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The problem of Diophantus for integers of Q(√−3)

Zrinka Franušić   ORCID icon orcid.org/0000-0003-3481-8057 ; Department of Mathematics, University of Zagreb, Bijenička cesta 30, HR-10 000 Zagreb, Croatia
Ivan Soldo   ORCID icon orcid.org/0000-0002-6195-6626 ; Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, HR-31 000 Osijek, Croatia

Puni tekst: engleski, pdf (199 KB) str. 15-25 preuzimanja: 289* citiraj
APA 6th Edition
Franušić, Z. i Soldo, I. (2014). The problem of Diophantus for integers of Q(√−3). Rad Hrvatske akademije znanosti i umjetnosti, (519=18), 15-25. Preuzeto s https://hrcak.srce.hr/127639
MLA 8th Edition
Franušić, Zrinka i Ivan Soldo. "The problem of Diophantus for integers of Q(√−3)." Rad Hrvatske akademije znanosti i umjetnosti, vol. , br. 519=18, 2014, str. 15-25. https://hrcak.srce.hr/127639. Citirano 31.10.2020.
Chicago 17th Edition
Franušić, Zrinka i Ivan Soldo. "The problem of Diophantus for integers of Q(√−3)." Rad Hrvatske akademije znanosti i umjetnosti , br. 519=18 (2014): 15-25. https://hrcak.srce.hr/127639
Harvard
Franušić, Z., i Soldo, I. (2014). 'The problem of Diophantus for integers of Q(√−3)', Rad Hrvatske akademije znanosti i umjetnosti, (519=18), str. 15-25. Preuzeto s: https://hrcak.srce.hr/127639 (Datum pristupa: 31.10.2020.)
Vancouver
Franušić Z, Soldo I. The problem of Diophantus for integers of Q(√−3). Rad Hrvatske akademije znanosti i umjetnosti [Internet]. 2014 [pristupljeno 31.10.2020.];(519=18):15-25. Dostupno na: https://hrcak.srce.hr/127639
IEEE
Z. Franušić i I. Soldo, "The problem of Diophantus for integers of Q(√−3)", Rad Hrvatske akademije znanosti i umjetnosti, vol., br. 519=18, str. 15-25, 2014. [Online]. Dostupno na: https://hrcak.srce.hr/127639. [Citirano: 31.10.2020.]

Sažetak
We solve the problem of Diophantus for integers of the
quadratic field Q(√−3) by finding a D(z)-quadruple in Z[(1+√−3)/2] for
each z that can be represented as a difference of two squares of integers in Q(√−3), up to finitely many possible exceptions.

Ključne riječi
Diophantine quadruples; quadratic field

Projekti
HRZZ / IP / IP-2013-11-6422 / DIOPHANTINE - Diofantove m-torke, eliptičke krivulje, Thueove i indeksne jednadžbe

Hrčak ID: 127639

URI
https://hrcak.srce.hr/127639

Posjeta: 491 *