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Math Help - Show that 2k+1 cannot be a prime unless...

  1. #1
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    Show that 2k+1 cannot be a prime unless...

    Show that 2k+1 cannot be a prime unless k is a power of 2.
    [Hint: Find a (polynomial) factor of Xp+1 for every odd prime p.]
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  2. #2
    MHF Contributor chisigma's Avatar
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    Setting k=6 we find that 2k+1= 13 is prime... but 6 is not a power of 2 !...

    Kind regards

    \chi \sigma
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  3. #3
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    Quote Originally Posted by NikoBellic View Post
    Show that 2k+1 cannot be a prime unless k is a power of 2.
    [Hint: Find a (polynomial) factor of Xp+1 for every odd prime p.]
    I suspect you mean 2^k+ 1.
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  4. #4
    MHF Contributor chiph588@'s Avatar
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  5. #5
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    Quote Originally Posted by HallsofIvy View Post
    I suspect you mean 2^k+ 1.
    Yeah, the formatting got lost for some reason.
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