A Pellian equation with primes and applications to D(-1)-quadruples (CROSBI ID 251334)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
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
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
Podaci o izdanju
42 (5)
2019.
2915-2926
objavljeno
0126-6705
2180-4206
10.1007/s40840-018-0638-5