Year: 2026
Type: article
Abstract: A generalization of the well-known Fibonacci sequence is the $ k $ -Fibonacci sequence for a fixed integer $ k\geq 2 $ . The first $ k $ terms of this sequence are $ 0,0,\dots,1 $ , and each subsequent term is the sum of the preceding $ k $ terms. In this paper, we find all Pell numbers that can be written as a product of two $ k $ -Fibonacci numbers. The proof of our main theorem uses lower bounds for linear forms in logarithms, properties of continued fractions, and a variation of a result of Dujella and Pethő in Diophantine approximation. This work generalizes a prior result of Alekseyev on the intersection of the Fibonacci and Pell sequences, a result of Ddamulira, Luca, and Rakotomalala on Pell numbers that are products of two Fibonacci numbers, and a result of Bravo, Gómez, and Herrera on Pell numbers that appear in the $ k $ -Fibonacci sequence.
Source: Siberian Mathematical Journal
Authors: J. J. Bravo, P. Das, J. L. Herrera, J. C. Saunders
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Universidad del Cauca
OpenAlex ID: W4416280673