Equal Sums of Like Powers

Non-negative Integer Solutions of

• This system has been considered by A.Golden (1949) [36], Xeroudakes and Moessner (1958) [17] who have obtained two-parameter solutions and by Lander (1968) [14] who has given three-parameter solutions.Numerical example by these method are
• [ 1, 13, 17, 23 ] = [ 3, 9, 21, 21 ]
• [ 0, 24, 33, 51 ] = [ 7, 13, 38, 50 ]
• In 1991, A.Choudhry obtained a four-parameter solution of this system. [18] Numerical example by his method is
• [ 53, 151, 187, 233] = [ 51, 165, 173, 235]
• Chen Shuwen made a computer search of this system in 1996. Here are the smallest solutions.
• [ 1, 13, 17, 23 ] = [ 3, 9, 21, 21 ]
• [ 6, 16, 18, 24 ] = [ 7, 13, 21, 23 ]
• [ 7, 21, 23, 33 ] = [ 11, 13, 29, 31 ]
• [ 5, 20, 22, 34 ] = [ 9, 12, 27, 33 ]