Question 159
Let $n$ be a positive integer larger than $1$, and let $a_0, a_1, \dots, a_{n-1}$ be integers. It is known that the equation
$$
x^n + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} + \dots + a_1x + a_0 = 0
$$
has $n$ pairwise relatively prime integer roots. Prove that $a_0$ and $a_1$ are relatively prime.
$$
x^n + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} + \dots + a_1x + a_0 = 0
$$
has $n$ pairwise relatively prime integer roots. Prove that $a_0$ and $a_1$ are relatively prime.