Given a finite set of real numbers A, not containing 0 and 1 and possessing the property: if the number a belongs to A, then numbers 1/a and 1-a also belong to A. How many numbers are in the set A?
(In reply to
Partial solution? by tomarken)
I think you have the full solution.
Here's a graph showing the relation among groups that must be in the set.
https://www.desmos.com/calculator/5snqqdthky
There's a slider for n and I plotted the six functions. You can see the vertical line passes through all six functions except at the unallowed {0,1} and the set of three {2,-1,0.5} where the functions intersect in pairs.
I suppose the answer to how many number are in set A is: any multiple of 3.
|
|
Posted by Jer
on 2021-04-19 13:29:17 |
re: Partial solution?
