Determining the small solutions to $S$-unit equations
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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.References
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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
- Received by editor(s): December 1, 1997
- Published electronically: March 11, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 1687-1699
- MSC (1991): Primary 11Y50, 11D61
- DOI: https://doi.org/10.1090/S0025-5718-99-01140-0
- MathSciNet review: 1653990