# Thirty-six Officers and their Code

## TL;DR

This paper provides a short proof of Euler's 36 officer conjecture, demonstrating the non-existence of an affine plane of order 6 through both indirect and direct methods.

## Contribution

It offers a concise proof of Euler's 36 officer conjecture and confirms the non-existence of an affine plane of order 6 with two different approaches.

## Key findings

- Confirmed no affine plane of order 6 exists
- Provided a short proof of Euler's 36 officer conjecture
- Presented a direct proof method

## Abstract

This note presents a short proof of Euler's 36 officer conjecture. This implies that there is no affine plane of order $6$, but we also give a direct proof.