Cheng, Zhi; Sun, Cuifang On partitioning \(\mathbb Z_m\) into pairs of prescribed differences. (English) Zbl 1399.05010 Adv. Math., Beijing 46, No. 6, 952-956 (2017). Summary: Let \(m=2n\) be a positive integer and \(\mathbb Z_m\) be the ring of residue classes modulo \(m\). Suppose that \(d_1\), \(d_2,\dots, d_n\) are any odd elements (not necessarily distinct) of \(\mathbb Z_m\). In this paper, we give the sufficient and necessary condition of partitioning \(\mathbb Z_m\) into \(n\) pairs with differences \(d_1\), \(d_2,\dots,d_n\). The conjecture on the seating couples problem can be seen as a corollary of our result. Based on this work, we obtain two corollaries and we also confirm a conjecture which is the special case of our first corollary. MSC: 05A18 Partitions of sets 05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) 11B13 Additive bases, including sumsets Keywords:partition; prescribed difference; ring of residue classes PDFBibTeX XMLCite \textit{Z. Cheng} and \textit{C. Sun}, Adv. Math., Beijing 46, No. 6, 952--956 (2017; Zbl 1399.05010) Full Text: DOI