Lagrange, central norms, and quadratic Diophantine equations
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 cen...
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| Language: | English |
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Hindawi Limited
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1039 |
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doaj-15c06cf48b784c1da5710345627e8d032020-11-24T22:59:20ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-01200571039104710.1155/IJMMS.2005.1039Lagrange, central norms, and quadratic Diophantine equationsR. A. Mollin0Department of Mathematics and Statistics, University of Calgary, Calgary, AB, T2N 1N4, CanadaWe 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.http://dx.doi.org/10.1155/IJMMS.2005.1039 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
R. A. Mollin |
| spellingShingle |
R. A. Mollin Lagrange, central norms, and quadratic Diophantine equations International Journal of Mathematics and Mathematical Sciences |
| author_facet |
R. A. Mollin |
| author_sort |
R. A. Mollin |
| title |
Lagrange, central norms, and quadratic Diophantine equations |
| title_short |
Lagrange, central norms, and quadratic Diophantine equations |
| title_full |
Lagrange, central norms, and quadratic Diophantine equations |
| title_fullStr |
Lagrange, central norms, and quadratic Diophantine equations |
| title_full_unstemmed |
Lagrange, central norms, and quadratic Diophantine equations |
| title_sort |
lagrange, central norms, and quadratic diophantine equations |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2005-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/IJMMS.2005.1039 |
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AT ramollin lagrangecentralnormsandquadraticdiophantineequations |
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1725644940172591104 |