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- W4292500657 abstract "For any positive integer $m$, let $mathbb{Z}_{m}$ be the set of residue classes modulo $m$. For $Asubseteq mathbb{Z}_{m}$ and $overline{n}in mathbb{Z}_{m}$, let $R_{A}(overline{n})$ denote the number of solutions of $overline{n}=overline{a}+overline{a'}$ with unordered pairs $(overline{a}, overline{a'})in A times A$. In this paper, we prove that if $m=2^{alpha}$ with $alphaneq 2$, $Acup B=mathbb{Z}_{m}$ and $|Acap B|=2$, then $R_{A}(overline{n})=R_{A}(overline{n})$ for all $overline{n}in mathbb{Z}_{m}$ if and only if $B=A+overline{frac{m}{2}}$." @default.
- W4292500657 created "2022-08-21" @default.
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- W4292500657 date "2020-07-01" @default.
- W4292500657 modified "2023-09-29" @default.
- W4292500657 title "On partitions of $mathbb{Z}_{m}$ with the same representation function" @default.
- W4292500657 doi "https://doi.org/10.48550/arxiv.2007.00414" @default.
- W4292500657 hasPublicationYear "2020" @default.
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