\documentclass{article}
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\begin{document}

\begin{center}
\includegraphics[width=0.5in]{../ltr-logo.jpg}
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\noindent{\Large{\textsc{Intro to Abstract Mathematics\hfill Assignment 7.3  \\ Spring 2020 \hfill Due March 18}}}

\large

\vspace{1cm}


\begin{exercise}
Let $a, b, c \in \Z$.  Prove that if $ab | ac$ and $a \ne 0$, then $b | c$.
\end{exercise}

\begin{exercise}
Let $n \in \Z^+$.  Prove that $X^n - 1 = (X-1)(X^{n-1} + X^{n-2} + \cdots + X + 1)$.
\end{exercise}

\begin{exercise}
Let $a, n \in \Z^+$.  Prove that if $n \ge 2$ and $a \ge 3$, then $a^n-1$ is composite.
\end{exercise}

\begin{exercise}
Let $n \in \Z^+$.  Prove that if $n$ is composite, then so is $2^n - 1$.
\end{exercise}


\end{document}
