Question 65
A point $(a, b)$ in the plane is a *primitive point* if $a, b$ are integers with $\gcd(a, b) = 1$. A graph whose vertices are the primitive points is constructed as follows: an edge is drawn between the points $(a_1, b_1)$ and $(a_2, b_2)$ if and only if $2a_1 = 2a_2 \in \{b_1 - b_2, b_2 - b_1\}$ or $2b_1 = 2b_2 \in \{a_1 - a_2, a_2 - a_1\}$. Later, some edges of this graph will be removed until a forest is obtained. At least how many edges must be removed from the graph? At least how many trees will be found in the forest?