  Kronecker observed that either all roots or only one root of a solvable
irreducible equation of odd prime degree with integer coefficients are real.
This gives a possibility to construct specific examples of equations not
solvable by radicals. A relatively elementary proof without using the full
power of Galois theory is due to Weber. We give a rather short proof of
Kronecker's theorem with a slightly different argument from Weber's. Several
modern presentations of Weber's proof contain inaccuracies, which can be traced
back to an error in the original proof. We discuss this error and how it can be
corrected.
