# Fibonacci Numbers - out of curiousity

1. Apr 5, 2010

### icystrike

This are some fibonacci numbers:

0,1,1,2,3,5,...

Such that

with seed values

Find the greatest integer n that satisfy the below equation.
p.s : That should be a + instead of -

#### Attached Files:

• ###### eqn.jpg
File size:
8.2 KB
Views:
207
Last edited by a moderator: May 4, 2017
2. Apr 5, 2010

### Max Faust

Shouldn't those more appropriately be called the Pingala numbers?

3. Apr 5, 2010

### icystrike

hmm.. would you tell me moer about it?
I was just trying to apply what i've learned in introductory number theory , linear algebra and calculus into fibonacci numbers...

4. Apr 5, 2010

### Max Faust

I seem to remember somebody telling me that Fibonacci published his "Liber Abaci" in 1202, but that his famous sequence was actually plagiarised form the Indian mathematician Pingala (as was common at that time).

5. Apr 5, 2010

### icystrike

Oh. I didn't know that . I was always been told that the sequence of numbers are called fibonacci numbers. =x Thanks btw

6. Apr 5, 2010

### Staff: Mentor

What's the equation? The attachment is still waiting to be approved.

Last edited by a moderator: May 4, 2017
7. Apr 5, 2010

8. Apr 6, 2010

### icystrike

$$\lfloor\frac{(\frac{(F_{m}}{F_{m-1})^{k}}{2\times\frac{(F_{m}}{F_{m-1})-1}+\frac{1}{2}\rfloor = F_{k}$$

9. Jul 23, 2011

### cubzar

Fn=($\phi$n-(1-$\phi$)n)/$\sqrt{}$5

If Fn=$\left\lfloor$(4/9)(13/8)n-1/2$\right\rfloor$ then 9(Fn-1/2)/4>(13/8)n. Since 13/8>$\phi$, the right hand side increases faster, and the right hand side for n=10 is already greater than the left hand side. 8 and 9 are the only integer solutions.