On extensions of $D(4)$-triples by adjoining smaller elements
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908878417952768 |
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| author | Trebješanin, Marija Bliznac Radić, Pavao |
| author_facet | Trebješanin, Marija Bliznac Radić, Pavao |
| contents | This paper examines the problem of obtaining a $D(4)$-quadruple by adding a smaller element to a $D(4)$-triple. We prove some relations between elements of observed hypothetical $D(4)$-quadruples under which conjecture of the uniqueness of such an extension holds. Also, it is shown that for any $D(4)$-triple there are at most two extensions with a smaller element. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_00850 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On extensions of $D(4)$-triples by adjoining smaller elements Trebješanin, Marija Bliznac Radić, Pavao Number Theory 11D09, 11B37, 11J68 This paper examines the problem of obtaining a $D(4)$-quadruple by adding a smaller element to a $D(4)$-triple. We prove some relations between elements of observed hypothetical $D(4)$-quadruples under which conjecture of the uniqueness of such an extension holds. Also, it is shown that for any $D(4)$-triple there are at most two extensions with a smaller element. |
| title | On extensions of $D(4)$-triples by adjoining smaller elements |
| topic | Number Theory 11D09, 11B37, 11J68 |
| url | https://arxiv.org/abs/2306.00850 |