For $A=\{\lfloor n \alpha \rfloor: n\in\Bbb Z \}$, where $\alpha$ irrational, $\alpha \gt 2$, we aim to show the following:
There exists $m$ elements contained in $A$ that form an arithmetic progression, for any $m \gt 2$, $m \in\Bbb N$.
There exists no infinite arithmetic progression in $A$.