121 is Square Number in All Bases greater than 2

Theorem
Let $b \in \Z$ be an integer such that $b \ge 3$.

Let $n$ be a positive integer which can be expressed in base $b$ as $121_b$.

Then $n$ is a square number.

Proof
Consider $11_b$.

By the Basis Representation Theorem:
 * $11_b = b + 1$

Thus:

Thus:
 * $121_b = {11_b}^2$

and so is a square number.