2
votes
1answer
52 views

What's the Lucas version of the Möbius test for Fibonacci numbers?

I recently came across the following, attributed to Möbius: $$(a\in\mathbb N)=F_n\iff\left[\varphi a-\tfrac{1}{a},\varphi a+\tfrac{1}{a}\right]\ni(b\in\mathbb N)$$ It is the lesser-known test used to ...
2
votes
2answers
82 views

How do I apply the $\pm4$ part of the equation $5F_n^2\pm~4=L_n^2$ without knowing $n$?

I'm trying to test a great many numbers $a^3+b^3$ to see if any of them are Fibonacci using the formula $$a^3+b^3=F_n \iff 5(a^3+b^3)^2\pm~4=L_n^2$$ I want to make my search more efficient by having ...
0
votes
1answer
39 views

Understanding Recursive algorithm using FIB

I am studying for an exam, and I came across this question, I think I got the answer correct, just need some validation. ...
1
vote
1answer
38 views

How do I calculate the number of members in a limited Fibonacci series? [duplicate]

Looking for an algorithm that will give me the number of members that will result from calculating a Fibonacci series, given a particular limit. For example, if I start the series at 1 and limit my ...
1
vote
1answer
123 views

Calculate Number of ways to make the grid

We wish to tile a grid of size Nx2 with rectangles (dominoes) of 2x1 (in either orientation).For given N I need to find the number of different ways to tile the grid. EXAMPLE : For N=1 answer is 1 ...
6
votes
5answers
279 views

Fibonacci-like sequence

Today I have to deal with something which reminds Fibonacci sequence. Let's say I have a certain number k, which is n-th number of certain sequence. This sequence however is created by recursive ...
1
vote
1answer
128 views

Register Machine on Fibonacci Numbers

This problem is easy to understand but I am struggling to come up with any solutions. According to Wikipedia a register machine is a generic class of abstract machines used in a manner similar to a ...
1
vote
0answers
112 views

Is this “Elegant” algorithm for logarithm by Zeckendorf representation, the same as an 'efficient' algorithm?

The algorithm here which computes the exponent $b$ given a base $a$, and given $n$ = $a$^$b$, appears no better to me than simply counting the number of times we divide $n$ through by the base $a$ ...
3
votes
5answers
218 views

Translating matrix fibonacci into c++ (how can we determine if a number is fibonacci?)

Is it possible to determine if a number is a fibonacci number in less than N time (where N is the Nth fibonacci number) using the matrix method? I'm trying to exclude external libraries like cmath or ...
5
votes
2answers
392 views

Computing nth term of fibonacci-like sequence for large n

Sum up to nth term of fibonacci sequence for very large n can be calculated in O($\log n$) time using the following approach: $$A = \begin{bmatrix} 1&1 \\\\1&0\end{bmatrix}^n$$ ...
0
votes
1answer
1k views

How to solve tribonacci series [duplicate]

Possible Duplicate: Fibonacci, tribonacci and other similar sequences Suppose my Tribonacci series is like this: \begin{equation} T(n) = T(n-1) + T(n-2) +T(n-3) \end{equation} with initial ...
1
vote
1answer
1k views

Smallest Fibonacci number having a common factor with a given number

We have a number $k$ and we have to find the smallest Fibonacci number that has common factor with it(except $1$). We also have $2 \leq k \leq 1,000,000$. The required Fibonacci number is guaranteed ...
4
votes
1answer
458 views

Finding the smallest prime number that divides $Fib(n)$ but not any other $Fib(k)$ smaller than $Fib(n)$

Let $F(n)$ be $n$-th Fibonacci number.$$F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 2, F(4) = 3 \text{ and so on. }$$Given a positive integer $n \gt 2$,Find the smallest prime number $P$ such that $P$ ...
2
votes
2answers
1k views

Finding index of a Fibonacci number: any mathematical solution possible?

The problem: Given a Fibonacci number,find its index. I am aware of the standard solution 'generate-hash-find'. I am just curious if there is ...