11-00-IndexOfAnIntegerWithRespectToAPrimitiveRoot.tex

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\pmtitle{index of an integer with respect to a primitive root}
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\begin{document}
\begin{defn}
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 $\operatorname{ind}_g a$.
\end{defn}

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