}$ Fibonacci number and ${{.}\brack {.}}_{F}$ denotes Fibonomial coefficient.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact:Here, $F_n$ is $n^{th}$ Fibonacci number and ${{.}\brack {.}}_{F}$ denotes Fibonomial coefficient.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fibonomial coefficient · Fibonacci number · Diophantine equation

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.

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Cite This Article

Irmak, N. (2023). A Diophantine equation including Fibonacci and Fibonomial coefficients. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 72 Issue: 4. https://doi.org/10.31801/cfsuasmas.1247415

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