# Brauer-Manin obstruction for Erd\H{o}s-Straus surfaces

## TL;DR

This paper investigates why certain solutions to the Erdős–Straus conjecture fail the integral Hasse principle and strong approximation, using the Brauer-Manin obstruction as a key tool.

## Contribution

It applies the Brauer-Manin obstruction to analyze failures of the integral Hasse principle for Erdős–Straus surfaces, providing new insights into their arithmetic properties.

## Key findings

- Identifies cases where the Brauer-Manin obstruction explains failures
- Provides criteria for the failure of strong approximation
- Enhances understanding of the arithmetic structure of Erdős–Straus surfaces

## Abstract

We study the failure of the integral Hasse principle and strong approximation for the Erd\H{o}s-Straus conjecture using the Brauer-Manin obstruction.