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Let Fq be a finite field with q elements. (a) Show that the polynomial x9 - r has exactly q distinct roots in Fq. (b)

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Let Fq be a finite field with q elements. (a) Show that the polynomial x9 - r has exactly q distinct roots in Fq. (b) Show that (F7 \\ {0}, .) is a cyclic group. (c) Find an example of a field K such that K \\ {0} is not a cyclic group

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