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Math Help - Coprime numbers

  1. #1
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    Coprime numbers

    Prove, that if
    (m,n) = 1 // m and n are two different primes
    then
    (2^m -1, 2^mn -1/2^m -1) = 1
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  2. #2
    Super Member PaulRS's Avatar
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    Oct 2007
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    We have \tfrac{2^{m\cdot n} - 1}{2^m - 1} = \left(2^m\right)^0 + .. + \left(2^m\right)^{n-1}\equiv n (\bmod. 2^m - 1)

    So basically we have to show that n doesn't divide 2^m - 1 (since n is prime)

    Now this cannot always happen since we may choose, say (3, 7).
    Last edited by PaulRS; November 19th 2010 at 04:00 PM. Reason: errors, sorry for making so many this time
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