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A Parametric Family of Quintic Thue Equations II

✍ Scribed by István Gaál; Günter Lettl

Publisher
Springer Vienna
Year
2000
Tongue
English
Weight
82 KB
Volume
131
Category
Article
ISSN
0026-9255

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In this paper, we solve a family of Diophantine equations associated with families of number fields of degree 3. In fact, we find all solutions to the Thue equation

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✍ Isao Wakabayashi 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 182 KB

We give a method of estimation for rational approximation to algebraic numbers of degree 4 of the form -1+(s+-t)ÂN+-1+(s&-t)ÂN with s, t # Z and large N # N. Our method is based on Pade approximation. As an application, we consider the Thue inequalities |x 4 &a 2 x 2 y 2 &by 4 | k(a, b), where a, b