\begin{definition}[Definition:Prime Decomposition/Multiplicity]
Let $n > 1 \in \Z$.
Let:
:$n = p_1^{k_1} p_2^{k_2} \cdots p_r^{k_r}$
be the prime decomposition of $n$, where:
:$p_1 < p_2 < \cdots < p_r$ are distinct primes
:$k_1, k_2, \ldots, k_r$ are (strictly) positive integers.
For each $p_j \in \set {p_1, p_2, \ldots, p_r}$, its power $k_j$ is known as the '''multiplicity of $p_j$'''.
\end{definition}