Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / B / 2 / v

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- Solution v

Solution

In characteristic two, the binomial theorem gives

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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