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On the Practical Solution of Genus Zero Diophantine Equations

โœ Scribed by Dimitrios Poulakis; Evaggelos Voskos

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
263 KB
Volume
30
Category
Article
ISSN
0747-7171

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โœฆ Synopsis

Let f (X, Y ) be an absolutely irreducible polynomial with integer coefficients such that the curve defined by the equation f (X, Y ) = 0 is of genus 0 having at least three infinite valuations. This paper describes a practical general method for the explicit determination of all integer solutions of the diophantine equation f (X, Y ) = 0. Some elaborated examples are given.

๐Ÿ“œ SIMILAR VOLUMES

Polynomial Bounds for the Solutions of a
Polynomial Bounds for the Solutions of a Class of Diophantine Equations
โœ Dimitrios Poulakis ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 320 KB

Let K be an algebraic number field such that all the embeddings of K into C are real. We denote by O K the ring of algebraic integers of K. Let F(X, Y) be an irreducible polynomial in K[X, Y ]&K[Y ] of total degree N and of degree n>0 in Y. We denote by F N (X, Y ) its leading homogeneous part. Supp