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'proper divisor'
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| Title of object: |
proper divisor |
| Canonical Name: |
ProperDivisor |
| Type: |
Definition |
| Created on: |
2006-04-23 15:44:07 |
| Modified on: |
2006-04-23 15:58:48 |
| Classification: |
msc:11A51 |
| Synonyms: |
proper divisor=aliquot part |
Revision comment (for changes between this and next version):
| Changes for correction #7856 ('positive divisor'). |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
If a divisor $d$ of $n$ (that is, $d|n$) satisfies $d < n$, then $d$ is a {\em proper divisor} of $n$.
By restricting the sum of divisors to proper divisors, some $n$ will be less than this sum (deficient numbers, including prime numbers), some will be equal (perfect numbers) and some will be greater (abundant numbers). |
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