On a generalization of Menon-Sury identity to number fields involving a Dirichlet Character

A generalization of Tóth identity in the ring of algebraic integers involving a Dirichlet Character

“…Recently, Ji and Wang [7] and Chattopadhyay and Sarkar [4] generalized Sita Ramaiah's identity in the ring of algebraic integers involving a Dirichlet character. Before we state the results of [4] and [7], we introduce the fundamental functions defined on the integral ideals of O K . In what follows, for an element α ∈ O K , the principal ideal αO K is denoted by α and gcd(α, a) will denote gcd( α , a).…”

“…It is also known that (cf. [7]), A special case of the result in [4] is the following generalization of Sita Ramaiah's identity: (6)…”

Proofs, generalizations and analogs of Menon's identity: a survey

“…Identities (4.24) and (4.25) by Tóth have been generalized by Sarkar[62] to the ring of algebraic integers O K and involving Dirichlet characters. The case k = 2, has been earlier investigated by Wang and Ji[101], Chattopadhyay and Sarkar[8].…”