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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA

Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp

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Recent progress in solving exponential Diophantine equations
by
Yann Bugeaud
Université L. Pasteur, Strasbourg, France

We give a survey of recent results concerning exponential Diophantine equations, including Catalan's equation xp - yq = 1 and the equations (xn-1)/(x-1)=yq and x2 + D = yq. We describe the different techniques which are used to handle with such equations. They include the theory of linear forms in logarithms of algebraic numbers, on which we will focus our attention.

Date received: February 20, 2000

Copyright © 2000 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 Conferences Inc. Document # cadx-30.