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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 6.1  \\ Spring 2020 \hfill Due March 4}}}

\large

\vspace{1cm}


\begin{exercise}
Let $m, n \in \N$.  Prove that if $n \ge 2$, then $n$ cannot divide both $m$ and $m+1$.
\end{exercise}

\begin{exercise}  Let $a, b, c \in \Z$.

\begin{itemize}

\item[\bf a.]  Prove that if $a+b+c$ is even, then $a$ is even, $b$ is even or $c$ is even.

\item[\bf b.]   Prove that if $ab$ is even, then $a$ is even or $b$ is even.

\end{itemize}

\end{exercise}

\begin{exercise}
Let $a, b, c \in \Z$ be odd.  Prove that the equation $ax^2 + bx + c = 0$ does not have a rational solution.
\end{exercise}


\end{document}
