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Mathematics of Computation

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On the resolution of inhomogeneous norm form equations in two dominating variables

Author: István Gaál
Journal: Math. Comp. 51 (1988), 359-373
MSC: Primary 11D57
MathSciNet review: 942162
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Abstract: Applying Baker's well-known method and the reduction procedure described by Baker and Davenport, we give a numerical algorithm for finding all solutions of inhomogeneous Thue equations of type

$\displaystyle {N_{K/Q}}(x + \alpha y + \lambda ) = 1$

in the variables $ x,y \in Z$ and $ \lambda \in {Z_K}$ with $ \lceil \lambda \rceil < (\max \vert x\vert,\vert y\vert){)^{1/2}}$, where $ K = Q(\alpha )$ is a totally real cubic field.

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Keywords: Computer solution of Diophantine equations, Thue equation, Davenport's lemma
Article copyright: © Copyright 1988 American Mathematical Society

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