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Turkey NMO 2012 Problem 3 functional equation

Source: Turkey NMO 2012

November 24, 2012
functionalgebrafunctional equationalgebra proposed

Problem Statement

Find all non-decreasing functions from real numbers to itself such that for all real numbers x,yx,y f(f(x2)+y+f(y))=x2+2f(y)f(f(x^2)+y+f(y))=x^2+2f(y) holds.
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