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A simple proof of a theorem of Hajdu–Jarden–Narkiewicz

Volume 147 / 2017

Paul Pollack 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 $G$.

Authors

  • Paul PollackDepartment of Mathematics University of Georgia
    Boyd Graduate Studies Research Center
    Athens, GA 30602, U.S.A.
    e-mail

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