Fourth Power is Sum of 2 Triangular Numbers/Proof 1

Proof
Note first that:
 * $\forall n \in \Z: \paren {-n}^4 = n^4$

Hence it is sufficient to consider the case where $n \ge 0$.

For $n = 0$:
 * $0^4 = 0 = 0 + 0 = T_0 + T_0$

Let $n > 0$.

Then:
 * $n^2 - 1 \ge 0$

and:
 * $n^2 \ge 0$

Hence: