Equal Sums of Like Powers

Non-negative Integer Solutions of

• The first nontrivial solution was given in 1934 by Subba-Rao. [3] [31]
• [ 3, 19, 22 ] = [ 10, 15, 23 ]
• In 1967, L.J.Lander, T.R.Parkin and J.L.Selfridge made a computer search using CDC6600 to the following Diophantine equation in least integers
a₁⁶ + a₂⁶ + a₃⁶ = b₁⁶ + b₂⁶ + b₃⁶
They found 10 primitive solutions of which 9 solutions were also satisfy the additional equality
a₁² + a₂² + a₃² = b₁² + b₂² + b₃²
Here are the primitive solutions in least integers by their computer search. [11]
• [ 3, 19, 22 ] = [ 10, 15, 23 ]
• [ 15, 52, 65 ] = [ 36, 37, 67 ]
• [ 23, 54, 73 ] = [ 33, 47, 74 ]
• [ 11, 65, 78 ] = [ 37, 50, 81 ]
• [ 3, 55, 80 ] = [ 32, 43, 81 ]
• Parametric solutions of this system were obtained by
• Simcha Brundo in 1968 [30]
• Simcha Brundo in 1970 [29]
• Simcha Brundo and Irving Kaplansky in 1974 [26]
• Simcha Brundo in 1976 [27]
• Andrew Bremner in 1979 [28]
• J .Delorme in 1990 [15]