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 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.b180417Published 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 :