Question

Proving Fibonacci Identity

score 88 · Answer 1 · 2018-03-20 07:18:45

88

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Proving Fibonacci Identity

Published on 20 Mar 2018 - 7:18

score 195 · Answer 2 · 2026-03-20 01:00:29

195

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On $3+\sqrt{11+\sqrt{11+\sqrt{11+\sqrt{11+\dots}}}}=\phi^4$ and friends

Published on 20 Mar 2026 - 1:00

score 80 · Answer 3 · 2018-03-23 03:35:27

proving that no positive integer can be written in two different ways as the sum of distinct non-consecutive Fibonacci numbers

score 391 · Answer 4 · 2018-03-23 20:38:01

391

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Prove that $F_{125n}$ is divisible by $125$.

Published on 23 Mar 2018 - 20:38

score 76 · Answer 5 · 2018-03-25 08:32:15

76

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How to prove that the sequence $\ln(F_n)$ isn't on a line?

Published on 25 Mar 2018 - 8:32

score 133 · Answer 6 · 2018-03-25 20:28:53

133

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N-th term of generating function of almost fibonacci sequence

Published on 25 Mar 2018 - 20:28

score 155 · Answer 7 · 2018-03-27 20:29:34

155

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If we have $\gcd(a_n,a_m)=a_{\gcd(n,m)}$ for each pair then $a_1,a_2,...$ is Fibonacci sequence?

Published on 27 Mar 2018 - 20:29

score 146 · Answer 8 · 2018-03-31 00:39:12

146

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Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.

Published on 31 Mar 2018 - 0:39

score 88 · Answer 9 · 2018-03-31 02:43:43

88

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Let $(F_n)_{n \in \mathbb{N}}$ be a Fibonacci sequence , then $(4 \mid n \Leftrightarrow 3 \mid F_n)$ for all $n \in \mathbb{N}$

Published on 31 Mar 2018 - 2:43

score 1k · Answer 10 · 2018-03-31 05:46:15

1k

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exponential generating function - Fibonacci recurrence relation

Published on 31 Mar 2018 - 5:46

score 188 · Answer 11 · 2018-03-31 11:27:10

188

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Is it possible to prove $(m\mid n \iff F_m \mid F_n)$ for a Fibonacci sequence by using only Principle of Strong Induction?

Published on 31 Mar 2018 - 11:27

score 450 · Answer 12 · 2018-04-01 15:58:07

450

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Prove that $\operatorname{fib}(n)$ is the closest integer to $\frac{\phi^{n}}{\sqrt{5}}$

Published on 01 Apr 2018 - 15:58

score 1.1k · Answer 13 · 2018-04-02 03:34:04

1.1k

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For Fibonacci sequence, $f_{m+n+1}=f_m f_n+ f_{m+1}f_{n+1}$ [Proof Verification]

Published on 02 Apr 2018 - 3:34

score 67 · Answer 14 · 2018-04-02 06:27:06

67

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Prove that the Fibonacci numbers obey the identity $\sum_{i=0}^{n} [f(i)]^2=f(n)f(n+1)$ for $n\ge 0$

Published on 02 Apr 2018 - 6:27

score 445 · Answer 15 · 2018-04-03 05:04:34

445

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What connects Fibonacci and Lucas numbers?

Published on 03 Apr 2018 - 5:04

List Question

Proving Fibonacci Identity

On $3+\sqrt{11+\sqrt{11+\sqrt{11+\sqrt{11+\dots}}}}=\phi^4$ and friends

proving that no positive integer can be written in two different ways as the sum of distinct non-consecutive Fibonacci numbers

Prove that $F_{125n}$ is divisible by $125$.

How to prove that the sequence $\ln(F_n)$ isn't on a line?

N-th term of generating function of almost fibonacci sequence

If we have $\gcd(a_n,a_m)=a_{\gcd(n,m)}$ for each pair then $a_1,a_2,...$ is Fibonacci sequence?

Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.

Let $(F_n)_{n \in \mathbb{N}}$ be a Fibonacci sequence , then $(4 \mid n \Leftrightarrow 3 \mid F_n)$ for all $n \in \mathbb{N}$

exponential generating function - Fibonacci recurrence relation

Is it possible to prove $(m\mid n \iff F_m \mid F_n)$ for a Fibonacci sequence by using only Principle of Strong Induction?

Prove that $\operatorname{fib}(n)$ is the closest integer to $\frac{\phi^{n}}{\sqrt{5}}$

For Fibonacci sequence, $f_{m+n+1}=f_m f_n+ f_{m+1}f_{n+1}$ [Proof Verification]

Prove that the Fibonacci numbers obey the identity $\sum_{i=0}^{n} [f(i)]^2=f(n)f(n+1)$ for $n\ge 0$

What connects Fibonacci and Lucas numbers?

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