Naslov
On the extensibility of some parametric families of D(-1)-pairs to quadruples in the ring Z[\sqrt{;;-t};;], t>0

Autori
Jukić Bokun ; Mirela

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
9th International Eurasian Conference on Mathematical Sciences and Applications - Book of Abstract / - , 2020, 21-21

Skup
9th International Eurasian Conference on Mathematical Sciences and Applications

Mjesto i datum
Skopje, Sjeverna Makedonija, 25.08.2020. - 28.08.2020

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Recenziran

Ključne riječi
Diophantine equation, Diophantine m-tuple, Fermat prime

Sažetak
Let R be a commutative ring. A set of m distinct elements in R such that the product of any two distinct elements increased by -1 is a perfect square is called a D(-1)-m-tuple in R. The existence of positive integer solutions of the equation x^2-(p^{; ; ; 2k+2}; ; ; +1)y^2=-p^{; ; ; 2l+1}; ; ; , l \in {; ; ; 0, 1, \dots, k}; ; ; , k \geq 0, (1) where p is a prime, is closely related to the existence of some D(-1)- quadruples in a certain ring. We discuss solubility of equation (1). By combining that result with other known results on the existence of Diophantine quadruples, we are able to prove results on the extensibility of some parametric families of D(-1)-pairs to quadruples in the ring Z[\sqrt{; ; ; -t}; ; ; ], t>0.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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