Solving Pell's Equation: I'm Stuck!

[wii]

I want to solve this equation

$$x^2 - 18 y^2 = 12$$

Any suggestion?

I thought , we have to find $\sqrt 18$and then find $$x/y$$

BUT I was confused and then stopped solving

 

[Dickfore]

This equation has 2 unknowns. If you don't specify what set x and y are elements of, for example integer, it has an infinite set of solutions that can be represented parametrically as:

$$\begin{array}{l}<br /> x = \pm 2 \sqrt{3} \, \cosh{t} \\<br /> <br /> y = \frac{2 \sqrt{3}}{3} \, \sinh{t}<br /> \end{array}$$

 

[wii]

Sorry,
Both x & y are integers.

 

[Buri]

You might get more help if you posted this in the Number Theory section...

 

[Dickfore]

There is no solution.