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Math Help - GCD Proof

  1. #1
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    GCD Proof

    I'm not sure at all how to start in answering the following:

    GCD (a^(m) - 1, a^(n) - 1) = a^GCD(m, n) - 1


    Are there any other properties of GCD other than GCD (a, b) = GCD (a - b, b)?

    djino
    "What that even help?"
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by djino View Post
    I'm not sure at all how to start in answering the following:

    GCD (a^(m) - 1, a^(n) - 1) = a^GCD(m, n) - 1


    Are there any other properties of GCD other than GCD (a, b) = GCD (a - b, b)?

    djino
    "What that even help?"
    Does a^{(m,n)}-1|a^m-1 and a^{(m,n)}-1|a^n-1? Why can't any value greater than a^(m,n)-1 divide both of them?
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