Prime ideal factorization and p-integral basis of quintic number fields defined by x^5+ax+b

Abstract

Based on Newton polygon techniques, for every prime integer p, a p-integral basis of ℤ_K, and the factorization of the principal ideal pℤ_K into prime ideals of ℤ_K are given, where K is a quintic number field defined by an irreducible trinomial X⁵ + aX + b ∈ ℤ[X].