Pell's Equation

[wii]

I want to solve this equation

x^2 - 18 y^2 = 12

Any suggestion?

I thought , we have to find \sqrt 18and 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}
x = \pm 2 \sqrt{3} \, \cosh{t} \\

y = \frac{2 \sqrt{3}}{3} \, \sinh{t}
\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.