Diophantine

Stupidly bruteforces Diophantine equations.

Motivation

The author wishes to find more solutions for the Diophantine equation given by

x^3 + y^3 n + z^3 n^2 - 3nxyz = 1

where n is not a cube root. It is also known as the Cubic Pell's equation due to its relation to the norm of cubic fields. Note that 富田清二 has already computed all solutions till 99.

Background

This project targets the NUS SoC compute cluster. It is characterised by the following.

• It's big, like 100~ish nodes with 20+ CPU cores each.
• I have no access and can't install stuff easily.
• Results can be persisted to a nfs share without any need for synchronisation.

Overview

There are 3 components.

• Master. A minimal networked endpoint which supplies work. Since all work is agreed beforehand all it has to do is to supply n.
• Slave has 2 parts,
  • Solver. Stupidly solves.
  • Client. Runs on each node, talks to master and keep multiple slaves alive.

Protocol (It's shit)

1. Slave connects to master
2. Slave asks for a number by sending a line that doing a HTTP GET on exactly matches /token
   • (Optional) Slave identifies itself with header X-Slave-Identifier
3. Master replies with parameters used to construct the parametrised equation