## Fall 2015, problem 4

Let $f\colon \mathbb{R}^2 \to \mathbb{R}$ be a function such that for any square $S$ in $\mathbb{R}^2$ with vertices $v_1,v_2,v_3,v_4$, we have

$$\sum_{j=1}^4 f(v_i) = 0.$$

Prove that $f$ is identically 0.