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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 16:24:08 |
| Classification: |
msc:11A51 |
| Synonyms: |
proper divisor=aliquot part |
Revision comment (for changes between this and next version):
| Clearer about positive divisors (I hope); restricted divisor; examples |
Preamble:
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\usepackage{amssymb}
\usepackage{amsmath}
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%\usepackage{psfrag}
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Content:
If a divisor $d$ of $n$ (that is, $d|n$) satisfies $0 < d < n$, 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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