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Solving Thue equations without the full unit group
Author(s):
Guillaume
Hanrot.
Journal:
Math. Comp.
69
(2000),
395-405.
MSC (1991):
Primary 11Y50;
Secondary 11B37
Posted:
May 19, 1999
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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:
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
Posted:
May 19, 1999
Additional Notes:
Partially supported by GDR AMI and GDR Théorie Analytique des Nombres.
Copyright of article:
Copyright
1999,
American Mathematical Society
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