A number is said to be @i{perfect} if it is
the sum of its divisors. For example, 6 is
perfect because
@tex $1+2+3 = 6$,
@end tex
@ifinfo
1+2+3 = 6,
@end ifinfo
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
@tex $$2^{p-1}(2^{p}-1)$$ where $p$ and $2^{p}-1$
@end tex
@ifinfo
@center 2^(p-1) (2^p - 1)
where p and 2^p - 1
@end ifinfo
are both prime.
The existence of @i{odd} perfect numbers is an
open question.
@bye
