Equal Sums of Like Powers

Non-negative Integer Solutions of

• L.E.Dickson gave the general solution for this system in 1910's.[7] [9] Numerial exampls are
• [ 0, 4, 7, 11 ] = [ 1, 2, 9, 10 ]
• [ 1, 8, 10, 17 ] = [ 2, 5, 13, 16 ]
• [ 0, 9, 11, 22 ] = [ 2, 4, 15, 21 ]
• Method for symmetric solution chain of this type was obtained by A.Golden in 1940's.[5] [3]
• [ 1, 79, 105, 183 ] = [ 3, 69, 115, 181 ] = [ 7, 57, 127, 177 ] = [ 13, 45, 139, 171 ] = [ 27, 27, 157, 157 ]
• Non-symmetric solution chain of this type was first obtained by Chen Shuwen in 1997.
• [ 0, 87, 93, 214 ] = [ 9, 52, 123, 210 ] = [ 24, 30, 133, 207 ]