Multiplicative independence in the sequence of $k$-generalized Lucas numbers

Abstract

Let $(L_n^{(k)}{)}_{n\ge 2-k}$ be the sequence of $k$-generalized Lucas numbers for some fixed integer $k\ge 2$, whose first $k$ terms are $0,\dots ,0,2,1$ and each term afterward is the sum of the preceding $k$ terms. In this paper, we find all pairs of the $k$-generalized Lucas numbers that are multiplicatively dependent.

16 pages. arXiv admin note: substantial text overlap with arXiv:2311.13047