Functiones et Approximatio Commentarii Mathematici

On Sidon sets which are asymptotic bases of order $4$

Sándor Z. Kiss, Eszter Rozgonyi, and Csaba Sándor

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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.

Article information

Source
Funct. Approx. Comment. Math., Volume 51, Number 2 (2014), 393-413.

Dates
First available in Project Euclid: 26 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.facm/1417010861

Digital Object Identifier
doi:10.7169/facm/2014.51.2.10

Mathematical Reviews number (MathSciNet)
MR3282635

Zentralblatt MATH identifier
1353.11016

Subjects
Primary: 11B13: Additive bases, including sumsets [See also 05B10]
Secondary: 11B75: Other combinatorial number theory

Keywords
additive number theory representation functions Sidon set asymptotic basis

Citation

Kiss, Sándor Z.; Rozgonyi, Eszter; Sándor, Csaba. On Sidon sets which are asymptotic bases of order $4$. Funct. Approx. Comment. Math. 51 (2014), no. 2, 393--413. doi:10.7169/facm/2014.51.2.10. https://projecteuclid.org/euclid.facm/1417010861


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