Naslov
D(-1)-triples of the form {;1, b, c}; in the ring Z[√-t], t > 0

Autori
Soldo, Ivan

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

Izvornik
Workshop on Number Theory and Algebra / - , 2014, 12-12

Skup
Workshop on Number Theory and Algebra on the occasion of 60th birthday of Ivica Gusić

Mjesto i datum
Zagreb, Hrvatska, 26.11.2014. - 28.11.2014

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Diophantine quadruples; quadratic field; simultaneous Pellian equations; linear form in logarithms

Sažetak
We study D(-1)-triple of the form {;1, b, c}; in the ring Z[√-t], t > 0, for positive integer b such that b is a prime, twice prime or twice prime squared. We prove that in those cases c has to be an integer. As a consequence of this result, in cases of b = 26, 37 or 50 we prove that D(−1)-triples of the form {;1, b, c}; cannot be extended to a D(−1)-quadruple in the ring Z[√-t], t > 0, except in cases of t ∈ {;1, 4, 9, 25, 36, 49};. For those exceptional cases of t we show that there exist infinitely many D(−1)-quadruples of the form {;1, b, −c, d};, c, d > 0 in Z[√−t].

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA