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Math Help - Greatest common divisor (different to last thread)

  1. #1
    Senior Member chella182's Avatar
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    Greatest common divisor (different to last thread)

    Let f(X) be a polynomial over \mathbb{Z}_3 such that d(X)=gcd(f(X),f(X)+(X^2+X+1)) is a polynomial of degree 1. Determine d(X).

    Quite literally stumped. I get why d(X) is of degree 1, but I don't know how to determine it at all.
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  2. #2
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    Quote Originally Posted by chella182 View Post

    Let f(X) be a polynomial over \mathbb{Z}_3 such that d(X)=gcd(f(X),f(X)+(X^2+X+1)) is a polynomial of degree 1. Determine d(X).

    Quite literally stumped. I get why d(X) is of degree 1, but I don't know how to determine it at all.
    well, it's pretty obvious that d(x)=x+2 because d(x) must divide f(x) + x^2+x+1 - f(x) = x^2+x+1=(x+2)^2.
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