MathNet 2019-part-05 — 184 problems (EN–VI) Question 12

Is it possible to express every positive integer $n$ congruent to $9$ modulo $25$ in the form $n = \frac{a(a+1)}{2} + \frac{b(b+1)}{2} + \frac{c(c+1)}{2}$, where $a$, $b$, $c$ are non-negative integers that do not share parity?