Multiplicative dependence between k-Fibonacci and k-Lucas numbers

Gómez, Carlos A.; Gómez, Jhonny C.; Luca, Florian

doi:10.1007/s10998-020-00336-z

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Multiplicative dependence between k-Fibonacci and k-Lucas numbers

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Luca, Florian
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Gómez, C. A., Gómez, J. C., & Luca, F. (2020). Multiplicative dependence between k-Fibonacci and k-Lucas numbers. Periodica Mathematica Hungarica, 81(2), 217-233. doi:10.1007/s10998-020-00336-z.

Cite as: https://hdl.handle.net/21.11116/0000-0007-7B4D-A

Abstract

A generalization of the well-known Fibonacci and Lucas sequences are the k-Fibonacci and
k-Lucas sequences with some fixed integer k ≥ 2. For these sequences the first k terms
are 0,..., 0, 1 and 0,..., 0, 2, 1, respectively, and each term afterwards is the sum of the
preceding k terms. Here we find all pairs of k-Fibonacci and k-Lucas numbers multiplicatively dependent.