Results 11 to 20 of about 254,556 (238)
On the Diophantine equation x^2+7^{alpha}.11^{beta}=y^n [PDF]
, 2012 In this paper, we give all the solutions of the Diophantine equation x^2+7^{alpha}.11^{beta}=y^n, in nonnegative integers x, y, n>=3 with x and y coprime, except for the case when alpha.x is odd and beta is even.Comment: to appear in Miskolc Mathematical
Soydan, Gokhan
core +2 more sources
Generalized Fibonacci-Lucas Sequence [PDF]
Turkish Journal of Analysis and Number Theory, 2014 The Fibonacci sequence is a source of many nice and interesting identities. A similar interpretation exists for Lucas sequence. The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field.
Bijendra Singh +2 more
openaire +1 more source
A lucas based cryptosystem analog to the ElGamal cryptosystem and elliptic curve cryptosystem [PDF]
, 2014 In this paper, a new cryptosystem will be developed which is analogue to ElGamal encryption scheme and based on Lucas sequence in the elliptic curve group over finite field. In this encryption scheme, an Elliptic curve Diffie-Hellman (ECDH) key agreement
Koo, Lee Feng +3 more
core +1 more source
Binomial Coefficients and Lucas Sequences
Journal of Number Theory, 2002 Let sequences \(\{u_n\}_{n\geq 0}\) and \(\{v_n\}_{n\geq 0}\) be defined by \(u_n= \frac{a^n-b^n}{a-b}\), \(v_n= a^n+b^n\) where \(a,b\) are integers such that \(a>|b|\). (Such sequences are Lucas sequences such that the associated quadratic polynomial has integer roots.
Flammenkamp, Achim, Luca, Florian
openaire +2 more sources
Repdigits in k-Lucas sequences
Proceedings - Mathematical Sciences, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bravo, Jhon J., Luca, Florian
openaire +1 more source
Primitive divisors of Lucas and Lehmer sequences [PDF]
, 1995 Stewart reduced the problem of determining all Lucas and Lehmer sequences whose $n$-th element does not have a primitive divisor to solving certain Thue equations.
Par Paul M Voutier, Paul M. Voutier
core +8 more sources
The GCD Sequences of the Altered Lucas Sequences [PDF]
Annales Mathematicae Silesianae, 2020 Abstract In this study, we give two sequences {L + n}n≥ 1 and {L− n}n≥ 1 derived by altering the Lucas numbers with {±1, ±3}, terms of which are called as altered Lucas numbers.
openaire +3 more sources
The density of numbers $n$ having a prescribed G.C.D. with the $n$th Fibonacci number [PDF]
, 2018 For each positive integer $k$, let $\mathscr{A}_k$ be the set of all positive integers $n$ such that $\gcd(n, F_n) = k$, where $F_n$ denotes the $n$th Fibonacci number.
Sanna, Carlo, Tron, Emanuele
core +5 more sources
Geometric Aspects of Lucas Sequences, I
Tokyo Journal of Mathematics, 2020 From the text: ``We present a way of viewing Lucas sequences in the framework of group scheme theory. This enables us to treat the Lucas sequences from a geometric and functorial viewpoint, which was suggested by \textit{R. R. Laxton} [Duke Math. J. 36, 721--736 (1969; Zbl 0226.10010)] ] and by \textit{M. Aoki} and \textit{Y. Sakai} [Rocky Mt. J. Math.
openaire +5 more sources
ON PERFECT POWERS IN LUCAS SEQUENCES [PDF]
International Journal of Number Theory, 2005 Let (un)n≥0be the binary recurrence sequence of integers given by u0= 0, u1= 1 and un+2= 2(un+1+ un). We show that the only positive perfect powers in this sequence are u1= 1 and u4= 16. We further discuss the problem of determining perfect powers in Lucas sequences in general.
Bugeaud, Yann +3 more
openaire +1 more source