Abstract
Let $h \geq 2$ be an integer. We say that a set $\mathcal{A}$ of positive integers is an asymptotic basis of order $h$ if every large enough positive integer can be represented as the sum of $h$ terms from $\mathcal{A}$. A set of positive integers $\mathcal{A}$ is called a Sidon set if all the sums $a+b$ with $a,b \in \mathcal{A}$, $a \leq b$ are distinct. In this paper we prove the existence of Sidon set $\mathcal{A}$ which is an asymptotic basis of order $4$ by using probabilistic methods.
Citation
Sándor Z. Kiss. Eszter Rozgonyi. Csaba Sándor. "On Sidon sets which are asymptotic bases of order $4$." Funct. Approx. Comment. Math. 51 (2) 393 - 413, December 2014. https://doi.org/10.7169/facm/2014.51.2.10
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