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 Make A Fib (Posted on 2010-07-09)
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

 No Solution Yet Submitted by Larry No Rating

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 Solution | Comment 1 of 8
`It can be constructed. The example in the problem givesit all.F(n)=F(n-1)+F(n-2)F(n) ≥ F(n-2)*2 + 1 for F(n) > 1So, 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)*..........=0The only case this fails when summing to 3 using 7 5sin 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

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