A simple proof of a theorem of Hajdu–Jarden–Narkiewicz
Volume 147 / 2017
Colloquium Mathematicum 147 (2017), 217-220
MSC: Primary 11R27; Secondary 11N56.
DOI: 10.4064/cm7054-9-2016
Published online: 9 January 2017
Abstract
Let $K$ be an algebraic number field, and let $G$ be a finitely generated subgroup of $K^{\times }$. We give a short proof that for every positive integer $n$, there is an element of $\mathcal {O}_K$ not expressible as a sum of $n$ elements of $G$.
