Question

Proving Fibonacci Identity

score 93 · Answer 1 · 2026-04-11 06:14:07

93

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Proving Fibonacci Identity

Published on 11 Apr 2026 - 6:14

score 202 · Answer 2 · 2026-05-02 05:19:11

202

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

Published on 02 May 2026 - 5:19

score 83 · Answer 3 · 2026-04-11 00:00:35

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

score 394 · Answer 4 · 2026-04-14 00:30:05

394

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

Published on 14 Apr 2026 - 0:30

score 79 · Answer 5 · 2026-04-15 17:48:57

79

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

Published on 15 Apr 2026 - 17:48

score 136 · Answer 6 · 2026-04-10 10:46:54

136

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N-th term of generating function of almost fibonacci sequence

Published on 10 Apr 2026 - 10:46

score 158 · Answer 7 · 2026-04-15 23:25:04

158

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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 15 Apr 2026 - 23:25

score 149 · Answer 8 · 2026-04-15 21:07:15

149

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

Published on 15 Apr 2026 - 21:07

score 91 · Answer 9 · 2026-04-17 23:58:30

91

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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 17 Apr 2026 - 23:58

score 1k · Answer 10 · 2026-04-10 17:51:48

1k

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exponential generating function - Fibonacci recurrence relation

Published on 10 Apr 2026 - 17:51

score 190 · Answer 11 · 2026-04-14 00:31:11

190

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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 14 Apr 2026 - 0:31

score 454 · Answer 12 · 2026-05-10 12:42:51

454

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

Published on 10 May 2026 - 12:42

score 1.1k · Answer 13 · 2026-04-15 21:18:04

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 15 Apr 2026 - 21:18

score 70 · Answer 14 · 2026-04-17 01:23:13

70

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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 17 Apr 2026 - 1:23

score 449 · Answer 15 · 2026-04-10 02:24:16

449

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What connects Fibonacci and Lucas numbers?

Published on 10 Apr 2026 - 2:24

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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