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Integral functional eqn

Source: INMO 1992 Problem 6

October 4, 2005
calculusintegrationalgebrapolynomial

Problem Statement

Let f(x)f(x) be a polynomial in xx with integer coefficients and suppose that for five distinct integers a1,…,a5a_1, \ldots, a_5 one has f(a1)=f(a2)=…=f(a5)=2f(a_1) = f(a_2) = \ldots = f(a_5) = 2. Show that there does not exist an integer bb such that f(b)=9f(b) = 9.
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