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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2010 Volume 383, Pages 53–62 (Mi znsl3871)

On the negative Pell equation

E. P. Golubeva

State University of Telecommunications, St. Petersburg, Russia

Abstract: Let $\varepsilon$ be the fundamental unit of a field $Q(\sqrt d)$. In the paper it is proved that $\varepsilon>d^{3/2}/\log^2d$ for almost all $d$ such that $N(\varepsilon)=-1$. Bibl. 6 titles.

Key words and phrases: negative Pell equation, fundamental unit of a field, continued fraction.

UDC: 511

Received: 27.10.2010


 English version:
Journal of Mathematical Sciences (New York), 2011, 178:2, 144–149

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© Steklov Math. Inst. of RAS, 2024