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

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