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A very beautiful problem

Source: Iran 2003

April 3, 2004
algebrapolynomialnumber theory unsolvednumber theory

Problem Statement

f1,f2,…,fnf_{1},f_{2},\dots,f_{n} are polynomials with integer coefficients. Prove there exist a reducible g(x)g(x) with integer coefficients that f1+g,f2+g,…,fn+gf_{1}+g,f_{2}+g,\dots,f_{n}+g are irreducible.
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