I need a proof that this equation has more than one solution

Question

I need a proof that this equation has more than one solution for $p$ and $q$. $$p^{q-2}= 1024$$, where $q\in N, q>2$

Answer 1

Here's a proof:

$(p,q) = (32,4)$ solves the equation, as does $(4,7)$.

QED.

Answer 2

It seems that everybody so far missed the solution $p=1024$, $q=3$. :-)

Answer 3

How about $2^{10}$ and $4^5$? that gives you $p=2$ and $q=12$, or $p=4$ and $q = 7$. The easiest way to see this is just to factor $1024$ and see the possibilities...