We have discussed different methods to find nth Fibonacci Number.

Following is another mathematically correct way to find the same.

nth Fibonacci Number :

Here φ is golden ratio with value as

The above formula seems to be good for finding nth Fibonacci Number in O(Logn) time as integer power of a number can be calculated in O(Logn) time. But this solution doesn’t work practically because φ is stored as a floating point number and when we calculate powers of φ, important bits may be lost in the process and we may get incorrect answer.

**References:**

https://www.youtube.com/watch?v=-EQTVuAhSFY

http://en.wikipedia.org/wiki/Fibonacci_number

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.