On a problem of partitions of $\mathbb{Z}_{m}$ with the same representation functions

30 Jun 2020 Sun Cui-Fang Xiong Meng-Chi

For any positive integer $m$, let $\mathbb{Z}_{m}$ be the set of residue classes modulo $m$. For $A\subseteq \mathbb{Z}_{m}$ and $\overline{n}\in \mathbb{Z}_{m}$, let representation function $R_{A}(\overline{n})$ denote the number of solutions of the equation $\overline{n}=\overline{a}+\overline{a'}$ with ordered pairs $(\overline{a}, \overline{a'})\in A \times A$... (read more)

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