 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2007/b/2/v/solution

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

. The only root is already in

F_{2}

, so the splitting field is the original field, despite the repeated root:

[K : F_{2}] = 1.

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