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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