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Note that $m\leq n$ because if $m\gt n$, then $m=n+k$ for some positive integer $k$.\\  Then,   \begin{align*}  e^{\frac{i(\theta+2\pi m)}{n}} &=e^{frac{i\theta}{n}}}e^{frac{i2\pi &=e^{\frac{i\theta}{n}}e^{\frac{i2\pi  (n+k)}{n}} \end{align*}  \end{solution}  \end{document}