summaryrefslogtreecommitdiff
path: root/info/maketexwork/ex-04-06
blob: cc95fc65a9a00c6b6aea182b413372e638addada (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
\input texinfo  @c -*- TeXinfo -*-
@setfilename perf-inf.inf
@ifinfo
  @paragraphindent 0
@end ifinfo
@iftex
  @defaultparindent=0pt @parindent=0pt
@end iftex

@node    Top, , (dir), (dir)
@chapter Unsolved Problems
@section Odd Perfect Numbers

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