Intersection of $\{ [n\sqrt{2}]\mid n \in \mathbb{N}^* \}$ and $\{ [n(2+\sqrt{2})]\mid n \in \mathbb{N}^* \}$ Find the intersection of sets $A$ and $B$ where
$$A = \{ [n\sqrt{2}]\mid n \in \mathbb{N}^* \}$$
$$B = \{ [n(2+\sqrt{2})]\mid n \in \mathbb{N}^* \}.$$
([$x$] is the integer part of $x$)
Using the computer, we found common elements.
Does anyone have an idea to solve?

Their intersection is the empty set
