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\Chapter Unsolved Problems
\Section Odd Perfect Numbers
A number is said to be {\it 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 {\it odd\/} perfect numbers is
an open question.
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