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 and $$k_1, k_2, \ldots, k_r$$ are positive integers.

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