Integer as Difference between Two Squares

Theorem
Let $n$ be a positive integer.

Then $n$ can be expressed as:
 * $n = a^2 - b^2$

$n$ has at least two distinct divisors of the same parity that multiply to $n$.

Proof
Thus $n = p q$ where:

Thus for $a$ and $b$ to be integers, both $p$ and $q$ must be:
 * distinct, otherwise $p = q$ and so $b = 0$
 * either both even or both odd, otherwise both $p + q$ and $p - q$ will be odd, and so neither $\dfrac {p + q} 2$ nor $\dfrac {p - q} 2$ are defined in $\Z$.

Hence the result.