Decomposition into Even-Odd Integers is not always Unique

Theorem
For every even integer $n$ such that $n > 1$, if $n$ can be expressed as the product of one or more even-times odd integers, it is not necessarily the case that this product is unique.

Proof
Let $n \in \Z$ be of the form $2^2 p q$ where $p$ and $q$ are odd primes.

Then:
 * $n = \paren {2 p} \times \paren {2 q} = 2 \times \paren {2 p q}$

A specific example that can be cited is $n = 60$:


 * $60 = 6 \times 10$

and:
 * $60 = 2 \times 30$.

Each of $2, 6, 10, 30$ are even-times odd integers:

Every $n \in \Z$ which has a divisor in that same form $2^2 p q$ can similarly be decomposed non-uniquely into even-times odd integers.