Definition:Prime Decomposition/Multiplicity

Definition
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 $p_j$.

Also see

 * Definition:P-adic Valuation