Abstract Algebra

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Finite Field: Generators of $\mathbf{F}_7$ & $\mathbf{F}_7^\ast$

ABSALG-D2AJ7B

Let $\mathbf{F}_7$ be a finite field with $7$ elements and let $\mathbf{F}_7^\ast$ be the non-zero elements of $\mathbf{F}_7$.
Let $+$ be addition and let $\times$ be multiplication in $\mathbf{F}_7$.
It is known that both $(\mathbf{F}_7, +)$ and $(\mathbf{F}_7^\ast, \times)$ are cyclic groups.

(1) There are

distinct elements $g\in\mathbf{F}_7$ such that $g$ generates $(\mathbf{F}_7, +)$.

(2) There are

distinct elements $g\in\mathbf{F}_7^\ast$ such that $g$ generates $(\mathbf{F}_7^\ast, \times)$.