MathNet 2010 — Part 05 Question 49

Let $D := \{1, 2, \dots, n\} \times \{1, 2, \dots, n\}$. Prove there exists a set $S \subset D$ with $|S| \ge \lfloor \frac{3}{5}n(n+1) \rfloor$, such that for any $(x_1, y_1), (x_2, y_2) \in S$ we have $(x_1 + x_2, y_1 + y_2) \notin S$.