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December 2010 On the sum of powers of two consecutive Fibonacci numbers
Diego Marques, Alain Togbé
Proc. Japan Acad. Ser. A Math. Sci. 86(10): 174-176 (December 2010). DOI: 10.3792/pjaa.86.174

Abstract

Let $(F_{n})_{n\geq 0}$ be the Fibonacci sequence given by $F_{n+2}=F_{n+1}+F_{n}$, for $n\geq 0$, where $F_{0}=0$ and $F_{1}=1$. In this note, we prove that if $s$ is an integer number such that $F_{n}^{s}+F_{n+1}^{s}$ is a Fibonacci number for all sufficiently large integer $n$, then $s=1$ or 2.

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Diego Marques. Alain Togbé. "On the sum of powers of two consecutive Fibonacci numbers." Proc. Japan Acad. Ser. A Math. Sci. 86 (10) 174 - 176, December 2010. https://doi.org/10.3792/pjaa.86.174

Information

Published: December 2010
First available in Project Euclid: 6 December 2010

zbMATH: 1222.11024
MathSciNet: MR2779831
Digital Object Identifier: 10.3792/pjaa.86.174

Subjects:
Primary: 11B39, 11J86

Rights: Copyright © 2010 The Japan Academy

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Vol.86 • No. 10 • December 2010
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