List questions from lucas-numbers

Published on 23 Apr 2016 - 8:18

750

Views

Proving the closed form of a generating function of the sum of n lucas numbers is equal to the n+2th lucas number

Published on 27 Apr 2016 - 10:31

351

Views

Proofing that the Lucas numbers come closer to the Phi rounded numbers then the Fibonacci numbers.

Published on 29 Apr 2016 - 8:46

281

Views

Prove by induction that $ F_{2n}=F_nL_n $

Published on 18 Mar 2026 - 10:26

89

Views

Lowest bounds of Lucas Numbers

Published on 21 Apr 2013 - 21:57

350

Views

Prove relation between Lucas and Fibonacci numbers using tilings

Published on 05 May 2013 - 16:36

149

Views

Proof Help dealing Lucas and Fibonacci Numbers

Published on 23 Nov 2013 - 3:06

159

Views

Converting Fibonacci number $F_{5n+3}$ to Lucas numbers $L_{n+k}$

Published on 16 Jan 2014 - 14:52

82

Views

Prove that $\gcd(F_{3K},L_{3k}) \equiv 2$

Published on 19 Apr 2017 - 5:08

250

Views

Prove that if $n$ is not a multiple of $3$ then $\gcd(F_n,L_n)=1$

Published on 20 Apr 2017 - 18:34

155

Views

Prove that $L_{6k} \equiv 2$ (mod $4$)

Published on 21 Apr 2017 - 5:59

109

Views

Fibonacci and Lucas linear relation proofs

Published on 03 May 2017 - 15:30

149

Views

Lucas sequence are elliptic sequence?

Published on 25 Jul 2017 - 13:12

60

Views

Gaussian primes and Lucas numbers

Published on 31 Jul 2017 - 23:28

94

Views

Pell-Lucas number

Published on 24 Mar 2026 - 18:45

List Question

Show that $\sum_{k=1}^{\infty}\frac{F_{2^{k-1}}}{L_{2^k}-2}=\frac{15-\sqrt{5}}{10}$

Proving the closed form of a generating function of the sum of n lucas numbers is equal to the n+2th lucas number

Proofing that the Lucas numbers come closer to the Phi rounded numbers then the Fibonacci numbers.

Prove by induction that $ F_{2n}=F_nL_n $

Lowest bounds of Lucas Numbers

Prove relation between Lucas and Fibonacci numbers using tilings

Proof Help dealing Lucas and Fibonacci Numbers

Converting Fibonacci number $F_{5n+3}$ to Lucas numbers $L_{n+k}$

Prove that $\gcd(F_{3K},L_{3k}) \equiv 2$

Prove that if $n$ is not a multiple of $3$ then $\gcd(F_n,L_n)=1$

Prove that $L_{6k} \equiv 2$ (mod $4$)

Fibonacci and Lucas linear relation proofs

Lucas sequence are elliptic sequence?

Gaussian primes and Lucas numbers

Pell-Lucas number

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