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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- May 7th 2011, 04:48 PMmickaeliusdivisibility/ 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! - May 7th 2011, 04:55 PMtopsquark