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Math Help - For p = 3, find the number of monic irreducible polynomials in...?

  1. #1
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    For p = 3, find the number of monic irreducible polynomials in...?

    1.) For p = 3, find the number of monic irreducible polynomials in Zp[x] of the following degrees

    (a) 5
    (b) 9
    (c) 10

    2.) Repeat Exercise 1 for a general prime p. Your answers will be formulas in p.

    Can anybody help me out, at least with part 1!? There must be any easier way than writing them all out.
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  2. #2
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    Re: For p = 3, find the number of monic irreducible polynomials in...?

    I have this formula from my problem session
    (p-1)p^k where k:=deg(p(x))

    so there are
    (p-1)p^k=(3-1)3^5=486 monic polynomials in \mathbb{Z}_{3}of deg 5

    (3-1)3^9=39366 monic polynomials in \mathbb{Z}_{3}of deg 9

    (3-1)3^{10}=118098 monic polynomials in \mathbb{Z}_{3}of deg 10

    so it would take quite long time to list them all by hand..
    Last edited by rayman; December 8th 2012 at 06:45 AM.
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