My questions is...
How many polynomials are there of degree n over Zp? Where p is a prime number and n is a positive integer.
I don't fully understand degrees.
Thanks, in advance, for any help.
How about we start with an easier question! How many polynomials of degree 2 are there over
Hint 1: A degree 2 polynomial has the form
where and we know that
Since our finite field has only 3 equivalence classes there are two choices for . Since there is no restriction on or (they do not affect the degree of the polynomial) they each have three choices. This gives
See if you can generalize this.