# Equal Sums of Like Powers

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

a1k + a2k + ... + an+2k = b1k + b2k + ... + bn+2k      ( k = k1 , k2 , ... , kn )

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 ]
• ( 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 ]
• ( 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.