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- Title
ON A PROBLEM OF CHEN AND LEV.
- Authors
CHEN, SHI-QIANG; TANG, MIN; YANG, QUAN-HUI
- Abstract
For a given set $S\subset \mathbb{N}$ , $R_{S}(n)$ is the number of solutions of the equation $n=s+s^{\prime },s. Suppose that $m$ and $r$ are integers with $m>r\geq 0$ and that $A$ and $B$ are sets with $A\cup B=\mathbb{N}$ and $A\cap B=\{r+mk:k\in \mathbb{N}\}$. We prove that if $R_{A}(n)=R_{B}(n)$ for all positive integers $n$ , then there exists an integer $l\geq 1$ such that $r=2^{2l}-1$ and $m=2^{2l+1}-1$. This solves a problem of Chen and Lev ['Integer sets with identical representation functions', Integers 16 (2016), A36] under the condition $m>r$.
- Subjects
PARTITION functions; CHARACTERISTIC functions; INTEGERS; SUBSET selection; MATHEMATICS theorems
- Publication
Bulletin of the Australian Mathematical Society, 2019, Vol 99, Issue 1, p15
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972718001107