Extensions of $D(4)$-pairs $\{a, ka\}$ with $k\in \{7,8,10,11,12,13\}$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911259316715520 |
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| author | Trebješanin, Marija Bliznac Radić, Pavao |
| author_facet | Trebješanin, Marija Bliznac Radić, Pavao |
| contents | We study the extensibility of $D(4)$-pairs $\{a,b\}$, where $b = ka$ and $k \in \{7,8,10,11,12,13\}$. Firstly, we show that it can be extended to a $D(4)$-triple with an element c, which is a member of a family of positive integers depending on a. Then, we prove that such a triple has a unique extension to a $D(4)$-quadruple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extensions of $D(4)$-pairs $\{a, ka\}$ with $k\in \{7,8,10,11,12,13\}$ Trebješanin, Marija Bliznac Radić, Pavao Number Theory 11D09, 11B37, 11J68, 11J86 We study the extensibility of $D(4)$-pairs $\{a,b\}$, where $b = ka$ and $k \in \{7,8,10,11,12,13\}$. Firstly, we show that it can be extended to a $D(4)$-triple with an element c, which is a member of a family of positive integers depending on a. Then, we prove that such a triple has a unique extension to a $D(4)$-quadruple. |
| title | Extensions of $D(4)$-pairs $\{a, ka\}$ with $k\in \{7,8,10,11,12,13\}$ |
| topic | Number Theory 11D09, 11B37, 11J68, 11J86 |
| url | https://arxiv.org/abs/2511.08099 |