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Math Help - Prime number 2

  1. #1
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    Prime number 2

    Hi,

    How to show (\forall n \in \mathbb{N}*) (2^{2n}+5) isn't a positive prime nimber????
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  2. #2
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    Quote Originally Posted by bhitroofen01 View Post
    Hi,

    How to show (\forall n \in \mathbb{N}*) (2^{2n}+5) isn't a positive prime nimber????

    2^2=4=1\!\!\!\pmod 3\Longrightarrow 2^{2n}=(2^2)^n=1\!\!\!\pmod n , and since 5=2\!\!\!\pmod 3 , we get 2^{2n}+5=1+2=0\!\!\!\pmod 3

    Tonio
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