Results 261 to 270 of about 21,260 (290)

On Fibonacci and Lucas sequences modulo a prime and primality testing

Arab Journal of Mathematical Sciences, 2018
We prove two properties regarding the Fibonacci and Lucas Sequences modulo a prime and use these to generalize the well-known property p∣Fp−p5. We then discuss these results in the context of primality testing.
Dorin Andrica, Fawzi Al-Thukair
exaly   +3 more sources

Some of the next articles are maybe not open access.

Related searches:

On the Completeness of the Lucas Sequence

The Fibonacci Quarterly, 1969
A sequence of positive integers is said to be complete if every positive integer is the sum of a finite number of distinct terms of the sequence. It is well-known that the Lucas sequence \(\{L_j\}\) where \(L_{n+1}=L_n+L_{n-1}\) for \(n>1\) and \(L_0=2\), \(L_1=1\) is complete. In this paper the author proves that if any term \(L_n\), where \(n>1\), is
openaire   +2 more sources

Palindromes in Lucas Sequences

Monatshefte f�r Mathematik, 2003
Say that \(\{w_n\}\) is a Lucas sequence if \(w_{n+2}= rw_{n+1}+sw_n\) where \(s\neq 0\) and \(r^2+4s\neq 0\). An integer is called a palindrome to base \(b\) if the base \(b\) representation of the integer is left unchanged when the digits are reversed. Let \(P(x)\) denote the number of integers \(n\leq x\) such that \(w_n\) is a base \(b\) palindrome.
openaire   +2 more sources

Relationship between Lucas Sequences and Gaussian Integers in Cryptosystems

, 2015
Both Gaussian integers and Lucas sequences have been applied in cryptography. This paper presents the mathematical relationship between Lucas sequences and Gaussian integers.
Aleksey Koval, Koval, Aleksey
exaly   +2 more sources

On the intersection of k-Lucas sequences and some binary sequences

Periodica Mathematica Hungarica, 2021
Lucas sequence \((L_n)\) is determined by \(L_0=2\); \(L_1=1\); \(L_n=L_{n-1}+L_{n-2}\), if \(n\ge 2\). The paper studies \(k\)-generalized \((k\ge 3)\) Lucas sequence. The sequence starts with the \(k\) terms \(0,\dots,0,2, 1\) and each term afterwards is the sum of the \(k\) preceding terms.
Salah Eddine Rihane, Alain Togbé
openaire   +2 more sources

CONGRUENCES CONCERNING LUCAS SEQUENCES

International Journal of Number Theory, 2014
Let p be a prime greater than 3. In this paper, by using expansions and congruences for Lucas sequences and the theory of cubic residues and cubic congruences, we establish some congruences for [Formula: see text] and [Formula: see text] modulo p, where [x] is the greatest integer not exceeding x, and m is a rational p-adic integer with m ≢ 0 ( mod p).
openaire   +1 more source

On k-Lucas sequences

AIP Conference Proceedings, 2014
For positive integers n and k, the k-Lucas sequence is defined by the recurrence relation Ln+1 = kLn+Ln−1 with the initial values L0 = 2, L1 = k. The Lucas sequence and Pell-Lucas sequence are two special cases of the k-Lucas sequence. Using a matrix approach, we uncover some new facts concerning the k-Lucas sequence.
C. K. Ho, Jye-Ying Sia, Chin-Yoon Chong
openaire   +1 more source

Two generalizations of Lucas sequence

Applied Mathematics and Computation, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

ON GENERALIZED LUCAS AND PELL-LUCAS SEQUENCES

2019
In this paper, we define the generaziled Lucas sequences and the Pell-Lucas sequences. Further we give Binet-like formulas, generating function, sums formulas and some important identities which involving the generalized Lucas and Pell-Lucas Numbers.
Tas, Zisan Kusaksiz, TAŞCI, DURSUN
openaire   +1 more source

Notes on the (s, t)-Lucas and Lucas Matrix Sequences.

Ars Comb., 2008
In this article, defining the matrix extensions of the Fibonacci and Lucas numbers we start a new approach to derive formulas for some integer numbers which have appeared, often surprisingly, as answers to intricate problems, in conventional and in recreational Mathematics.
Civciv, Hacı, Türkmen, Ramazan
openaire   +1 more source