Question 199
Let us denote by $\Omega(n)$ and $\omega(n)$ the largest and the smallest prime divisors of $n$, respectively. Alireza and Amin decided to play the following game. Starting with Alireza, he chooses 1400 polynomials with integer coefficients. Then, Amin chooses 700 polynomials among them and denotes their sets by $A$ and $B$, respectively. Amin shall win the game if for each positive integer $n$
$$
\max_{\{P \in A\}}(\Omega(P(n))) \geq \min_{\{Q \in B\}}(\omega(Q(n))),
$$
otherwise, Alireza shall win the game. Which player has the winning strategy?
$$
\max_{\{P \in A\}}(\Omega(P(n))) \geq \min_{\{Q \in B\}}(\omega(Q(n))),
$$
otherwise, Alireza shall win the game. Which player has the winning strategy?