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- Jun 20, 2014

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Let $f,g : \Bbb R \to \Bbb R$ such that $$f(x) = \sum_{n =1}^{\lfloor x\rfloor} g\left(\frac{x}{n}\right)$$ Show that $$g(x) = \sum_{n = 1}^{\lfloor x\rfloor} \mu(n)\, f\left(\frac{x}{n}\right)$$ where $\mu(n)$ is the Möbius function.

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