Prove whether or not any Fibonacci number, F(n), can be constructed by using
F(n) F(n-1)'s and the operators +,-,*,/
(Provided that F(n-1)>0 )
For example I can make a 5 using 5 3's: 3 + 3/3 + 3/3

It can be constructed. The example in the problem gives
it all.
F(n)=F(n-1)+F(n-2)

F(n) ≥ F(n-2)*2 + 1 for F(n) > 1

So, produce F(n-2)
=F(n-1)/F(n-1)+F(n-1)/F(n-1)+............

remaining F(n-1)s to produce 0.

{F(n-1)-F(n-1)}*F(n-1)*F(n-1)*..........=0

The only case this fails when summing to 3 using 7 5s

in that case 3 = 5 - 5/5 - 5/5 + 5 - 5

Edited on July 10, 2010, 1:31 am

Posted by Praneeth on 2010-07-09 18:12:10