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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Solving Thue equations
without the full unit group


Author: Guillaume Hanrot
Journal: Math. Comp. 69 (2000), 395-405
MSC (1991): Primary 11Y50; Secondary 11B37
Published electronically: May 19, 1999
MathSciNet review: 1651759
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Abstract: The main problem when solving a Thue equation is the computation of the unit group of a certain number field. In this paper we show that the knowledge of a subgroup of finite index is actually sufficient. Two examples linked with the primitive divisor problem for Lucas and Lehmer sequences are given.


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Additional Information

Guillaume Hanrot
Affiliation: Algorithmique Arithmétique Expérimentale, UPRES A CNRS 5465, Université Bordeaux 1, 351, Cours de la Libération, F-33405 Talence Cedex, FRANCE
Address at time of publication: LORIA, 615, rue du Jardin Botanique, B.P. 101, F-54600 Villers-lès-Nancy, FRANCE
Email: Guillaume.Hanrot@loria.fr.

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01124-2
PII: S 0025-5718(99)01124-2
Keywords: Diophantine equations, Thue equation, linear recurrence sequences, Lucas sequences, Lehmer sequences, fundamental units
Received by editor(s): April 7, 1997
Received by editor(s) in revised form: March 31, 1998
Published electronically: May 19, 1999
Additional Notes: Partially supported by GDR AMI and GDR Théorie Analytique des Nombres.
Article copyright: © Copyright 1999 American Mathematical Society