Show that Zp contains all the (p-1)th roots of unity.

For which primes p does Zp contains primitive fourth roots of unity.

Here Zp is the set of p-adic integers.

Proving that it has a (p-1)th root of unity is easy, but ALL roots is another matter. Please help me with these questions..

I think for the second question, p has to be 5, but maybe there are other answers that i didn't think of.