Geodesic
Simplifying Method for Algebraic Approximation of Certain Algebraic Numbers
Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 426-439

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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.
Mots-clés : Diophantine equation
Keywords: Padè approximation, effective approximation. 
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     author = {X. Jingbo and Ch. Jianhua and Zh. Silan},
     title = {Simplifying {Method} for {Algebraic} {Approximation} of {Certain} {Algebraic} {Numbers}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a10/}
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X. Jingbo; Ch. Jianhua; Zh. Silan. Simplifying Method for Algebraic Approximation of Certain Algebraic Numbers. Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 426-439. http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a10/