IMO Shortlist 2002 problem A3


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2. travnja 2012.
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Let P be a cubic polynomial given by P(x)=ax^3+bx^2+cx+d, where a,b,c,d are integers and a\ne0. Suppose that xP(x)=yP(y) for infinitely many pairs x,y of integers with x\ne y. Prove that the equation P(x)=0 has an integer root.
Izvor: Međunarodna matematička olimpijada, shortlist 2002