# All pairs of (a,b) of positive integers satisfying a given condition.

I have to determine all pairs $(a,b)$ of positive integers satisfying the condition $a^{b^2}=b^a$. So far i have found only one, namely $(1,1)$. How can i do it? Thanks for any help.

2. $\log_b(a)\in\mathbb Q\Leftrightarrow \exists n\in\mathbb N:a=b^n$