HMMT November 2012 E7

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Find the number of ordered 2012-tuples of integers $\left(x_{1}, x_{2}, \ldots, x_{2012}\right)$ , with each integer between 0 and 2011 inclusive, such that the sum $x_{1}+2 x_{2}+3 x_{3}+\cdots+2012 x_{2012}$ is divisible by 2012 .

Dataset text NuminaMath olympiads. Quoted with source.

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2012^{2011}

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