# Goldbach's Conjecture and Euler's $\phi$-Function

## TL;DR

This paper introduces a novel approach to Goldbach's conjecture by reformulating it as systems of equations involving Euler's phi-function, offering a new perspective on these longstanding problems.

## Contribution

It presents an alternative formulation of Goldbach's conjectures using Euler's phi-function, potentially opening new avenues for analytical or computational investigation.

## Key findings

- New formulation of Goldbach's conjecture as phi-function equations
- Potential for new methods to approach the conjectures
- Provides a different mathematical perspective on the problem

## Abstract

In this paper we propose an alternative formulation of the binary and ternary Goldbach conjectures as the systems of equations involving the Euler $\phi$-function.