Equal Sums of Like Powers

Non-negative Integer Solutions of

• Nuutti Kuosa discovered the following solution in 3 Sep1999, using a program written by Jean-Charles Meyrignac.
• 151¹⁰+140¹⁰+127¹⁰+86¹⁰+61¹⁰+22¹⁰=148¹⁰+146¹⁰+121¹⁰+94¹⁰+47¹⁰+35¹⁰
• See Computing Minimal Equal Sums Of Like Powers for detail.
• Chen Shuwen noticed in 7 Sep1999 that the above result is also a solution of ( k = 2, 4, 6, 8, 10 ) .
• [ 22, 61, 86, 127, 140, 151 ] = [ 35, 47, 94, 121, 146, 148 ]
• David Broadhurst found the second solution in 2007._[0701]
  • [ 257, 891, 1109, 1618, 1896, 2058 ] = [ 472, 639, 1294, 1514, 1947, 2037 ]
• In 2008, A.Choudhry and Jaroslaw Wroblewski proved that this system has infinitely many solutions and give a method to produce new numerical solutions. The smallest new solution found by their method is
  • [ 107, 622, 700, 1075, 1138, 1511 ] = [ 293, 413, 886, 953, 1180, 1510 ]
• In 2016, Chen Shuwen found that there is no other new solution in the range of of max {a_i, b_i } <= 1800.
• See also ( k = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ) for more information.