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Pell Equations: Non-Principal Lagrange Criteria and Central Norms
R. A. Mollin, A. Srinivasan
Journal:

Canadian Mathematical Bulletin / Volume 55 / Issue 4 / 01 December 2012

Published online by Cambridge University Press:

20 November 2018, pp. 774-782

Print publication:

01 December 2012
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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 $D$.