MathDB
IMC 2008 Day 2 P4 - Polynomial with degree > 5

Source: Problem 4

July 28, 2008
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Problem Statement

Let Z[x] \mathbb{Z}[x] be the ring of polynomials with integer coefficients, and let f(x),g(x)āˆˆZ[x] f(x), g(x) \in\mathbb{Z}[x] be nonconstant polynomials such that g(x) g(x) divides f(x) f(x) in Z[x] \mathbb{Z}[x]. Prove that if the polynomial f(x)\minus{}2008 has at least 81 distinct integer roots, then the degree of g(x) g(x) is greater than 5.
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