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Mat. Sb. (N.S.), 1969, Volume 80(122), Number 3(11), Pages 445–452 (Mi msb3628)  

This article is cited in 1 scientific paper (total in 1 paper)

On the representation of numbers by binary biquadratic forms

V. A. Dem'yanenko


Abstract: In this paper it is proved that if the rank of the equation $ax^4+bx^2y^2+cy^4=kz^2$ over the field $R(1)$ does not exceed unity, and if $k$ is not divisible by any fourth power and is relatively prime to the discriminant, then, provided that $\frac{(b^2-4ac)}{\max\{|a|,|c|\}}$ is sufficiently large relative to $k$, the equation $ax^4+bx^2y^2+cy^4=k$ does not have more than three positive integer solutions.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1969, 9:3, 415–422

Bibliographic databases:

UDC: 511.46
MSC: 11E16, 11E25, 11E04
Received: 04.03.1969

Citation: V. A. Dem'yanenko, “On the representation of numbers by binary biquadratic forms”, Mat. Sb. (N.S.), 80(122):3(11) (1969), 445–452; Math. USSR-Sb., 9:3 (1969), 415–422

Citation in format AMSBIB
\Bibitem{Dem69}
\by V.~A.~Dem'yanenko
\paper On~the representation of numbers by binary biquadratic forms
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 80(122)
\issue 3(11)
\pages 445--452
\mathnet{http://mi.mathnet.ru/msb3628}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=250977}
\zmath{https://zbmath.org/?q=an:0191.05201|0206.33704}
\transl
\jour Math. USSR-Sb.
\yr 1969
\vol 9
\issue 3
\pages 415--422
\crossref{https://doi.org/10.1070/SM1969v009n03ABEH001360}


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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. V. A. Dem'yanenko, “On Tate height and the representation of numbers by binary forms”, Math. USSR-Izv., 8:3 (1974), 463–476  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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