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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Diophantine approximation of ternary linear forms

Author: T. W. Cusick
Journal: Math. Comp. 25 (1971), 163-180
MSC: Primary 10F99
MathSciNet review: 0296022
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Abstract: The paper gives an efficient method for finding arbitrarily many solutions in integers x, y, z of the Diophantine inequality $|x + \alpha y + \beta z|\max ({y^2},{z^2}) < c$, where $\alpha$ defines a totally real cubic field F over the rationals, the numbers 1, $\alpha ,\beta$ form an integral basis for F, and c is a constant which can be calculated in terms of parameters of the method. For certain values of c, the method generates all solutions of the inequality.

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Keywords: Diophantine inequality, ternary linear forms, totally real cubic field
Article copyright: © Copyright 1971 American Mathematical Society