Lagrange, central norms, and quadratic Diophantine equations

R. A. Mollin

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-9

Abstract:

We consider the Diophantine equation of the form x 2 − D y 2 = c , where c = ± 1 , ± 2 , and provide a generalization of results of Lagrange with elementary proofs using only basic properties of simple continued fractions. As a consequence, we achieve a completely general, simple, and elegant criterion for the central norm to be 2 in the simple continued fraction expansion of D .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:213076

DOI: 10.1155/IJMMS.2005.1039

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