Pregled bibliografske jedinice broj: 827072
There are infinitely many rational Diophantine sextuples
There are infinitely many rational Diophantine sextuples // 5th International Conference on Uniform Distribution Theory / Gueth, Krisztián ; Herendi, Tamás ; Németh, László ; Szalay, László (ur.).
Šopron: Walter de Gruyter, 2017. str. 10-10 doi:10.1515/udt-2017-0010 (pozvano predavanje, međunarodna recenzija, sažetak, znanstveni)
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Naslov
There are infinitely many rational Diophantine sextuples
Autori
Dujella, Andrej ; Kazalicki, Matija ; Mikić, Miljen ; Szikszai, Marton
Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni
Izvornik
5th International Conference on Uniform Distribution Theory
/ Gueth, Krisztián ; Herendi, Tamás ; Németh, László ; Szalay, László - Šopron : Walter de Gruyter, 2017, 10-10
Skup
5th International Conference on Uniform Distribution Theory (UDT 2016)
Mjesto i datum
Sopron, Mađarska, 05.07.2016. - 08.07.2016
Vrsta sudjelovanja
Pozvano predavanje
Vrsta recenzije
Međunarodna recenzija
Ključne riječi
Diophantine sextuples ; elliptic curves
Sažetak
A rational Diophantine m-tuple is a set of $m$ nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The fi rst rational Diophantine quadruple was found by Diophantus, while Euler proved that there are in finitely many rational Diophantine quintuples. In 1999, Gibbs found the fi rst example of a rational Diophantine sextuple. In this talk, we describe construction of infi nitely many rational Diophantine sextuples. The construction involves elliptic curves, induced by rational Diophantine triples, with torsion group Z/2Z x Z/6Z.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
HRZZ-IP-2013-11-6422 - Diofantove m-torke, eliptičke krivulje, Thueove i indeksne jednadžbe (DIOPHANTINE) (Dujella, Andrej, HRZZ - 2013-11) ( CroRIS)
Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb
