3) Let m = i=1 where p1 2 be an integer, and denote by [x] the congruence class of r E Z modulo n. (i) The sets [0], [1], ..., [n - 1] are all congruence classes modulo n. We have [i] n[i] = 0 for all i # j in the set {0, . .., n - 1} and n-1 Z = [ , 1=0 i.e. Z is the disjoint union of the congruence classes [0], . . ., [n - 1]. (ii) The following three statements are equivalent for all integers a, be Z: (a) [a] = [b]; (b) [a]n [b] # 0; and (c) a = b mod n