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If $n>2$, and $\zeta$ is a primitive nth root of unity, and we have an integer $a$ where $\zeta^a=1$, can we simply say that $\zeta^a=\zeta$? Or is there some other way to prove that $n|a$?

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    If $\zeta\ne1$ but $\zeta^a=1$ then $\zeta^a\ne\zeta$.2011-10-12

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