# Cracking the problem with 33

## TL;DR

This paper explores solutions to the equation x^3 + y^3 + z^3 = k for small k, successfully finding the first known solution for k=33, inspired by a popular number theory video.

## Contribution

It presents the first known solution for the specific case of k=33 in the sum of three cubes problem.

## Key findings

- First known solution for k=33
- Methodology for finding solutions to sum of three cubes
- Insight into the difficulty of solving for specific k values

## Abstract

Inspired by the Numberphile video "The uncracked problem with 33" by Tim Browning and Brady Haran, we investigate solutions to $x^3+y^3+z^3=k$ for a few small values of $k$. We find the first known solution for $k=33$.