Pell's equation are equations of the form

x² - n*y² = 1

The fundamental solution is the pair (x, y) that solves the equation with the minimum x. The trivial solution always exist (x=1, y=0), but if you obtain a non-trivial solution, you can generate the rest of the inifinite solutions.

(There is only 1 possible solution, the trivial, if n is a perfect square)

This implementation uses the continued fractions method.

To solve Pell's equation for an arbitrary n, download pell.py and do:

python pell.py n

Where n is the integer to solve for