MathDB

8

Part of 1996 Austrian-Polish Competition

Problems(1)

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

Source: Austrian - Polish 1996 APMC

5/3/2020
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.
algebrapolynomialfunctional equationfunctional