Let p be a prime, show that the sum of all the primitive roots module p is congruent to $\displaystyle u(p-1)$ module p. u is the mobius function.

I am considering the polymonial $\displaystyle \Pi (x-g^k)$ in $\displaystyle Z/pZ[x]$, where g is a primitive root, and the product is taken over all k such that g^k is also a primitive root. and...???

Any help or new idea would be appriciated.