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Show that x^n+ax+p is irreducible if p>|a|+1, p prime

Source: Romanian IMO Team Selection Test TST 1999, problem 11

September 24, 2005
algebrapolynomialinequalitiesabsolute valuealgebra proposed

Problem Statement

Let a,na,n be integer numbers, pp a prime number such that p>∣a∣+1p>|a|+1. Prove that the polynomial f(x)=xn+ax+pf(x)=x^n+ax+p cannot be represented as a product of two integer polynomials. Laurentiu Panaitopol
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