\documentclass[12pt, letterpaper]{amsart}

\usepackage{amsmath, amssymb, amsthm}
\usepackage[margin=.5in]{geometry}
\usepackage[pdflang={en-US}]{hyperref}

\theoremstyle{definition}
\newtheorem{dfn}{Definition}
\newtheorem{problem}{}
\newtheorem*{instructions}{Instructions}

\title{Portfolio proofs C}
\date{\today}

\begin{document} \ 

\vspace{-.25in}

\maketitle

\vspace{-.2in} 

\begin{instructions}
Choose one of the following statements and determine if it is true or false.
Use \LaTeX\ to write your proof (or disproof) nicely.
Drop your proof (both pdf and tex) in your OneDrive folder by the end of the day Wednesday, November 3.
\end{instructions}

\begin{problem}
There are integers $m$ and $n$ such that $m^2 + mn + n^2$ is a perfect square.
\end{problem}


% \begin{problem}
% There is an integer $n$ such that $ 4 \mid (n^2 -3)$.
% \end{problem}


\begin{problem}
If $n \in \mathbb{N}$, then $11 \nmid (2^n -1)$.
\end{problem}


\begin{problem}
Suppose $A$, $B$, and $C$ are sets. If $A \times C \subseteq  B \times C$, then $A \subseteq B$.
\end{problem}


\begin{problem}
For any sets  $A$, $B$, and $C$, $(A \cap B) \times C = (A \times C) \cap (B \times C)$.
\end{problem}
\end{document}