# Equal Sums of Like Powers

## Integer Solutions of

a1h + a2h + a3h + a4h+ a5h+ a6h = b1h + b2h + b3h + b4h + b5h+ b6h
( h = 1, 2, 4, 6, 8, 10 )
• Nuutti Kuosa discovered the following solution in 3 Sep1999, using a program written by Jean-Charles Meyrignac.
• Chen Shuwen noticed that the above result is also a solution of ( k = 2, 4, 6, 8, 10 ) .
• [ 22, 61, 86, 127, 140, 151 ] = [ 35, 47, 94, 121, 146, 148 ]
• Using this solution of ( k = 2, 4, 6, 8, 10 ), Chen Shuwen checked all the posible cases in 8 Sep1999, and found the following 7 solutions of ( h = 1, 2, 4, 6, 8, 10 ).
• [ 22, 61, 86, -127, 140, 151 ] = [ -35, 47, -94, 121, 146, 148 ]
• [ 22, 61, -86, -127, 140, 151 ] = [ 35, 47, -94, -121, 146, 148 ]
• [ 22, 61, 86, -127, -140, 151 ] = [ 35, 47, 94, -121, 146, -148 ]
• [ 22, 61, -86, 127, -140, 151 ] = [ -35, -47, 94, 121, -146, 148 ]
• [ 22, -61, 86, 127, -140, 151 ] = [ -35, -47, 94, -121, 146, 148 ]
• [ -22, 61, -86, 127, -140, 151 ] = [ -35, 47, -94, -121, 146, 148 ]
• [ 22, -61, -86, 127, -140, 151 ] = [ 35, -47, -94, 121, 146, -148 ]

Last revised March,31, 2001.