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1 - Ineffective Results for Diophantine Equations over Finitely Generated Domains

Published online by Cambridge University Press:  31 August 2022

Jan-Hendrik Evertse  and
Kálmán Győry
Jan-Hendrik Evertse
Affiliation:
Universiteit Leiden
Kálmán Győry
Affiliation:
Debreceni Egyetem, Hungary
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Summary

We give an overview of the history of the classical Diophantine equations treated in our book and describe the ineffective finiteness results for those. We consider unit equations, Thue equations, hyper- and superelliptic equations, the Schinzel–Tijdeman equation, Catalan’s equation, decomposable form equations, and discriminant equations.

Keywords

Diophantine equationshistoryineffective results
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Chapter
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Effective Results and Methods for Diophantine Equations over Finitely Generated Domains , pp. 1 - 17
Publisher: Cambridge University Press
Print publication year: 2022

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