index of an integer with respect to a primitive root

Definition.

Let $m\mathrm{>}\mathrm{1}$ be an integer such that the integer $g$ is a primitive root for $m$. Suppose $a$ is another integer relatively prime to $g$. The index of $a$ (to base $g$) is the smallest positive integer $n$ such that $g^n\mathrm{\equiv }a\mathrm{mod}m$, and it is denoted by $\mathrm{ind}\mathit{}a$ or ${\mathrm{ind}}_g\mathit{}a$.

If $m$ has a primitive root the index with respect to a primitive root is a very useful tool to solve polynomial congruences modulo $m$.