IMO Shortlist 1974 problem 3


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2. travnja 2012.
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Let P(x) be a polynomial with integer coefficients. We denote \deg(P) its degree which is \geq 1. Let n(P) be the number of all the integers k for which we have (P(k))^{2}=1. Prove that n(P)- \deg(P) \leq 2.
Izvor: Međunarodna matematička olimpijada, shortlist 1974