Pregled bibliografske jedinice broj: 640830
D(z)-quadruples in the ring Z[√ -2], for some exceptional cases of z
D(z)-quadruples in the ring Z[√ -2], for some exceptional cases of z // Electronic Notes in Discrete Mathematics
Budimpešta, Mađarska: Elsevier, 2013. str. 51-56 (poster, međunarodna recenzija, sažetak, znanstveni)
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Naslov
D(z)-quadruples in the ring Z[√ -2], for some exceptional cases of z
Autori
Soldo, Ivan
Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni
Izvornik
Electronic Notes in Discrete Mathematics
/ - : Elsevier, 2013, 51-56
Skup
Erdős Centennial
Mjesto i datum
Budimpešta, Mađarska, 01.07.2013. - 05.07.2013
Vrsta sudjelovanja
Poster
Vrsta recenzije
Međunarodna recenzija
Ključne riječi
Diophantine quadruples; quadratic field; congruence
Sažetak
By the work of Abu Muriefah, Al-Rashed, Dujella and Soldo, 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. 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. These new formulas then together with previous results on this subject allow us to almost completely characterize elements z of Z[√−2] for which a Diophantine quadruple with the property D(z) exists.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
Citiraj ovu publikaciju:
Časopis indeksira:
- Scopus
