I think that is a very simple/silly question but i can't find the meaning of the asterisk in $\mathbb{Z}_n^*$.
I'm trying to understand some basic concepts in number theory, while studying cryptography (for example yesterday i came across these lectures) and I've been seeing this symbolism.
I know that $\mathbb{Z}_n = {0, 1, …, n-1}$, but what the extra $'*'$ stands for?
Until today, i knew that the asterisk above a set of numbers "means" the same set with $'0'$ excluded, but i don't think it's the same in this case.
Also i found that it may mean the non-negative integers of the set, but (at least in my lectures), the $\mathbb{Z}_n$ already doesn't have negative integers.
In every cryptography – number theory lectures/course i've came across they just write it down without exlain it, but it really confuses me.
Any help?
Best Answer
It stands for the set of elements of $\mathbb{Z}_n$ which are invertible modulo $n$. In particular, if $n$ is prime, then (and only then) $\mathbb{Z}_n^*=\mathbb{Z}_n\setminus\{0\}$.