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Matematicheskie Zametki, 2009, Volume 86, Issue 4, Pages 588–600
DOI: https://doi.org/10.4213/mzm4068 (Mi mzm4068) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Determination of Integer Solutions of a System of Simultaneous Pell Equations

A. Yu. Nesterenko

M. V. Lomonosov Moscow State University
Full-text PDF (484 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm4068
Abstract: 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, Diophantine equation, linear and quadratic forms, continued fraction, iterative algorithm, quadratic field, algebraic number, quadratic irrationality.
Received: 14.04.2005
Revised: 29.06.2006
English version:
Mathematical Notes, 2009, Volume 86, Issue 4, Pages 556–566
DOI: https://doi.org/10.1134/S0001434609090326
Bibliographic databases:
UDC: 511.5
Language: Russian
Citation: A. Yu. Nesterenko, “Determination of Integer Solutions of a System of Simultaneous Pell Equations”, Mat. Zametki, 86:4 (2009), 588–600; Math. Notes, 86:4 (2009), 556–566
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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