All solutions of the Diophantine equation a^6+b^6=c^6+d^6+e^6+f^6+g^6 for a,b,c,d,e,f,g < 250000 found with a distributed Boinc project

TL;DR

This paper reports on a distributed computing project that found all solutions to a specific high-degree Diophantine equation, demonstrating the effectiveness of volunteer computing for complex mathematical problems.

Contribution

It introduces a large-scale distributed search for solutions to the Euler(6,2,5) system, providing comprehensive solutions and showcasing the application of Boinc in number theory research.

Findings

All solutions with variables less than 250000 were found.

The project demonstrated the feasibility of distributed computing for complex Diophantine equations.

The approach can be applied to other similar mathematical systems.

Abstract

The above equation is also called as Euler(6,2,5) system. By computational aspect these systems are very interesting. And we can also apply these methods to other Diophantine equations. We give a brief history of these systems and how we searched for these big solutions on Boinc. Our two Boinc projects ran from April of 2010 to July of 2011.