ABSTRACT
In 1937, R. Vaidyanathaswamy [ 4 ] introduced a ‘class-division’ of integers modulo r (r > 1) which is closed under ‘addition’ and in which the factor https://www.w3.org/1998/Math/MathML"> γ i j k https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351023344/b6c68d68-1226-4347-aaa8-58dfe0c0d0a9/content/eq1833.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> occurring in https://www.w3.org/1998/Math/MathML"> C i C i = Σ k γ i j k C k https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351023344/b6c68d68-1226-4347-aaa8-58dfe0c0d0a9/content/eq1834.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> is evaluated in closed form, where {C 1, C 2, …, Ct } is the set of classes into which the set {1, 2, …, r} of residues (mod r) fall. An application is pointed out.
