1.

If 1,alpha,alpha^2,alpha^3,…,alpha^(n-1) be the n^(th) roots of unity, then prove that 1^p+alpha^p+(alpha^2)^p+(alpha^3)^p+…+(alpha^(n-1))^p={{:(0,if" "pnekn),(n,if" "p=kn):}" where p,k"epsilonN

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