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Math Help - Composite number proof help

  1. #1
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    Smile Composite number proof help

    Hello, I am having trouble with following proof:

    Prove that all integers

    2^2^(2n+1) +3 2^2^(4n+1) +7 , n = 1, 2, 3 ...

    are composite.


    Any help is appreciated , Thanks - Kate
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by katie07 View Post
    Hello, I am having trouble with following proof:

    Prove that all integers

    2^2^(2n+1) +3 2^2^(4n+1) +7 , n = 1, 2, 3 ...

    are composite.


    Any help is appreciated , Thanks - Kate
    I don't have time to do this in more detail, but my impression is that this might be doable by an induction proof.

    -Dan

    Edit: If it's going to be done by induction, it will take a better Mathematician than me!
    Last edited by topsquark; November 6th 2007 at 09:18 PM.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    this is supposed to be  2^{2^{2n + 1}} + 3 \cdot 2^{2^{4n + 1}} + 7 right?

    i'm having trouble proving this is composite for n = 1, but i'm not that good with divisibility on such a large scale, the number is huge.
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