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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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