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Math Help - Algebraic Numbers Proof

  1. #1
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    Algebraic Numbers Proof

    A number r is algebraic if there is a nonzero polynomial p(x) with integer coefficients such that r is a root of p(x) = 0.


    Prove that every kth root of a rational number r is an algebraic number.
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  2. #2
    Junior Member
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    Sep 2011
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    Re: Algebraic Numbers Proof

    Let r be the k'th root of a rational number \frac{a}{b} where a and b are integers and b is not 0. (i.e. r^k = \frac{a}{b})

    We know that p(x) = x^k - \frac{a}{b} is a polynomial with a root at r

    To ensure the coefficients are all integer we simply multiply the right hand side by b
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