engleski

Pellian equations of special type

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

Pellian equation, Diophantine m-tuple, quadratic field

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