# Rational Diophantine sextuples containing two regular quadruples and one regular quintuple

## TL;DR

This paper constructs infinite families of rational Diophantine sextuples that include specific types of quadruples and quintuples, advancing understanding of their structure and existence.

## Contribution

It introduces new infinite families of rational Diophantine sextuples with particular structural properties, expanding known classifications.

## Key findings

- Existence of infinitely many rational Diophantine sextuples.
- Construction methods for sextuples containing special quadruples and quintuples.
- Structural characterization of these sextuples.

## Abstract

A set of $m$ distinct nonzero rationals $\{a_1,a_2,\ldots,a_m\}$ such that $a_ia_j+1$ is a perfect square for all $1\leq i<j\leq m$, is called a rational Diophantine $m$-tuple. It is proved recently that there are infinitely many rational Diophantine sextuples. In this paper, we construct infinite families of rational Diophantine sextuples with special structure, namely the sextuples containing quadruples and quintuples of certain type.