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\headers{Math373}{Homework 10}{Due Fri, Apr. 4, 2014}

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\noindent
\textbf{Directions:} Solve the following problems.  All written work must be your own.  See the course syllabus for detailed rules.

\begin{enumerate}

\newcommand{\dr}[3]%
{%
	$x^{#1} \equiv #2 \pmod{#3}$%
}

\item {} [JJJ 3.1] Solve the following congruences.
\begin{enumerate}
\item \dr{19}{36}{97}.
\item \dr{137}{428}{541}.
\item \dr{73}{614}{1159}.
\item \dr{751}{677}{8023}.
\item \dr{38993}{328047}{401227}.  \emph{Hint:} $401227 = 607\cdot 661$.
\end{enumerate}

\item {} \textbf{[Challenge]} Solve the following congruence:  \dr{162881}{89}{794577}.
\end{enumerate}
\end{document}
