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f(X) is irreducible. when p >\sum_{i=1}^n |a_i|

Source: 2013 Saudi Arabia GMO TST II p2

July 26, 2020
polynomialalgebraIrreducible

Problem Statement

Let f(X)=anXn+an−1Xn−1+...+a1X+pf(X) = a_nX^n + a_{n-1}X^{n-1} + ...+ a_1X + p be a polynomial of integer coefficients where pp is a prime number. Assume that p>∑i=1n∣ai∣p >\sum_{i=1}^n |a_i|. Prove that f(X)f(X) is irreducible.
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