17.3.16

Exponentiation tables in Z sub power of a prime

I already discussed two different types of exponentiation tables, namely those of Zn where n is the product of two distinct odd primes p and q and of Zp when p is a prime.

Another interesting type of exponentiation tables is that of Zpk when p is prime and k is any integer. If p is prime then pk has a primitive root so the only universal exponent mod pk is strictly φ(pk). In this case this is equal to:

φ(pk) = pk − pk−1 = pk−1(p − 1)

Additionally, Zpk has elements i, j > 0 such that ij = 0 when i is any multiple of p. Therefore the rows i of the exponentiation table of Zpk  that are multiples of p are simply 0 for j > 1