List questions from fibonacci-numbers

247

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Without resorting to induction show that $L_n^2=L_{n+1}L_{n-1}+5(-1)^n$,Where $L_n$ is $n^{th}$ Lucas number.

Published on 22 Mar 2026 - 16:05

86

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How many ways can dominoes cover a $2 \times n$ rectangle? Justify proposed solution.

Published on 25 Mar 2026 - 3:07

75

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Closed Form Equation for Finding Roots of Fibonacci Series Given Any Two Consecutive Numbers in that Series

Published on 25 Mar 2026 - 8:10

211

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Fibonacci numbers proof

Published on 18 May 2018 - 15:21

64

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Stuck Simplifying for a Fibonacci Series

Published on 25 Mar 2026 - 8:07

82

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Prove that $9\vert F_{n+24}$ iff $9\vert F_n$.

Published on 20 May 2018 - 10:26

37

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If $F_n<a<F_{n+1}<b<F_{n+2}$ for $n\ge4$,establish that the sum $a+b$ cannot be a Fibonacci number

Published on 20 May 2018 - 11:06

182

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An equation for Fibonacci numbers

Published on 20 May 2018 - 12:40

145

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Use induction to show that $F_{2n} \equiv n(-1)^{n + 1} \pmod 5 \forall n \ge 1$

Published on 20 May 2018 - 23:44

777

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Experimental identities with Fibonacci series

Published on 24 May 2018 - 11:23

186

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Showing $ F_{n}=\sum_{k=0}^n\binom{n}{k}F_{k}(-1)^{k+1}$ without Binet's formula

Published on 24 May 2018 - 20:06

168

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Is the Fibonacci sequence the only increasing strong divisibility sequence such that u_0=0 and u_1=1?

Published on 28 May 2018 - 13:46

580

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Recurrences for even and odd indexed of Fibonacci Numbers

Published on 03 Jun 2018 - 10:45

991

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Generating Function for even and odd Fibonacci Numbers, Missing Steps

Published on 03 Jun 2018 - 11:37

90

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Every $k$th Fibonacci generating function

Published on 03 Jun 2018 - 17:23

List Question

Without resorting to induction show that $L_n^2=L_{n+1}L_{n-1}+5(-1)^n$,Where $L_n$ is $n^{th}$ Lucas number.

How many ways can dominoes cover a $2 \times n$ rectangle? Justify proposed solution.

Closed Form Equation for Finding Roots of Fibonacci Series Given Any Two Consecutive Numbers in that Series

Fibonacci numbers proof

Stuck Simplifying for a Fibonacci Series

Prove that $9\vert F_{n+24}$ iff $9\vert F_n$.

If $F_n<a<F_{n+1}<b<F_{n+2}$ for $n\ge4$,establish that the sum $a+b$ cannot be a Fibonacci number

An equation for Fibonacci numbers

Use induction to show that $F_{2n} \equiv n(-1)^{n + 1} \pmod 5 \forall n \ge 1$

Experimental identities with Fibonacci series

Showing $ F_{n}=\sum_{k=0}^n\binom{n}{k}F_{k}(-1)^{k+1}$ without Binet's formula

Is the Fibonacci sequence the only increasing strong divisibility sequence such that u_0=0 and u_1=1?

Recurrences for even and odd indexed of Fibonacci Numbers

Generating Function for even and odd Fibonacci Numbers, Missing Steps

Every $k$th Fibonacci generating function

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