Results 1 to 3 of 3

Math Help - GCD of polynomials in Z3[x]

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    2

    GCD of polynomials in Z3[x]

    There seems to be an error in the following calculation, I'm not quite sure what it is though. Could someone point it out?
    Thanks.

    Find the GCD of p(x) = 2x^5 + x^3 + 2^x + 1 and q(x) = x^4 + x^3 + x + 1 in z3[x]
    Use the Euclidean algorithm:
    2x^5 + x^3 + 2x + 1 = (2x + 1)(x^4 + x^3 + x + 1) + x^2 + 2x
    x^4 + x^3 + x + 1 = (x^2 + 2x + 2)(x^2 + 2x) + 1
    x^2 + 2x = (1)(x^2 + 2x) + 0
    So the answer is 1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Zoird View Post
    There seems to be an error in the following calculation, I'm not quite sure what it is though. Could someone point it out?
    Thanks.

    Find the GCD of p(x) = 2x^5 + x^3 + 2^x + 1 and q(x) = x^4 + x^3 + x + 1 in z3[x]
    Use the Euclidean algorithm:
    2x^5 + x^3 + 2x + 1 = (2x + 1)(x^4 + x^3 + x + 1) + x^2 + 2x
    x^4 + x^3 + x + 1 = (x^2 + 2x + 2)(x^2 + 2x) + 1
    x^2 + 2x = (1)(x^2 + 2x) + 0
    So the answer is 1
    What is the problem? It seems you did everything correctly.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2007
    Posts
    2

    Gcd

    I was told there was something wrong with the calculation, but didn't really get a proper explanation of why. I'm quite sure that the first two lines are right, and the answer should be too. So that really only leaves the third row

    x^2 + 2x = (1)(x^2 + 2x) + 0

    But it's really simple, so how could it be wrong.. It drives me mad

    Oh, and I noticed I wrote 2^x instead of 2x in the initial description, it should be 2x as in the calculation. Sorry about that.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: April 7th 2011, 12:38 PM
  2. GCD of polynomials in Zn[x]
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 18th 2010, 06:22 AM
  3. Polynomials
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 16th 2010, 06:52 AM
  4. Replies: 7
    Last Post: January 8th 2010, 03:13 AM
  5. Replies: 5
    Last Post: November 29th 2005, 03:22 PM

Search Tags


/mathhelpforum @mathhelpforum