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P(x)^2+1=(x^2+1)Q(x^2), der(P)=?

Source: 10th European Mathematical Cup - Problem S4

December 22, 2021

polynomialalgebraEuropean Mathematical Cup

Problem Statement

Find all positive integers

d

for which there exist polynomials

P(x)

and

Q(x)

with real coefficients such that degree of

P

equals

d

and

P(x)^2+1=(x^2+1)Q(x)^2.