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Zapiski Nauchnykh Seminarov POMI, 1995, Volume 227, Pages 52–60 (Mi znsl4263)  
This article is cited in 2 scientific papers (total in 2 papers)

Diophantine representations of linear recurrences. I

M. A. Vsemirnov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (387 kB) Citations (2)
Abstract: Direct constructions of Diophantine representations of linear recurrent sequences are discussed. These constructions generalize already known results for second-order recurrences. Some connections of this problem with the theory of units in rings of algebraic integers are shown. It is proved that the required representations erist only for second-, third-, and fourth-order sequences. In the two last-mentioned cases certain additional restrictions on their coefficients must be imposed. Bibliography: 14 titles.
Received: 03.03.1995
English version:
Journal of Mathematical Sciences (New York), 1998, Volume 89, Issue 2, Pages 1113–1118
DOI: https://doi.org/10.1007/BF02355857
Bibliographic databases:
Document Type: Article
UDC: 511.216+511.5
Language: Russian
Citation: M. A. Vsemirnov, “Diophantine representations of linear recurrences. I”, Problems in the theory of representations of algebras and groups. Part 4, Zap. Nauchn. Sem. POMI, 227, POMI, St. Petersburg, 1995, 52–60; J. Math. Sci. (New York), 89:2 (1998), 1113–1118
Citation in format AMSBIB
\Bibitem{Vse95}
\by M.~A.~Vsemirnov
\paper Diophantine representations of linear recurrences.~I
\inbook Problems in the theory of representations of algebras and groups. Part~4
\serial Zap. Nauchn. Sem. POMI
\yr 1995
\vol 227
\pages 52--60
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4263}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1374557}
\zmath{https://zbmath.org/?q=an:0938.11004}
\transl
\jour J. Math. Sci. (New York)
\yr 1998
\vol 89
\issue 2
\pages 1113--1118
\crossref{https://doi.org/10.1007/BF02355857}
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  • https://www.mathnet.ru/eng/znsl/v227/p52
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    Citing articles in Google Scholar: Russian citations, English citations
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