Question 108
You are given $n$ different primes $p_1, p_2, \dots, p_n$. Consider the polynomial
$$
x^n + a_1x^{n-1} + a_2x^{n-2} + \dots + a_{n-1}x + a_n,
$$
where $a_i$ is the product of the first $i$ given prime numbers. For what $n$ can it have an integer root?
$$
x^n + a_1x^{n-1} + a_2x^{n-2} + \dots + a_{n-1}x + a_n,
$$
where $a_i$ is the product of the first $i$ given prime numbers. For what $n$ can it have an integer root?