Oooh...I almost forgot to add this.. notice the relation between the proof for part (ii) and the discrete logarithm problem. The proof is no mere coincidence. This is the reason behind using primes in encryption schemes that rely on the hardness of the discrete logarithm problem. This will ensure that given b^k mod p (since p is prime , p%b is definitely not zero) k has uniform probability because if p were not prime we would not be getting the remainders the equal number of times and hence the probability would be biased making it easier to crack.
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