## 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}
= b_{1}^{k} + b_{2}^{k}
+ b_{3}^{k} + b_{4}^{k}
+ b_{5}^{k} + b_{6}^{k}
+ b_{7}^{k}
( k = 1, 2, 3, 4,
5, 6 )
- The first solution of this type was found out
by E.B.Escott in 1910.
`[2]`
- [ 0, 18, 27, 58, 64, 89, 101 ] = [ 1, 13, 38,
44, 75, 84, 102 ]

- J.Chernick gave a two-parameter solution of this
type in 1937.
`[7]` Numerical examples
by his method are
- [ 0, 59, 68, 142, 181, 221, 267 ] = [ 1, 47,
87, 126, 200 , 209, 268 ]

- No non-symmetric solution of this type is first
found Chen Shuwen in 1997.
- [ 0, 18, 19, 50, 56, 79, 81 ] = [ 1, 11, 30,
39, 68, 70, 84 ]
- This one is also the smallest solution of this
type that have been found out.

- [ 0, 14, 43, 141, 156, 193, 199 ] = [ 3, 9, 46,
133, 175, 176, 204 ]
- [ 0, 24, 31, 74, 106, 137, 147 ] = [ 4, 11, 52,
57, 119, 126, 150 ]

- Each non-symmetric solution has its "co-symmetric"
solution., For example
- [ 0, 18, 19, 50, 56, 79, 81 ] = [ 1, 11, 30,
39, 68, 70, 84 ]
- [ 0, 14, 16, 45, 54, 73, 83 ] = [ 3, 5, 28, 34,
65, 66, 84 ]

*Last revised March,31, 2001.*

Copyright 1997-2001, Chen Shuwen