Naslov
A Pellian equation with primes and its applications

Autori
Soldo, Ivan

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

Izvornik
Representation Theory XVI / - , 2019, 18-18

Skup
Representation Theory XVI

Mjesto i datum
Dubrovnik, Hrvatska, 24.06.2019. - 29.06.2019

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Diophantine triple ; quadratic field ; Diophantine equation ; Diophantine quadruple

Sažetak
We consider the equation $x^2- (p^{; ; 2k+2}; ; +1)y^2=- p^{; ; 2l+1}; ; $, $l \in \{; ; 0, 1, \dots, k\}; ; , k \geq 0$, where $p$ is an odd prime and prove that it is not solvable in positive integers $x$ and $y$. 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 $\mathbb{; ; Z}; ; [\sqrt{; ; - t}; ; ], t>0$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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