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

Let p=1009

(a) What is the order n of the group Z^{*}_p? Write n as a product of prime powers.
(b) Show that if g\in Z^{*}_p then either g is a generator for Z^{*}_p or at least one of the following equations holds: 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 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 Z^{*}_p.Estimate the probability that at least one of them will be a generator

For (a) I've Calculated...


But the others i need help please =)