MathDB
Two variable polynomial and function

Source: 239 2008 S6

July 28, 2020
polynomialalgebrafunction

Problem Statement

Given a polynomial P(x,y)P(x,y) with real coefficients, suppose that some real function f:R→Rf:\mathbb R \to \mathbb R satisfies P(x,y)=f(x+y)−f(x)−f(y)P(x,y) = f(x+y)-f(x)-f(y)for all x,y∈Rx,y\in\mathbb R. Show that some polynomial qq satisfies P(x,y)=q(x+y)−q(x)−q(y)P(x,y) = q(x+y)-q(x)-q(y)
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