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arXiv · 2504.02514

The Discriminant of the Characteristic Polynomial of the $k$th Fibonacci sequence is not a member of the $k$th Lucas sequence

Herbert Batte·Florian Luca
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Abstract

Let $k\ge 2$ and $\{L_n^{(k)}\}_{n\geq 2-k}$ be the sequence of $k$-generalized Lucas numbers whose first $k$ terms are $0,\ldots,0,2,1$ and each term afterwards is the sum of the preceding $k$ terms. In this paper, we show that this sequence does not contain the discriminant of its characteristic polynomial.

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Herbert Batte, Florian Luca. 2025-04-03. The Discriminant of the Characteristic Polynomial of the $k$th Fibonacci sequence is not a member of the $k$th Lucas sequence. https://arxiv.org/abs/2504.02514

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