Let $m > 0$ be a positive integer and let $C=\{a_1,\ldots,a_m\}$ a complete residue system modulo $m$. We call $R$ a reduced residue system modulo $m$, if $R$ is a subset $R\subseteq C$ consisting only of those integers, which are co-prime to $m.$
Note: With the Euler function $\phi$, it follows that $R$ has $\phi(m)$ elements.
Lemmas: 1
Proofs: 2 3 4 5 6
Propositions: 7 8 9 10
