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On the Pellian equation. (English. Russian original) Zbl 1077.11021

J. Math. Sci., New York 122, No. 6, 3600-3602 (2004); translation from Zap. Nauchn. Semin. POMI 286, 36-39 (2002).
Summary: Let \(\varepsilon(d)\) be the least solution of the Pell equation \(x^2-dy^2= 1\). It is proved that there exists a sequence of values of \(d\) having a positive density and such that \(\varepsilon(d)> d^{2-\delta}\), where \(\delta\) is an arbitrary positive constant.

MSC:

11D09 Quadratic and bilinear Diophantine equations
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