Show that $16$ is a $8th$ power $\mod{}$ $p$ for any prime number $p$.
I have no idea how to approach this.
I tried,
$$a^8\equiv16\pmod{p}$$
$$(a^4+4)(a^4-4)\equiv 0 \pmod{p}$$
$$a^4 \equiv \pm4\pmod{p}$$
$$a^4 \equiv 2,p-2\pmod{p}$$
But this doesn't seem to lead anywhere.
