Solving Some Quadratic Diophantine Equations with Clifford Algebra
| Audiencia | Público en general | es_ES |
| Cobertura | México | es_ES |
| Fecha de ingreso | 2026-10-05T16:34:23Z | |
| Fecha de publicación | 2011-01-01 | |
| Resumen | In this work, the equivalence class representatives of integer solutions of the Diophantine equation of the type a<sub>1x1</sub> <sup>2</sup> +...+ a<sub>p</sub>x<sub>p</sub> <sup>2</sup>= a<sub>p</sub>+1x<sup>2</sup> <sub>p+1</sub> +...+a<sub>p+q</sub>x<sup>2</sup> <sub>p+q</sub> + a<sub>1</sub>x<sup>2</sup> <sub>n+1</sub> (a<sub>i</sub>>0, i=1,...,p+q, x<sub>n+1</sub>≠0) are found using simple reflections of orthogonal vectors, manipulated using the Clifford algebra over orthogonal spaces R<sup>p,q</sup>. These solutions are obtained from the application of a useful Lemma: given two different non-zero vectors of the same norm, we can map one onto the other, or its negative, by means of a simple reflection. With this Lemma, we extend and improve a previous work [1] concerning generalized Pythagorean numbers, which now can be obtained as a Corollary. We also show that our technique is promising for solving others Diophantine equations. | es_ES |
| Doi | https://doi.org/10.1007/s00006-010-0247-3 | es_ES |
| URI | https://riuat.uat.edu.mx/handle/123456789/6159 | |
| Idioma | en | es_ES |
| Editorial | Birkhauser Verlag AG | es_ES |
| Relación | Advances in Applied Clifford Algebras | es_ES |
| URL relacionado | https://doi.org/10.1007/s00006-010-0247-3 | es_ES |
| Derechos | Acceso restringido / Suscripción (Metadatos de producción científica) | es_ES |
| Licencia | http://purl.org/coar/access_right/c_16ec | es_ES |
| Fuente | Advances in Applied Clifford Algebras | |
| Palabra clave | Clifford algebras | es_ES |
| Palabra clave | Diophantine equations | es_ES |
| Título | Solving Some Quadratic Diophantine Equations with Clifford Algebra | es_ES |
| Tipo | Artículo | es_ES |
| Arbitrado | Ha sido Arbitrado | es_ES |
| Autor | Aragón-González, G. | |
| Autor | Aragón, J.L. | |
| Autor | Rodríguez-Andrade, M.A. | |
| Autor | Aragón-González, G. | es_ES |
| Autor | Aragón, J.L. | es_ES |
| Autor | Rodríguez-Andrade, M.A. | es_ES |
| Institución | Universidad Autónoma de Tamaulipas | |
| Institución | Universidad Autónoma de Tamaulipas | es_ES |
| Número | 2 | es_ES |
| Rango de páginas | 259-272 | es_ES |
| URL relacionada | https://doi.org/10.1007/s00006-010-0247-3 | |
| Tipo de artículo | Indexado | |
| Tipo de artículo | Indexado | es_ES |
| Volumen | 21 | es_ES |