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Keldysh Institute preprints, 2016, 001, 20 pages (Mi ipmp2077)  

This article is cited in 2 scientific papers (total in 3 papers)

From Diophantine approximations to Diophantine equations

A. D. Bruno


Abstract: We consider the global generalization of the continued fraction giving the best Diophantine approximations. The generalization allows to compute the fundamental units of the algebraic rings and to find all solutions of a certain class of Diophantine equations.

Keywords: generalization of continued fraction, Diophantine approximations, set of fundamental units, fundamental domain, Diophantine equation.

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UDC: 517.36

Citation: A. D. Bruno, “From Diophantine approximations to Diophantine equations”, Keldysh Institute preprints, 2016, 001, 20 pp.

Citation in format AMSBIB
\Bibitem{Bru16}
\by A.~D.~Bruno
\paper From Diophantine approximations to Diophantine equations
\jour Keldysh Institute preprints
\yr 2016
\papernumber 001
\totalpages 20
\mathnet{http://mi.mathnet.ru/ipmp2077}


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  • http://mi.mathnet.ru/eng/ipmp2077
  • http://mi.mathnet.ru/eng/ipmp/y2016/p1

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Aptekarev, A. B. Batkhin, A. D. Bryuno, “Vladimir Igorevich Parusnikov”, Chebyshevskii sb., 17:1 (2016), 286–298  mathnet  elib
    2. A. D. Bryuno, “Ot diofantovykh priblizhenii do diofantovykh uravnenii”, Chebyshevskii sb., 17:3 (2016), 38–52  mathnet  elib
    3. A. D. Bryuno, “Vychislenie osnovnykh edinits chislovykh kolets s pomoschyu obobschënnoi tsepnoi drobi”, Preprinty IPM im. M. V. Keldysha, 2017, 046, 28 pp.  mathnet  crossref
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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