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Journal of the London Mathematical Society 1997 56(3):455-462; doi:10.1112/S0024610797005619
© 1997 by London Mathematical Society
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© The London Mathematical Society

Thue and Thue–Mahler Equations over Rings of Integers

N. P. Smart

Institute of Mathematics and Statistics, University of Kent at Canterbury Canterbury, Kent CT2 7NF

Received 26 April 1995. Revision received 7 September 1995.

A method is given to solve any Thue–Mahler equation when the coefficients and variables come from the ring of integers of a number field. The method involves using an algorithm for solving an S-unit equation and a method of reducing the number of exponential variables. The method is used to solve the equation


Formula

Hewlett-Packard Laboratories Filton Road, Stoke Gifford, Bristol BS12 6QZ. E-mail: nsma{at}hplb.hpl.hp.com


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