\documentclass[12pt,reqno]{amsart} 

\usepackage{amsmath,amssymb,amsfonts,amsthm}
\usepackage{graphicx}
\usepackage{enumerate}
\usepackage[top=1in,bottom=1in,left=1in,right=1in]{geometry}
\usepackage{circuitikz}

\renewcommand{\baselinestretch}{1.25}

\newtheorem{thm}{Theorem}
\newtheorem{ex}{Exercise}

\begin{document}

\begin{flushright}
Your Name Here\\
Math 220\\
HW \# 4\\
\today
\end{flushright}

%Please write your solutions in the designated solution area!

\begin{ex}
Prove that if $x$ is an odd integer, then $9x+5$ is even.
\end{ex}

\begin{proof}

\end{proof}

\begin{ex}
Prove that if $a$ and $c$ are odd integers, then $ab+bc$ is even for every integer $b$.
\end{ex}

\begin{proof}

\end{proof}

\begin{ex}
Prove that if $n\in\mathbb{Z}$, then $n^2-3n+9$ is odd.
\end{ex}

\begin{proof}

\end{proof}

\begin{ex}
Let $x\in\mathbb{Z}$. Prove that if $7x+5$ is odd, then $x$ is even.
\end{ex}

\begin{proof}

\end{proof}

\begin{ex}
Let $n\in\mathbb{Z}$. Prove that $(n+1)^2-1$ is even if and only if $n$ is even.
\end{ex}

\begin{proof}

\end{proof}

\begin{ex}
Disprove the statement: If $n\in\{1,2,3,4,5\}$, then $2n^2+1$ is divisible by $3$.
\end{ex}

\begin{proof}

\end{proof}

\begin{ex}
Prove that $200$ cannot be written as the sum of an odd integer and two even integers.
\end{ex}

\begin{proof}

\end{proof}

\begin{ex}
Prove that if $n$ is an odd integer, then $7n-5$ is even by (a) a direct proof, (b) a proof by contrapositive, and (c) a proof by contradiction.
\end{ex}

\begin{proof}

\end{proof}

\begin{ex}
Prove for every integer $n\geq8$ that there exist nonnegative integers $a$ and $b$ such that $n=3a+5b$.
\end{ex}

\begin{proof}

\end{proof}

\begin{ex}
Disprove the statement: There is an integer $n$ such that $n^4+n^3+n^2+n$ is odd.
\end{ex}

\begin{proof}

\end{proof}

\end{document}