There are no Diophantine quadruples of Pell numbers

In this paper, we prove that there are no positive integers [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] such that [Formula: see text] is a Diophantine quadruple, where for a positive integer [Formula: see text], [Formula: see text] is the [Formula: see text]th Pell number.