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Math Help - Math problem?

  1. #1
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    Math problem?

    Let n be a positive integer. Show that K=2^(2n-1)-9n^2+21n-14 is a multiple of 27.

    To try to attempt solving this, I actually used a trial and error method where I plugged in various numbers just to see what I got. For instance, I did K(1), K(2), and K(3), but my answers were just 0. I'm sure there's an algebraic approach to this, but I need some guidance.
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by EPark View Post
    Let n be a positive integer. Show that K=2^(2n-1)-9n^2+21n-14 is a multiple of 27.

    To try to attempt solving this, I actually used a trial and error method where I plugged in various numbers just to see what I got. For instance, I did K(1), K(2), and K(3), but my answers were just 0. I'm sure there's an algebraic approach to this, but I need some guidance.
    And 0 is a multiple of 27

    What you can do is a proof by induction, (supposing it's true for n, and checking for n+1)
    I haven't thought of another way yet.
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  3. #3
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    Yeh the method I would use here would be proof by induction, assuming true for n, making it equal to 27a, and then trying for n+1.

    As moo stated though, 0 is a multiple of 27
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