Find the number of positive integers m for which there exist nonnegative integers x_{0}, x_{1}, \ldots, x_{2011}, such that

m^{x_{0}}=\sum_{k=1}^{2011} m^{x_{k}}

Find the number of positive integers m for which there exist nonnegative integers x_{0}, x_{1}, \ldots, x_{2011}, such that

m^{x_{0}}=\sum_{k=1}^{2011} m^{x_{k}}