Results 1 to 3 of 3

Math Help - gcd in F5

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    204

    gcd in F5

    calculate gcd(x^3 + 2x^2 + 3x - 1, 2x^2 - x - 1) in F_{5}

    i know how to go about this question, im just a little confused...
    does 6x^2 \equiv 0, because we are working in F_{5}?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: gcd in F5

    Quote Originally Posted by wik_chick88 View Post
    calculate gcd(x^3 + 2x^2 + 3x - 1, 2x^2 - x - 1) in F_{5}

    i know how to go about this question, im just a little confused...
    does 6x^2 \equiv 0, because we are working in F_{5}?
    No, if that were the case it would be the additive identity. Just reduce the coefficient mod 5

    6x^2=1x^2=x^2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: gcd in F5

    Quote Originally Posted by wik_chick88 View Post
    calculate gcd(x^3 + 2x^2 + 3x - 1, 2x^2 - x - 1) in F_{5}

    i know how to go about this question, im just a little confused...
    does 6x^2 \equiv 0, because we are working in F_{5}?
    Roots of: g(x)=2x^2 - x - 1=0 are: 1 and -1/2

    Say f(x)=x^3 + 2x^2 + 3x - 1,

    f(1)!=f(-1/2)!=0

    gcd((f(X),g(x))=1
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum