\documentclass[11pt]{amsart}

\usepackage{fullpage}

\newcommand{\makeheading}[2]%
        {\hspace*{-\marginparsep minus \marginparwidth}%
         \begin{minipage}[t]{\textwidth}%
                {\large \bfseries #1\hfill#2}\\[-0.15\baselineskip]%
                 \rule{\columnwidth}{1pt}%
         \end{minipage}\bigskip
}

\theoremstyle{definition}
\newtheorem{prob}{Problem}
 
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\begin{document}
\makeheading{Math 6211 Autumn 2020, Homework 1}{Names}
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\begin{prob}
Here is the problem.
\end{prob}
\begin{proof}
Here is my solution.
\end{proof}

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\end{document}