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I got this on an exam and struggled to complete it, could anyone offer a proof? Thanks!

Let $X$ be a finite set. Let $f: X \longrightarrow X$ be a bijection. For $n \in \mathbb{Z}^+$, set $$f^n = \underbrace{f \circ f \circ \cdots \circ f}_{n \text{ times}}.$$

Prove that there exists $m \in \mathbb{Z}^+$ such that $f^m = \mathrm{Id}_X$.

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