Let $F$ be a field of 8 elements and $A$= {$x\in F$| $x^7$=1 and $x^k$$\neq$1 for all natural number k<1}. Then the number of elements in A is

Question

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

a) 1

b) 2

c) 3

d) 6

Please give me some hints. I am very new in Algebra.

Answer 1

Hint: the nonzero elements of a field form a group under multiplication. Do you know something about groups with $7$ elements?