Integers form Unique Factorization Domain

Theorem
The fundamental theorem of arithmetic can be stated as:


 * The integral domain $$\left({\Z, +, \times}\right)$$ is a unique factorization domain.

Proof
Follows directly from:


 * 1) the fundamental theorem of arithmetic;
 * 2) the fact that $\left({\Z, +, \times}\right)$ is an integral domain;
 * 3) the definitions complete factorization and equivalent factorizations.