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\begin{document} %(
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\title{Problem Set 04}
% YOUR NAME GOES HERE under Author
\author{Your Name}
\maketitle

\begin{enumerate} %(

\item $N$-year cicadas breed once every $N$ years.  How often will the
breeding year for 17-year cicadas coincide with that of 13-year
cicadas?
% Answer below this line

\item What is $14600926_{10}$ in hexadecimal (base 16)?
% Answer below this line

\item 
\begin{enumerate} %( 
\item What is the the prime factorization of $18!$?  (Note, that's 18
factorial, not just 18.)
% Answer below this line

\item  What is the smallest positive integer that's evenly divisible
by all integers from 2 to 18?
% Answer below this line
\end{enumerate} %)

\item
\begin{enumerate} %( 
\item Write a {\em closed form} formula (i.e.\ one with no
``$\cdots$'' or ``$\sum$'') for $7 + 14 + 21 + 28 + 35 + \cdots + 7
n$. 
% Answer below this line

\item Prove that your answer is valid.
% Answer below this line

\end{enumerate} %)

\item 
\begin{enumerate} %( 
\item Prove or disprove that $4^k - 1$ is evenly divisible by 3 (for
all $k$ where $k$ is a positive integer).
% Answer below this line

\item BONUS: Prove or disprove that $N^k - 1$ is evenly divisible by
$N-1$ (for all $k$ and $N-1$ where $k$ and $N-1$ are positive
integers).
% Answer below this line

\end{enumerate} %)





\end{enumerate} %)
\end{document} %)