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Matematicheskie Zametki, 2012, Volume 92, Issue 3, Pages 426–439
DOI: https://doi.org/10.4213/mzm6375 (Mi mzm6375) 		 
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
Full-text PDF (469 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm6375
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
English version:
Mathematical Notes, 2012, Volume 92, Issue 3, Pages 383–395
DOI: https://doi.org/10.1134/S0001434612090118
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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