“…It is easily seen that s is ultimately periodic modulo M , for every positive integer M , and purely periodic if (c r , M ) = 1. Indeed, properties of linear recurrences modulo M have been studied intensively, including: which residues modulo M appear in the s and how frequently [4,6,9,12,15,17], and for which positive integers M the linear recurrence s contains a complete system of residues modulo M [2,5,16,18]. Let M(g) denote the set of positive integers m such that there exist initial conditions s 0 , .…”