On the intersection of $k$-Fibonacci and Pell numbers
Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 535-547
https://doi.org/10.4134/BKMS.b180417
Published online 2019 Mar 01
Jhon J. Bravo, Carlos A. G\'omez, Jose L. Herrera
Universidad del Cauca; Universidad del Valle; Universidad del Cauca
Abstract : 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
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang.co., Ltd