Naslov
Asymptotic estimates for the number of Diophantine m-tuples

Autori
Dujella, Andrej

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

Izvornik
XXIV-iemes Journees Arithmetiques / - Marseille : Universite de Provence, 2005, 26-26

Skup
Journees Arithmetiques 2005

Mjesto i datum
Marseille, Francuska, 04.07.2005. - 08.07.2005

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Diophantine m-tuples

Sažetak
A set of m positive integers is called a Diophantine m-tuple if the product of any two of them is one less than a perfect square. It has been proved recently that there does not exist a Diophantine sextuple and that there are only finitely many Diophantine quintuples. On the other hand, there are infinitely many Diophantine m-tuples for m=2, 3 and 4. For example, the set {; ; k-1, k+1, 4k, 16k^3-4k}; ; is a Diophantine quadruple for k >= 2. In this talk, we will present asymptotic estimates for the numbers of Diophantine pairs, triples and quadruples with elements less than a given positive integer N.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA