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A Pellian equation with primes and applications to D(-1)-quadruples (CROSBI ID 251334)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Dujella, Andrej ; Jukić Bokun, Mirela ; Soldo, Ivan A Pellian equation with primes and applications to D(-1)-quadruples // Bulletin of the Malaysian Mathematical Sciences Society, 42 (2019), 5; 2915-2926. doi: 10.1007/s40840-018-0638-5

Podaci o odgovornosti

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

engleski

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

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.

Diophantine equation, quadratic eld, Diophantine triple

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Podaci o izdanju

42 (5)

2019.

2915-2926

objavljeno

0126-6705

2180-4206

10.1007/s40840-018-0638-5

Povezanost rada

Matematika

Poveznice
Indeksiranost