page1929 Rings Matthias Lorentzen...mattegrisenforlag.com
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Question
In the finite field ℤ, 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.
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