MathDB

Let

f: \mathbb{R}^2\to\mathbb{R}

be a function such that f(x,y)\plus{}f(y,z)\plus{}f(z,x)\equal{}0 for real numbers

x,y,

and

z.

Prove that there exists a function

g: \mathbb{R}\to\mathbb{R}

such that f(x,y)\equal{}g(x)\minus{}g(y) for all real numbers

x

and

y.

A1