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This part $k=a*t +b$ is used in proving that that smallest degree $t=r(w)$ for which one of roots of unity is w^t=1 divides all other roots of unity. I already know that the difference vetween two neighbour roots is constant $2sin(pi/n)$. Is that the reason why we can express any root $k$ as linear function of $r(w)$

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