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Math Help - Need help doing a proof

  1. #1
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    Need help doing a proof

    Prove:
    If a positive integer n is not prime, then 2^(n)-1 is not prime.

    If n is not prime, then it factors into n = a*b. Use the identity
    x^(b) = (x-1)(x^(b-1) + x^(b-2) + ...+ x + 1) and substitute x = 2^(a).
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  2. #2
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    Quote Originally Posted by noles2188 View Post
    Prove:
    If a positive integer n is not prime, then 2^(n)-1 is not prime.

    If n is not prime, then it factors into n = a*b. Use the identity
    x^(b) = (x-1)(x^(b-1) + x^(b-2) + ...+ x + 1) and substitute x = 2^(a).
    There's a "-1" missing in that identity. It should be x^b {\color{red}{} - 1} = (x-1)(x^{b-1} + x^{b-2} + \ldots + x + 1). Substitute x=2^a in that and you should have no trouble getting the result.
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