A Method to Solve the Diophantine Equation $ax^2-by^2+c=0$
| dc.creator | Smarandache, Florentin | |
| dc.date | 2006-09-24 | |
| dc.date.accessioned | 2026-07-07T07:25:12Z | |
| dc.date.available | 2026-07-07T07:25:12Z | |
| dc.description | It is a generalization of Pell's equation $x^2-Dy^2=0$. Here, we show that: if our Diophantine equation has a particular integer solution and $ab$ is not a perfect square, then the equation has an infinite number of solutions; in this case we find a close expression for $(x_n,y_n)$, the general positive integer solution, by an original method. More, we generalize it for any Diophantine equation of second degree and with two unknowns $f(x,y)=0$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609671 | |
| dc.identifier | http://arxiv.org/abs/math/0609671 | |
| dc.identifier | Gaceta Matematica, 2a Serie, Vol. 1, No. 2, 1988, pp. 151-157; translated into Spanish by Francisco Bellot Rosado, "Un metodo de resolucion de la ecuacion diofantica" | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116638 | |
| dc.subject | General Mathematics | |
| dc.subject | 11D09 | |
| dc.title | A Method to Solve the Diophantine Equation $ax^2-by^2+c=0$ | |
| dc.type | text |