Geodesic
Determination of Integer Solutions of a System of Simultaneous Pell Equations
Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 588-600

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We describe an algorithm for finding integer solutions of a system of simultaneous Pell equations whose effective estimates can be obtained using the theory of linear forms in the logarithms of algebraic numbers. We use Matveev's estimate for forms in three logarithms. To decrease the resulting estimate, we use an iterative algorithm. At the end of the paper, results of the practical implementation of the proposed algorithm are given.
Keywords: simultaneous Pell equations, linear and quadratic forms, continued fraction, iterative algorithm, quadratic field, algebraic number, quadratic irrationality.
Mots-clés : Diophantine equation 
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     author = {A. Yu. Nesterenko},
     title = {Determination of {Integer} {Solutions} of a {System} of {Simultaneous} {Pell} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
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     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a10/}
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A. Yu. Nesterenko. Determination of Integer Solutions of a System of Simultaneous Pell Equations. Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 588-600. http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a10/