Hi just a few questions I'm having trouble with:

Let p=1009

(a) What is the order n of the group $\displaystyle Z^{*}_p$? Write n as a product of prime powers.

(b) Show that if $\displaystyle g\in Z^{*}_p$ then either g is a generator for $\displaystyle Z^{*}_p$ or at least one of the following equations holds: $\displaystyle g^{144}=1,g^{336}=1,g^{504}=1$ (Hint: Find the factors of n and apply Lagrange's Theorem.)

(c)Use the result from part(b) to find a generator for $\displaystyle Z^{*}_p$.Use fast exponentiation to compute the necessary powers of your generator, and show your working.

(d) Suppose you choose 10 elements at random from $\displaystyle Z^{*}_p$.Estimate the probability that at least one of them will be a generator

For (a) I've Calculated...

$\displaystyle p=1009$

$\displaystyle \phi(1009)=1009-1=1008$

$\displaystyle 1008=2^4.3^2.7$

But the others i need help please =)