# Integral points on twisted Markoff surfaces

## TL;DR

This paper investigates the integral Hasse principle on twisted Markoff surfaces using Brauer-Manin obstruction, providing explicit examples with 4-torsion Brauer group elements and detailed local invariant computations.

## Contribution

It introduces new examples of twisted Markoff surfaces with nontrivial Brauer groups and explicit representatives, advancing understanding of the Brauer-Manin obstruction in this context.

## Key findings

- Identified examples with 4-torsion elements in the Brauer group
- Constructed explicit representatives for these Brauer group elements
- Computed local invariants at special places for these examples

## Abstract

We study the integral Hasse principle for affine varieties of the form ax^2+y^2+z^2-xyz=m ,using Brauer-Manin obstruction, and we produce examples whose Brauer groups include 4-torsion elements .We will construct their explicit representatives and compute local invariants in special places.