`Equal Sums of Like Powers`

Non-negative Integer Solutions of

a₁^k + a₂^k + a₃^k+ a₄^k+ a₅^k+ a₆^k = b₁^k + b₂^k + b₃^k + b₄^k + b₅^k + b₆^k

( k = 1, 2, 3, 4, 6 )

Chen Shuwen Studied this type since 1995. He found a method to solve this system and obtained the following examples.

[ 116, 166, 206, 331, 336, 411 ] = [ 131, 136, 236, 291, 366, 406 ]

This one is the first solution obtained by Chen in 1995. ( It took a 386SX/33 PC run one night.)

[ 11, 23, 24, 47, 64, 70 ] = [ 14, 15, 31, 44, 67, 68 ]
[ 42, 48, 59, 74, 76, 85 ] = [ 43, 46, 62, 69, 80, 84 ]
[ 23, 31, 60, 80, 91, 103 ] = [ 25, 28, 65, 73, 96, 101 ]
[ 19 , 29 , 89 , 123 , 127 , 152 ] = [ 23 , 24 , 97 , 107 , 139 , 149 ]
[ 73 , 85 , 116 , 146 , 147 , 164 ] = [ 74 , 83 , 120 , 136 , 157 , 161 ]

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