Square of 1 Less than Number Base

Theorem
Let $b \in \Z$ be an integer such that $b > 2$.

Let $n = b - 1$.

The square of $n$ is expressed in base $b$ as:


 * $n^2 = \left[{c1}\right]_b$

where $c = b - 2$.

Proof
The result follows by definition of number base.