Non-negative Integer
Solutions of
a1k
+ a2k + a3k+
a4k+ a5k
= b1k + b2k
+ b3k + b4k
+ b5k
( k = 1, 2, 4, 6)
- Only one solution, which was found by G.Palama
in 1953, seem to have appeared in the literature.[19]
- [ 3, 7, 10, 16, 16 ] = [ 4, 5, 12, 14, 17 ]
- How Palama obtained this solution is unknown.
- Chen Shuwen obtained a parameter solution of
this type in 1994.Numerical Examples are
- [ 7, 44, 48, 79, 90 ] = [ 9, 33, 64, 70, 92 ]
- [ 10, 46, 48, 83, 91 ] = [ 13, 32, 69, 70, 94
]
- [ 13, 50, 56, 95, 102 ] = [ 17, 35, 78, 80, 106
]
- Chen Shuwen made a computer search in 1997 and
obtained the smallest solutions.
- [ 3, 7, 10, 16, 16 ] = [ 4, 5, 12, 14, 17 ]
- [ 1, 19, 22, 37, 42 ] = [ 2, 14, 29, 33, 43 ]
- [ 17, 26, 31, 42, 45 ] = [ 18, 23, 35, 39, 46
]
- [ 13, 25, 32, 48, 50 ] = [ 15, 20, 38, 43, 52
]
Last revised March,31, 2001.
Copyright 1997-2001, Chen Shuwen