Solving Skolem problem for negative indexed $k-$generalized Pell numbers
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911392867549184 |
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| author | Mohapatra, Monalisa Bhoi, Pritam Kumar Panda, Gopal Krishna |
| author_facet | Mohapatra, Monalisa Bhoi, Pritam Kumar Panda, Gopal Krishna |
| contents | In this paper, we address the Skolem problem for the $k$-generalized Pell sequence $(P_n^{(k)})_{n\geq2-k}$ extended to negative indices. We focus on identifying and bounding the indices $n<0$ for which $P_n^{(k)}=0.$ In particular, we establish that the zero multiplicity of $P_n^{(k)}$ is $ χ_k = \lfloor k^2/4\rfloor$ for all $k \in [4, 500].$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving Skolem problem for negative indexed $k-$generalized Pell numbers Mohapatra, Monalisa Bhoi, Pritam Kumar Panda, Gopal Krishna Number Theory Primary 11B39, Secondary 11J86, 11D61 In this paper, we address the Skolem problem for the $k$-generalized Pell sequence $(P_n^{(k)})_{n\geq2-k}$ extended to negative indices. We focus on identifying and bounding the indices $n<0$ for which $P_n^{(k)}=0.$ In particular, we establish that the zero multiplicity of $P_n^{(k)}$ is $ χ_k = \lfloor k^2/4\rfloor$ for all $k \in [4, 500].$ |
| title | Solving Skolem problem for negative indexed $k-$generalized Pell numbers |
| topic | Number Theory Primary 11B39, Secondary 11J86, 11D61 |
| url | https://arxiv.org/abs/2509.04503 |