Definition:Prime Decomposition

Definition
Let $n > 1 \in \Z$.

From the Fundamental Theorem of Arithmetic, $n$ has a unique factorization of the form:
 * $n = p_1^{k_1} p_2^{k_2} \cdots p_r^{k_r}$

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 $n$.

Also known as
The prime decomposition of $n$ is also known as the prime factorization of $n$.

Linguistic Note
The UK English spelling of prime factorization is prime factorisation.