\documentclass{article}
\usepackage{amsmath, amssymb,verbatim, amsthm, graphicx}

%exercise environment
\newcounter{exercise}
\setcounter{exercise}{0}
\newenvironment{exercise}{\addtocounter{exercise}{1} \noindent{\bf{Exercise \theexercise.}}}{\vspace{.5cm}}

\newcommand{\R}{\mathbb{R}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\C}{\mathbb{C}}

\textwidth 6.5in
\textheight 9in
\oddsidemargin 0in
\evensidemargin 0in
\headsep -0.5in

\setlength{\parskip}{0.25cm}

\pagenumbering{gobble}

\begin{document}

\begin{center}
\includegraphics[width=0.5in]{../ltr-logo.jpg}
\end{center}

\noindent{\Large{\textsc{Modern Algebra \hfill Assignment 2.1  \\ Spring 2023 \hfill Due January 25}}}

\large

\vspace{1cm}

\begin{exercise}
Construct Cayley tables for the groups $\Z_7^{\times}$, $\Z_{15}^{\times}$ and $\Z_{16}^{\times}$.
\end{exercise}

\begin{exercise}
Prove that if $G$ is a group in which every element is its own inverse, then $G$ is abelian.  
\end{exercise}

\begin{exercise}
Lang, exercise II.1.3.
\end{exercise}

\end{document}
