Naslov
On the strong version of Diophantine quintuple conjecture

Autori
Filipin, Alan ; Fujita, Yasutsugu ; Togbe, Alain

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

Izvornik
Conference on Elementary and analytic number theory (ELAZ 2016) / - , 2016, 21-21

Skup
Conference on Elementary and analytic number theory (ELAZ 2016)

Mjesto i datum
Strobl, Austrija, 05.09.2016. - 09.09.2016

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Diophnatine m-tuples
(Diophantine m-tuples)

Sažetak
A set of m positive integers is called a Diophantine m-tuple if the product of any two of its distinct elements increased by 1 is a perfect square. One of the interesting question is how large those sets can be. There is a folklore conjecture that there does not exist a Diophantine quintuple. Furthermore, there is a stronger version of that conjecture, that every Diophantine triple can be extended to a quadruple with a larger element in the unique way. In 2004, Dujella proved that there does not exist a Diophantine sextuple and that there are only finitely many quintuples. His results were improved in recent years, but the conjecture still remains open. Let {;a, b, c, d}; such that a < b < c < d be a Diophantine quadruple. In this talk we give an upper bound for minimal c such that d is not unique. It helps us to prove the strong version of the conjecture for various families of Diophantine triples and as corollary it implies the non-extendibility of some parametric families of Diophantine pairs to a quintuple.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA