The Discriminant of the Characteristic Polynomial of the $k$th Fibonacci sequence is not a member of the $k$th Lucas sequence
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915225688604672 |
|---|---|
| author | Batte, Herbert Luca, Florian |
| author_facet | Batte, Herbert Luca, Florian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Discriminant of the Characteristic Polynomial of the $k$th Fibonacci sequence is not a member of the $k$th Lucas sequence Batte, Herbert Luca, Florian Number Theory 11B39, 11D61, 11D45 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. |
| title | The Discriminant of the Characteristic Polynomial of the $k$th Fibonacci sequence is not a member of the $k$th Lucas sequence |
| topic | Number Theory 11B39, 11D61, 11D45 |
| url | https://arxiv.org/abs/2504.02514 |