My questions is...

How many polynomials are there of degree n overZp? Where p is a prime number and n is a positive integer.

I don't fully understand degrees.

Thanks, in advance, for any help.

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- February 8th 2011, 08:01 AMpage929Polynomials of degree n over Zp
My questions is...

How many polynomials are there of degree n over**Z**p? Where p is a prime number and n is a positive integer.

I don't fully understand degrees.

Thanks, in advance, for any help. - February 8th 2011, 08:48 AMTheEmptySet
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. - February 8th 2011, 09:23 AMpage929
Thank you. I believe I have it now.