Burton- Number theory p.163
Let $n\in\mathbb{Z}^+$.
Let $r$ be a primitive root mod $n$, so that $<r>=\mathbb{Z}_n^*$
Let $a\in \mathbb{Z}_n^*$
Let $k$ be the smallest positive integer such that $a=r^k$
Then, $k$ is called the index of $a$ relative to $r$ and denoted by $ind_r(a)$.
Well.. this definition can be extended to any cyclic group and since the term "index" is really ambiguous, if this tool is useful, I am sure that there is another terminology for "index" here.
Is there another name for "index" here?
This is not on wikipedia so I think this term is not standard..
Usually it's referred to as the discrete logarithm of $a$ with respect to $r$, denoted by $$k = \log_r a \pmod{\varphi(n)}$$ Where $\varphi(n)$ is the euler totient function wich counts the elements of $\mathbb Z_n^\ast$.