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If E = F2[ x ]/( p ( x )), where p ( x ) = x^ 3 + x + 1, then E is a field with 8 elements.

If E = F2[x]/(p(x)), where p(x) = x^3 + x + 1, then E is a field with 8 elements. Show that a root π of p(x) is a primitive element of E by writing every nonzero element of E as a power of π.

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