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Polynomials

Source: Greek mathematical olympiad,Problem 2

February 29, 2016

algebrapolynomial

Problem Statement

Find all monic polynomials

P,Q

which are non-constant, have real coefficients and they satisfy

2P(x)=Q(\frac{(x+1)^2}{2})-Q(\frac{(x-1)^2}{2})

and

P(1)=1

for all real

x