Rational Diophantine sextuples with strong pair
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917623526064128 |
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| author | Dujella, Andrej Kazalicki, Matija Petričević, Vinko |
| author_facet | Dujella, Andrej Kazalicki, Matija Petričević, Vinko |
| contents | A set of $m$ distinct nonzero rationals $\{a_1, a_2,\ldots, a_m\}$ such that $a_i a_j+1$ is a perfect square for all $1\le i <j \le m$, is called a rational Diophantine $m$-tuple. If in addition, $a_i^2+1$ is a perfect square for $1\le i\le m$, then we say the $m$-tuple is strong. In this paper, we construct infinite families of rational Diophantine sextuples containing a strong Diophantine pair. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational Diophantine sextuples with strong pair Dujella, Andrej Kazalicki, Matija Petričević, Vinko Number Theory A set of $m$ distinct nonzero rationals $\{a_1, a_2,\ldots, a_m\}$ such that $a_i a_j+1$ is a perfect square for all $1\le i <j \le m$, is called a rational Diophantine $m$-tuple. If in addition, $a_i^2+1$ is a perfect square for $1\le i\le m$, then we say the $m$-tuple is strong. In this paper, we construct infinite families of rational Diophantine sextuples containing a strong Diophantine pair. |
| title | Rational Diophantine sextuples with strong pair |
| topic | Number Theory |
| url | https://arxiv.org/abs/2403.17959 |