`Equal Sums of Like Powers`

Integer Solutions of

a₁^h + a₂^h + a₃^h + a₄^h = b₁^h + b₂^h + b₃^h + b₄^h

( h = 1, 2, 4, 6 )

G.Palama gave a solution of this system in 1953.[19] .

[ -5, -14, 23, 24 ] = [ -16, -2, 21, 25 ]

Chen Shuwen obtained a parameter solution of this type based on Crussol's method for the system ( k =2, 4, 6 ) [9].Numerical examples are

[ -43, -1, 49, 72 ] = [ -27, -23, 56, 71 ]
[ -70, -13, 96, 127 ] = [ -47, -42, 104, 125 ]
[ -107, -21, 116, 145 ] = [ -131, 31, 93, 140 ]
[ -41, 5, 23, 48 ] = [ -43, 15, 16, 47 ]

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