Non-negative Integer
Solutions of
a1k
+ a2k + a3k+
a4k+ a5k
= b1k + b2k
+ b3k + b4k
+ b5k
( k = 1, 2, 3, 5 )
- The first known solutions of this type was obtained
by Chen Shuwen in 1995.
- [ 12, 25, 55, 55, 73] = [ 13, 31, 43, 67, 69
]
- Smallest solutions can be easily found by directly
computer searching.
- [ 1, 8, 13, 24, 27 ] = [ 3, 4, 17, 21, 28 ]
- [ 1, 17, 20, 42, 42 ] = [ 2, 12, 26, 37, 45 ]
- [ 11, 24, 36, 52, 53 ] = [ 12, 21, 43, 44, 56
]
- [ 5, 17, 35, 55, 55 ] = [ 7, 13, 41, 47, 59 ]
- [ 3, 14, 34, 51, 57 ] = [ 6, 9, 42, 43, 59 ]
- Chen Shuwen gave a parametric solution of this
type in 1995. Numerical examples are
- [ 829, 877, 887, 971, 1003 ] = [ 841, 847, 913,
959, 1007 ]
- [ 719, 879, 1039, 1409, 1249 ] = [ 739, 829,
1109, 1199, 1419 ]
Last revised March,31, 2001.
Copyright 1997-2001, Chen Shuwen