%%
%% The LaTeX Companion, 3ed
%%
%% Example 11-4-19 on page II-171 in "Modular relations".
%%
%% Copyright (C) 2022 Frank Mittelbach
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%%
%% See https://www.latex-project.org/lppl.txt for details.
%%

\documentclass{tlc3examargin}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{183.0pt}

  % Shorten the vertical size of the example ...
  \AtBeginDocument{%
    \setlength\abovedisplayskip{.8\abovedisplayskip}%
    \setlength\belowdisplayskip{.8\belowdisplayskip}%
  }

%StartShownPreambleCommands
\usepackage{amsmath}
%StopShownPreambleCommands

\begin{document}
\begin{align*}
   u & \equiv v + 1 \mod{n^2}      \\
   u & \equiv v + 1 \bmod{n^2}     \\
   u &   =    v + 1 \pmod{n^2}     \\
   u &   =    v + 1 \pod{n^2}  \end{align*}
The in-text layout: $ u = v + 1 \pmod{n^2} $
\begin{align*}
   k^2 &= (m \bmod n)    \, ;  &
     x &\equiv y \pmod b \, ;     \\
     x &\equiv y \mod c  \, ;  &
     x &\equiv y \pod d  \, .  \end{align*}
\end{document}