Exponential complete residue system
Paolo Leonetti · arXiv (Cornell University) · 2013
This article deals with a question about the existence (and non uniqueness) of a complete residue system in the quotient ring $\mathbb{Z}/n\mathbb{Z}$, where $n$ is a fixed integer greater than 1. In particular it is asked when there exists a permutation $\sigma$ of the complete residue system $\{1,2,\ldots,n\}$ such that $\{1^{\sigma(1)},2^{\sigma(2)},\ldots,n^{\sigma(n)}\}$ is a complete residue system too. The characterization of the set of such integers will be given for almost all $n$.