Equal Sums of Like Powers

Non-negative Integer Solutions of

• T.N.Sinha found a two-parametric integer solution of this type in 1984, but his method cannot lead to non-negative integer solutions. [6]
• In 1988, R.N.Singh gave a method on how to construct infinitely many integral solutions to the system of equations
a₁^k + a₂^k + a₃^k = b₁^k + b₂^k + b₃^k + b₄^k      ( k = 1, 3, 4 )
However, his method also just gives integer solutions, not non-negative integer solutions. [16]
• Non-negative integer solutions of this type were first found by Chen Shuwen in 1995. Examples are
• [ 3, 140, 149, 252 ] = [ 50, 54, 201, 239 ]
• [ 127, 324, 1740, 2023 ] = [ 24, 439, 1711, 2040 ]
• [ 1059, 1444, 2476, 2763 ] = [ 1179, 1288, 2632, 2643 ]
• Chen had made a computer search recently, and found that there are no non-negative integer solutions of this type in the range R<=200.