AMCA: Parametric solutions of the Diophantine equation $x^3 + D*y^3 = 1$ by Karl Dilcher

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Canadian Number Theory Association VIII Meeting
June 20-25, 2004
The Fields Institute
Toronto, ON, Canada

Organizers
John Friedlander (Toronto) and Cam Stewart (Waterloo)

Parametric solutions of the Diophantine equation x³ + D*y³ = 1
by
Karl Dilcher
Dalhousie University

In this talk I will describe a simple algorithm for the fast computation of the solutions of the equation in the title, and thus of fundamental units of the corresponding pure cubic fields. The method is mostly elementary and is related to work of Ljunggren and others. However, some results, computations and conjectures on the integral points of the Mordell curve y² = x³ + k are also used.

Date received: April 30, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # caok-13.