On the existence of rational Diophantine quintuples with the property D(q) (CROSBI ID 622630)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa
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