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Asymptotic estimates for the number of Diophantine m-tuples (CROSBI ID 507346)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Dujella, Andrej Asymptotic estimates for the number of Diophantine m-tuples // XXIV-iemes Journees Arithmetiques. Marseille: Universite de Provence, 2005. str. 26-26-x

Podaci o odgovornosti

Dujella, Andrej

engleski

Asymptotic estimates for the number of Diophantine m-tuples

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.

Diophantine m-tuples

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Podaci o prilogu

26-26-x.

2005.

objavljeno

Podaci o matičnoj publikaciji

XXIV-iemes Journees Arithmetiques

Marseille: Universite de Provence

Podaci o skupu

Journees Arithmetiques 2005

predavanje

04.07.2005-08.07.2005

Marseille, Francuska

Povezanost rada

Matematika