Fourth Power is Sum of 2 Triangular Numbers

Theorem
Let $n \in \Z$ be an integer.

Then:
 * $\exists a, b \in \Z_{\ge 0}: n^4 = T_a + T_b$

where $T_a$ and $T_b$ are triangular numbers.

That is, the $4$th power of an integer equals the sum of two triangular numbers.

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 $n = 0$, $0^4 = 0 = 0 + 0 = T_0 + T_0$.

For $n > 0$, $n^2 - 1 \ge 0$ and $n^2 \ge 0$.