## Lagrange's theorem/generator/probability

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...

$p=1009$
$\phi(1009)=1009-1=1008$
$1008=2^4.3^2.7$

But the others i need help please =)