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Math Help - prove(easy for you all):

  1. #1
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    prove(easy for you all):

    if 2^p-1 is prime prove that p is also a prime
    Last edited by great_math; November 22nd 2008 at 03:48 AM.
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  2. #2
    o_O
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    The typical way is to prove the contrapositive: If n is composite, i.e. n = ab, then 2^{n} - 1 is composite.

    Then notice that: 2^{n} - 1 = 2^{ab}-1 = (2^a-1)\left(2^{a(b-1)} + 2^{a(b-2)} + \cdots + 2^{a} + 1\right)
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