How to show a harmonic function is a polynomial?

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Can anyone give me a hint to show the following?

Let $m$ be a positive integer and $u : \mathbb{R}^{n} \rightarrow \mathbb{R}$ be a harmonic function. If $u(x) = O(\left|x \right|)^m$ when $\left|x \right| \to \infty$, show that $u$ is polynomial of degree at most $m$.

Any clue will be great.

Thanks