Hello,

the task is to solve (find all integer solutions) following quadratic Diophantine equation:

$\displaystyle x^2-4y^2=65$

I think I need to use modular arithmetic for obtaining solutions. Maybe I should start investigating squares of integers $\displaystyle mod \ x$, $\displaystyle x = 1,2,...$

Also I peeled answer from WolframAlpha, but that doesn't give me any hint how to get it myself. WolframAlpha gave the following solutions:

$\displaystyle x = \pm 33, \ y = \pm 16$

$\displaystyle x = \pm 9, \ y = \pm 2$

So, any help is appreciated. Thanks!