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Determine all polynomials such that f(x^2-2x)=f^2(x-2)

Source: 4-th Hungary-Israel Binational Mathematical Competition 1993

May 26, 2007
algebrapolynomialalgebra proposed

Problem Statement

Determine all polynomials f(x)f (x) with real coeffcients that satisfy f(x2−2x)=f2(x−2)f (x^{2}-2x) = f^{2}(x-2) for all x.x.
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