Let p be a prime. Determine the number of irreducible quadratic polynomials over Z_p

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- Dec 11th 2008, 02:02 PMmandy123determine irreducible quadratic polynomials
Let p be a prime. Determine the number of irreducible quadratic polynomials over Z_p

(Worried) - Dec 11th 2008, 09:07 PMThePerfectHacker
The polynomial factors into a product of monic irreducible polynomials of order dividing .

There are linear monic polynomials. Let be the number of monic irreducible quadradic polynomials.

Then by counting degrees of polynomials in

We see that .

(This formula can be generalized to polynomials of degree by applying Mobius inversion formula) - Dec 12th 2008, 08:22 AMmandy123
So then what if p is not a prime, what if we are told to

Determine the number of irreducible quadratic polynomials over Z_p?

how would that change the answer? - Dec 12th 2008, 09:28 AMThePerfectHacker