On the intersection of $k$-Fibonacci and Pell numbers
Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 535-547
Published online March 1, 2019
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
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