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

Jaitra Chattopadhyay, Subha Sarkar

For every positive integer $n$, Sita Ramaiah's identity states that \medskip \begin{equation*} \sum_{a_1, a_2, a_1+a_2 \in (\mathbb{Z}/n\mathbb{Z})^*} \gcd(a_1+a_2-1,n) = ϕ_2(n)σ_0…