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Mat. Zametki, 2012, Volume 92, Issue 3, Pages 426–439 (Mi mz6375)  

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

DOI: https://doi.org/10.4213/mzm6375

Full text: PDF file (469 kB)
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English version:
Mathematical Notes, 2012, 92:3, 383–395

Bibliographic databases:

UDC: 511
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

Citation in format AMSBIB
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  • Математические заметки Mathematical Notes
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