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On the Resolution of F(x,y)=G(x,y)

✍ Scribed by István Gaál

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
222 KB
Volume
16
Category
Article
ISSN
0747-7171

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✦ Synopsis

Let (F(x, y), G(x, y) \in \mathbf{Z}[x, y]) be polynomials of degree (n) and (m), respectively. Assume, that (F) is homogeneous and (n-m \geq 3). We give a fast algorithm for the resolution of the inequality (|F(x, y)| \leq|G(x, y)|) in (x, y \in \mathbf{Z}, \max (|x|,|y|)<C). We illustrate the method by solving (\left|x^{5}-x y^{4}-y^{5}\right| \leq 200\left(x^{2}+y^{2}\right), \max (|x|,|y|) \leq 10^{500}).

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