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Lagrange, central norms, and quadratic Diophantine equations

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  • R. A. Mollin

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 .

Suggested Citation

  • R. A. Mollin, 2005. "Lagrange, central norms, and quadratic Diophantine equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:213076
    DOI: 10.1155/IJMMS.2005.1039
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