Question

Proving the Fibonacci identity $(−1)^{m−k}(F_{m+k+1}F_{m−k−1}−F_{m+k}F_{m−k}) =F_{k}^2+F_{k+1}^2$

score 313 · Answer 1 · 2019-01-04 12:40:18

313

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Proving the Fibonacci identity $(−1)^{m−k}(F_{m+k+1}F_{m−k−1}−F_{m+k}F_{m−k}) =F_{k}^2+F_{k+1}^2$

Published on 04 Jan 2019 - 12:40

score 81 · Answer 2 · 2019-01-07 17:53:39

81

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Generating function for Fibonacci-like sequence

Published on 07 Jan 2019 - 17:53

score 497 · Answer 3 · 2019-01-07 23:36:19

497

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Prove Fibonacci Sequence Property: $x^2_n + x^2_{n+1}=x_{2n+1}$

Published on 07 Jan 2019 - 23:36

score 145 · Answer 4 · 2019-01-10 00:06:21

145

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Given a Fibonacci number, find what number in the sequence it is

Published on 10 Jan 2019 - 0:06

score 106 · Answer 5 · 2019-01-11 02:02:47

106

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Prove $F(n+2) - 1 = 1 + n(h-1) + n(h-2)$ by mathematical induction

Published on 11 Jan 2019 - 2:02

score 203 · Answer 6 · 2019-01-11 21:15:28

203

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Calculating how many 2's appear in the last digits of the first 2004 Fibonacci numbers.

Published on 11 Jan 2019 - 21:15

score 41 · Answer 7 · 2019-01-12 14:35:08

41

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How to show this inequality involving generalized Fibonacci sequence?

Published on 12 Jan 2019 - 14:35

score 126 · Answer 8 · 2026-03-25 20:27:40

126

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Show that $F_{3n} = F_{n}(L_{2n} + (-1)^n)$

Published on 25 Mar 2026 - 20:27

score 85 · Answer 9 · 2019-01-16 18:42:34

85

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Formula for the Tribonacci sequence

Published on 16 Jan 2019 - 18:42

score 239 · Answer 10 · 2019-01-16 23:01:04

239

Views

Asymptotic for general Fibonacci sequence.

Published on 16 Jan 2019 - 23:01

score 182 · Answer 11 · 2026-03-25 07:16:37

182

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Have I discovered a new significance to a previously discovered constant?

Published on 25 Mar 2026 - 7:16

score 162 · Answer 12 · 2026-03-25 06:06:26

162

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Are all Fibonacci words uniquely represented as concatenation of two palindromes?

Published on 25 Mar 2026 - 6:06

score 472 · Answer 13 · 2019-01-20 14:35:37

472

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Proving that there are infinitely-many prime numbers that are not Fibonacci numbers

Published on 20 Jan 2019 - 14:35

score 114 · Answer 14 · 2019-01-23 01:46:52

114

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Let $(F_n)_{n\in \mathbb{N}}$ be the Fibonacci sequence. Prove that $F_{n+1}F_n - F_{n-1}F_{n-2} = F_{2n-1}$.

Published on 23 Jan 2019 - 1:46

score 87 · Answer 15 · 2019-01-24 01:52:51

87

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Fibonacci inequality proved by induction.

Published on 24 Jan 2019 - 1:52

List Question

Proving the Fibonacci identity $(−1)^{m−k}(F_{m+k+1}F_{m−k−1}−F_{m+k}F_{m−k}) =F_{k}^2+F_{k+1}^2$

Generating function for Fibonacci-like sequence

Prove Fibonacci Sequence Property: $x^2_n + x^2_{n+1}=x_{2n+1}$

Given a Fibonacci number, find what number in the sequence it is

Prove $F(n+2) - 1 = 1 + n(h-1) + n(h-2)$ by mathematical induction

Calculating how many 2's appear in the last digits of the first 2004 Fibonacci numbers.

How to show this inequality involving generalized Fibonacci sequence?

Show that $F_{3n} = F_{n}(L_{2n} + (-1)^n)$

Formula for the Tribonacci sequence

Asymptotic for general Fibonacci sequence.

Have I discovered a new significance to a previously discovered constant?

Are all Fibonacci words uniquely represented as concatenation of two palindromes?

Proving that there are infinitely-many prime numbers that are not Fibonacci numbers

Let $(F_n)_{n\in \mathbb{N}}$ be the Fibonacci sequence. Prove that $F_{n+1}F_n - F_{n-1}F_{n-2} = F_{2n-1}$.

Fibonacci inequality proved by induction.

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