Diophantine number theory is an active area that has seen tremendous growth over the past
century, and in this theory unit equations play a central role. This comprehensive treatment …

The aim of this book is to give a survey of results in the theory of algebraic numbers
achieved in the first half of the twentieth century and may be viewed as a companion to my …

For a cyclic group G generated by some a∈ G, ie G=〈 a〉, the atom of a is defined as the set
of all elements generating G. Given any two elements a, b of a finite cyclic group G, we study …

For a cyclic group G and a∈ G, we define〈 a〉 as the subgroup generated by a and the
atom of a as the set of all elements generating〈 a〉. In this paper, given t (t≥ 2) atoms, we …

We give an overview on recent results concerning additive unit representations. Furthermore
the solutions of some open questions are included. The central problem is whether and how …

At a conference in Debrecen in October 2010 Nathanson announced some results
concerning the arithmetic diameters of certain sets. He proposed some related results on the …

1. Introduction. Let K be an algebraic number field of degree k, and let ai,..., an be linearly
independent elements of K over Q. Denote by D e Z the common denominator of ai,..., an …

Let P be a finite set of at least two prime numbers and A the set of positive integers that are
products of powers of primes from P. Let F (k) denote the smallest positive integer which …

We give an affirmative answer to the following question by Jarden and Narkiewicz: Is it true
that every number field has a finite extension L such that the ring of integers of L is …

We extend a result of Hajdu and Tijdeman concerning the smallest number which cannot be
obtained as a sum of less than k power products of fixed primes. For this, we also generalize …