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Monic polynomial of degree 1991 with integer coefficients

Source: IMO ShortList 1991, Problem 21 (HKG 6)

August 15, 2008
algebrapolynomialfunctional equationrootsIMO Shortlist

Problem Statement

Let f(x) f(x) be a monic polynomial of degree 1991 1991 with integer coefficients. Define g(x) \equal{} f^2(x) \minus{} 9. Show that the number of distinct integer solutions of g(x) \equal{} 0 cannot exceed 1995. 1995.
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