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Putnam 2010 A2


Find all differentiable functions f: \Bbb{R} \to \Bbb{R} such that \displaystyle f^\prime(x)=\frac{f(x+n)-f(x)}{n} for all x \in \Bbb{R},\ \forall n \in \Bbb{Z}_+^*.

Putnam 2010 A2

Hint: Prove that f^\prime is periodic of period 1.

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