Solving a specific Thue-Mahler equation

Authors:
N. Tzanakis and B. M. M. de Weger

Journal:
Math. Comp. **57** (1991), 799-815

MSC:
Primary 11D25; Secondary 11D61, 11Y50

DOI:
https://doi.org/10.1090/S0025-5718-1991-1094961-0

MathSciNet review:
1094961

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Abstract: The diophantine equation is completely solved as follows. First, a large upper bound for the variables is obtained from the theory of linear forms in *p*-adic and real logarithms of algebraic numbers. Then this bound is reduced to a manageable size by *p*-adic and real computational diophantine approximation, based on the -algorithm. Finally the complete list of solutions is found in a sieving process. The method is in principle applicable to any Thue-Mahler equation, as the authors will show in a forthcoming paper.

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DOI:
https://doi.org/10.1090/S0025-5718-1991-1094961-0

Article copyright:
© Copyright 1991
American Mathematical Society