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    • Thread Starter


    Show that f(k+1) - f(k) is divisible by 15.

    f(n) = 3^4n + 2^4n+2

    b) Prove that f(n) is divisible by 5

    Check for 1, assume for K etc.

    3^4(k+1) + 2^(4(k+1)+2) - (3^4k + 2^4k+2)
    = 3^(4k + 4) + 2^(4k+6) - (3^4k + 2^4k+2)
    = 81.3^4k + 16.2^(4k+2) - (3^4k + 2^4k+2)
    = 80.3^4k + 15.2^4k+2

    80 isn't divisible by 15. Stuck.

    and for part be, how do you show that it's divisible by 5? You know it's divisible by 15 which is 5 multiplied by 3 hence divisible by 5 but how do you show that?

    Many Thanks!

    80 x 3^(4k) = 16 x 5 x 3^(4k) = 16 x 15 x 3^(4k-1)
    • Thread Starter

    (Original post by Glutamic Acid)
    80 x 3^(4k) = 16 x 5 x 3^(4k) = 16 x 15 x 3^(4k-1)
    Aha, that is sneaky! Thanks!
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Updated: January 31, 2010
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