Is it possible to construct an equilateral triangle with coordinates on a grid of integers?
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?