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June 2021 Fibonacci numbers which are products of two Jacobsthal numbers
Fatih Erduvan, Refik Keskin
Tbilisi Math. J. 14(2): 105-116 (June 2021). DOI: 10.32513/tmj/19322008126

Abstract

In this paper, we find all Fibonacci numbers which are products of two Jacobsthal numbers. Also we find all Jacobsthal numbers which are products of two Fibonacci numbers. More generally, taking $k,m,n$ as positive integers, it is proved that $F_{k}=J_{m}J_{n}$ implies that \begin{align*} (k,m,n) = &(1,1,1),(2,1,1),(1,1,2),(2,1,2),\\ & (1,2,2),(2,2,2),(4,1,3),(4,2,3),\\ & (5,1,4),(5,2,4),(10,4,5),(8,1,6),(8,2,6) \end{align*} and $J_{k}=F_{m}F_{n}$ implies that \begin{align*} (k,m,n) =&(1,1,1),(2,1,1),(1,2,1),(2,2,1),\\ & (1,2,2),(2,2,2),(3,4,1),(3,4,2),\\ & (4,5,1),(4,5,2),(6,8,1),(6,8,2). \end{align*}

Citation

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Fatih Erduvan. Refik Keskin. "Fibonacci numbers which are products of two Jacobsthal numbers." Tbilisi Math. J. 14 (2) 105 - 116, June 2021. https://doi.org/10.32513/tmj/19322008126

Information

Received: 21 September 2020; Accepted: 21 January 2021; Published: June 2021
First available in Project Euclid: 2 July 2021

Digital Object Identifier: 10.32513/tmj/19322008126

Subjects:
Primary: 11B39
Secondary: 11D61, 11J86

Rights: Copyright © 2021 Tbilisi Centre for Mathematical Sciences

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Vol.14 • No. 2 • June 2021
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