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\chapter{Unsolved Problems}
\section{Odd Perfect Numbers}
A number is said to be {\em perfect\/} if it
is the sum of its divisors. For example, $6$ is
perfect because \(1+2+3 = 6\), and $1$, $2$, and $3$
are the only numbers that divide evenly into $6$
(apart from 6 itself).
It has been shown that all even perfect numbers
have the form \[2^{p-1}(2^{p}-1)\] where $p$
and \(2^{p}-1\) are both prime.
The existence of {\em odd\/} perfect numbers is
an open question.
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