Is it possible to have four points on a plane, which the length between each of those points (six lengths) can be divided by an integer to get 1? Give an example of this, with the lengths between each point shown.
If you can, what about 5? What about 6?
For any Pythagorean triple $a,b,c \in \mathbb{N}$ with $a^2 + b^2 = c^2$ the four points \begin{equation} (0,0), (a,0), (a,b) \text{ and } (0, b) \end{equation} satisfy the given constraints.