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f(x - t, y) + f(x + t, y) + f(x, y - t) + f(x, y + t) = 2010

Source: Thailand Mathematical Olympiad 2010 day 2 p5

August 17, 2020
functional equationfunctionalalgebra

Problem Statement

Determine all functions f:R×R→Rf : R \times R \to R satisfying the equation f(x−t,y)+f(x+t,y)+f(x,y−t)+f(x,y+t)=2010f(x - t, y) + f(x + t, y) + f(x, y - t) + f(x, y + t) = 2010 for all real numbers x,yx, y and for all nonzero tt
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