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Determining the small solutions to  -unit equations
Author(s):
N.
P.
Smart.
Journal:
Math. Comp.
68
(1999),
1687-1699.
MSC (1991):
Primary 11Y50, 11D61
Posted:
March 11, 1999
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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  -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
DOI:
10.1090/S0025-5718-99-01140-0
PII:
S 0025-5718(99)01140-0
Keywords:
$S$-unit equations
Received by editor(s):
December 1, 1997
Posted:
March 11, 1999
Copyright of article:
Copyright
1999,
American Mathematical Society
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