Is it possible to construct an equilateral triangle with vertices on lattice points?
I think the answer is no, but how can I prove this?
I started with a triangle with coordinates $(0,0)$ $(a,b)$ and $(c,d)$. Equating the size of the 3 sides, I get
How should I continue?
I see there are solutions based on the fact that the angle between two edges can not be 60°. Is it possible to have a solution based on the fact that the length of the edges can not be the same?