How to insert rational cubic residue symbol in LaTeX

Question

I would like this symbol, except with a dotted horizontal line. Thank you. :)

Answer 1

Using elements from Frac or inference rule with dotted line you can define \rcr{<num>}{<denom>}:

\documentclass{article}

\usepackage{amsmath}

\newcommand{\dashdfrac}[2]{%
  {\sbox0{$\genfrac{}{}{0pt}{0}{#1}{#2}$}%
   \vphantom{\copy0}%
   \ooalign{%
     \hidewidth
     $\vcenter{\moveright\nulldelimiterspace
       \hbox to\wd0{%
         \xleaders\hbox{\kern.5pt\vrule height 0.4pt width 1.5pt\kern.5pt}\hfill
         \kern-1.5pt
       }%
     }$
     \hidewidth\cr
   \box0\cr}}%
}

\newcommand{\rcr}[2]{\biggl[\dashdfrac{#1}{#2}\biggr]_3}

\begin{document}

For relatively prime integers~$m$ and~$n$ define the \textbf{rational cubic residue symbol} as
\[
  \rcr{m}{n} = \begin{cases}
    1  & \text{$m$ is a cubic residue mod~$n$} \\
    -1 & \text{$m$ is a cubic non-residue mod~$n$}
  \end{cases}
\]

\end{document}

It would be possible to modify \rcr to set according to the math style, if needed.

You can also try with

\newcommand{\rcr}[2]{\Bigl[\dashdfrac{#1}{#2}\Bigr]_3}