HP Labs Technical Reports

Determining the Small Solutions to S-unit Equations

Smart, Nigel P.

HPL-97-146

Keyword(s): S-unit equations; diophantine equation; computational number theory

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.

13 Pages

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