In this paper, we discuss the extensibility of Diophantine D(-1) pairs {a, b}, where a,b are positive integers in the ring Z[\sqrt{-k}], k>0. We prove that families of such D(-1)-pairs with b=pⁱq^j, where p,q are different odd primes and i,j are positive integers, cannot be extended to quadruples in certain rings Z[\sqrt{-k}], where k depends on pⁱ,qⁱ and a. Further, we present the result on non-existence of D(-1)-quintuples of a specific form in certain imaginary quadratic rings.

Authors were supported by the Croatian Science Foundation under the project no. IP-2022-10-5008.