A new result in combinatorial number theory
Fan Ge, Zhi‐Wei Sun · arXiv (Cornell University) · 2016
Let $G$ be a finite abelian group with exponent $n>1$. For $a_1,\ldots,a_{n-1}\in G$, we determine completely when there is a permutation $\sigma$ on $\{1,\ldots,n-1\}$ such that $sa_{\sigma(s)} ot=0$ for all $s=1,\ldots,n-1$. When $G$ is the cyclic group $\mathbb Z/n\mathbb Z$, this confirms a conjecture of Z.-W. Sun.