Naslov
Applications of Pellian equations of a special type

Autori
Jukić Bokun, Mirela

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
Conference on Diophantine m-tuples and related problems III

Mjesto i datum
Zagreb, Hrvatska, 14.16.9.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Recenziran

Ključne riječi
Pellian equation ; Diophantine m-tuple ; commutative ring

Sažetak
We consider the solvability of the Pellian equation x^2 − (d^2 + 1)y^2 = −m, (2) in the case d = n^k, m = n^{;2l−1};, where k, l are positive integers and n is a composite positive integer. Moreover, we completely solve the problem of the solvability of equation (2) in integers in the case d = pq, m = pq^2, and p, q are primes. By combining that results with other known results on the existence of Diophantine m- tuples, we proved results on the extensibility of some parametric families of D(−1)-pairs to quadruples in the ring Z[√−t], t > 0.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA