On the intersection of $k-$Fibonacci and Pell numbers
Bull. Korean Math. Soc.
Published online 2019 Jan 14
Jhon Jairo Bravo, Carlos Alexis Gómez, and José Luis Herrera
Universidad del Cauca, Universidad del Valle
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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