 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2007/b/b2/v/solution

In characteristic two, repeated squaring gives

x^{8} - 1 = (x - 1)^{8}

. There is only the root one, already in the base field. Thus

K = F_{2}, [K : F_{2}] = 1

. Repeated roots do not require a larger splitting field.

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