For integers a,b, call the lattice point with coordinates (a,b) basic if gcd(a,b)=1. A graph takes the basic points as vertices and the edges are drawn in such way: There is an edge between (a1,b1) and (a2,b2) if and only if 2a1=2a2∈{b1−b2,b2−b1} or 2b1=2b2∈{a1−a2,a2−a1}. Some of the edges will be erased, such that the remaining graph is a forest. At least how many edges must be erased to obtain this forest? At least how many trees exist in such a forest? combinatoricsgraph theorynumber theoryGCDTrees