AIME 2011a Problem 7

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Answer

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

Dataset text AIME 1983 to 2026. Quoted with source.

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