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Functional equation: x p(y/x) + y p(x/y) = x + y

Source: XIII Rioplatense Mathematical Olympiad (2004), Level 3

July 26, 2011

algebrapolynomialalgebra unsolved

Problem Statement

Find all polynomials

P(x)

with real coefficients such that

xP\bigg(\frac{y}{x}\bigg)+yP\bigg(\frac{x}{y}\bigg)=x+y

for all nonzero real numbers

x

and

y