Question 99
Determine all polynomials $P \in \mathbb{Z}[X]$ such that:
(i) $P(n) \geqslant 1$ for all $n \geqslant 1$
(ii) $P(mn)$ and $P(m) P(n)$ have the same number of prime divisors for all $m, n \geqslant 1$.
(i) $P(n) \geqslant 1$ for all $n \geqslant 1$
(ii) $P(mn)$ and $P(m) P(n)$ have the same number of prime divisors for all $m, n \geqslant 1$.