`Equal Sums of Like Powers`

Non-negative Integer Solutions of

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

( k = 2, 4, 6 )

Parametric solutions of this system were obtained by Crussol in 1913 [9] and J.Chernick in 1913 [7] . Numerical examples are :

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

[ 7, 24, 25, 34 ] = [ 14, 15, 31, 32 ]
[ 7, 31, 36, 50 ] = [ 18, 20, 41, 49 ]
[ 9, 47, 49, 67 ] = [ 23, 31, 61, 63 ]

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