`Equal Sums of Like Powers`

Non-negative Integer Solutions of

a₁^k + a₂^k + a₃^k+ a₄^k+ a₅^k+ a₆^k = b₁^k + b₂^k + b₃^k + b₄^k + b₅^k + b₆^k

( k = 1, 3, 5, 7, 9 )

Non-negative integer solution of this type is first obtained by Chen Shuwen in 2000.

Jarosław Wróblewski found the following four solutions in 2009. _[1001] _[0901]
- [ 23, 163, 181, 341, 347, 407 ] = [ 37, 119, 221, 311, 371, 403 ]
- [ 43, 161, 217, 335, 391, 463 ] = [ 85, 91, 283, 287, 403, 461 ]
- [ 57, 399, 679, 995, 1167, 1293 ] = [ 115, 299, 767, 925, 1205, 1279 ]
- [ -13, 365, 689, 1111, 1115, 1325 ] = [ 23, 305, 731, 1037, 1177, 1319 ]
In 2016，Chen Shuwen finished a computer search in the range of Max{a_i,b_i}<=5600 and found that there is no new positive integer solution.
In 2016，Chen Shuwen finished a computer search in the range of a₁=0 and Max{a_i,b_i}<=25000 and found that there is no any positive integer solution. That is to say, there is no ideal symmetric non-negative solutions of the the Prouhet-Tarry-Escott problem for ( k = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ) in the range of Max{a_i,b_i} <= 50000.