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Math Help - Divisibility of Binomial Coefficients

  1. #1
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    Divisibility of Binomial Coefficients

    Hello!

    My question is simple: how do I proof that 9 | binomial(2^(k+1),2^k), where k >= 3 integer?

    I have an idea: from 1 to 2^k there are n numbers that divisible by 9, from 2^k+1 to 2^(k+1) there are n+1 numbers that divisible by 9.

    Is that the correct way to proof?

    Thanks in advance!
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  2. #2
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    Hint: Play with the Binomial on the right...
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  3. #3
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    I do not understand what you exactly think. Can you explain?
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Ben92 View Post
    I do not understand what you exactly think. Can you explain?
    Expand the binomial coefficient into its factorial form. I think induction works better but I have not tried it.
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