Publications (80)
Pell Numbers with Lehmer property
Bernadette Faye, Florian Luca
Finiteness results for Diophantine triples with repdigit values
Attila Bérczes, Florian Luca, István Pink +1
Diophantine triples with values in $k$-generalized Fibonacci sequences
Clemens Fuchs, Christoph Hutle, Florian Luca +1
Collinear CM-points
Yuri Bilu, Florian Luca, David Masser
Integers without divisors from a fixed arithmetic progression
William D. Banks, John B. Friedlander, Florian Luca
On arithmetic lattices in the plane
Lenny Fukshansky, Pavel Guerzhoy, Florian Luca
On two functions arising in the study of the Euler and Carmichael quotients
Florian Luca, Min Sha, Igor E. Shparlinski
On a divisibility relation for Lucas sequences
Yuri Bilu, Takao Komatsu, Florian Luca +2
Number Fields in Fibers: the Geometrically Abelian Case with Rational Critical Values
Yuri Bilu, Florian Luca
Uniform Distribution of Fractional Parts Related to Pseudoprimes
William D. Banks, Moubariz Z. Garaev, Florian Luca +1
Noncototients and Nonaliquots
William D. Banks, Florian Luca
On perfect powers that are sums of two Fibonacci numbers
Florian Luca, Vandita Patel
On members of Lucas sequences which are products of factorials
Shanta Laishram, Florian Luca, Mark Sias
Lucas Numbers with Lehmer Property
Bernadette Faye, Florian Luca
Pell Numbers whose Euler Function is a Pell Number
Bernadette Faye, Florian Luca
On the Diophantine equation x^2+2^a.3^b.11^c=y^n
Ismail Naci Cangul, Musa Demirci, Ilker Inam +2
Counting Keith numbers
Martin Klazar, Florian Luca
On the proximity of large primes
Minjia Shi, Florian Luca, Patrick Solé
Arithmetic properties of the Ramanujan function
Florian Luca, Igor E Shparlinski
A variation on the theme of Nicomachus
Florian Luca, GeremÃas Polanco, Wadim Zudilin
Common values of the arithmetic functions phi and sigma
Kevin Ford, Florian Luca, Carl Pomerance
Powers of two as sums of two $k-$Fibonacci numbers
Jhon J. Bravo, Carlos A. Gómez, Florian Luca
The number of solutions of lambda(x)=n
Kevin Ford, Florian Luca
On a variant of Giuga numbers
Jose Maria Grau, Florian Luca, Antonio M. Oller-Marcen
On the largest prime factor of $x^2-1$
Florian Luca, Filip Najman
Exponential Sums and Congruences with Factorials
Moubariz Z. Garaev, Florian Luca, Igor E. Shparlinski
On a problem of Pillai with $k$-generalised Fibonacci numbers and powers of $2$
Mahadi Ddamulira, Carlos A. Gómez, Florian Luca
Carmichael numbers in the sequence (k2^n+1)_{n\ge 1}
Javer Cilleruelo, Florian Luca, Amalia Pizarro
Heron triangles with two fixed sides
Eugen J. Ionascu, Florian Luca, Pantelimon Stanica
Diophantine triples in linear recurrence sequences of Pisot type
Clemens Fuchs, Christoph Hutle, Florian Luca
Products of Factorials Modulo p
Florian Luca, Pantelimon Stanica
On the Fixed Points of the Map x -> x^x Modulo a Prime
Pär Kurlberg, Florian Luca, Igor Shparlinski
On the prime power factorization of n!
Florian Luca, Pantelimon Stanica
Every positive integer is a sum of three palindromes
Javier Cilleruelo, Florian Luca, Lewis Baxter
On the largest prime factor of the Mersenne numbers
Kevin Ford, Florian Luca, Igor E. Shparlinski
Compositions of n Satisfying Some Coprimality Conditions
Daniela Bubboloni, Florian Luca, Pablo Spiga
A note on odd perfect numbers
Jose Arnaldo B. Dris, Florian Luca
Quadratic forms representing the $p$-th Fibonacci number
Pedro Berrizbeitia, Florian Luca, Alberto Mendoza
The $r$th moment of the divisor function: an elementary approach
Florian Luca, László Tóth
On some monotonic combinatorial sequences conjectures
Florian Luca, Pantelimon Stanica
On the Typical Size and Cancelations Among the Coefficients of Some Modular Forms
Florian Luca, Maksym Radziwill, Igor E. Shparlinski
Only finitely many Tribonacci Diophantine triples exist
Clemens Fuchs, Christoph Hutle, Nurettin Irmak +2
On the $X$-coordinates of Pell equations which are Tribonacci numbers
Florian Luca, Amanda Montejano, Laszlo Szalay +1
On the maximal order of numbers in the "factorisatio numerorum" problem
Martin Klazar, Florian Luca
Some Diophantine equations from finite group theory: $Φ_m(x)=2p^n-1$
Florian Luca, Pieter Moree, Benne de Weger
On the period of the continued fraction expansion of ${\sqrt {2^{2n+1}+1}}$
Yann Bugeaud, Florian Luca
A note on the number of $S$-Diophantine quadruples
Florian Luca, Volker Ziegler
Functional Graphs of Polynomials over Finite Fields
Sergei V. Konyagin, Florian Luca, Bernard Mans +3
Zeckendorf representations with at most two terms to x-coordinates of Pell equations
Carlos Alexis Gómez, Florian Luca
Linear independence of powers of singular moduli of degree 3
Florian Luca, Antonin Riffaut
An elliptic sequence is not a sampled linear recurrence sequence
Florian Luca, Tom Ward
On the period mod $m$ of polynomially-recursive sequences: a case study
Cyril Banderier, Florian Luca
Values of the Euler phi-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields
Kevin Ford, Florian Luca, Pieter Moree
Diversity in Parametric Families of Number Fields
Yuri Bilu, Florian Luca
Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms
Yuri Bilu, Jean-Marc Deshouillers, Sanoli Gun +1
Fibonacci Numbers which are Products of two Pell Numbers
Mahadi Ddamulira, Florian Luca, Mihaja Rakotomalala
Rational Products of Singular Moduli
Yuri Bilu, Florian Luca, Amalia Pizarro-Madariaga
The Distribution of Self-Fibonacci Divisors
Florian Luca, Emanuele Tron
Character Sums and Congruences with n!
Moubariz Z. Garaev, Florian Luca, Igor E. Shparlinski
Denominators of Bernoulli polynomials
Olivier Bordellès, Florian Luca, Pieter Moree +1
Corrigendum to "Cullen numbers with the Lehmer Property"
José MarÃa Grau, Florian Luca
Sylvester's Theorem and the Non-integrality of a certain Binomial Sum
Daniel López-Aguayo, Florian Luca
On the largest prime factor of the $k-$Fibonacci numbers
Jhon J. Bravo, Florian Luca
On a problem of Pillai with Fibonacci numbers and powers of 2
Mahadi Ddamulira, Florian Luca, Mihaja Rakotomalala
Non-Holonomicity of Sequences Defined via Elementary Functions
Jason P. Bell, Stefan Gerhold, Martin Klazar +1
Power of Two as sums of Three Pell Numbers
Jhon J. Bravo, Bernadette Faye, Florian Luca
On $X$-coordinates of Pell equations which are repdigits
Bernadette Faye, Florian Luca
The image of Carmichael's $λ$-function
Kevin Ford, Florian Luca, Carl Pomerance
Residue Classes Having Tardy Totients
John Friedlander, Florian Luca
Coincidences in generalized Lucas sequences
Eric F. Bravo, Jhon J. Bravo, Florian Luca
Cullen Numbers with the Lehmer Property
Jose Maria Grau, Florian Luca
Some Additive Combinatorics Problems in Matrix Rings
Ron Ferguson, Corneliu Hoffman, Florian Luca +2
On numbers $n$ dividing the $n$th term of a linear recurrence
Juan Jose Alba Gonzalez, Florian Luca, Carl Pomerance +1
On the error term of a lattice counting problem
Florian Luca, Igor E. Shparlinski
On the Oppenheim's "factorisatio numerorum" function
Florian Luca, Anirban Mukhopadhyay, Kotyada Srinivas
On the $x$--coordinates of Pell equations which are $k$--generalized Fibonacci numbers
Mahadi Ddamulira, Florian Luca
An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers
Salah E. Rihane, Bernadette Faye, Florian Luca +1
Divisibility of class numbers: enumerative approach
Yuri F. Bilu, Florian Luca
On shifted primes with large prime factors and their products
Florian Luca, Ricardo Menares, Amalia Pizarro-Madariaga
Prime chains and Pratt trees
Kevin Ford, Sergei V. Konyagin, Florian Luca