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Math Help - Can any one beat this?(Polynomials)

  1. #1
    Junior Member
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    Talking Can any one beat this?(Polynomials)

    If g.c.d(f(x),g(x))=1,

    where f(x) \in \mathbb{K}[x] and g(x) \in \mathbb{K}[x],

    where \mathbb{K} is a field of number.

    for \forall m \in \mathbb{Z} and m>0

    show that:

    g.c.d(f(x^m),g(x^m))=1
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  2. #2
    Senior Member Shanks's Avatar
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    If gcd (f(x), g(x))=1, then there exist u(x) and v(x) in K[x] such that
    u(x)f(x)+v(x)g(x)=1,
    Thus for any integer m>0,
    u(x^m)f(x^m)+v(x^m)g(x^m)=1
    gcd(f(x^m),g(x^m))=1
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