Pellian equations of a special type

Abstract

In this paper, we consider the solvability of the Pellian equation
x² - (d² + 1)y² = -m;
in cases d = n^k, m = n^2l-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], with t > 0.