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\begin{document}

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\noindent{\Large{\textsc{Number Theory\hfill Assignment 3.2  \\ Fall 2020 \hfill Due September 16}}}

\large

\vspace{1cm}


\begin{exercise}
Textbook exercise 3.1.6(b).
\end{exercise}

\begin{exercise}
Textbook exercise 3.1.16.
\end{exercise}

\begin{exercise}
Textbook exercise 3.1.17.
\end{exercise}

\begin{exercise}
We have shown that every prime number $p$ has the property that if $p|ab$ for some $a, b \in \Z$, then $p|a$ or $p|b$.  Prove that the converse is also true.  That is, show that if a natural number $p \ge 2$ has the property that $p|ab$ implies $p|a$ or $p|b$, for any $a, b \in \Z$, then $p$ is prime.
\end{exercise}

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