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Polynomial Equation

Source: Azerbaijan IMO TST 2016,D1 P2

May 26, 2018
algebrapolynomial

Problem Statement

Find all polynomials P(x)P(x) with real coefficents, such that for all x,y,zx,y,z satisfying x+y+z=0x+y+z=0, the equation below is true: P(x+y)3+P(y+z)3+P(z+x)3=3P((x+y)(y+z)(z+x))P(x+y)^3+P(y+z)^3+P(z+x)^3=3P((x+y)(y+z)(z+x))
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