Equal Sums of Like Powers

Non-negative Integer Solutions of

• Chen Shuwen studied this type in 1995 and got a parameter solution.
• Smallest solutions of this type are very easy to be found by computer search.
• [ 2, 7, 11, 15 ] = [ 3, 5, 13, 14 ]
• [ 0, 7, 14, 19 ] = [ 1, 5, 16, 18 ]
• [ 3, 10, 13, 19 ] = [ 5, 6, 17, 17 ]
• [ 5, 14, 14, 21 ] = [ 6, 10, 19, 19 ]
• Chen Shuwen also studied the system
a₁^k + a₂^k + a₃^k+ a₄^k = b₁^k + b₂^k + b₃^k + b₄^k = c₁^k + c₂^k + c₃^k + c₄^k
( k = 1, 2, 4 )
and obtained the following solutions:
• [ 14, 37, 39, 64 ] = [ 16, 29, 46, 63 ] = [ 19, 24, 49, 62 ]
• [ 19, 68, 83, 129 ] = [ 27, 47, 101, 124 ] = [ 29, 44, 103 , 123 ]
• [ 3, 89, 97, 166 ] = [ 11, 58, 127, 159 ] = [ 13, 54, 131, 157 ]