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Math Help - Another GCD problem

  1. #1
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    Another GCD problem

    prove that gcd(((a^m)-1)/(a-1));(a-1))=((a-1);m)

    Help would be really appreciated.
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  2. #2
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    Re: Another GCD problem

    Quote Originally Posted by RuyHayabusa View Post
    prove that gcd(((a^m)-1)/(a-1));(a-1))=((a-1);m)

    Help would be really appreciated.
    Please show us what you've been able to do so far.

    -Dan
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  3. #3
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    Re: Another GCD problem

    First prove then use the following

    a^m = 1 + \sum _{k=1}^m c_k (a-1)^k

    where the c_k are integers
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  4. #4
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    Re: Another GCD problem

    I've finally solved it using Bezout's theorem.
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  5. #5
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    Re: Another GCD problem

    I would like to see a solution of this problem using Bezout's theorem.

    Here is a reference to Bezout's theorem as seen in Wikipedia

    Bézout's theorem - Wikipedia, the free encyclopedia

    .....X and Y are two algebraic curves in the Euclidean plane whose implicit equations are polynomials of degrees m and n without any non-constant common factor, then the number of intersection points does not exceed mn.

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