Authors: Florentin Smarandache
We consider the equation (1) ax2 - by2 + c = 0, with a,b ε N* and c ε Z*. It is a generalization of Pell's equation: x2 -Dy2 = 1. Here, we show that: if the equation has an integer solution and a.b is not a perfect square, then (1) has an infinitude of integer solutions; in this case we find a closed expression for (xn,yn), the general positive integer solution, by an original method. More, we generalize it for any Diophantine equation of second degree and with two unknowns.
Comments: 10 pages.
[v1] 13 Mar 2010
Unique-IP document downloads: 76 times
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.