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P(x^2 + 1) = P(x)^2 - 1, polynomial of degree 998

Source: Austrian - Polish 1996 APMC

May 3, 2020
algebrapolynomialfunctional equationfunctional

Problem Statement

Show that there is no polynomial P(x)P(x) of degree 998998 with real coefficients which satisfies P(x2+1)=P(x)2āˆ’1P(x^2 + 1) = P(x)^2 - 1 for all xx.
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