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Mathematics of Computation

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Determining the small solutions
to $S$-unit equations


Author: N. P. Smart
Journal: Math. Comp. 68 (1999), 1687-1699
MSC (1991): Primary 11Y50, 11D61
Published electronically: March 11, 1999
MathSciNet review: 1653990
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Abstract: In this paper we generalize the method of Wildanger for finding small solutions to unit equations to the case of $S$-unit equations. The method uses a minor generalization of the LLL based techniques used to reduce the bounds derived from transcendence theory, followed by an enumeration strategy based on the Fincke-Pohst algorithm. The method used reduces the computing time needed from MIPS years down to minutes.


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Additional Information

N. P. Smart
Affiliation: Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol, BS12 6QZ, U.K.
Email: nsma@hplb.hpl.hp.com

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01140-0
Keywords: $S$-unit equations
Received by editor(s): December 1, 1997
Published electronically: March 11, 1999
Article copyright: © Copyright 1999 American Mathematical Society