## Non-negative Integer
Solutions of

*a*_{1}^{k}
+ a_{2}^{k} + a_{3}^{k}+
a_{4}^{k}+ a_{5}^{k}
+ a_{6}^{k} = b_{1}^{k}
+ b_{2}^{k} + b_{3}^{k}
+ b_{4}^{k} + b_{5}^{k}+
b_{6}^{k}
( k = 2, 4, 6, 8,
10 )
- Nuutti Kuosa discovered the following solution
in 3 Sep1999, using a program written by Jean-Charles Meyrignac.
- 151
^{10}+140^{10}+127^{10}+86^{10}+61^{10}+22^{10}=148^{10}+146^{10}+121^{10}+94^{10}+47^{10}+35^{10}

- Chen Shuwen noticed in 7 Sep1999 that the above
result is also a solution of ( k = 2, 4, 6, 8, 10
) .
- [ 22, 61, 86, 127, 140, 151 ] = [ 35, 47, 94,
121, 146, 148 ]

- David Broadhurst found the second solution in 2007.
_{[0701]}
- [ 257, 891, 1109, 1618, 1896, 2058 ] = [ 472, 639, 1294, 1514, 1947, 2037 ]

- In 2008, A.Choudhry and Jaroslaw Wroblewski proved that this system has
infinitely many solutions and give a method to produce new numerical solutions.
The smallest new solution found by their method is
- [ 107, 622, 700, 1075, 1138, 1511 ] = [ 293, 413, 886, 953, 1180, 1510 ]

- In 2016, Chen Shuwen found that there is no other new solution in the range
of of max {
*a*_{i}, *b*_{i}
} <= 1800.
- See also ( k = 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 11 ) for more information.

*Last revised March,19, 2017.*

Copyright 1997-2017, Chen Shuwen