Question 70
Does there exist a nonzero polynomial $P(x)$ with integer coefficients satisfying both of the following conditions?
* $P(x)$ has no rational root;
* For every positive integer $n$, there exists an integer $m$ such that $n$ divides $P(m)$.
* $P(x)$ has no rational root;
* For every positive integer $n$, there exists an integer $m$ such that $n$ divides $P(m)$.