## Non-negative Integer
Solutions of

*a*_{1}^{k}
+ a_{2}^{k} + a_{3}^{k}
= b_{1}^{k} + b_{2}^{k}
+ b_{3}^{k}
( k = 2, 6 )
- The first nontrivial solution was given in 1934
by Subba-Rao.
`[3]` `[31]`
- [ 3, 19, 22 ] = [ 10, 15, 23 ]

- In 1967, L.J.Lander, T.R.Parkin and J.L.Selfridge
made a computer search using CDC6600 to the following Diophantine equation
in least integers
*a*_{1}^{6}*
+ a*_{2}^{6}* + a*_{3}^{6}*
= b*_{1}^{6}* + b*_{2}^{6}*
+ b*_{3}^{6}

- They found 10 primitive solutions of which 9
solutions were also satisfy the additional equality
*a*_{1}^{2}*
+ a*_{2}^{2}* + a*_{3}^{2}*
= b*_{1}^{2}* + b*_{2}^{2}*
+ b*_{3}^{2}

- Here are the primitive solutions in least integers
by their computer search.
`[11]`
- [ 3, 19, 22 ] = [ 10, 15, 23 ]
- [ 15, 52, 65 ] = [ 36, 37, 67 ]
- [ 23, 54, 73 ] = [ 33, 47, 74 ]
- [ 11, 65, 78 ] = [ 37, 50, 81 ]
- [ 3, 55, 80 ] = [ 32, 43, 81 ]

- Parametric solutions of this system were obtained
by
- Simcha Brundo in 1968
`[30]`
- Simcha Brundo in 1970
`[29]`
- Simcha Brundo and Irving Kaplansky in 1974
`[26]`
- Simcha Brundo in 1976
`[27]`
- Andrew Bremner in 1979
`[28]`
- J .Delorme in 1990
`[15]`

*Last revised March,31, 2001.*

Copyright 1997-2001, Chen Shuwen