MathDB
19th kmo #4

Source: KMO round 2, problem 4

February 3, 2006
functioninductioncalculusderivativealgebrafunctional equationalgebra unsolved

Problem Statement

Find all f:R→Rf: \mathbb R \to\mathbb R such that for all real numbers xx, f(x)≥0f(x) \geq 0 and for all real numbers xx and yy, f(x+y)+f(x−y)−2f(x)−2y2=0. f(x+y)+f(x-y)-2f(x)-2y^2=0.
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