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Bull. Korean Math. Soc. 2019; 56(2): 535-547
Online first article January 14, 2019 Printed March 1, 2019
https://doi.org/10.4134/BKMS.b180417
Copyright © The Korean Mathematical Society.
On the intersection of $k$-Fibonacci and Pell numbers
Jhon J. Bravo, Carlos A. G\'omez, Jose L. Herrera
Universidad del Cauca; Universidad del Valle; Universidad del Cauca
In this paper, by using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and Peth\H o, we find all generalized Fibonacci numbers which are Pell numbers. This paper continues a previous work that searched for Pell numbers in the Fibonacci sequence.
Keywords: $k$-Fibonacci numbers, Pell numbers, linear forms in logarithms, reduction method
MSC numbers: 11B39, 11J86
Supported by: J. J. Bravo was supported in part by Projects VRI ID 4689 (Universidad del Cauca) and Colciencias 110371250560. C. A. G´omez was supported in part by Project 71079 (Universidad del Valle). J. L. Herrera was supported by Colciencias (Colombia) through the Program J´ovenes investigadores e innovadores Project VRI ID 4402 (Universidad del Cauca)
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