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Math Help - abstract algebra proof

  1. #1
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    abstract algebra proof

    a)let a be a positive integer.If square root of a is rational, prove that square root of a is an integer.

    b)let r be a rational number and a an integer such that r^n = a .Prove that r is an integer.


    PLease help me this one.
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  2. #2
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    Quote Originally Posted by Deepu View Post
    a)let a be a positive integer.If square root of a is rational, prove that square root of a is an integer.
    This is proved here:

    Quadratic irrational - Wikipedia, the free encyclopedia

    b)let r be a rational number and a an integer such that r^n = a .Prove that r is an integer.
    Let r=\frac{p}{q}, reduced. Then q^n\big|p^n and so q\big|p. So r\in\mathbb{Z}.
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