Equal Sums of Like Powers

Non-negative Integer Solutions of

• The first known solution is obtained by A.Letac in 1940's.[5] [25]
• [ 12, 11881, 20231, 20885, 23738 ] = [ 436, 11857, 20449, 20667 , 23750 ]
• The second known solution is obtained by G.Palama in 1950[33] and by C.J.Smyth in 1990 independently.[22]
• [ 87647378809, 243086774390, 308520455907, 441746154196, 527907819623 ] = [ 133225698289, 189880696822, 338027122801, 432967471212, 529393533005 ]
• Peter Borwein, Petr Lisonek and Colin Percival found these two smallest solutions by computer search in 2000. _[0201]  
• [ 71, 131, 180, 307, 308 ] = [ 99, 100, 188, 301 , 313 ]
• [ 18, 245, 331, 471, 508 ] = [ 103, 245, 331, 471, 508 ]
• Chen Shuwen found the third smallest solution in 2023 by computer search.
  • [ 498, 3773, 3783, 4567, 4787 ] = [ 517, 3598, 4017, 4463, 4827 ]
• See also ( h = 1, 2, 4, 6, 8 ) for more information.