Field Theory: We show that g(x)=x^5-x+1 is irreducible over the rationals using techniques from finite fields. This leads to the definition of an Artin-Schreier polynomial, and in turn we obtain a class of irreducible polynomials over the rationals and prime characteristic.
Tagged under: mathematics,field,theory,ring,abstract,algebra,Artin,Schreier,polynomial,quintic,irreducible,root,modular,arithmetic,Fermat,theorem,Gauss,lemma
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