ABSTRACT
Given k, r positive integers, the notion of a reduced residue system (mod k, r), due to Eckford Cohen [ 6 ] is introduced. Jordan’s totient Jk (r) is interpreted arithmetically in the new terminology. The extension C (k)(n, r) of Ramanujan sums C(n, r) is derived. Certain applications to linear congruences with side conditions are pointed out.
