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Math Help - a squence question

  1. #1
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    Question a squence question

    Please see the " Microsoft word" attachment.
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  2. #2
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    There seems to be something wrong.
    If n=5
    Then,
    2=2
    2^2=4
    2^4=16=1
    2^1=2
    This is non-constant.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker View Post
    There seems to be something wrong.
    If n=5
    Then,
    2=2
    2^2=4
    2^4=16=1
    2^1=2
    This is non-constant.
    2^{2^4}=2^{16}=65536\equiv 1\ \mod\ 5

    Also

    <br />
2^{4k}=(2^4)^k \equiv 1 \ \mod \ 5<br />

    and since the \log_2 of all the numbers in the sequence after 2^{2^2} are divisible by 4 the result follows for \mod\ 5.

    By a similar argument we can show that if any element in the sequence is ever congurent to 0 or 1 so
    are all subsequent terms.


    RonL
    Last edited by CaptainBlack; December 28th 2006 at 12:03 AM.
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