Question 101
Let the odd positive integer $a$ not be a perfect square, let $b$ and $c$ be odd primes, and
$$
a^2 + a + 1 = 3(b^2 + b + 1)(c^2 + c + 1).
$$
Prove that at least one of $b^2 + b + 1$ and $c^2 + c + 1$ is composite.
$$
a^2 + a + 1 = 3(b^2 + b + 1)(c^2 + c + 1).
$$
Prove that at least one of $b^2 + b + 1$ and $c^2 + c + 1$ is composite.