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Bounds for the solutions of some diophantine equations in terms of discriminants

Part of: Diophantine equations

Published online by Cambridge University Press:  09 April 2009

B. Brindza ,
J. H. Evertse  and
K. Györy
B. Brindza
Affiliation:
Mathematical Institute Kossuth Lajos University4010 Debrecen Hungary
J. H. Evertse
Affiliation:
Department of Mathematics and Computer Science 2300 RA Leiden P.O. Box 9512 The Netherlands
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Abstract

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Several effective upper bounds are known for the solutions of Thue equations, Thue-Mahler equations and superelliptic equations. One of the basic parameters occurring in these bounds is the height of the polynomial involved in the equation. In the present paper it is shown that better (and, in certain important particular cases, best possible) upper bounds can be obtained in terms of the height, if one takes into consideration also the discriminant of the polynomial.

MSC classification

Secondary: 11D41: Higher degree equations; Fermat's equation 11D61: Exponential equations

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 1 , August 1991 , pp. 8 - 26
Copyright
Copyright © Australian Mathematical Society 1991

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