  A rational Diophantine m-tuple is a set of m nonzero rationals such that the
product of any two of them increased by 1 is a perfect square. The first
rational Diophantine quadruple was found by Diophantus, while Euler proved that
there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found
the first example of a rational Diophantine sextuple, and in 2016 Dujella,
Kazalicki, Miki\'c and Szikszai proved that there are infinitely many of them.
In this paper, we prove that there exist infinitely many rational Diophantine
sextuples such that the denominators of all the elements in the sextuples are
perfect squares.
