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Math Help - Divisible

  1. #1
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    Divisible

    Prove that 7|5^{2n}+(3)(2^{5n-2})

    I tried to use induction on this one. The statement is true for n = 1, assume k is true.

    I have 5^{2k+2}+3(2^{5k+3})

    Then 5^{2k}(25)+3(2^{5k-2})(32) \equiv 5^{2k}(4)+3(2^{5k-2})(4) \equiv 0 \ (mod \  7)

    This right?
    Last edited by tttcomrader; February 9th 2008 at 05:59 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tttcomrader View Post
    Prove that 7|5^{2n}+(3)(2^{5n-2})

    I tried to use induction on this one. The statement is true for n = 1, assume k is true.

    I have 5^{2k+2}+3(2^{5k+3})

    Then 5^{2k}(25)+3(2^{5k-2})(32) \equiv 5^{2k}(4)+3(2^{5k-2})(4) \equiv 0 \ (mod \  7)

    This right?
    The idea is OK but you should tighten up the wording/presentation.

    RonL
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