Rational Diophantine sextuples with strong pair

Abstract: 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 $1\le i &lt;j \le m$, is called a rational Diophantine $m$-tuple. If in addition, $a_i<sup>2+1$ 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.