IMO 1989 LL POR85

Let P(x) be a polynomial with integer coefficients such that

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IMO 1989 LL POR85

Origin: POR

Problem

Let P(x) be a polynomial with integer coefficients such that P(m1) = P(m2) = P(m3) = P(m4) = 7 for given distinct integers m1, m2, m3, and m4. Show that there is no integer m such that P(m) = 14.