With field extension is odd the nonsquare element in $GF(p)$ is also a nonsquare in $GF(p^e)$ where $p$ is odd prime

Question

I just want to know how to get this little thing, for $\theta\in GF(p)$ is a nonsquare element where $p$ is an odd prime, $\theta\in GF(p^e)$ is also a nonsquare element since $e$ is odd. I hope someone can hint me in caculation of finite field, and I think field extension theorem will be used.

Answer 1

Hint: $a\in GF(p)$ is a square iff $a^{(p-1)/2}=1$