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.