  The study of Diophantine triples taking values in linear recurrence sequences
is a variant of a problem going back to Diophantus of Alexandria which has been
studied quite a lot in the past. The main questions are, as usual, about
existence or finiteness of Diophantine triples in such sequences. Whilst the
case of binary recurrence sequences is almost completely solved, not much was
known about recurrence sequences of larger order, except for very specialized
generalizations of the Fibonacci sequence. Now, we will prove that any linear
recurrence sequence with the Pisot property contains only finitely many
Diophantine triples, whenever the order is large and a few more not very
restrictive conditions are met.
