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This article is cited in 1 scientific paper (total in 1 paper)
Simplifying Method for Algebraic Approximation of Certain Algebraic Numbers
X. Jingboa, Ch. Jianhuaa, Zh. Silanb a Huazhong Agricultural University, Китай
b Wuhan University, Китай
Abstract:
A new simple method for approximating certain algebraic numbers is developed. By applying this method, an effective upper bound is derived for the integral solutions of the quartic Thue equation with two parameters
$$
tx^4-4sx^3y-6tx^2y^2+4sxy^3+ty^4=N,
$$
where $s>32t^3$. As an application, Ljunggren's equation is solved in an elementary way.
Keywords:
Diophantine equation, Padè approximation, effective approximation.
Received: 03.08.2008
Citation:
X. Jingbo, Ch. Jianhua, Zh. Silan, “Simplifying Method for Algebraic Approximation of Certain Algebraic Numbers”, Mat. Zametki, 92:3 (2012), 426–439; Math. Notes, 92:3 (2012), 383–395
Linking options:
https://www.mathnet.ru/eng/mzm6375https://doi.org/10.4213/mzm6375 https://www.mathnet.ru/eng/mzm/v92/i3/p426
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Abstract page: | 340 | Full-text PDF : | 174 | References: | 49 | First page: | 8 |
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