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2001 Spanish Mathematical Olympiad, Problem 1

Source: Spanish Mathematical Olympiad 2001

June 4, 2017
polynomialgeometryalgebra

Problem Statement

Prove that the graph of the polynomial P(x)P(x) is symmetric in respect to point A(a,b)A(a,b) if and only if there exists a polynomial Q(x)Q(x) such that: P(x)=b+(x−a)Q((x−a)2)).P(x) = b + (x-a)Q((x-a)^2)).
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