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

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.