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Thread: composite

  1. January 27th 2009, 05:06 PM #1
    Sally_Math
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    composite

    prove that n is composite, then 2^(n)-1 is composite.

    I need a prove, but I just want to know can I also prove using a counter example.
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  2. January 27th 2009, 06:46 PM #2
    ThePerfectHacker
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    Quote Originally Posted by Sally_Math View Post
    prove that n is composite, then 2^(n)-1 is composite.

    I need a prove, but I just want to know can I also prove using a counter example.
    Hint: x^m - 1 = (x-1)(x^{n-1}+x^{n-2}+...+x+1).
    Now assume that n=ab and consider \left( 2^a\right)^b - 1 and expand.
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