Naslov
Pellian equations of special type

Autori
Jukić Bokun, Mirela ; Soldo, Ivan

Izvornik
Mathematica slovaca (0139-9918) 71 (2021), 6; 1599-1607

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Pellian equation, Diophantine m-tuple, quadratic field

Sažetak
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 $t>0$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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