Be $\displaystyle \alpha\in\mathbb{R}$ and $\displaystyle p_{0}, p_{1}, p_{2},\cdots, p_{n} $ distintict positive intergers. I must prove there's an interger $\displaystyle r$ and indices $\displaystyle i$ and $\displaystyle j$ with $\displaystyle 0\le i<j \le n$ such that $\displaystyle \mid\alpha(p_{i} - p_{j}) - r\mid < \frac{1}{n}$

I've been trying to prove this using Dirichlet's principle but I only got to a few results using all possible values for $\displaystyle r = \lfloor\mid\alpha(p_{i} - p_{j}) - r\mid\rfloor$ and considering the sets $\displaystyle [\frac{2}{n},\frac{3}{n}),\cdots\,[\frac{n-1}{n},1)$. I don't see it