Let X3+AX+B be an irreducible abelian cubic polynomial in Z[X]. We determine explicitly integers a1,…,at, F such that, except for finitely many primes p, x3+Ax+B≡0(modp) has three solutions⇔p≡a1,…,at(modF).

Additional Metadata
Persistent URL dx.doi.org/10.3836/tjm/1270127967
Journal Tokyo Journal of Mathematics
Huard, J.G. (James G.), Spearman, B.K. (Blair K.), & Williams, K.S. (1994). The primes for which an abelian cubic polynomial splits. Tokyo Journal of Mathematics, 17(2), 467–478. doi:10.3836/tjm/1270127967