Is it possible for $\langle a \rangle =\mathbb Z/n\mathbb Z^*$ for $a\in \mathbb Z/n\mathbb Z^*$?
I think I recall hearing it is, what is the name this element takes? I remember hearing generator but i'm not sure.
2026-05-06 10:57:09.1778065029
Generator of all congruence classes
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Such an $a$ is a generator of the multiplicative group modulo $n$, and is called a primitive root modulo $n$. They don't exist for all $n$, but they do always exist when $n$ is a prime number.