  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. In this paper, we prove
that there exist infinitely many rational Diophantine sextuples.
