# Category:Definitions/Prime Decompositions

This category contains definitions related to Prime Decompositions.
Related results can be found in Category:Prime Decompositions.

Let $n > 1 \in \Z$.

From the Fundamental Theorem of Arithmetic, $n$ has a unique factorization of the form:

 $\displaystyle n$ $=$ $\displaystyle \prod_{p_i \mathop \divides n} {p_i}^{k_i}$ $\quad$ $\quad$ $\displaystyle$ $=$ $\displaystyle {p_1}^{k_1} {p_2}^{k_2} \cdots {p_r}^{k_r}$ $\quad$ $\quad$

where:

$p_1 < p_2 < \cdots < p_r$ are distinct primes
$k_1, k_2, \ldots, k_r$ are (strictly) positive integers.

This unique expression is known as the prime decomposition of $n$.

## Pages in category "Definitions/Prime Decompositions"

The following 3 pages are in this category, out of 3 total.