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Possible Duplicate:
Simple formulation, nontrivial problem

I have the following problem: let $f : \mathbb{R} \rightarrow \mathbb{R}$ be infinitely differentiable, such that for each $x \in \mathbb{R}$ there is an $n(x) \in \mathbb{N}$ such that $f^{(n(x))}(x) = 0$. We must prove $f$ is a polynomial. Note that the difficulty of this problem lies in the fact that $n(x)$ depends on $x$. If we could find an $n$ such that $f^{(n)} = 0$ the problem would be easy.

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    See [here](http://math.stackexchange.com/questions/119436/simple-formulation-nontrivial-problem)2012-03-16

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