The Discriminant of the Characteristic Polynomial of the kth Fibonacci sequence is not a member of the kth Lucas sequence

2025/04/03 by Batte, Herbert, Luca, Florian
#11B39 #11D45 #11D61 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.02514

Abstract

Let k≥ 2 and \L_n^(k)\_{n≥ 2-k} be the sequence of k-generalized Lucas numbers whose first k terms are 0,…,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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