Equal Sums of Like Powers

Non-negative Integer Solutions of

• During 1750-1751, Goldbach and Euler had studied this system.[2] [9]
• The general solutions are easy to obtain. [2] [5]
• [ 0, 3, 3 ] = [ 1, 1, 4 ]
• [ 0, 4, 5 ] = [ 1, 2, 6 ]
• [ 0, 7, 7 ] = [ 1, 4, 9 ]
• [ t + mn, t + pq, t + mp + nq ] = [ t + mp, t + nq, t + mn + pq ]
• Solution chain of this system was obtained by A.Golden in 1940's. [3] [5]
• [ 1, 17, 18 ] = [ 6, 7, 23 ] = [ 2, 13, 21 ] = [ 3, 11, 22 ]
• [ 1, 17, 18 ] = [ 6, 7, 23 ]              ( Symmetric )
• [ 2, 13, 21 ] = [ 3, 11, 22 ]            ( Symmetric )
• [ 6, 7, 23 ] = [ 2, 13, 21 ]              ( Non-symmetric )
• [ 6, 7, 23 ] = [ 3, 11, 22 ]              ( Non-symmetric )
• [ 1, 17, 18 ] = [ 2, 13, 21 ]            ( Non-symmetric )
• [ 1, 17, 18 ] = [ 3, 11, 22 ]            ( Non-symmetric )
• [ 0, 71, 73 ] = [ 1, 63, 80 ] = [ 3, 56, 85 ] = [ 5, 51, 88] = [ 8, 45, 91] = [ 11, 40, 93 ] = [ 16, 33, 95 ] = [23, 25, 96 ]