# Pell's Equation

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

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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:

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

Last edited:
Sorry,
Both x & y are integers.

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

There is no solution.