\documentclass{article}

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\begin{document} \pagestyle{empty} \begin{flushleft}

\scs{Name(s):} 

\scs{Math 301 \hfill Proof and disproof \hfill March 18, 2015}

\vspace{.1in}

Determine if each statement is true or false.
If it is true, prove it.
If it is false, give a disproof.

\prob{
There is an integer $n$ such that $n^2 \equiv -1 \m[13]$.
}

\prob{
For all $a,b,c \in \ZZ$, if $a|bc$, then $a|b$ or $a|c$.
}

\prob{
There are integers $a$ and $b$ such that $12 a + 15 b = 2$.
}

\prob{
There are integers $a$ and $b$ such that $11 a + 15 b = 1$.
}

\prob{
If $X \subseteq A \cup B$, then $X \subseteq A$ or $X \subseteq B$.
}

\chal{
There is an integer $n$ such that $n^2 \equiv -1 \m[3]$.
}

\end{flushleft} 
\end{document}