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    Irreducible Polynomials and Isomorphic Fields

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    Let F=Z7 and let p(x)=x^3 - 2 and q(x)= x^3 + 2 in F[x]. Show that p(x) and q(x) are irreducible in F[x] and that the fields F[x]/p(x) and F[x]/q(x) are isomorphic.

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    Solution Summary

    Irreducible polynomials and isomorphic fields are investigated and discussed in the solution.