| Version 9 |
Version 8 |
| Each natural number $n \geq 1$ can be decomposed uniquely, up to the order of the factors, as a product of positive prime numbers. This allows us to write $n$ in the unique representation |
Each natural number $n \geq 1$ can be decomposed uniquely, up to the order of the factors, as a product of positive prime numbers. This allows us to write $n$ in the unique representation |
| $$ |
$$ |
| n = {p_1}^{a_1} {p_2}^{a_2} {p_3}^{a_3} \cdots {p_k}^{a_k} |
n = {p_1}^{a_1} {p_2}^{a_2} {p_3}^{a_3} \cdots {p_k}^{a_k} |
| $$ |
$$ |
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for some nonnegative integer $k$ with $a_l$ positive integers, $p_i$ positive primes and $p_i \neq p_j$ for $i \neq j$. For some results it is also useful to assume that $p_i < p_j$ for $i < j$. The $p_i$ are called the prime factors of $n$.
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for some nonnegative integer $k$ with $a_l$ positive integers, $p_i$ positive primes and $p_i \neq p_j$ for $i \neq j$. For some results it is also useful to assume that $p_i < p_j$ for $i < j$.$.
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