On a generalization of the Gauss's formula

TL;DR

This paper extends Gauss's formula using a group-theoretic approach and a generalized Euler's totient function, providing a broader mathematical framework.

Contribution

It introduces a new generalization of Gauss's formula based on group theory and a generalized Euler's totient function.

Findings

New group-theoretic generalization of Gauss's formula

Introduction of a generalized Euler's totient function

Broader mathematical framework for classical formulas

Abstract

In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].