# On the Diophantine Equation Gn(x) = Gm(y) with Q (x, y)=0

Ontology type: schema:Chapter      Open Access: True

### Chapter Info

DATE

2008-01-01

AUTHORS ABSTRACT

Let K denote an algebraically closed field of characteristic 0, and let A0,..., Ad–1, G0,..., Gd-1 ∈ K[X] and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {Gn\left( X \right)} \right)_{n = 0}^\infty$$\end{document} be a sequence of polynomials defined by the d- th order linear recurring relation (1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{n + d} \left( X \right) = A_{d - 1} \left( X \right)G_{n + d - 1} \left( X \right) + \cdots + A_0 \left( X \right)G_n \left( X \right), for n \geqslant 0.$$\end{document} Furthermore, let P(X) ∈ K[X], deg P ≥ 1. Recently, we investigated the question, what can be said about the number of solutions of the Diophantine equation (2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Gn\left( X \right) = Gm\left( {P\left( X \right)} \right).$$\end{document} More... »

PAGES

199-209

### Book

TITLE

Diophantine Approximation

ISBN

978-3-211-74279-2
978-3-211-74280-8

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-211-74280-8_10

DOI

http://dx.doi.org/10.1007/978-3-211-74280-8_10

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1022121577

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