7

Part of 2003 Iran MO (3rd Round)

Problems(1)

A very beautiful problem

Source: Iran 2003

f_{1},f_{2},\dots,f_{n}

are polynomials with integer coefficients. Prove there exist a reducible

g(x)

with integer coefficients that

f_{1}+g,f_{2}+g,\dots,f_{n}+g

are irreducible.

algebrapolynomialnumber theory unsolvednumber theory