Hi just a few questions I'm having trouble with:
Let p=1009
(a) What is the order n of the group ? Write n as a product of prime powers.
(b) Show that if then either g is a generator for or at least one of the following equations holds: (Hint: Find the factors of n and apply Lagrange's Theorem.)
(c)Use the result from part(b) to find a generator for .Use fast exponentiation to compute the necessary powers of your generator, and show your working.
(d) Suppose you choose 10 elements at random from .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 =)