## A Method to Solve the Diophantine Equation a X^{2}-B Y^{2} + C = 0

**Authors:** Florentin Smarandache

We consider the equation
(1) ax^{2} - by^{2} + c = 0, with a,b ε N* and c ε Z*.
It is a generalization of Pell's equation: x^{2} -Dy^{2} = 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 (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.

**Comments:**
10 pages.

**Download:** **PDF**

### Submission history

[v1] 13 Mar 2010

**Unique-IP document downloads:** 66 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.*

*
*