Question

Prove that $F^3_n \mid F_{mn} - F^m_{n + 1} + F^m_{n - 1} (m, n \in \mathbb N, m, n \ge 1)$.

score 110 · Answer 1 · 2019-09-01 04:01:45

110

Views

Prove that $F^3_n \mid F_{mn} - F^m_{n + 1} + F^m_{n - 1} (m, n \in \mathbb N, m, n \ge 1)$.

Published on 01 Sep 2019 - 4:01

score 296 · Answer 2 · 2026-03-25 11:06:57

296

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Does a spiral generated using Fibonacci squares do a good job of approximating a Golden Spiral?

Published on 25 Mar 2026 - 11:06

score 400 · Answer 3 · 2019-09-05 19:04:17

400

Views

Fibonacci number vector space

Published on 05 Sep 2019 - 19:04

score 591 · Answer 4 · 2019-09-05 19:59:50

591

Views

Need help figure out a Fibonacci related math trick

Published on 05 Sep 2019 - 19:59

score 55 · Answer 5 · 2019-09-11 22:21:52

Prove that $a_1 ≤ a_3 ≤ \cdots ≤ a_{2n+1} ≤ a_{2n} ≤ a_{2n-2} ≤ \cdots ≤ a_2$ where $a_i=f_{i+1}/f_i$ and $\{f_i\}$ is the Fibonacci sequence

score 38 · Answer 6 · 2019-09-14 17:41:31

38

Views

Sum of $1/f_{2^k}$

Published on 14 Sep 2019 - 17:41

score 128 · Answer 7 · 2026-03-26 07:34:48

128

Views

Primality test $n \mid F_{n+1}+F_{n-1}-1$

Published on 26 Mar 2026 - 7:34

score 73 · Answer 8 · 2019-09-17 13:31:26

73

Views

What will be the formula to find how many Fibonacci terms are there below a given no., $n$?

Published on 17 Sep 2019 - 13:31

score 108 · Answer 9 · 2019-09-17 19:18:07

108

Views

Why does this alternate Fibonacci relation appear to be true?

Published on 17 Sep 2019 - 19:18

score 58 · Answer 10 · 2019-09-18 06:25:47

58

Views

Then $F_a$ divides $F_{an}$, $n \in \Bbb{N}$ where $F_i$ denotes the $i$-th Fibonacci number.

Published on 18 Sep 2019 - 6:25

score 76 · Answer 11 · 2019-09-24 17:18:58

76

Views

Show $f_n^2+2f_{n-1}f_n = f_{2n}$

Published on 24 Sep 2019 - 17:18

score 110 · Answer 12 · 2019-09-25 20:35:34

110

Views

How is $ F(2,m) = \langle a_1, a_2,\ldots, a_m \mid a_i a_{i+1} = a_{i+2} \rangle $ a group?

Published on 25 Sep 2019 - 20:35

score 101 · Answer 13 · 2019-09-26 13:48:20

101

Views

Proof of the identity $F_{(n+1)k}=\frac{F_{2k}}{F_k}F_{nk}+(-1)^{k+1}F_{(n-1)k}\quad\forall k,n\in\mathbb{N}$

Published on 26 Sep 2019 - 13:48

score 160 · Answer 14 · 2014-03-12 20:52:34

160

Views

Generalisation of Fibonacci

Published on 12 Mar 2014 - 20:52

score 156 · Answer 15 · 2014-03-12 21:21:30

156

Views

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

Published on 12 Mar 2014 - 21:21

List Question

Prove that $F^3_n \mid F_{mn} - F^m_{n + 1} + F^m_{n - 1} (m, n \in \mathbb N, m, n \ge 1)$.

Does a spiral generated using Fibonacci squares do a good job of approximating a Golden Spiral?

Fibonacci number vector space

Need help figure out a Fibonacci related math trick

Prove that $a_1 ≤ a_3 ≤ \cdots ≤ a_{2n+1} ≤ a_{2n} ≤ a_{2n-2} ≤ \cdots ≤ a_2$ where $a_i=f_{i+1}/f_i$ and $\{f_i\}$ is the Fibonacci sequence

Sum of $1/f_{2^k}$

Primality test $n \mid F_{n+1}+F_{n-1}-1$

What will be the formula to find how many Fibonacci terms are there below a given no., $n$?

Why does this alternate Fibonacci relation appear to be true?

Then $F_a$ divides $F_{an}$, $n \in \Bbb{N}$ where $F_i$ denotes the $i$-th Fibonacci number.

Show $f_n^2+2f_{n-1}f_n = f_{2n}$

How is $ F(2,m) = \langle a_1, a_2,\ldots, a_m \mid a_i a_{i+1} = a_{i+2} \rangle $ a group?

Proof of the identity $F_{(n+1)k}=\frac{F_{2k}}{F_k}F_{nk}+(-1)^{k+1}F_{(n-1)k}\quad\forall k,n\in\mathbb{N}$

Generalisation of Fibonacci

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

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