Results 1 to 5 of 5

Math Help - number of monic irreducible polyynomials

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    44

    number of monic irreducible polyynomials

    I need help with irreducible polynomials. Could anybody help me please?
    The problem is:
    Find the pattern for the number of monic irreducible polynomials of degree 6 in Z_2[x]!
    Is it different to look for monic irreducible and irreducible polynomials?
    Thank you very much
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by sidi View Post
    I need help with irreducible polynomials. Could anybody help me please?
    The problem is:
    Find the pattern for the number of monic irreducible polynomials of degree 6 in Z_2[x]!
    Is it different to look for monic irreducible and irreducible polynomials?
    Thank you very much
    In the case of \mathbb{Z}_2[x] all polynomials are monic. Therefore, finding the monic irreducible polynomials is equivalent to finding the irreducible polynomials. There is a formula by Gauss that gives you the number of such irreducible polynomials. Are you asking for a formula?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2009
    Posts
    44
    yes, I think I am looking for that formula...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by sidi View Post

    yes, I think I am looking for that formula...
    \frac{1}{6} \sum_{d \mid 6} \mu(6/d) 2^d = 9, where \mu is the Mobius function.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2009
    Posts
    44
    Is there any other way how to derive the number of these polynomials without using this formula?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 10th 2011, 11:41 AM
  2. Finding monic irreducible polynomials.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 13th 2011, 11:32 AM
  3. Find all monic irreducible polynomicals
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 8th 2011, 11:06 AM
  4. Irreducible factorization in number ring.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 24th 2010, 02:43 PM
  5. Irreducible Monic Polynomials
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: November 30th 2009, 08:07 PM

Search Tags


/mathhelpforum @mathhelpforum