Abel's Lemma

The pure equation

$$x^p=C$$

of Prime degree $p$ is irreducible over a Field when $C$ is a number of the Field but not the $p$th Power of an element of the Field.

See also Abel's Irreducibility Theorem, Gauss's Polynomial Theorem, Kronecker's Polynomial Theorem, Schoenemann's Theorem

References

Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 118, 1965.