The Experts below are selected from a list of 7098 Experts worldwide ranked by ideXlab platform
Florian Luca - One of the best experts on this subject based on the ideXlab platform.
-
on the x coordinates of pell equations which are Fibonacci Numbers
Mathematica Scandinavica, 2018Co-Authors: Florian Luca, Alain TogbéAbstract:For an integer $d>2$ which is not a square, we show that there is at most one value of the positive integer $x$ participating in the Pell equation $x^2-dy^2=\pm 1$ which is a Fibonacci Number.
-
on a problem of pillai with Fibonacci Numbers and powers of 2
arXiv: Number Theory, 2017Co-Authors: Mahadi Ddamulira, Florian Luca, Mihaja RakotomalalaAbstract:In this paper, we find all integers c having at least two representations as a difference between a Fibonacci Number and a power of 2.
-
Quadratic forms representing the $p$-th Fibonacci Number
arXiv: Number Theory, 2015Co-Authors: Pedro Berrizbeitia, Florian Luca, Alberto MendozaAbstract:In this paper, we show that if $p\equiv 1\pmod 4$ is prime, then $4F_p$ admits a representation of the form $u^2-pv^2$ for some integers $u$ and $v$, where $F_n$ is the $n$th Fibonacci Number. We prove a similar result when $p\equiv -1\pmod 4$.
-
On the formula Fp = u2 + pv2
International Journal of Number Theory, 2014Co-Authors: Juan José Alba González, Pedro Berrizbeitia, Florian LucaAbstract:In this paper, we show that if p ≡ 1 (mod 4) is prime, then Fp admits a representation of the form u2 + pv2 for some integers u and v, where Fn is the nth Fibonacci Number.
-
There are No Multiply-Perfect Fibonacci Numbers
Integers, 2011Co-Authors: Kevin A. Broughan, Florian Luca, Marcos J. González, Ryan H. Lewis, V. Janitzio Mejía Huguet, Alain TogbéAbstract:AbstractWe show that no Fibonacci Number (larger than 1) divides the sum of its divisors.
Li Chao - One of the best experts on this subject based on the ideXlab platform.
-
Series of Fibonacci Type and Its Properties
Natural Science Journal of Hainan University, 2007Co-Authors: Li ChaoAbstract:A series of Fibonacci type is constructed using the application of the basic properties of Fibonacci Number and Lucas Number and the generated function and the concerned properties are studied from which some results are obtained.
-
On a Group of Identity of linear Combination of Fibonacci Number and Lucas Number
Journal of Shangluo Teachers College, 2005Co-Authors: Li ChaoAbstract:With the use of generating function of Fibonacci Number and Lucas Number, and the relationship with generating function of Gagenbauer polynomials, on a group of identity of linear combination of Fibonacci Number and Lucas Number is obtained.
-
Self-assembly on core/shell microstructures driven by stress into triangular and Fibonacci Number patterns
Physics, 2005Co-Authors: Li ChaoAbstract:Triangular and Fibonacci Number phyllotactic patterns in nature have attracted much interest amongst scientists in multidisciplinary fields. By controlling the geometry along with the stress developed during cooling, these patterns can be reproduced on the surface of Ag core/SiO_x shell microstructures. The significance of our work lies in the revelation that, under proper geometrical constraint, the various patterns can develop through minimization of the strain energy. This provides a physical mechanism without involving the growth dynamics of the formation of phyllotactic patterns. Moreover, it demonstrates that highly-ordered microstructures, even with desirable defects, can be prepared across large areas simultaneously by stress engineering.
-
self assembly on core shell microstructures driven by stress into triangular and Fibonacci Number patterns
Physics, 2005Co-Authors: Li ChaoAbstract:Triangular and Fibonacci Number phyllotactic patterns in nature have attracted much interest amongst scientists in multidisciplinary fields. By controlling the geometry along with the stress developed during cooling, these patterns can be reproduced on the surface of Ag core/SiO_x shell microstructures. The significance of our work lies in the revelation that, under proper geometrical constraint, the various patterns can develop through minimization of the strain energy. This provides a physical mechanism without involving the growth dynamics of the formation of phyllotactic patterns. Moreover, it demonstrates that highly-ordered microstructures, even with desirable defects, can be prepared across large areas simultaneously by stress engineering.
Pedro Berrizbeitia - One of the best experts on this subject based on the ideXlab platform.
-
Quadratic forms representing the $p$-th Fibonacci Number
arXiv: Number Theory, 2015Co-Authors: Pedro Berrizbeitia, Florian Luca, Alberto MendozaAbstract:In this paper, we show that if $p\equiv 1\pmod 4$ is prime, then $4F_p$ admits a representation of the form $u^2-pv^2$ for some integers $u$ and $v$, where $F_n$ is the $n$th Fibonacci Number. We prove a similar result when $p\equiv -1\pmod 4$.
-
On the formula Fp = u2 + pv2
International Journal of Number Theory, 2014Co-Authors: Juan José Alba González, Pedro Berrizbeitia, Florian LucaAbstract:In this paper, we show that if p ≡ 1 (mod 4) is prime, then Fp admits a representation of the form u2 + pv2 for some integers u and v, where Fn is the nth Fibonacci Number.
Shichong Tan - One of the best experts on this subject based on the ideXlab platform.
-
elliptic curve scalar multiplication based on Fibonacci Number
Intelligent Networking and Collaborative Systems, 2013Co-Authors: Ning Zhang, Shichong TanAbstract:The paper presents a series algorithms of Elliptic curve scalar multiplication based on Fibonacci Numbers. The double free addition chain is used to develop new scalar multiplication. Zeckendorf and Pell representation is analyzed and used to construct scalar multiplication. We analyzed the efficiency and the security to power analysis, it shows that with sophisticated designation, double free method can both have efficiency and security.
-
INCoS - Elliptic Curve Scalar Multiplication Based on Fibonacci Number
2013 5th International Conference on Intelligent Networking and Collaborative Systems, 2013Co-Authors: Ning Zhang, Shichong TanAbstract:The paper presents a series algorithms of Elliptic curve scalar multiplication based on Fibonacci Numbers. The double free addition chain is used to develop new scalar multiplication. Zeckendorf and Pell representation is analyzed and used to construct scalar multiplication. We analyzed the efficiency and the security to power analysis, it shows that with sophisticated designation, double free method can both have efficiency and security.
Indhumathi Raman - One of the best experts on this subject based on the ideXlab platform.
-
A Note on Closed-Form Representation of Fibonacci Numbers Using Fibonacci Trees
International Scholarly Research Notices, 2014Co-Authors: Indhumathi RamanAbstract:We give a new representation of the Fibonacci Numbers. This is achieved using Fibonacci trees. With the help of this representation, the th Fibonacci Number can be calculated without having any knowledge about the previous Fibonacci Numbers.
-
A note on closed-form representation of Fibonacci Numbers using Fibonacci trees
arXiv: Combinatorics, 2013Co-Authors: Indhumathi RamanAbstract:In this paper, we give a new representation of the Fibonacci Numbers. This is achieved using Fibonacci trees. With the help of this representation, the nth Fibonacci Number can be calculated without having any knowledge about the previous Fibonacci Numbers.