In the finite field `ZZ_2(alpha)`, where `alpha` is a root of the irreducible polynomial
`x^3 + x^2 + 1` over `ZZ_2` ,
consider the following statements:
I `alpha^7 = 1`
II `alpha^8 = alpha`
Which of the following is correct:
A) Only statement I is true.
B) Both statements I and II are true.
Hint: The multiplicative group has
8 - 1 = 7 elements. ?