Kronecker's Polynomial Theorem

An algebraically soluble equation of Odd Prime degree which is irreducible in the natural Field possesses either

1. Only a single Real Root, or

2. All Real Roots.

See also Abel's Irreducibility Theorem, Abel's Lemma, Schoenemann's Theorem

References

Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover p. 127, 1965.