Resolution of the Skolem Problem for $k$-Generalized Lucas Sequences
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917321497378816 |
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| author | Mohapatra, Monalisa Bhoi, Pritam Kumar Panda, Gopal Krishna |
| author_facet | Mohapatra, Monalisa Bhoi, Pritam Kumar Panda, Gopal Krishna |
| contents | This paper provides a complete solution to Skolem's problem for the $k$-generalized Lucas sequence $(L_n^{(k)})_{n \in \mathbb{Z}}$ with a primary focus on its behavior at negative indices. We characterize the zero-distribution of this sequence by identifying and bounding all indices $n < 0$ such that $L_n^{(k)} = 0$. Our central result establishes that the zero-multiplicity $δ_k$ of the sequence is $(k-1)(k-2)/2$ for all $k.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07172 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Resolution of the Skolem Problem for $k$-Generalized Lucas Sequences Mohapatra, Monalisa Bhoi, Pritam Kumar Panda, Gopal Krishna Number Theory This paper provides a complete solution to Skolem's problem for the $k$-generalized Lucas sequence $(L_n^{(k)})_{n \in \mathbb{Z}}$ with a primary focus on its behavior at negative indices. We characterize the zero-distribution of this sequence by identifying and bounding all indices $n < 0$ such that $L_n^{(k)} = 0$. Our central result establishes that the zero-multiplicity $δ_k$ of the sequence is $(k-1)(k-2)/2$ for all $k.$ |
| title | Resolution of the Skolem Problem for $k$-Generalized Lucas Sequences |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.07172 |