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Let F be a field containing primitive p-th root of unity (i.e., n = 1 if and only if n is divisible by p). a)

Let F be a field containing primitive p-th root of unity (i.e., n = 1 if and only if n is divisible by p).

a) Show that 1 + ⁱ+ ²ⁱ + + ^(p1)i = 0 for i = 1, . . . , p 1.

b) What happens for i = p?

With some explanation please.

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