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Results tagged with galois-theory
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user 407413
Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.
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Existence of an irreducible polynomial that does not divide $x^n + a$
The question:
Can one characterize all fields $K$ over which there exists an irreducible polynomial $f(x)$ that does not divide a polynomial of the form $x^n + a$?
Examples:
Such a polynomial clearly …
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