Proceedings of the Japan Academy, Series A, Mathematical Sciences

An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers

Florian Luca and Roger Oyono

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 4 (2011), 45-50.

Dates
First available in Project Euclid: 26 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.pja/1303823878

Digital Object Identifier
doi:10.3792/pjaa.87.45

Mathematical Reviews number (MathSciNet)
MR2803898

Zentralblatt MATH identifier
1253.11046

Subjects
Primary: 11B39: Fibonacci and Lucas numbers and polynomials and generalizations 11J86: Linear forms in logarithms; Baker's method

Keywords
Fibonacci numbers Applications of linear forms in logarithms

Citation

Luca, Florian; Oyono, Roger. An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 4, 45--50. doi:10.3792/pjaa.87.45. https://projecteuclid.org/euclid.pja/1303823878


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References

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