`Equal Sums of Like Powers`

Non-negative Integer Solutions of

a₁^k + a₂^k + a₃^k + a₄^k+ a₅^k + a₆^k + a₇^k + a₈^k + a₉^k

= b₁^k + b₂^k + b₃^k + b₄^k + b₅^k + b₆^k + b₇^k + b₈^k+ b₉^k

( k = 1, 2, 3, 4, 5, 6, 7, 8 )

A.Latec gave two symmetric solutions in 1942.[5] [25]

[ 0, 24, 30, 83, 86, 133, 157, 181, 197 ] = [ 1, 17, 41, 65, 112, 115, 168, 174, 198 ]
[ 0, 26, 42, 124, 166, 237, 293, 335, 343 ] = [ 5, 13, 55, 111, 182, 224, 306, 322, 348 ]

No any new result was obtained on this type during the pass sixty years.
Chen Shuwen made a computer search in 1997, and found that there is no other symmetric solution of this type in the range max { a_i, b_i }< 400.

Last revised March,31, 2001.
Copyright 1997-2001, Chen Shuwen