Lagrange, central norms, and quadratic Diophantine equations

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IJMMS.2005.213076.pdf (508.29 KB)
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2005-01-01
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Abstract
We consider the Diophantine equation of the form x2−Dy2=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.
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R. A. Mollin, “Lagrange, central norms, and quadratic Diophantine equations,” International Journal of Mathematics and Mathematical Sciences, vol. 2005, no. 7, pp. 1039-1047, 2005. doi:10.1155/IJMMS.2005.1039
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http://hdl.handle.net/1880/108559
 https://doi.org/10.11575/PRISM/44153
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