Let $f(X) = a_nX^n + a_{n-1}X^{n-1} + ...+ a_1X + p$ be a polynomial of integer coefficients where $p$ is a prime number. Assume that $p >\sum_{i=1}^n |a_i|$. Prove that $f(X)$ is irreducible.
Source: 2013 Saudi Arabia GMO TST II p2
Tags: polynomial, algebra, Irreducible
Let $f(X) = a_nX^n + a_{n-1}X^{n-1} + ...+ a_1X + p$ be a polynomial of integer coefficients where $p$ is a prime number. Assume that $p >\sum_{i=1}^n |a_i|$. Prove that $f(X)$ is irreducible.