Equal Sums of Like Powers

Non-negative Integer Solutions of

• Solutions of this type is obvious.
• [ 0, 2 ] = [ 1, 1 ]
• [ 1, 4 ] = [ 2, 3 ]
• [ 0, 7 ] = [ 1, 6 ] = [ 2, 5 ] = [ 3, 4 ]
• From 1 + 9 = 4 + 6, applying Theorem 2 successively with T = 2, 1, 7, 8, 13, 11, we have, respectively[2]
• [ 1, 8, 9 ] = [ 3, 4 11 ]     ( k = 1, 2 )
• [ 1, 5, 8, 12 ] = [ 2, 3, 10, 11 ]    ( k = 1, 2, 3 )
• [ 1, 5, 9, 17, 18 ] = [ 2, 3, 11, 15, 19]    ( k = 1, 2, 3, 4 )
• [ 1, 5, 10, 18, 23, 27 ] = [ 2, 3, 13, 15, 25, 26 ]    ( k = 1, 2, 3, 4, 5 )
• [ 1, 5, 10, 16, 27, 28, 38, 39 ] = [ 2, 3, 13, 14, 25, 31, 36, 40 ]    ( k = 1, 2, 3, 4, 5, 6 )
• [ 1, 5, 10, 24, 28, 42, 47, 51 ] = [ 2, 3, 12, 21, 31, 40, 49, 50 ]    ( k = 1, 2, 3, 4, 5, 6, 7 )