Pregled bibliografske jedinice broj: 623725
On the existence of Diophantine quadruples in Z[√ -2]
On the existence of Diophantine quadruples in Z[√ -2] // Miskolc Mathematical Notes, 14 (2013), 1; 265-277 (međunarodna recenzija, članak, znanstveni)
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Naslov
On the existence of Diophantine quadruples in Z[√ -2]
Autori
Soldo, Ivan
Izvornik
Miskolc Mathematical Notes (1787-2405) 14
(2013), 1;
265-277
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Diophantine quadruples; quadratic field
Sažetak
By the work of Abu Muriefah, Al-Rashed, Dujella and the author, the problem of the existence of D(z)-quadruples in the ring Z[√ -2] has been solved, except for the cases z=24a+2+(12b+6)√ -2, z=24a+5+(12b+6)√ -2, z=48a+44+(24b+12)√ -2. In this paper, we present some new formulas for D(z)-quadruples in these remaining cases, involving some congruence conditions modulo 11 on integers a and b. We show the existence of D(z)-quadruple for significant proportion of the remaining three cases.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
Citiraj ovu publikaciju:
Časopis indeksira:
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
