One of the classical problems in algebraic number theory, going back among others to
Dedekind [De78], Hensel [He08], and Hasse [Ha63], is to decide if an algebraic number field …

Discriminant equations are an important class of Diophantine equations with close ties to
algebraic number theory, Diophantine approximation and Diophantine geometry. This book …

Let K= Q (θ) be the octic number field generated by a complex root θ of a monic irreducible
trinomial F (x)= x 8+ ax+ b∈ Z [x]. In this paper, we study the monogenity of K. More …

Abstract top The problem of determining power integral bases in algebraic number fields is
equivalent to solving the corresponding index form equations. As is known (cf. Győry [25]) …

Let $ K=\mathbb {Q}(\theta) $ be a number field generated by a complex root $\theta $ of a
monic irreducible trinomial $ F (x)= x^ n+ ax+ b\in\mathbb {Z}[x] $. There is an extensive …

Monogenity is a classical area of algebraic number theory that continues to be actively
researched. This paper collects the results obtained over the past few years in this area …

Let K be an octic number field generated by a complex root θ of a monic irreducible trinomial
F (x)= x 8+ ax+ b∈ Z [x], where a and b are two non-zero rational integers. Let i (K) be the …

LetQ1, Q2∈ Z [X, Y, Z] be two ternary quadratic forms andu1, u2∈ Z. In this paper we
consider the problem of solving the system of equations [formula] According to Mordell [12] …

Let K= ℚ (𝜃) be a number field generated by a complex root 𝜃 of a monic irreducible
trinomial F (x)= xn+ axm+ b∈ ℤ [x]. In this paper, we deal with the problem of the …

Monogenity of pure fields is recently intensively investigated. There are several papers on
conditions for the monogenity and non-monogenity of pure fields of various degrees …