1 Jul
2016
1 Jul
'16
9:27 a.m.
I wrote:
(What if we require all the numbers to be rational? I haven't figured this part out yet.)
It can be done with 4 numbers:
More generally, it can be done with n numbers if and only if n >= 4. Consider: 0: {} 5: {-18, -1/36, 1/36, 6, 12} 6: {-6, -1/6, 1/6, 1, 2, 3} 7: {-63, -2/21, -1/21, -1/42, 1/6, 21, 42} and append k different copies of {-a/b, -b/a, b/a, a/b} to the solution of cardinality n - 4k. Best wishes, Adam P. Goucher