Mollin, R. A.2018-09-272018-09-272005-01-01R. 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.2005.1039http://hdl.handle.net/1880/108559https://doi.org/10.11575/PRISM/44153We 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.Journal Article2018-09-27enCopyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.https://doi.org/10.1155/IJMMS.2005.1039