## Non-negative Integer
Solutions of

*a*_{1}^{k}
+ a_{2}^{k} + a_{3}^{k}+
a_{4}^{k}+ a_{5}^{k}+
a_{6}^{k}+ a_{7}^{k}
+ a_{8}^{k} = b_{1}^{k}
+ b_{2}^{k} + b_{3}^{k}
+ b_{4}^{k} + b_{5}^{k}
+ b_{6}^{k} + b_{7}^{k}
+ b_{8}^{k}
( k = 1, 2, 3, 4,
5, 6, 7 )
- The first solution of this type was obtained
by G.Tarry in 1913.
`[2]` However,
his method only can give one solution of this type.
- [ 0, 4, 9, 23, 27, 41, 46, 50 ] = [ 1, 2, 11,
20, 30, 39 , 48, 49 ]

- Crussol gave a parameter solution in 1913.
`[9]`
- J.Chernick gave a two-parameter symmetric solution
of this type in 1937.
`[7]` Numerical
examples by his method are
- [ 0, 9, 10, 27, 41, 58, 59, 68 ] = [ 2, 3, 19,
20, 48, 49, 65, 66 ]
- [ 0, 14, 19, 43, 57, 81, 86, 100 ] = [ 1, 9,
30, 32, 68, 70, 91, 99 ]

- Non-symmetric solution of this type is first
found by Chen Shuwen in 1997.
- [ 0, 7, 23, 50, 53, 81, 82, 96 ] = [ 1, 5, 26,
42, 63, 72, 88, 95 ]
** **
- [ 0, 21, 82, 149, 155, 262, 278, 321 ] = [ 2,
17, 91, 126 , 174, 253, 285, 320 ]

*Last revised March,31, 2001.*

Copyright 1997-2001, Chen Shuwen