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

Abstract

Let $k\ge 2$ and $\{L_n^{(k)}{\}}_{n\ge 2-k}$ be the sequence of $k$-generalized Lucas numbers whose first $k$ terms are $0,\dots ,0,2,1$ 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.

13 pages