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Math Help - Multiplicative Inverse

  1. #1
    Member elninio's Avatar
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    Multiplicative Inverse

    Find the multiplicative inverse in the given field.

    [x^2-2x+1] in Z_3[x]/<x^3+x^2+2x+1>

    Thank you!
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  2. #2
    Member Haven's Avatar
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    Hint: \mathbb{Z}_{3}[x]{/}(x^3 + x^2 +2x + 1) =  \{0,1,2,x,x+1,x+2,2x,2x+1,2x+2,x^2,x^{2} +1, x^{2}+2,x^{2}+x,x^{2}+2x,x^{2}+x+1, x^{2}+x+2,x^{2}+2x+1,x^{2}+2x+2\}

    And x^2 -2x +1 = x^2 +x + 1
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  3. #3
    Member elninio's Avatar
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    I think I've got it!
    Is the answer (x-2) (or should I say x+1?)?

    Correct me if I've done this wrong, but:
    x^2-2x+1)(x-2)=x^3-2x^2+x-2x^2+4x-2
    =x^3-4x^2+5x-2
    =x^3+x^2+2x+1
    Last edited by elninio; December 2nd 2009 at 10:47 AM.
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  4. #4
    Member elninio's Avatar
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    Actually, it seems I am going about this the wrong way.
    I am trying the find an a^-1 in which:
    a*a^-1=1 in Z_3.

    where a=x^2+x+1
    Is this right? By doing a case by case basis I still cant find a suitable answer.
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  5. #5
    Member elninio's Avatar
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    I'm not sure if I'm allowed to bump this, but it would be nice to have an answer.
    Thank you!
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