# index of an integer with respect to a primitive root

###### Definition.

Let $m>1$ 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 $g^{n}\equiv a\mod m$, and it is denoted by $\operatorname{ind}a$ or $\operatorname{ind}_{g}a$.

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

Title index of an integer with respect to a primitive root IndexOfAnIntegerWithRespectToAPrimitiveRoot 2013-03-22 16:20:50 2013-03-22 16:20:50 alozano (2414) alozano (2414) 4 alozano (2414) Definition msc 11-00