A power pseudo-random number generator is the following

Question

A power pseudo-random number generator is the following: start with a prime p, exponent d>1 and seed x₀ such that (d,p-1)=1. Then form x_n+1=x_n^d(mod p) for each n.

a)Determine the period of the random number generator in terms of p, d and x₀.

b)Also find what is the maximum possible period for a given prime p, and what values of p and x₀ should be chosen to achieve this maximum.