Naslov
A Pellian equation with primes and applications to D(-1)-quadruples

Autori
Dujella, Andrej ; Jukić Bokun, Mirela ; Soldo, Ivan

Izvornik
Bulletin of the Malaysian Mathematical Sciences Society (0126-6705) 42 (2019), 5; 2915-2926

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

Ključne riječi
Diophantine equation, quadratic eld, Diophantine triple

Sažetak
In this paper, we prove that the equation x^2- (p^{; ; ; ; ; ; 2k+2}; ; ; ; ; ; +1)y^2=-p^{; ; ; ; ; ; 2l+1}; ; ; ; ; ; , l in {; ; ; ; ; ; 0, 1, ..., k}; ; ; ; ; ; , k > 0, where p is an odd prime number, 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 D(-1)- pairs to quadruples in the ring Z[sqrt(-t)], t>0.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA