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11
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'fundamental theorem of arithmetic'
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| Title of object: |
fundamental theorem of arithmetic |
| Canonical Name: |
FundamentalTheoremOfArithmetic |
| Type: |
Theorem |
| Created on: |
2001-10-15 20:50:09 |
| Modified on: |
2005-09-24 00:59:43 |
| Classification: |
msc:11A05 |
| Keywords: |
number theory |
| Defines: |
prime divisor, prime factor |
Revision comment (for changes between this and next version):
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic} |
Content:
Each positive integer $n$ has a unique decomposition as a product
\[
n = \prod_{i=0}^{\ell} {p_i}^{a_i}
\]
of positive powers of its positive {\it prime divisors} $p_i$. The decomposition is unique up to the order of the divisors and for $n=1$ is an empty product.
For some results it is useful to assume that
$p_i < p_j$ whenever $i < j$. |
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