Let $n$ be a positive integer. Suppose $(x_1, y_1), (x_2, y_2), \dots, (x_k, y_k)$ with $\sqrt{n} \le x_1 < x_2 < \dots < x_k$ are integer lattice points on the hyperbola $x y = n$ near the center $(\sqrt{n}, \sqrt{n})$. In this talk, we will discuss repulsion among these lattice points through a lower bound on $x_k - y_k$. It turns out that this lower bound is sharp when $k = 2$ and $k = 3$ but not $k \ge 4$. We apply elementary, Pell equation, and Diophantine approximation techniques. This is joint work with Jorge Jim'{e}nez-Urroz.