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 $m$.

Title	index of an integer with respect to a primitive root
Canonical name	IndexOfAnIntegerWithRespectToAPrimitiveRoot
Date of creation	2013-03-22 16:20:50
Last modified on	2013-03-22 16:20:50
Owner	alozano (2414)
Last modified by	alozano (2414)
Numerical id	4
Author	alozano (2414)
Entry type	Definition
Classification	msc 11-00