A counterexample to the Pellian equation conjecture of Mordell

Let d 2 be a squarefree integer, let \d, 1+{d2\} be such that Z is the ring of algebraic integers of the real quadratic number field Q (d), let >1 be the fundamental unit of Z and let x and y be the unique nonnegative integers with =x+y. In this note, we extend and study the list of known squarefree integers d 2, for which y is divisible by d (cf. OEIS A135735). As a byproduct, we present a counterexample to a conjecture of L. J. Mordell.