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Math Help - divisibility/ binomial theorem question

  1. #1
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    divisibility/ binomial theorem question

    Given positive integers k, m, and n, how do you show k divides m^(k-1)+m^(k-2)*n+...+mn^(k-2)+n^(k-1) ?

    I have tried using the binomial theorem, but to no avail (problems when k is composite).

    Any help would be greatly appreciated!
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  2. #2
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    Quote Originally Posted by mickaelius View Post
    Given positive integers k, m, and n, how do you show k divides m^(k-1)+m^(k-2)*n+...+mn^(k-2)+n^(k-1) ?

    I have tried using the binomial theorem, but to no avail (problems when k is composite).

    Any help would be greatly appreciated!
    The problem statement is incorrect somehow. For k = 2: m + n is not necessarily divisible by k. Again for k = 3: m^2 + mn + n^2 is not necessarily divisible by 3.

    -Dan
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