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\begin{document}

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\noindent{\Large{\textsc{Number Theory\hfill Assignment 2.1  \\ Fall 2020 \hfill Due September 9}}}

\large

\vspace{1cm}


\begin{exercise}
Let $a \in \Z$.  Show that for any $n \in \Z$, $(a,a+n)$ divides $n$.  Conclude that $(a,a+1)=1$.
\end{exercise}

\begin{exercise}
Use the Euclidean Algorithm to find integers $r$ and $s$ satisfying the following:
\begin{itemize}

\item[\bf a.]  $(24,138) = 24 r + 138 s$.

\item[\bf b.]  $(119, 272) = 119 r + 272 s$.

\item[\bf c.] $(1769,2378) = 1769 r + 2378 s$.

\end{itemize}
\end{exercise}

\begin{exercise}
Let $a, b, c \in \Z$.  Prove that if $(a,b) = 1$ and $c | (a+b)$, then $(a,c) = (b,c) = 1$.
\end{exercise}

\end{document}
