This paper shows that the discriminant does not appear in the k-th Lucas sequence, indicating a unique mathematical relationship.
Let k≥ 2 and ₙ⁽ᵏ⁾≥ 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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Batte et al. (2025) studied this question.
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