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Math Help - gcd

  1. #1
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    Apr 2010
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    gcd

    I need a little help on this problem.....Prove that is a is a relatively prime to b and a>b then gcd(a^m-b^m,a^n-b^n)=a^gcd(m,n)-b^gcd(m,n)

    I am suppose to use the Euclidean algorithm

    thanks
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  2. #2
    Super Member
    Joined
    Apr 2009
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    Quote Originally Posted by bugal402 View Post
    I need a little help on this problem.....Prove that is a is a relatively prime to b and a>b then gcd(a^m-b^m,a^n-b^n)=a^gcd(m,n)-b^gcd(m,n)

    I am suppose to use the Euclidean algorithm

    thanks

    An idea (I haven't tried it myself but my guess is it should work) - Prove that if x|RHS => x|LHS and vice a versa
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