### References & Citations

# Mathematics > Number Theory

# Title: Rational $D(q)$-quadruples

(Submitted on 5 Feb 2020 (v1), last revised 13 May 2021 (this version, v3))

Abstract: 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 $(q,m).$

## Submission history

From: Goran Dražić [view email]**[v1]**Wed, 5 Feb 2020 22:01:58 GMT (8kb)

**[v2]**Thu, 18 Feb 2021 13:25:49 GMT (9kb)

**[v3]**Thu, 13 May 2021 18:50:54 GMT (11kb)

Link back to: arXiv, form interface, contact.