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 …

We obtain good estimates on the ranks of universal quadratic forms over Shanks' family of
the simplest cubic fields and several other families of totally real number fields. As the main …

1. Introduction. While the contributions of Wilhelm Ljunggren to the study of Diophantine
equations are significant, perhaps what is as interesting are the problems that remain open …

A family of quartic Thue inequalities 1 Introduction Page 1 A family of quartic Thue inequalities
Andrej Dujella and Borka Jadrijevic Abstract In this paper we prove that the only primitive …

If F (x, y) ϵ ℤ [x, y] is an irreducible binary form of degree k≥ 3, then a theorem of Darmon
and Granville implies that the generalized superelliptic equation F (x, y)= zl has, given an …

Let m⩾− 1 be an integer. We give a correspondence between integer solutions to the
parametric family of cubic Thue equations where λ> 0 is a divisor of m2+ 3m+ 9 and …

In this paper we completely solve a simple quartic family of Thue equations over C (T).
Specifically, we apply the ABC-Theorem to find all solutions (x, y)∈ C [T]× C [T] to the set of …

Acta Mathematica et Informatica Universitatis Ostraviensis Page 1 Acta Mathematica et
Informatica Universitatis Ostraviensis Clemens Heuberger; Attila Pethő; Robert Franz Tichy …

A standard formula (1.1) leads to a proof of HT90, but requires proving the existence of θ
such that α= 0, so that β= α/σ (α). We instead impose the condition (M), that taking θ= 1 …

On a Family of Quartic Thue Inequalities I Page 1 Journal of Number Theory NT2161 journal of
number theory 66, 70 84 (1997) On a Family of Quartic Thue Inequalities I Isao Wakabayashi …