Word Count : 271

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Consider the map (f: \mathbb{F} \to \mathbb{F}) defined by (f(x) = x^3 - x). We want to show that this map is not surjective, which will imply that there exists some (a \in \mathbb{F}) such that the polynomial (x^3 - x + a) has no root in (\mathbb{F}) and is therefore irreducible over (\mathbb{F}). ____ _______ _________ _______ _____ ___.
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