Let D ∈ ℤ and let CD be the set of all monic cubic polynomials x3 + ax2 + bx + c ∈ ℤ[x] with the discriminant equal to D. Along the line of our preceding papers, the following Theorem has been proved: If D is square-free and 3 ∤ h(−3D) where h(−3D) is the class number of
then all polynomials in CD have the same type of factorization over the Galois field 𝔽p where p is a prime, p > 3. In this paper, we prove the validity of the above implication also for primes 2 and 3.
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process.