Rational $D(q)$-quadruples
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866908735424692224 |
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| author | Dražić, Goran Kazalicki, Matija |
| author_facet | Dražić, Goran Kazalicki, Matija |
| contents | For a rational number $q$, a rational $D(q)$-$n$-tuple is a set of $n$ distinct nonzero rationals $\{a_1, a_2, \dots, a_n\}$ such that $a_ia_j+q$ is a rational square for all $1 \leqslant i < j \leqslant n$. For every $q$ we find all rational $m$ such that there exists a $D(q)$-quadruple with product $abcd=m$. We describe all such quadruples using points on a specific elliptic curve depending on $(q,m).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_02006 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Rational $D(q)$-quadruples Dražić, Goran Kazalicki, Matija Number Theory 11D09, 11G05 For a rational number $q$, a rational $D(q)$-$n$-tuple is a set of $n$ distinct nonzero rationals $\{a_1, a_2, \dots, a_n\}$ such that $a_ia_j+q$ is a rational square for all $1 \leqslant i < j \leqslant n$. For every $q$ we find all rational $m$ such that there exists a $D(q)$-quadruple with product $abcd=m$. We describe all such quadruples using points on a specific elliptic curve depending on $(q,m).$ |
| title | Rational $D(q)$-quadruples |
| topic | Number Theory 11D09, 11G05 |
| url | https://arxiv.org/abs/2002.02006 |