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ON MINIMAL ASYMPTOTIC $g$-ADIC BASES
Published online by Cambridge University Press: 05 August 2015
Abstract
Let $g\geq 2$ be a fixed integer. Let $\mathbb{N}$ denote the set of all nonnegative integers and let $A$ be a subset of $\mathbb{N}$. Write $r_{2}(A,n)=\sharp \{(a_{1},a_{2})\in A^{2}:a_{1}+a_{2}=n\}.$ We construct a thin, strongly minimal, asymptotic $g$-adic basis $A$ of order two such that the set of $n$ with $r_{2}(A,n)=2$ has density one.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 374 - 379
- Copyright
- © 2015 Australian Mathematical Publishing Association Inc.
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