Problem:
For each natural number $n$, we define: $A_{n}=\left \{ (n+1)k:k\in \mathbb{N} \right \}$. It seems obvious to me that $\bigcap_{n=1}^{\infty }A_{n}=\varnothing $ where $\varnothing$ is the empty set. However, I couldn't come up with a proof for that. Any help please? Thanks.