| Version 14 |
Version 13 |
| Each positive integer $n$ has a unique \PMlinkescapetext{decomposition} as a product |
Each positive integer $n$ has a unique \PMlinkescapetext{decomposition} as a product |
| \[ |
\[ |
| n = \prod_{i=0}^{\ell} {p_i}^{a_i} |
n = \prod_{i=0}^{\ell} {p_i}^{a_i} |
| \] |
\] |
| of positive powers of its distinct positive {\it prime divisors} $p_i$. The {\it prime divisor} of $n$ means a (rational) prime number \PMlinkname{dividing}{Divisibility} $n$. A synonymous name is {\it prime factor}. |
of positive powers of its distinct positive {\it prime divisors} $p_i$. The {\it prime divisor} of $n$ means a (rational) prime number \PMlinkname{dividing}{Divisibility} $n$. A synonymous name is {\it prime factor}. |
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| The \PMlinkescapetext{decomposition is unique up to the order} of the prime divisors and for\, $n=1$\, is an empty product. |
The \PMlinkescapetext{decomposition is unique up to the order} of the prime divisors and for\, $n=1$\, is an empty product. |
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| For some results it is useful to assume that |
For some results it is useful to assume that |
| $p_i < p_j$ whenever $i < j$. |
$p_i < p_j$ whenever $i < j$. |
