On a problem of Chen and Fang related to infinite additive complements
Volume 200 / 2021
Acta Arithmetica 200 (2021), 213-220
MSC: Primary 11B13; Secondary 11B34.
DOI: 10.4064/aa201217-2-3
Published online: 7 September 2021
Abstract
Two infinite sets $A$ and $B$ of nonnegative integers are called additive complements if their sumset contains every nonnegative integer. In 1964, Danzer constructed infinite additive complements $A$ and $B$ with $A(x)B(x) = (1 + o(1))x$ as $x \rightarrow \infty $, where $A(x)$ and $B(x)$ denote the counting function of the sets $A$ and $B$, respectively. In this paper we solve a problem of Chen and Fang by extending the construction of Danzer.
