# Equal Sums of Like Powers

## Non-negative Integer Solutions of

a1k + a2k + a3k = b1k + b2k + b3k
( k = 2, 6 )
• The first nontrivial solution was given in 1934 by Subba-Rao.  
• [ 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. 
• [ 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 
• Simcha Brundo in 1970 
• Simcha Brundo and Irving Kaplansky in 1974 
• Simcha Brundo in 1976 
• Andrew Bremner in 1979 
• J .Delorme in 1990 

Last revised March,31, 2001.
Copyright 1997-2001, Chen Shuwen