A counterexample to the Pellian equation conjecture of Mordell

Let d≥ 2 be a squarefree integer, let ω∈\√d,1+√d2\ be such that Z[ω] is the ring of algebraic integers of the real quadratic number field Q(√d), let ε>1 be the fundamental unit of Z[ω] and let x and y be the unique nonnegative integers with ε=x+yω. 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.