On the sumsets of exceptional units in ${\mathbb{Z}}_n$

Quan-Hui Yang, Qing-Qing Zhao

Let $R$ be a commutative ring with $1\in R$ and $R^{\ast }$ be the multiplicative group of its units. In 1969, Nagell introduced the exceptional unit $u$ if both $u$ and $1-u$ belon…