Can $ x^2-4a^n$ be a square? Let $ x,y,a,n \in {Z}>1$, Does the diophantine equation $ x^2-4a^n=y^2$ have any solutions? or How can I solve this?

Note that if $n=2$ you can rewrite as $x^2=y^2+(2a)^2$ - which essentially means you are looking for a pythagorean triple since if positive integers satisfy $x^2=y^2+z^2$ at least one of $y, z$ must be even.
