Prove that the given polynomial is irreducible
Source: Balkan MO ShortList 2009 A7
April 6, 2020
Problem Statement
Let be a positive integer and
\begin{align*} P(x) = c_0 X^n + c_1 X^{n-1} + \ldots + c_{n-1} X +c_n \end{align*}
be a polynomial with integer coefficients, such that is a prime number and
\begin{align*} |c_0| + |c_1| + \ldots + |c_{n-1}| < |c_n| \end{align*}
Prove that the polynomial is irreducible in the