List questions from lucas-numbers

Published on 28 Jun 2021 - 12:28

143

Views

Confusion on the original Lucas test

Published on 05 Jul 2021 - 10:32

186

Views

When is $L_n-1$ a prime?

Published on 11 Sep 2021 - 4:53

71

Views

Does $(L_{p+1}+2)\equiv0 \mod p$ only when $p^2$ have digits in nondecreasing order?

Published on 12 Sep 2021 - 21:10

181

Views

A Lucas sequence

Published on 25 Mar 2026 - 8:22

89

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How to find a complementary subspace for the subspace of sequences where $u_{n+2}=u_{n} + u_{n+1}$, in $\mathbb{R}^\infty$?

Published on 21 Sep 2021 - 16:17

81

Views

How can this relation between Lucas and Fibonacci numbers be proved?

Published on 14 Oct 2021 - 12:54

82

Views

Proof recursion is a subset of Lucas numbers

Published on 20 Oct 2021 - 0:40

195

Views

If $(3p_n\pm \sqrt{5p_n^2-4})\Delta/(2p_n)$ is an integer then $p_n$ is an odd-indexed Fibonacci number

Published on 26 Mar 2026 - 1:47

133

Views

Primality test for numbers of the form $(10^p-1)/9$ (and maybe $((10 \cdot 2^n)^p-1)/(10 \cdot 2^n-1)$)

Published on 23 Feb 2026 - 6:41

266

Views

A pattern of periodic continued fraction

Published on 11 Apr 2022 - 17:15

61

Views

How to prove that $a_{2n} = a_nb_n$ in a Lucas sequence?

Published on 05 May 2022 - 10:56

73

Views

Closed form representation for $\sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n-k}k$

Published on 30 May 2022 - 15:23

87

Views

Generalizing Fibonacci/Lucas-like series' in terms of the Fibonacci Sequence

Published on 11 Jun 2022 - 2:13

53

Views

Lucas numbers relation to Φ

Published on 13 Jun 2022 - 8:08

List Question

What is the fastest method to compute the $nth$ number in Lucas sequences?

Confusion on the original Lucas test

When is $L_n-1$ a prime?

Does $(L_{p+1}+2)\equiv0 \mod p$ only when $p^2$ have digits in nondecreasing order?

A Lucas sequence

How to find a complementary subspace for the subspace of sequences where $u_{n+2}=u_{n} + u_{n+1}$, in $\mathbb{R}^\infty$?

How can this relation between Lucas and Fibonacci numbers be proved?

Proof recursion is a subset of Lucas numbers

If $(3p_n\pm \sqrt{5p_n^2-4})\Delta/(2p_n)$ is an integer then $p_n$ is an odd-indexed Fibonacci number

Primality test for numbers of the form $(10^p-1)/9$ (and maybe $((10 \cdot 2^n)^p-1)/(10 \cdot 2^n-1)$)

A pattern of periodic continued fraction

How to prove that $a_{2n} = a_nb_n$ in a Lucas sequence?

Closed form representation for $\sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n-k}k$

Generalizing Fibonacci/Lucas-like series' in terms of the Fibonacci Sequence

Lucas numbers relation to Φ

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