The extensibility of the Diophantine triple $\{2, b, c\}$
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| Format: | Preprint |
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2026
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| _version_ | 1866912853513994240 |
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| author | Adžaga, Nikola Filipin, Alan Jurasić, Ana |
| author_facet | Adžaga, Nikola Filipin, Alan Jurasić, Ana |
| contents | The aim of this paper is to consider the extensibility of the Diophantine triple $\{2,b,c\}$, where $2<b<c$, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of $c$'s (depending on $b$). As corollary, for example, we prove that for $b/2-1$ prime, all Diophantine quadruples $\{2,b,c,d\}$ with $2<b<c<d$ are regular. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_19803 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The extensibility of the Diophantine triple $\{2, b, c\}$ Adžaga, Nikola Filipin, Alan Jurasić, Ana Number Theory 11D09 (Primary), 11D45, 11B37, 11J86 (Secondary) The aim of this paper is to consider the extensibility of the Diophantine triple $\{2,b,c\}$, where $2<b<c$, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of $c$'s (depending on $b$). As corollary, for example, we prove that for $b/2-1$ prime, all Diophantine quadruples $\{2,b,c,d\}$ with $2<b<c<d$ are regular. |
| title | The extensibility of the Diophantine triple $\{2, b, c\}$ |
| topic | Number Theory 11D09 (Primary), 11D45, 11B37, 11J86 (Secondary) |
| url | https://arxiv.org/abs/2601.19803 |