Structure of digraphs associated with quadratic congruences with composite moduli

AbstractWe assign to each positive integer n a digraph G(n) whose set of vertices is H={0,1,…,n-1} and for which there exists a directed edge from a∈H to b∈H if a2≡b(modn). Associated with G(n) are two disjoint subdigraphs: G1(n) and G2(n) whose union is G(n). The vertices of G1(n) correspond to those residues which are relatively prime to n. The structure of G1(n) is well understood. In this paper, we investigate in detail the structure of G2(n)