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On the existence of rational Diophantine quintuples with the property D(q) (CROSBI ID 622630)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa

Dujella, Andrej On the existence of rational Diophantine quintuples with the property D(q) // Explicit Problems in Diophantine Analysis and Geometry. 2013. str. 3-3

Podaci o odgovornosti

Dujella, Andrej

engleski

On the existence of rational Diophantine quintuples with the property D(q)

We investigate for which rational numbers q there are infinitely many sets consisting of ve nonzero rationals such that the product of any two of them plus q is a square of a rational number. We will present recent joint work with Clemens Fuchs, where we show that there are infinitely many square-free such q, and on assuming the Parity Conjecture for the twists of an explicitly given elliptic curve we derive that the density of such q is at least one half. We will mention some other known results and open problems concerning integer and rational Diophantine m-tuples.

Diophantine quintuples; elliptic curves

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Podaci o prilogu

3-3.

2013.

objavljeno

Podaci o matičnoj publikaciji

Explicit Problems in Diophantine Analysis and Geometry

Podaci o skupu

ESI-Miniworkshop on Explicit Problems in Diophantine Analysis and Geometry

pozvano predavanje

29.11.2013-30.11.2013

Beč, Austrija

Povezanost rada

Matematika