## ABSTRACT

A cyclic group of order n may be realized as the additive group Z/nZ, that is, as the integers modulo n. When we interpret Theorem 3.19 (on page 59) in this way we obtain the following result.

THEOREM 7.1

Let m and n be relatively prime positive integers. If A = {a1, . . . , am} and B = {b1, . . . , bn} are sets of integers such that their sum set

A+B = {ai + bj : 1 ≤ i ≤ m, 1 ≤ j ≤ n} is a complete set of representatives modulo mn, then A is a complete set of residues modulo m and B is a complete set of residues modulo n.