IMO Shortlist 1976 problem 9


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2. travnja 2012.
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Let P_{1}(x)=x^{2}-2 and P_{j}(x)=P_{1}(P_{j-1}(x)) for j=2,\ldots Prove that for any positive integer n the roots of the equation P_{n}(x)=x are all real and distinct.
Izvor: Međunarodna matematička olimpijada, shortlist 1976