# My problems #18

Algebra Level 3

Find the number of positive integers $$m$$for which there exist nonnegative integers $$x_0$$, $$x_1$$, $$\dots$$ , $$x_{2011}$$ such that $m^{x_0} = \displaystyle\sum_{k = 1}^{2011} m^{x_k}.$

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