For n ≥ 2 a reduced set of residues modulo n is a set of integers, one congruent (modulo n) to each of the positive integers less than n which are coprime with n. Thus, {1, 5, 7, 11} is a reduced set of residues modulo 12, as is {1,−1,5,−5}. A reduced set of residues forms an abelian group under multiplication, denoted ${\mathbb{Z}}_n^{*}$, which has order ϕ‎(n) (see totient function).