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Polynomial equation

Source: Moscow Olympiad 2018, Grade 11, P3

April 7, 2018
algebrapolynomial

Problem Statement

Are there such natural nn, that exist polynomial of degree nn and with nn different real roots, and a) P(x)P(x+1)=P(x2)P(x)P(x+1)=P(x^2) b) P(x)P(x+1)=P(x2+1)P(x)P(x+1)=P(x^2+1)
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