BALTIC-WAY 2019 Problem 18

Let $a,b$ , and $c$ be odd positive integers such that $a$ is not a perfect square and $$a^2+a+1 = 3(b^2+b+1)(c^2+c+1).$$ Prove that at least one of the numbers $b^2+b+1$ and $c^2+c+1$ is composite.