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April 2011 An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers
Florian Luca, Roger Oyono
Proc. Japan Acad. Ser. A Math. Sci. 87(4): 45-50 (April 2011). DOI: 10.3792/pjaa.87.45

Abstract

Here, we show that there is no integer $s\ge 3$ such that the sum of $s$th powers of two consecutive Fibonacci numbers is a Fibonacci number.

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Florian Luca. Roger Oyono. "An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers." Proc. Japan Acad. Ser. A Math. Sci. 87 (4) 45 - 50, April 2011. https://doi.org/10.3792/pjaa.87.45

Information

Published: April 2011
First available in Project Euclid: 26 April 2011

zbMATH: 1253.11046
MathSciNet: MR2803898
Digital Object Identifier: 10.3792/pjaa.87.45

Subjects:
Primary: 11B39 , 11J86

Keywords: Applications of linear forms in logarithms , Fibonacci numbers

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 4 • April 2011
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