Equal Sums of Like Powers

Non-negative Integer Solutions of

• Chen Shuwen studied this type first and found a parameter solution in 1995. Numerical examples are
• [ 53, 113, 156, 204 ] = [ 74, 78, 183, 191 ]
• [ 36, 329, 407, 608 ] = [ 88, 199, 537, 556 ]
• Chen had searched the smallest solutions of this type by using a Pentium. There are eight solutions in the range of R<100. Here R = max { a_i, b_i }.
• [ 1, 28, 39, 58 ] = [ 8, 14, 51, 53 ]
• [ 21, 37, 46, 58 ] = [ 23, 32, 51, 56 ]
• [ 29, 42, 83, 92 ] = [ 32, 38, 87, 89 ]
• [ 3, 52, 54, 97 ] = [ 12, 27, 73, 94 ]
• [ 16, 57, 71, 98 ] = [ 21, 43, 86, 92 ]