Give a conjecture describing the values of $n$ for which all of the nonzero elements of $Z_n = {0, 1, 2, . . . , n − 1}$ have multiplicative inverses.
I am guessing the point of not having $0$ included is so nonprime numbers of $n$ will now have inverses, but I want to make sure this is the case.
It is not necessarily the case that all nonprime numbers less than $n$ have inverses.
Hint: $r\in\{0,1,2,\dotsc, n-1\}$ has a multiplicative inverse if there is some $s$ such that $rs-1$ is divisible by $n$, i.e., such that $rs-1 = kn$, or $rs-kn = 1$. What does that tell you about $r$ and $n$?
