NL-NWO 1975 Problem 4

Given is a rectangular plane coordinate system.

(a) Prove that it is impossible to find an equilateral triangle whose vertices have integer coordinates.

(b) In the plane the vertices $A, B$ and $C$ lie with integer coordinates in such a way that $AB = AC$ . Prove that $\frac{d(A,BC)}{BC}$ is rational.