`Equal Sums of Like Powers`

Non-negative integer solutions of the m=n+2 case

a₁^k + a₂^k + ... + a_n₊₂^k = b₁^k + b₂^k + ... + b_n₊₂^k ( k = k₁ , k₂ , ... , k_n )

To the following types, non-negative integer solutions have not been found when m=n+1, but for the m=n+2 case, we have some results.

( k = 5 )

[ 26, 85, 118 ] = [ 53, 90, 116 ] [11]
[ 0, 220, 14132 ] = [ 5027, 6237, 14068 ]

This solution is found by Bob Scher and Ed Seidl using computer in 1997. ( See Massively Parallel Number Theory )

( k = 6 )

[ 25, 62, 138 ] = [ 82, 92, 135 ] [11]

( k = 3, 4 )

[ 2, 21, 28, 37 ] = [ 11, 16, 31, 36 ]
[ 6, 35, 67, 86 ] = [ 9, 22, 77, 80 ]

This two solutions are found by Chen Shuwen using a PC in 1995.

( k = 1, 3, 7 )

[ 2, 8, 27, 39, 43 ] = [ 4, 5, 30, 36, 44 ] [11]

( k = 2, 4, 8 )

[ 25, 33, 79, 92, 116 ] = [ 31, 44, 60, 103, 113 ]

Chen Shuwen find it from the results of (8,5,5) in Randy L. Ekl's article.

( k = 1, 3, 5, 7, 9 )

[ 1, 13, 25, 55, 75, 87, 97 ] = [ 7, 11, 19, 61, 69, 91, 93 ]

This solution is obtained by Chen Shuwen in 1992.

( k = 2, 4, 6, 8, 10 )

[ 1, 28, 31, 32, 55, 61, 68 ] = [ 17, 20, 23, 44, 49, 64, 67 ] [13]

A.Moessner discovered it in 1939.

Last revised Augest 16, 1999.
Copyright 1997-1999, Chen Shuwen