Abstract
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 X-3-Y-3 root 2=+/-5(n) for X,Y is an element of Z[root 2].
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