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Let $F$ be a field of $8$ elements and $A =\{x\in F:x^7=1\text{ and }x^k\neq 1\}$ for all natural numbers $k<7$. Then the number of elements in $A$ is
1. $1$
2. $2$
3. $3$
4. $6$

How can I solve this problem, I am completely stuck on it. Can anyone help me? Thanks

2 Answers 2