A Method of Solving a Dophantine Equation of Second Degree with N Variables
| dc.creator | Smarandache, Florentin | |
| dc.date | 2004-05-12 | |
| dc.date.accessioned | 2026-07-07T05:08:09Z | |
| dc.date.available | 2026-07-07T05:08:09Z | |
| dc.description | First, we consider the equation $ax^2 - by^2 + c = 0$, with $a,b \in N*$ and $c \in Z*$, which is a generalization of Pell's equation. Here, we show that: if this equation has an integer solution and $ab$ is not a perfect square, then it has infinitely many integer solutions; in this case we find a closed expression for $(x_{n}, y_{n})$, the general positive integer solution, by an original method. More, we generalize it for a Diophantine equation of second degree and with n variables of the form: $\sum_{i=1}^{n} a_{i}x_{i}^{2} = b$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0405206 | |
| dc.identifier | http://arxiv.org/abs/math/0405206 | |
| dc.identifier | "Gaceta Matematica," Madrid, 2a Serie, Volumen 1, Numero 2, 1988, 151-157; translated to Spanish by Francisco Bellot Rosado as <Un metodo de resolucion de la ecuacion diofantica $ax^2 - by^2 + c = 0$> | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71146 | |
| dc.subject | General Mathematics | |
| dc.subject | 11D09 | |
| dc.title | A Method of Solving a Dophantine Equation of Second Degree with N Variables | |
| dc.type | text |