A note on non-integrality of the $(k,l)$-Göbel sequences
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913623217012736 |
|---|---|
| author | Kobayashi, Yuh Seki, Shin-ichiro |
| author_facet | Kobayashi, Yuh Seki, Shin-ichiro |
| contents | The $(k,l)$-Göbel sequences defined by Ibstedt remain integers for the first (in some cases, many) terms, but for selected values of $(k,l)$, computations show that the terms eventually stop being integers. It is still unresolved whether the integrality of these sequences breaks down for all $k, l\geq 2$. In this article, we prove the non-integrality for a specific class of $(k,l)$ values. Our proof is based on geometric arguments related to the distribution of quadratic residues modulo a prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on non-integrality of the $(k,l)$-Göbel sequences Kobayashi, Yuh Seki, Shin-ichiro Number Theory 11B37, 11B50 The $(k,l)$-Göbel sequences defined by Ibstedt remain integers for the first (in some cases, many) terms, but for selected values of $(k,l)$, computations show that the terms eventually stop being integers. It is still unresolved whether the integrality of these sequences breaks down for all $k, l\geq 2$. In this article, we prove the non-integrality for a specific class of $(k,l)$ values. Our proof is based on geometric arguments related to the distribution of quadratic residues modulo a prime. |
| title | A note on non-integrality of the $(k,l)$-Göbel sequences |
| topic | Number Theory 11B37, 11B50 |
| url | https://arxiv.org/abs/2410.23240 |