Suppose the polynomial

\(f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_2x^2 + a_1x + a_0\)

has integer coefficients, and its roots are distinct integers.

Given that \(a_n=2 \) and \(a_0=66 \), what is the least possible value of \(|a_{n-1}|\)?

AoPS.Morrisville Dec 14, 2019