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Pell Equations: Non-Principal Lagrange Criteria and Central Norms
Published online by Cambridge University Press: 20 November 2018
Abstract
We provide a criterion for the central norm to be any value in the simple continued fraction expansion of $\sqrt{D}$ for any non-square integer $D\,>\,1$. We also provide a simple criterion for the solvability of the Pell equation ${{x}^{2}}\,-\,D{{y}^{2}}\,=\,-1$ in terms of congruence conditions modulo $D$.
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- Research Article
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- Copyright © Canadian Mathematical Society 2012
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