I apologize if this is silly - let $k$ be a separably closed field, I wish to calculate $\pi_1(\mathbb{A}^n)$ completed away from the characteristic :($Hom(\hat{\pi_1(\mathbb{A}^n)}, G)$ classifies $G$-torsors where $G$ is a finite group with order prime to the characteristic.
I know how to do it for $\mathbb{A}^1$ using Riemann-Hurwitz (the answer is $= \{1\}$) but I am not sure what I have available to go up to arbitrary $n$. Thanks!