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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| Format: | Article |
| Language: | English |
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Wiley
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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| _version_ | 1832565490759761920 |
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| author | R. A. Mollin |
| author_facet | R. A. Mollin |
| author_sort | R. A. Mollin |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-15c06cf48b784c1da5710345627e8d03 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-15c06cf48b784c1da5710345627e8d032025-02-03T01:07:25ZengWileyInternational 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 |
| spellingShingle | R. A. Mollin Lagrange, central norms, and quadratic Diophantine equations International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Lagrange, central norms, and quadratic Diophantine equations |
| title_sort | lagrange central norms and quadratic diophantine equations |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1039 |
| work_keys_str_mv | AT ramollin lagrangecentralnormsandquadraticdiophantineequations |