Equal Sums of Like Powers

Non-negative Integer Solutions of

• Some systems like this type had been studied by A.Golden since 1940's. [35] He gave a parametric solution of the following system
a₁^k + a₂^k + a₃^k+ a₄^k+ a₅^k+ a₆^k+ a₇^k = b₁^k + b₂^k + b₃^k + b₄^k + b₅^k + b₆^k+ b₇^k
( k =1, 2, 4, 6, 8 )
• Non-negative integer solution of the system in the title was first obtained by Chen Shuwen in 1995. He got the following solution by two ways.
• [ 1, 7, 17, 30, 31, 36 ] = [ 3, 4, 19, 27, 34, 35 ]
• With the help of a Pentium-100MHz PC, Chen Shuwen obtained these two solutions in 1997.
• [ 64, 169, 184, 277, 347, 417 ] = [ 69, 139, 233, 248, 353 , 416 ]
• [ 111, 242, 243, 445, 446, 596 ] = [ 148, 149, 353, 354, 485 , 594 ]