## Abstract

Let *D* ∈ *ℤ* and let *C _{D}* be the set of all monic cubic polynomials with integer coefficients having a discriminant equal to

*D*. In this paper, we devise a general method of establishing whether, for a prime

*p*, all polynomials in

*C*have the same type of factorization over the Galois field ${\mathbb{F}}_{p}$.

_{D}
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