Pellian equations of special type.

In this paper, we consider the solvability of the Pellian equation x 2 − (d 2 + 1) y 2 = − m , $$\begin{array}{} \displaystyle x^2-(d^2+1)y^2 = -m, \end{array} $$ in cases d = nk, m = n2l−1, where k, l are positive integers, n is a composite positive integer and d = pq, m = pq2, p, q are primes. We use the obtained results to prove results on the extendibility of some D(−1)-pairs to quadruples in the ring Z [ − t ] $\begin{array}{} {\mathbb{Z}}[\sqrt{-t}] \end{array} $ , with t > 0. [ABSTRACT FROM AUTHOR]