Florian Luca

发表

An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers

Salah E. Rihane, Bernadette Faye, Florian Luca, 2018, Annales Mathematicae et Informaticae.

Remarks on a Sequence of Minimal Niven Numbers

Pantelimon Stanica, Florian Luca, H. Fredricksen, 2007, SSC.

On finite fields for pairing based cryptography

Igor E. Shparlinski, Florian Luca, 2007, Adv. Math. Commun..

Squares in a certain sequence related to L-functions of elliptic curves

Florian Luca, Aynur Yalçiner, 2013, Finite Fields Their Appl..

Number fields in fibers: the geometrically abelian case with rational critical values

Florian Luca, Yuri Bilu, 2017, Period. Math. Hung..

x-Coordinates of Pell equations which are Tribonacci numbers II

Florian Luca, Alain Togbé, Bir Kafle, 2019, Period. Math. Hung..

On the lower bound of the linear complexity over F/sub p/ of Sidelnikov sequences

Igor E. Shparlinski, Arne Winterhof, Florian Luca, 2006, IEEE Transactions on Information Theory.

On a conjecture of Erdos and Stewart

Florian Luca, F. Luca, 2000, Math. Comput..

Euler to the Rescue: 10869

Lenny Jones, Florian Luca, 2003, Am. Math. Mon..

A Remark on Prime Divisors of Lengths of Sides of Heron Triangles

István Gaál, Florian Luca, István Járási, 2003, Exp. Math..

A generalization of a classical zero-sum problem

Florian Luca, 2007, Discret. Math..

Problem 11090

Florian Luca, 2004, Am. Math. Mon..

Power Totients with Almost Primes

Florian Luca, William D. Banks, 2011, Integers.

Coincidences of Catalan and q-Catalan Numbers

Paul Thomas Young, Florian Luca, F. Luca, 2011, Integers.

Power Values of Divisor Sums

Florian Luca, Frans Oort, Frits Beukers, 2012, Am. Math. Mon..

The Number of Solutions of λ(x) = n

Florian Luca, Kevin Ford, F. Luca, 2011, Integers.

On the Multiplicative Order of Fn+1/Fn Modulo Fm

Florian Luca, Takao Komatsu, Yohei Tachiya, 2012, Integers.

Common factors of shifted Fibonacci numbers

Florian Luca, Santos Hernández, F. Luca, 2003, Period. Math. Hung..

On the equation 1k+2k+···+nk=x2

Florian Luca, 2002, Period. Math. Hung..

Appendix. Basic complex analysis theory

Florian Luca, Jean-Marie De Koninck, 2012 .

Rectangles Of Nonvisible Lattice Points

Florian Luca, Shanta Laishram, 2015, J. Integer Seq..

Integer Roots Chromatic Polynomials of Non-Chordal Graphs and the Prouhet-Tarry-Escott Problem

Florian Luca, Santos Hernández, 2005, Graphs Comb..

Prime divisors of some shifted products

Igor E. Shparlinski, Éric Levieil, Florian Luca, 2005, Int. J. Math. Math. Sci..

A note on odd perfect numbers pdf

Florian Luca, Jose Arnaldo B. Dris, 2011, ArXiv.

Values of the Euler Φ-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields

Florian Luca, Kevin Ford, Pieter Moree, 2013, Math. Comput..

Elliptic Curves with Low Embedding Degree

Igor E. Shparlinski, Florian Luca, F. Luca, 2006, Journal of Cryptology.

Primitive Root Bias for Twin Primes

Stephan Ramon Garcia, Florian Luca, Elvis Kahoro, 2019, Exp. Math..

On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves

Igor E. Shparlinski, Jorge Jiménez Urroz, Florian Luca, 2011, Math. Comput..

Carmichael numbers in the sequence (2n k+1)n≥1

Javier Cilleruelo, Florian Luca, Amalia Pizarro-Madariaga, 2015, Math. Comput..

Sometimes Divides σk(): 11090

Florian Luca, John Ferdinands, 2006, Am. Math. Mon..

Fermat Primes and Heron Triangles with Prime Power Sides

Florian Luca, 2003, Am. Math. Mon..

Repdigits as sums of three Pell numbers

Florian Luca, Alain Togbé, Benedict Vasco Normenyo, 2018, Period. Math. Hung..

Uniform distribution of some ratios involving the number of prime and integer divisors

Igor E. Shparlinski, Florian Luca, 2006 .

X-coordinates of Pell equations as sums of two tribonacci numbers

Florian Luca, Eric F. Bravo, Carlos Alexis Gómez Ruiz, 2018, Period. Math. Hung..

The Anti-Social Fermat Number

Florian Luca, 2000, Am. Math. Mon..

Problem 10793

Florian Luca, 2000, Am. Math. Mon..

A Note on r-Full Numbers of the Form lm + k

Florian Luca, 2000, Period. Math. Hung..

Perfect repdigits

Kevin A. Broughan, Florian Luca, Sergio Guzman Sanchez, 2013, Math. Comput..

Powers of Two as Sums of Two Lucas Numbers

Florian Luca, Jhon J. Bravo, Jhon J. Bravo, 2014, J. Integer Seq..

The global behavior of arithmetic functions

Florian Luca, Jean-Marie De Koninck, 2012 .

Prime divisors of binary holonomic sequences

Florian Luca, F. Luca, 2008, Adv. Appl. Math..

On a Conjecture Regarding Balancing with Powers of Fibonacci Numbers

Florian Luca, Andrej Dujella, Saúl Díaz Alvarado, 2012, Integers.

Counting permutation equivalent degree six binary polynomials invariant under the cyclic group

Pantelimon Stanica, Florian Luca, 2016, Applicable Algebra in Engineering, Communication and Computing.

Every positive integer is a sum of three palindromes

Javier Cilleruelo, Florian Luca, Lewis Baxter, 2018, Math. Comput..

On Multiplicative Magic Squares

Javier Cilleruelo, Florian Luca, F. Luca, 2010, Electron. J. Comb..

On the X-coordinates of Pell equations which are rep-digits, II

Florian Luca, Alain Togbé, Sossa Victorin Togan, 2019, Annales Mathematicae et Informaticae.

On the largest prime factor of x2-1

Florian Luca, Filip Najman, F. Luca, 2010, Math. Comput..

VSH and multiplicative modular relations between small primes with polynomial exponents

Igor E. Shparlinski, Ian F. Blake, Florian Luca, 2014, Applicable Algebra in Engineering, Communication and Computing.

On Fibonacci numbers which are elliptic Carmichael

Pantelimon Stanica, Florian Luca, 2016, Period. Math. Hung..

Proceedings of the Fourteenth International Conference on Fibonacci Numbers and Their Applications

Florian Luca, Pantelimon Stănică, 2011 .

On the sum of two divisors of (n2 + 1)/2

Florian Luca, Andrej Dujella, F. Luca, 2012, Period. Math. Hung..

On the Local Minima of the Order of Appearance Function

Florian Luca, Thato Mosima, 2015, Int. J. Math. Math. Sci..

Prime factors of Motzkin numbers

Florian Luca, F. Luca, 2006, Ars Comb..

On the Diophantine Equation x2+2alpha5beta13gamma=yn

Florian Luca, Alain Togbé, Edray Goins, 2008, ANTS.

A Number and Its Totient Are Not Amicable: 10793

Florian Luca, Nasha Komanda, 2002, Am. Math. Mon..

Can Two Consecutive Numbers Both Be Perfect?: 10711

Florian Luca, Francis B. Coghlan, 2001, Am. Math. Mon..

Errata to "On the largest prime factor of x2-1"

Florian Luca, Filip Najman, 2014, Math. Comput..

The rth Moment of the Divisor Function: An Elementary Approach

Florian Luca, L'aszl'o T'oth, 2017, J. Integer Seq..

On the Period mod m of Polynomially-Recursive Sequences: a Case Study

Cyril Banderier, Florian Luca, F. Luca, 2019, J. Integer Seq..

Catalan and Apéry numbers in residue classes

Igor E. Shparlinski, Florian Luca, Moubariz Z. Garaev, 2006, J. Comb. Theory, Ser. A.

On Giuga numbers

Igor E. Shparlinski, Florian Luca, Carl Pomerance, 2009 .

Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem

Igor E. Shparlinski, Kevin A. Broughan, Florian Luca, 2010, Integers.

Markov Type Equations with Solutions in Lucas Sequences

Florian Luca, Alaa Altassan, 2021 .

On the divisibility Fk|Fx2 + Fx + 1

Florian Luca, László Szalay, Prapanpong Pongsriiam, 2021 .

On a nonintegrality conjecture

Florian Luca, Carl Pomerance, C. Pomerance, 2021, European Journal of Mathematics.

There are no Diophantine quadruples of Pell numbers

Florian Luca, Alain Togbé, Salah Eddine Rihane, 2021, International Journal of Number Theory.

Coprime partitions and Jordan totient functions

Daniela Bubboloni, Florian Luca, F. Luca, 2020, Journal of Number Theory.

Trinomials, singular moduli and Riffaut's conjecture

Florian Luca, Yuri Bilu, Amalia Pizarro-Madariaga, 2020, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE.

Common values of generalized Fibonacci and Pell sequences

Florian Luca, Jhon J. Bravo, José Luis Arciniegas Herrera, 2021 .

Fibonacci and Lucas numbers as difference of two repdigits

Refik Keskin, Florian Luca, Fatih Erduvan, 2021, Rendiconti del Circolo Matematico di Palermo Series 2.

k-generalized Fibonacci numbers which are concatenations of two repdigits

Florian Luca, Adel Alahmadi, Alaa Altassan, 2021, Glasnik Matematicki.

k-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k-$$\end{document}Fibonacci powers as sums of powers of some fixed p

Florian Luca, Jhonny C. Gómez, Carlos A. Gómez, 2021, Monatshefte für Mathematik.

The Orbit Problem for Parametric Linear Dynamical Systems pdf

Christel Baier, James Worrell, Markus A. Whiteland, 2021, CONCUR.

Product of repdigits with consecutive lengths in the Fibonacci sequence.

Florian Luca, Jhonny C. Gómez, F. Luca, 2021, Boletín de la Sociedad Matemática Mexicana.

Universal Skolem Sets

Joël Ouaknine, James Worrell, Florian Luca, 2021, 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

Big prime factors in orders of elliptic curves over finite fields

Florian Luca, Yuri Bilu, Haojie Hong, 2021 .

On the number of divisors of the least common multiples of shifted prime powers

Florian Luca, Francesco Pappalardi, 2021, Functiones et Approximatio Commentarii Mathematici.

On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences

Florian Luca, Mahadi Ddamulira, 2021, The Ramanujan journal.

ON THE EQUATION x 2 + 2 a · 3 b = y n

Florian Luca, F. Luca, 2002 .

Palindromes in linear recurrence sequences

Javier Cilleruelo, Florian Luca, Rafael Tesoro, 2013 .

On the largest prime factor of the mersenne numbers

Igor E. Shparlinski, Florian Luca, Kevin Ford, 2007, 0704.1327.

On Fibonacci Numbers Which Are Elliptic Korselt Numbers

Pantelimon Stanica, Florian Luca, 2014 .

On the x-coordinates of Pell equations which are Fibonacci numbers II

Florian Luca, Alain Togbé, Bir Kafle, 2017 .

Estimates for Wieferich numbers

Igor E. Shparlinski, Florian Luca, William D. Banks, 2007 .

Powers of two as sums of two k-Fibonacci numbers

Florian Luca, Jhon J. Bravo, F. Luca, 2014, 1409.8514.

ON THE DIOPHANTINE EQUATION x2 + 2a · 5b = yn

Florian Luca, Alain Togbé, 2008 .

ON PILLAI'S PROBLEM WITH TRIBONACCI NUMBERS AND POWERS OF 2

Florian Luca, Jhon J. Bravo, F. Luca, 2017 .

Pseudoprime reductions of elliptic curves

Igor E. Shparlinski, Florian Luca, Alina Carmen Cojocaru, 2009, Mathematical Proceedings of the Cambridge Philosophical Society.

Fibonacci numbers at most one away from a perfect power

Maurice Mignotte, Yann Bugeaud, Samir Siksek, 2008 .

On Pillai’s problem with the Fibonacci and Pell sequences

Florian Luca, Luis Manuel Rivera, F. Luca, 2018, Boletín de la Sociedad Matemática Mexicana.

Irrationality of Power Series for Various Number Theoretic Functions

Igor E. Shparlinski, Florian Luca, William D. Banks, 2005 .

Average multiplicative orders of elements modulo n

Igor E. Shparlinski, Florian Luca, 2003 .

Non-Holonomicity of Sequences Defined via Elementary Functions

Martin Klazar, Stefan Gerhold, Florian Luca, 2006 .

Distinct digits in base b expansions of linear recurrence sequences

Florian Luca, F. Luca, 2000 .

Analytic Number Theory: Exploring the Anatomy of Integers

Florian Luca, Jean-Marie De Koninck, 2012 .

On the average number of divisors of the Euler function

Florian Luca, Carl Pomerance, 2007 .

The diophantine equation x 2 = p a p b + 1

Florian Luca, F. Luca, 2004 .

Fibonacci and Lucas numbers with only one distinct digit.

Florian Luca, F. Luca, 2000 .

Multiperfect numbers on lines of the Pascal triangle

Florian Luca, Juan L. Varona, F. Luca, 2009 .

Pseudoprime values of the Fibonacci sequence, polynomials and the Euler function

Igor E. Shparlinski, Florian Luca, 2006 .

Repdigits as sums of two $$k$$k-Fibonacci numbers

Florian Luca, Jhon J. Bravo, F. Luca, 2015 .

On binary palindromes of the form 10n±1⁎

Florian Luca, Alain Togbé, F. Luca, 2008 .

On barycentric constants

Oscar Ordaz, Florian Luca, María Teresa Varela, 2012 .

On X-coordinates of Pell equations which are repdigits

Bernadette Faye, Florian Luca, F. Luca, 2016, Research in Number Theory.

On the $X$-coordinates of Pell equations which are Tribonacci numbers

Amanda Montejano, Florian Luca, F. Luca, 2016, 1612.09546.

On the exponent of the group of points on elliptic curves in extension fields

Igor E. Shparlinski, Florian Luca, F. Luca, 2005 .

Linear combinations of factorials and $$S$$S-units in a binary recurrence sequence

Florian Luca, F. Luca, Sergio Guzmán Sanchez, 2014 .

Composite positive integers with an average prime factor

Florian Luca, Francesco Pappalardi, 2007 .

Power values of palindromes

Igor E. Shparlinski, Javier Cilleruelo, Florian Luca, 2009 .

On the Counting Function of Elliptic Carmichael Numbers

Igor E. Shparlinski, Florian Luca, 2014, Canadian Mathematical Bulletin.

The average Smarandache function

Florian Luca, F. Luca, 2001 .

MOV attack in various subgroups on elliptic curves

Igor E. Shparlinski, Florian Luca, David Jose Mireles, 2004 .

Some Mean Values Related to Average Multiplicative Orders of Elements in Finite Fields

Florian Luca, 2005 .

Some results on Oppenheim's ``Factorisatio Numerorum'' function

Florian Luca, Anirban Mukhopadhyay, Kotyada Srinivas, 2010 .

Power of Two as sums of Three Pell Numbers

Bernadette Faye, Florian Luca, Jhon J. Bravo, 2016, 1608.06086.

On the Diophantine equation $x^2 + 2^{\alpha} 13^{\beta}=y^{n}$

Florian Luca, Alain Togbé, F. Luca, 2009 .

Control of coupled parabolic systems and Diophantine approximations

Florian Luca, Luz de Teresa, F. Luca, 2013 .

ON THE DIOPHANTINE EQUATION x2 + 5a 13b = yn

Fadwa S. Abu Muriefah, Florian Luca, Alain Togbé, 2008, Glasgow Mathematical Journal.

On a conjecture about repdigits in k-generalized Fibonacci sequences

Florian Luca, Jhon J. Bravo, F. Luca, 2013 .

Diophantine Approximations and a Problem from the 1988 IMO

Florian Luca, P. G. Walsh, F. Luca, 2006 .

Repdigits as Sums of Four Fibonacci or Lucas Numbers

Florian Luca, Alain Togbé, Florian Luca, 2018, J. Integer Seq..

Repdigits as sums of four Pell numbers

Florian Luca, Alain Togbé, Benedict Vasco Normenyo, 2019 .

On a problem of Pillai with k–generalized Fibonacci numbers and powers of 2

Florian Luca, Mahadi Ddamulira, Carlos A. Gómez, 2017, International Journal of Number Theory.

On the radical of a perfect number

Florian Luca, Carl Pomerance, 2010 .

Multiperfect numbers with identical digits

Paul Pollack, Florian Luca, F. Luca, 2011 .

On the $X$-coordinates of Pell equations which are Tribonacci numbers

Amanda Montejano, Florian Luca, László Szalay, 2016 .

On the values of the divisor function

Igor E. Shparlinski, Florian Luca, 2007 .

Fibonacci Numbers of the Form k2+k+2

Florian Luca, F. Luca, 1999 .

On Integers for Which the Sum of Divisors is the Square of the Squarefree Core

Kevin A. Broughan, Florian Luca, Jean-Marie De Koninck, 2012 .

On The diophantine equation Fn+Fm=2a

Florian Luca, Jhon J. Bravo, F. Luca, 2016 .

Palindromes in Lucas Sequences

Florian Luca, F. Luca, 2003 .

INTEGERS : ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 8 ( 2008 ) , # A 06 ON TOTIENT ABUNDANT NUMBERS

Florian Luca, F. Luca, Paul Loomis, 2008 .

A Generalization of a Lemma of Sullivan

Florian Luca, Myriam Maldonado-Ramírez, Martha Rzedowski-Calderón, 2012 .

Repdigits as sums of three Lucas numbers

Florian Luca, Alain Togbé, Benedict Vasco Normenyo, 2019, Colloquium Mathematicum.

Counting Keith numbers

Martin Klazar, Florian Luca, 2006 .

Perfect fibonacci and lucas numbers

Florian Luca, F. Luca, 2000 .

Fibonacci Numbers with the Lehmer Property

Florian Luca, F. Luca, 2007 .

Average order in cyclic groups

Arnold Knopfmacher, Igor E. Shparlinski, Joachim von zur Gathen, 2004 .

On the Lower Bound of the Linear Complexity Over of

Igor E. Shparlinski, Arne Winterhof, Florian Luca, 2006 .

On the binary expansion of the odd Catalan numbers

Paul Thomas Young, Florian Luca, F. Luca, 2010 .

Repdigits as sums of three Fibonacci numbers

Florian Luca, F. Luca, 2012 .

On the Oppenheim's "factorisatio numerorum" function

Florian Luca, Anirban Mukhopadhyay, Kotyada Srinivas, 2008 .

Common values of the arithmetic functions ϕ and σ

Florian Luca, Kevin Ford, Carl Pomerance, 2009, 0906.3380.