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Luca, Florian

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Author ID: luca.florian Recent zbMATH articles by "Luca, Florian"
Published as: Luca, F.; Luca, Florian
Homepage: https://www.wits.ac.za/staff/academic-a-z-listing/l/florianlucawitsacza/
External Links: MGP · Math-Net.Ru · Wikidata · ORCID · dblp · GND
Documents Indexed: 696 Publications since 1993, including 7 Books
Reviewing Activity: 303 Reviews
all top 5

Co-Authors

97 single-authored
77 Shparlinski, Igor E.
38 Stănică, Pantelimon
38 Togbé, Alain
29 De Koninck, Jean-Marie
25 Banks, William D.
24 Pomerance, Carl Bernard
21 Bravo, Jhon Jairo
19 Szalay, László
17 Gómez, Carlos Alexis
16 Faye, Bernadette
15 Gómez Ruiz, Carlos Alexis
13 Garaev, Moubariz Z.
12 Bilu, Yuri F.
12 Cilleruelo, Javier
11 Mignotte, Maurice
10 Bugeaud, Yann
10 Ford, Kevin B.
10 Hernández, Santos Hernández
9 Walsh, Peter Gareth
8 Dujella, Andrej
8 Kafle, Bir
8 Mejía-Huguet, V. Janitzio
8 Moree, Pieter
7 Bérczes, Attila
7 Garcia, Stephan Ramon
7 Komatsu, Takao
7 Pappalardi, Francesco
7 Siksek, Samir
7 Somer, Lawrence E.
7 Tachiya, Yohei
6 Bravo, Eric F.
6 Broughan, Kevin A.
6 Ddamulira, Mahadi
6 Friedlander, John Benjamin
6 Fuchs, Clemens
6 Hajdu, Lajos
6 Křížek, Michal
6 Pizarro-Madariaga, Amalia
5 Berrizbeitia, Pedro
5 Grytczuk, Aleksander
5 Klazar, Martin
5 Knopfmacher, Arnold
5 Shorey, Tarlok Nath
5 Thangadurai, Ravindranathan
5 Wójtowicz, Marek
5 Yalçiner, Aynur
5 Young, Paul Thomas
4 Balasubramanian, Ramachandran
4 Ballot, Christian
4 Cipu, Mihai
4 Deshouillers, Jean-Marc
4 Doyon, Nicolas
4 Gómez, Jhonny C.
4 Kihel, Omar
4 Konyagin, Sergeĭ Vladimirovich
4 Normenyo, Benedict Vasco
4 Pintér, Ákos
4 Pollack, Paul
4 Rihane, Salah Eddine
4 Sankaranarayanan, Ayyadurai
4 Ziegler, Volker
3 Alba González, Juan José
3 Altassan, Alaa
3 Chakraborty, Kalyan
3 Dress, Andreas W. M.
3 Filaseta, Michael A.
3 González, Marcos José
3 Grau, José María
3 Hutle, Christoph
3 Iannucci, Douglas E.
3 Ionaşcu, Eugen Julien
3 Laishram, Shanta
3 Mukhopadhyay, Anirban
3 Munagi, Augustine O.
3 Nicolae, Florin
3 Nowak, Werner Georg
3 Oyono, Roger
3 Porubsky, Stefan
3 Ralaivaosaona, Dimbinaina
3 Soydan, Gokhan
3 Tall, Amadou Makhtar
2 Abu Muriefah, Fadwa S.
2 Adamczewski, Boris
2 Adegbindin, Chèfiath Awero
2 Alvarado, Saúl Díaz
2 Ayad, Mohamed
2 Balasuriya, Sanka
2 Bazsó, András
2 Bordellès, Olivier
2 Cangul, Ismail Naci
2 Ciolan, Alexandru
2 de Weger, Benne
2 Demirci, Musa
2 Flammenkamp, Achim
2 Fredricksen, Harold M.
2 Fujita, Yasutsugu
2 García, Victor Cuauhtemoc
2 Gun, Sanoli
2 Heim, Bernhard Ernst
2 Hernane, Mohand-Ouamar
...and 213 more Co-Authors
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Serials

48 Journal of Number Theory
41 Acta Arithmetica
27 The Fibonacci Quarterly
25 International Journal of Number Theory
21 Colloquium Mathematicum
21 Journal of Integer Sequences
18 Publicationes Mathematicae
18 Integers
14 Indagationes Mathematicae. New Series
13 Periodica Mathematica Hungarica
12 Monatshefte für Mathematik
12 Glasnik Matematički. Serija III
12 Boletín de la Sociedad Matemática Mexicana. Third Series
11 Bulletin of the Australian Mathematical Society
11 Annales Mathematicae et Informaticae
10 Rocky Mountain Journal of Mathematics
10 Proceedings of the American Mathematical Society
10 Journal de Théorie des Nombres de Bordeaux
9 Glasgow Mathematical Journal
8 Mathematics of Computation
8 Archiv der Mathematik
8 Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. Nouvelle Série
8 Uniform Distribution Theory
7 Mathematica Slovaca
7 The Ramanujan Journal
6 Functiones et Approximatio. Commentarii Mathematici
6 Proceedings of the Edinburgh Mathematical Society. Series II
6 The New York Journal of Mathematics
6 Journal of Combinatorics and Number Theory
5 American Mathematical Monthly
5 Annales des Sciences Mathématiques du Québec
5 Canadian Mathematical Bulletin
5 Proceedings of the Japan Academy. Series A
5 Revista Colombiana de Matemáticas
5 Congressus Numerantium
5 Smarandache Notions Journal
4 Lithuanian Mathematical Journal
4 Bulletin of the London Mathematical Society
4 International Journal of Mathematics and Mathematical Sciences
4 Mathematika
4 Mathematica Bohemica
4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
4 Acta Academiae Paedagogicae Agriensis. Nova Series. Sectio Matematicae
4 Journal of the Australian Mathematical Society
4 Portugaliae Mathematica. Nova Série
3 Mathematical Proceedings of the Cambridge Philosophical Society
3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
3 Indian Journal of Mathematics
3 Journal für die Reine und Angewandte Mathematik
3 Quaestiones Mathematicae
3 Studia Scientiarum Mathematicarum Hungarica
3 Transactions of the American Mathematical Society
3 Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica
3 IMRN. International Mathematics Research Notices
3 Aequationes Mathematicae
3 Divulgaciones Matemáticas
3 Mathematical Communications
3 Revista Matemática Complutense
3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
3 Communications in Mathematics
3 Moscow Journal of Combinatorics and Number Theory
3 Research in Number Theory
2 Houston Journal of Mathematics
2 Archivum Mathematicum
2 Journal of Algebra
2 Michigan Mathematical Journal
2 Results in Mathematics
2 Bulletin of the Greek Mathematical Society
2 Bulletin of the Korean Mathematical Society
2 Acta Mathematica Hungarica
2 Forum Mathematicum
2 Journal of the Ramanujan Mathematical Society
2 Elemente der Mathematik
2 Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică
2 Applicable Algebra in Engineering, Communication and Computing
2 Experimental Mathematics
2 Bulletin of the Belgian Mathematical Society - Simon Stevin
2 Turkish Journal of Mathematics
2 Finite Fields and their Applications
2 Analele Ştiinţifice ale Universităţii “Ovidius” Constanţa. Seria: Matematică
2 Annals of Combinatorics
2 Acta Mathematica Sinica. English Series
2 The Quarterly Journal of Mathematics
2 La Gaceta de la Real Sociedad Matemática Española
2 Nieuw Archief voor Wiskunde. Vijfde Serie
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 JP Journal of Algebra, Number Theory and Applications
2 Missouri Journal of Mathematical Sciences
2 Algebra & Number Theory
2 Albanian Journal of Mathematics
2 Annales Mathématiques du Québec
1 Communications in Algebra
1 Discrete Mathematics
1 IEEE Transactions on Information Theory
1 Indian Journal of Pure & Applied Mathematics
1 Revue Roumaine de Mathématiques Pures et Appliquées
1 Acta Scientiarum Mathematicarum
1 Ars Combinatoria
1 Canadian Journal of Mathematics
1 Collectanea Mathematica
...and 64 more Serials

Publications by Year

Citations contained in zbMATH

451 Publications have been cited 1,635 times in 890 Documents Cited by Year
On a conjecture about repdigits in \(k\)-generalized Fibonacci sequences. Zbl 1274.11035
Bravo, Jhon J.; Luca, Florian
30
2013
On the complexity of algebraic numbers. Zbl 1119.11019
Adamczewski, Boris; Bugeaud, Yann; Luca, Florian
27
2004
Powers of two in generalized Fibonacci sequences. Zbl 1353.11020
Bravo, Jhon J.; Luca, Florian
24
2012
Analytic number theory. Exploring the anatomy of integers. Zbl 1247.11001
De Koninck, Jean-Marie; Luca, Florian
21
2012
Linear combinations of factorials and \(S\)-units in a binary recurrence sequence. Zbl 1361.11007
Sanchez, Sergio Guzmán; Luca, Florian
20
2014
Fibonacci numbers at most one away from a perfect power. Zbl 1156.11008
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
20
2008
Fibonacci and Lucas numbers with only one distinct digit. Zbl 0958.11007
Luca, F.
18
2000
On the equation \(x^2 + 2^a \cdot 3^b = y^n\). Zbl 1085.11021
Luca, Florian
17
2002
Powers of two as sums of two \(k\)-Fibonacci numbers. Zbl 1389.11041
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
14
2016
On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions \(\varphi\) and \(\sigma\). Zbl 1027.11007
Luca, Florian; Pomerance, Carl
14
2002
On numbers \(n\) dividing the \(n\)th term of a linear recurrence. Zbl 1262.11015
Alba González, Juan José; Luca, Florian; Pomerance, Carl; Shparlinski, Igor E.
13
2012
A generalization of a classical zero-sum problem. Zbl 1123.11012
Luca, Florian
13
2007
17 lectures on Fermat numbers. From number theory to geometry. With a foreword by Alena Šolcová. Zbl 1010.11002
Křížek, Michal; Luca, Florian; Somer, Lawrence
13
2001
Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers. Zbl 1289.11021
Komatsu, Takao; Luca, Florian
12
2013
Coincidences in generalized Fibonacci sequences. Zbl 1272.11028
Bravo, Jhon J.; Luca, Florian
12
2013
Repdigits as sums of three Fibonacci numbers. Zbl 1305.11008
Luca, Florian
12
2012
Character sums and congruences with \(n!\). Zbl 1060.11046
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
12
2004
Distinct digits in base \(b\) expansions of linear recurrence sequences. Zbl 1030.11004
Luca, Florian
12
2000
On a Diophantine equation. Zbl 0997.11027
Luca, Florian
12
2000
On the largest prime factor of the \(k\)-Fibonacci numbers. Zbl 1292.11034
Bravo, Jhon J.; Luca, Florian
11
2013
On the Diophantine equation \(x^2+2^a\cdot 5^b=y^n\). Zbl 1231.11041
Luca, Florian; Togbé, Alain
11
2008
Diophantine equations with products of consecutive terms in Lucas sequences. Zbl 1081.11023
Luca, F.; Shorey, T. N.
11
2005
On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
10
2017
Values of the Euler \(\varphi\)-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields. Zbl 1294.11164
Ford, Kevin; Luca, Florian; Moree, Pieter
10
2014
Fibonacci numbers which are sums of two repdigits. Zbl 1287.11021
Díaz Alvarado, Saúl; Luca, Florian
10
2011
Irreducible radical extensions and Euler-function chains. Zbl 1172.11029
Luca, Florian; Pomerance, Carl
10
2007
On the \(x\)-coordinates of Pell equations which are rep-digits. Zbl 1389.11076
Dossavi-Yovo, Appolinaire; Luca, Florian; Togbé, Alain
9
2016
Functional graphs of polynomials over finite fields. Zbl 1327.05323
Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E.
9
2016
The distribution of self-Fibonacci divisors. Zbl 1390.11119
Luca, Florian; Tron, Emanuele
9
2015
Almost powers in the Lucas sequence. Zbl 1204.11030
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
9
2008
On Pillai’s Diophantine equation. Zbl 1136.11026
Bugeaud, Yann; Luca, Florian
9
2006
On the exponent of the group of points on elliptic curves in extension fields. Zbl 1082.11041
Luca, Florian; Shparlinski, Igor E.
9
2005
Divisibility of class numbers: enumerative approach. Zbl 1072.11084
Bilu, Yuri F.; Luca, Florian
9
2005
On the \(X\)-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007
Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain
8
2017
An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Zbl 1253.11046
Luca, Florian; Oyono, Roger
8
2011
Fibonacci Diophantine triples. Zbl 1218.11020
Luca, Florian; Szalay, László
8
2008
On the lower bound of the linear complexity over \(\mathbb F_p\) of Sidelnikov sequences. Zbl 1296.94073
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor; Winterhof, Arne
8
2006
Catalan and Apéry numbers in residue classes. Zbl 1101.11010
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
8
2006
The Diophantine equation \(P(x)=n!\) and a result of M. Overholt. Zbl 1085.11023
Luca, Florian
8
2002
On \(X\)-coordinates of Pell equations that are repdigits. Zbl 06985805
Faye, Bernadette; Luca, Florian
7
2018
On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027
Luca, Florian; Togbé, Alain
7
2018
On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013
Bravo, Jhon J.; Luca, Florian; Yazán, Karina
7
2017
\(p\)-adic quotient sets. Zbl 1428.11023
Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam
7
2017
Rational products of singular moduli. Zbl 1400.11113
Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia
7
2016
Pell and Pell-Lucas numbers with only one distinct digit. Zbl 1349.11023
Faye, Bernadette; Luca, Florian
7
2015
On shifted primes with large prime factors and their products. Zbl 1370.11110
Luca, Florian; Menares, Ricardo; Pizarro-Madariaga, Amalia
7
2015
On the exponential local-global principle. Zbl 1330.11019
Bartolome, Boris; Bilu, Yuri; Luca, Florian
7
2013
On stable quadratic polynomials. Zbl 1241.11027
Ahmadi, Omran; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E.
7
2012
Some additive combinatorics problems in matrix rings. Zbl 1208.11037
Ferguson, Ron; Hoffman, Corneliu; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E.
7
2010
Common values of the arithmetic functions \(\varphi\) and \(\sigma\). Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
7
2010
Generalized balancing numbers. Zbl 1239.11035
Liptai, Kálmán; Luca, Florian; Pintér, Ákos; Szalay, László
7
2009
On the Diophantine equation \(x^2 + 2^{\alpha}5^{\beta}13^{\gamma} = y^n\). Zbl 1232.11130
Goins, Edray; Luca, Florian; Togbé, Alain
7
2008
On the Diophantine equation \(x^2 + 5^a 13^b = y^n\). Zbl 1186.11016
Abu Muriefah, Fadwa S.; Luca, Florian; Togbé, Alain
7
2008
Fibonacci numbers of the form \(p^a\pm p^b+1\). Zbl 1228.11021
Luca, Florian; Szalay, László
7
2007
On a diophantine equation related to a conjecture of Erdös and Graham. Zbl 1132.11319
Luca, F.; Walsh, P. G.
7
2007
On factorials which are products of factorials. Zbl 1132.11017
Luca, Florian
7
2007
Fibonacci numbers with the Lehmer property. Zbl 1112.11007
Luca, Florian
7
2007
On the maximal order of numbers in the “factorisatio numerorum” problem. Zbl 1169.11043
Klazar, Martin; Luca, Florian
7
2007
Exponential sums and congruences with factorials. Zbl 1071.11051
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
7
2005
Average order in cyclic groups. Zbl 1079.11003
von zur Gathen, Joachim; Knopfmacher, Arnold; Luca, Florian; Lucht, Lutz G.; Shparlinski, Igor E.
7
2004
On the largest prime factor of \((ab+1)(ac+1)(bc+1)\). Zbl 1108.11030
Hernández, Santos; Luca, Florian
7
2003
The number of non-zero digits of \(n\)! Zbl 1043.11008
Luca, Florian
7
2002
Some remarks on Heron triangles. Zbl 1062.11019
Kramer, Alpar-Vajk; Luca, Florian
7
2000
On a problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of 2. Zbl 1437.11051
Ddamulira, Mahadi; Gómez, Carlos A.; Luca, Florian
6
2018
On perfect powers that are sums of two Fibonacci numbers. Zbl 06865878
Luca, Florian; Patel, Vandita
6
2018
Powers of two as sums of three Pell numbers. Zbl 1433.11032
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian
6
2017
Quotients of Fibonacci numbers. Zbl 1391.11027
Garcia, Stephan Ramon; Luca, Florian
6
2016
Powers of two as sums of two Lucas numbers. Zbl 1358.11026
Bravo, Jhon J.; Luca, Florian
6
2014
Control of coupled parabolic systems and Diophantine approximations. Zbl 1272.93029
Luca, Florian; De Teresa, Luz
6
2013
On equal values of power sums of arithmetic progressions. Zbl 1330.11020
Bazsó, András; Kreso, Dijana; Luca, Florian; Pintér, Ákos
6
2012
On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves. Zbl 1329.11063
Jiménez-Urroz, Jorge; Luca, Florian; Shparlinski, Igor E.
6
2012
On composite integers \(n\) for which \(\varphi(n)\mid n-1\). Zbl 1294.11005
Luca, Florian; Pomerance, Carl
6
2011
Fibonacci numbers which are sums of three factorials. Zbl 1259.11038
Bollman, Mark; Hernández Hernández, Santos; Luca, Florian
6
2010
On factorials expressible as sums of at most three Fibonacci numbers. Zbl 1253.11048
Luca, Florian; Siksek, Samir
6
2010
Some results on Oppenheim’s “factorisatio numerorum” function. Zbl 1213.11020
Luca, Florian; Mukhopadhyay, Anirban; Srinivas, Kotyada
6
2010
Non-holonomicity of sequences defined via elementary functions. Zbl 1189.11007
Bell, Jason P.; Gerhold, Stefan; Klazar, Martin; Luca, Florian
6
2008
On the Diophantine equation \(x^2+7^{2k}=y^n\). Zbl 1221.11091
Luca, Florian; Togbé, Alain
6
2007
Composite integers \(n\) for which \(\varphi (n)\mid n-1\). Zbl 1215.11094
Banks, William D.; Luca, Florian
6
2007
Perfect powers from products of terms in Lucas sequences. Zbl 1137.11011
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
6
2007
Elliptic curves with low embedding degree. Zbl 1133.14303
Luca, Florian; Shparlinski, Igor E.
6
2006
Diophantine \(m\)-tuples for primes. Zbl 1085.11019
Dujella, Andrej; Luca, Florian
6
2005
On shifted products which are powers. Zbl 1123.11011
Luca, Florian
6
2005
Fibonacci numbers that are not sums of two prime powers. Zbl 1113.11011
Luca, Florian; Stănică, Pantelimon
6
2005
MOV attack in various subgroups on elliptic curves. Zbl 1072.11094
Luca, Florian; Mireles, David Jose; Shparlinski, Igor E.
6
2004
A quantitative lower bound for the greatest prime factor of \((ab+1)(bc+1)(ca+1)\). Zbl 1122.11060
Bugeaud, Yann; Luca, Florian
6
2004
The Diophantine equation \(x^2=p^a\pm p^b+1\). Zbl 1067.11016
Luca, Florian
6
2004
On the prime power factorization of \(n\)! Zbl 1049.11092
Luca, Florian; Stănică, Pantelimon
6
2003
Palindromes in Lucas sequences. Zbl 1027.11012
Luca, Florian
6
2003
Squares in Lehmer sequences and some Diophantine applications. Zbl 1006.11011
Luca, Florian; Walsh, P. G.
6
2001
On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
5
2019
Fibonacci numbers which are products of two Pell numbers. Zbl 1400.11040
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
5
2016
On the fixed points of the map \(x \mapsto x^x\) modulo a prime. Zbl 1393.11029
Kurlberg, Pär; Luca, Florian; Shparlinski, Igor E.
5
2015
On the counting function of irregular primes. Zbl 1356.11067
Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl
5
2015
Members of Lucas sequences whose Euler function is a power of 2. Zbl 1351.11015
Taoufiq Damir, Mohamed; Faye, Bernadette; Luca, Florian; Tall, Amadou
5
2014
On the \(g\)-ary expansions of middle binomial coefficients and Catalan numbers. Zbl 1221.11020
Luca, Florian; Shparlinski, Igor E.
5
2011
On the number of factorizations of an integer. Zbl 1245.11100
Balasubramanian, Ramachandran; Luca, Florian
5
2011
On the largest prime factor of \(x^2-1\). Zbl 1221.11080
Luca, Florian; Najman, Filip
5
2011
On the Diophantine equation \(x^2 + 2^a \cdot 11^b = y^n\). Zbl 1219.11056
Cangül, Ismail Naci; Demirci, Musa; Luca, Florian; Pintér, Ákos; Soydan, Gökhan
5
2010
Prime chains and Pratt trees. Zbl 1218.11085
Ford, Kevin; Konyagin, Sergei V.; Luca, Florian
5
2010
Representing integers as linear combinations of \(S\)-units. Zbl 1230.11044
Ádám, Zs.; Hajdu, L.; Luca, F.
5
2009
Primitive root bias for twin primes. II: Schinzel-type theorems for totient quotients and the sum-of-divisors function. Zbl 1450.11002
Garcia, Stephan Ramon; Luca, Florian; Shi, Kye; Udell, Gabe
3
2020
On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers. Zbl 1447.11025
Ddamulira, Mahadi; Luca, Florian
3
2020
The \(x\)-coordinates of Pell equations and sums of two Fibonacci numbers. II. Zbl 07271355
Ddamulira, Mahadi; Luca, Florian
1
2020
Lucas factoriangular numbers. Zbl 07217178
Kafle, Bir; Luca, Florian; Togbé, Alain
1
2020
On a Diophantine equation involving powers of Fibonacci numbers. Zbl 07192786
Gueth, Krisztián; Luca, Florian; Szalay, László
1
2020
Zeckendorf representations with at most two terms to \(x\)-coordinates of Pell equations. Zbl 1455.11031
Gómez, Carlos A.; Luca, Florian
1
2020
Pell and Pell-Lucas numbers as sums of two repdigits. Zbl 1452.11020
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
1
2020
On \(Y\)-coordinates of Pell equations which are members of a fixed binary recurrence. Zbl 07179055
Faye, Bernadette; Luca, Florian
1
2020
Correction to: \(X\)-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1449.11051
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian
1
2020
On certain sums concerning the gcd’s and lcm’s of \(k\) positive integers. Zbl 1452.11007
Hilberdink, Titus; Luca, Florian; Tóth, László
1
2020
Trinomials with given roots. Zbl 07152833
Bilu, Yuri; Luca, Florian
1
2020
On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
5
2019
Repdigits as sums of four Pell numbers. Zbl 1455.11019
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
4
2019
Primitive root bias for twin primes. Zbl 1450.11001
Garcia, Stephan Ramon; Kahoro, Elvis; Luca, Florian
4
2019
Repdigits as sums of three Lucas numbers. Zbl 07053960
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
4
2019
\(X\)-coordinates of Pell equations which are Lucas numbers. Zbl 07137965
Kafle, Bir; Luca, Florian; Togbé, Alain
3
2019
Lucas numbers as sums of two repdigits. Zbl 1427.11013
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
2
2019
On Pillai’s problem with the Fibonacci and Pell sequences. Zbl 1440.11018
Hernández Hernández, Santos; Luca, Florian; Rivera, Luis Manuel
2
2019
\(x\)-Coordinates of Pell equations which are Tribonacci numbers. II. Zbl 1449.11030
Kafle, Bir; Luca, Florian; Togbé, Alain
2
2019
On Pillai’s problem with \(X\)-coordinates of Pell equations and powers of 2. Zbl 07081797
Erazo, Harold S.; Gómez, Carlos A.; Luca, Florian
2
2019
Recurrence relations for polynomials obtained by arithmetic functions. Zbl 1435.11055
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
2
2019
On the discriminator of Lucas sequences. Zbl 07068791
Faye, Bernadette; Luca, Florian; Moree, Pieter
2
2019
On the zero-multiplicity of a fifth-order linear recurrence. Zbl 1450.11009
Gómez Ruiz, Carlos Alexis; Luca, Florian
2
2019
Diophantine equations with the Ramanujan \(\tau\) function of factorials, Fibonacci numbers, and Catalan numbers. Zbl 07099365
Luca, Florian; Mabaso, Sibusiso
1
2019
On the \(x\)-coordinates of Pell equations which are products of two Fibonacci numbers. Zbl 1420.11061
Kafle, Bir; Luca, Florian; Montejano, Amanda; Szalay, László; Togbé, Alain
1
2019
On the typical size and cancellations among the coefficients of some modular forms. Zbl 1450.11100
Luca, Florian; Radziwiłł, Maksym; Shparlinski, Igor E.
1
2019
Linear independence of powers of singular moduli of degree three. Zbl 1451.11069
Luca, Florian; Riffaut, Antonin
1
2019
On \(X\)-coordinates of Pell equations that are repdigits. Zbl 06985805
Faye, Bernadette; Luca, Florian
7
2018
On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027
Luca, Florian; Togbé, Alain
7
2018
On a problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of 2. Zbl 1437.11051
Ddamulira, Mahadi; Gómez, Carlos A.; Luca, Florian
6
2018
On perfect powers that are sums of two Fibonacci numbers. Zbl 06865878
Luca, Florian; Patel, Vandita
6
2018
On the difference in values of the Euler totient function near prime arguments. Zbl 1455.11127
Garcia, Stephan Ramon; Luca, Florian
4
2018
Repdigits as sums of three Pell numbers. Zbl 1413.11008
Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain
4
2018
Repdigits as sums of four Fibonacci or Lucas numbers. Zbl 1453.11006
Normenyo, Benedict Vasco; Luca, Florian; Togb, Alain
4
2018
Polynomial values of sums of products of consecutive integers. Zbl 1442.11055
Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F.
4
2018
Every positive integer is a sum of three palindromes. Zbl 1441.11016
Cilleruelo, Javier; Luca, Florian; Baxter, Lewis
4
2018
Primitive root biases for prime pairs. I: Existence and non-totality of biases. Zbl 1431.11112
Garcia, Stephan Ramon; Luca, Florian; Schaaff, Timothy
4
2018
On Pillai’s problem with Pell numbers and powers of 2. Zbl 1448.11042
Ouamar Hernane, Mohand; Luca, Florian; Rihane, Salah; Togbé, Alain
3
2018
Diophantine triples and \(k\)-generalized Fibonacci sequences. Zbl 1447.11054
Fuchs, Clemens; Hutle, Christoph; Luca, Florian; Szalay, László
3
2018
Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms. Zbl 1444.11071
Bilu, Yuri F.; Deshouillers, Jean-Marc; Gun, Sanoli; Luca, Florian
2
2018
\(X\)-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian
2
2018
Arithmetic properties of coefficients of \(L\)-functions of elliptic curves. Zbl 1423.11169
Güloğlu, Ahmet M.; Luca, Florian; Yalçiner, Aynur
1
2018
Markov equation with Fibonacci components. Zbl 06985849
Luca, Florian; Srinivasan, Anitha
1
2018
Denominators of Bernoulli polynomials. Zbl 1415.11121
Bordellès, Olivier; Luca, Florian; Moree, Pieter; Shparlinski, Igor E.
1
2018
A Diophantine equation in \(k\)-Fibonacci numbers and repdigits. Zbl 1407.11026
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
1
2018
On the error term of a lattice counting problem. Zbl 1380.11085
Bordellès, Olivier; Luca, Florian; Shparlinski, Igor E.
1
2018
On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
10
2017
On the \(X\)-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007
Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain
8
2017
On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013
Bravo, Jhon J.; Luca, Florian; Yazán, Karina
7
2017
\(p\)-adic quotient sets. Zbl 1428.11023
Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam
7
2017
Powers of two as sums of three Pell numbers. Zbl 1433.11032
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian
6
2017
On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. II. Zbl 1420.11037
Kafle, Bir; Luca, Florian; Togbé, Alain
4
2017
Diversity in parametric families of number fields. Zbl 1414.11150
Bilu, Yuri; Luca, Florian
2
2017
On Diophantine quadruples of Fibonacci numbers. Zbl 1386.11065
Fujita, Yasutsugu; Luca, Florian
2
2017
Only finitely many Tribonacci Diophantine triples exist. Zbl 1440.11042
Fuchs, Clemens; Hutle, Christoph; Irmak, Nurettin; Luca, Florian; Szalay, László
2
2017
The \(r\)th moment of the divisor function: an elementary approach. Zbl 1366.11103
Luca, Florian; Tóth, László
2
2017
Palindromes in several sequences. Zbl 1429.11018
Luca, Florian
2
2017
On the number of non-zero digits of integers in multi-base representations. Zbl 1399.11027
Bertók, Cs.; Hajdu, L.; Luca, F.; Sharma, D.
2
2017
Generalized incomplete poly-Bernoulli polynomials and generalized incomplete poly-Cauchy polynomials. Zbl 1409.11015
Komatsu, Takao; Luca, Florian
2
2017
On arithmetic lattices in the plane. Zbl 1358.11074
Fukshansky, Lenny; Guerzhoy, Pavel; Luca, Florian
2
2017
Counting terms \(U_n\) of third order linear recurrences with \(u_n = u^2 + nv^2\). Zbl 1425.11024
Ciolan, Alexandru; Luca, Florian; Moree, Pieter
1
2017
Local behavior of the composition of the aliquot and co-totient functions. Zbl 1421.11076
Luca, Florian; Pomerance, Carl
1
2017
Number fields in fibers: the geometrically abelian case with rational critical values. Zbl 1413.12001
Bilu, Yuri; Luca, Florian
1
2017
Diophantine triples with values in the sequences of Fibonacci and Lucas numbers. Zbl 1417.11011
Luca, Florian; Munagi, Augustine O.
1
2017
Corrigendum to “Positive integers divisible by the product of their nonzero digits”, portugaliae math. 64 (2007), 1: 75 – 85. Zbl 1434.11195
De Koninck, Jean-Marie; Luca, Florian
1
2017
Lucas numbers with the Lehmer property. Zbl 1389.11043
Faye, Bernadette; Luca, Florian
1
2017
On polynomials whose roots have rational quotient of differences. Zbl 1435.11061
Luca, Florian
1
2017
On two functions arising in the study of the Euler and Carmichael quotients. Zbl 1425.11009
Luca, Florian; Sha, Min; Shparlinski, Igor E.
1
2017
Fibonacci factoriangular numbers. Zbl 1373.11011
Gómez Ruiz, Carlos Alexis; Luca, Florian
1
2017
Collinear CM-points. Zbl 1432.11061
Bilu, Yuri; Luca, Florian; Masser, David
1
2017
Pell numbers with the Lehmer property. Zbl 1439.11015
Faye, Bernadette; Luca, Florian
1
2017
Monotonic phinomial coefficients. Zbl 1437.11006
Luca, Florian; Stănică, Pantelimon
1
2017
Powers of two as sums of two \(k\)-Fibonacci numbers. Zbl 1389.11041
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
14
2016
On the \(x\)-coordinates of Pell equations which are rep-digits. Zbl 1389.11076
Dossavi-Yovo, Appolinaire; Luca, Florian; Togbé, Alain
9
2016
Functional graphs of polynomials over finite fields. Zbl 1327.05323
Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E.
9
2016
Rational products of singular moduli. Zbl 1400.11113
Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia
7
2016
Quotients of Fibonacci numbers. Zbl 1391.11027
Garcia, Stephan Ramon; Luca, Florian
6
2016
Fibonacci numbers which are products of two Pell numbers. Zbl 1400.11040
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
5
2016
An explicit bound for the number of partitions into roots. Zbl 1343.05031
Luca, Florian; Ralaivaosaona, Dimbinaina
3
2016
Visual properties of generalized Kloosterman sums. Zbl 1338.11077
Burkhardt, Paula; Chan, Alice Zhuo-Yu; Currier, Gabriel; Garcia, Stephan Ramon; Luca, Florian; Suh, Hong
3
2016
On the Diophantine equation \(F_n + F_m=2^a\). Zbl 1419.11024
Bravo, Jhon J.; Luca, Florian
2
2016
Cyclotomic coefficients: gaps and jumps. Zbl 1405.11032
Camburu, Oana-Maria; Ciolan, Emil-Alexandru; Luca, Florian; Moree, Pieter; Shparlinski, Igor E.
2
2016
A note on odd perfect numbers. Zbl 1400.11010
Dris, Jose Arnaldo B.; Luca, Florian
1
2016
Sylvester’s theorem and the non-integrality of a certain binomial sum. Zbl 1400.11061
López-Aguayo, Daniel; Luca, Florian
1
2016
Repdigits as Euler functions of Lucas numbers. Zbl 1389.11040
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian; Tall, Amandou
1
2016
Multiplicative independence in \(k\)-generalized Fibonacci sequences. Zbl 1355.11010
Gómez Ruiz, Carlos Alexis; Luca, Florian
1
2016
An elliptic sequence is not a sampled linear recurrence sequence. Zbl 1367.11020
Luca, F.; Ward, T.
1
2016
Diophantine triples of Fibonacci numbers. Zbl 1359.11028
He, Bo; Luca, Florian; Togbé, Alain
1
2016
On a divisibility relation for Lucas sequences. Zbl 1402.11023
Bilu, Yuri F.; Komatsu, Takao; Luca, Florian; Pizarro-Madariaga, Amalia; Stănică, Pantelimon
1
2016
Carmichael numbers in the sequence \((2^{n} k+1)_{n\geq 1}\). Zbl 1400.11017
Cilleruelo, Javier; Luca, Florian; Pizarro-Madariaga, Amalia
1
2016
The distribution of self-Fibonacci divisors. Zbl 1390.11119
Luca, Florian; Tron, Emanuele
9
2015
Pell and Pell-Lucas numbers with only one distinct digit. Zbl 1349.11023
Faye, Bernadette; Luca, Florian
7
2015
On shifted primes with large prime factors and their products. Zbl 1370.11110
Luca, Florian; Menares, Ricardo; Pizarro-Madariaga, Amalia
7
2015
On the fixed points of the map \(x \mapsto x^x\) modulo a prime. Zbl 1393.11029
Kurlberg, Pär; Luca, Florian; Shparlinski, Igor E.
5
2015
On the counting function of irregular primes. Zbl 1356.11067
Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl
5
2015
On the largest prime factor of the ratio of two generalized Fibonacci numbers. Zbl 1393.11012
Gómez Ruiz, Carlos Alexis; Luca, Florian
4
2015
Tribonacci Diophantine quadruples. Zbl 1387.11013
Gómez Ruiz, Carlos Alexis; Luca, Florian
4
2015
Rectangles of nonvisible lattice points. Zbl 1390.11117
Laishram, Shanta; Luca, Florian
3
2015
Sierpiński and Carmichael numbers. Zbl 1325.11010
Banks, William; Finch, Carrie; Luca, Florian; Pomerance, Carl; Stănică, Pantelimon
3
2015
Diophantine quadruples in the sequence of shifted Tribonacci numbers. Zbl 1349.11024
Gómez Ruiz, Carlos Alexis; Luca, Florian
2
2015
...and 351 more Documents
all top 5

Cited by 842 Authors

201 Luca, Florian
46 Shparlinski, Igor E.
26 Togbé, Alain
20 Pollack, Paul
19 Bugeaud, Yann
19 Hajdu, Lajos
16 Sanna, Carlo
14 Marques, Diego
14 Szalay, László
13 Bravo, Jhon Jairo
13 Komatsu, Takao
13 Pomerance, Carl Bernard
12 De Koninck, Jean-Marie
12 Dubickas, Artūras
12 Dujella, Andrej
12 Stănică, Pantelimon
11 Chen, Yonggao
11 Garaev, Moubariz Z.
10 Adamczewski, Boris
10 Gómez, Carlos Alexis
10 Pink, István
9 Bennett, Michael A.
9 Cilleruelo, Javier
9 Ddamulira, Mahadi
9 Gómez Ruiz, Carlos Alexis
9 Siksek, Samir
9 Soydan, Gokhan
9 Ziegler, Volker
8 Banks, William D.
8 Bilu, Yuri F.
8 Fuchs, Clemens
8 Garcia, Stephan Ramon
8 Keskin, Refik
8 Moree, Pieter
8 Shorey, Tarlok Nath
7 Bérczes, Attila
7 Heim, Bernhard Ernst
7 Neuhauser, Markus
7 Sha, Min
7 Tengely, Szabolcs
7 Ulas, Maciej
6 Faye, Bernadette
6 Ford, Kevin B.
6 Grau, José María
6 Mignotte, Maurice
6 Panda, Gopal Krishna
6 Somer, Lawrence E.
6 Tijdeman, Robert
6 Winterhof, Arne
5 Adhikari, Sukumar Das
5 Bazsó, András
5 Broughan, Kevin A.
5 Irmak, Nurettin
5 Kátai, Imre
5 Křížek, Michal
5 Le, Maohua
5 Leonetti, Paolo
5 Pappalardi, Francesco
5 Rout, Sudhansu Sekhar
4 Berrizbeitia, Pedro
4 Bertók, Csanád
4 Bordellès, Olivier
4 Chattopadhyay, Jaitra
4 Chim, Kwok Chi
4 Coons, Michael
4 Drungilas, Paulius
4 Elsholtz, Christian
4 Hernández, Santos Hernández
4 Hu, Su
4 Kafle, Bir
4 Kihel, Omar
4 Laishram, Shanta
4 Miska, Piotr
4 Oller-Marcén, Antonio M.
4 Pizarro-Madariaga, Amalia
4 Raggi-Cárdenas, Alberto Gerardo
4 Rihane, Salah Eddine
4 Roy, Bidisha
4 Sarkar, Subha
4 Sun, Xuegong
4 Thangadurai, Ravindrananathan
4 Trojovský, Pavel
4 Wu, Jie
4 Zhu, Huilin
3 Abu Muriefah, Fadwa S.
3 Balasubramanian, Ramachandran
3 Bell, Jason P.
3 Berend, Daniel
3 Brandstätter, Nina
3 Bridy, Andrew
3 Bubboloni, Daniela
3 Chakraborty, Kalyan
3 Dai, Lixia
3 Deshouillers, Jean-Marc
3 Erduvan, Fatih
3 Freiberg, Tristan
3 Fu, Ruiqin
3 Fujita, Yasutsugu
3 Fukshansky, Lenny
3 Guzmán, Sergio
...and 742 more Authors
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Cited in 182 Serials

124 Journal of Number Theory
55 International Journal of Number Theory
28 Proceedings of the American Mathematical Society
25 Periodica Mathematica Hungarica
24 Mathematics of Computation
23 Monatshefte für Mathematik
22 Journal de Théorie des Nombres de Bordeaux
21 Bulletin of the Australian Mathematical Society
20 Indagationes Mathematicae. New Series
20 Journal of Integer Sequences
18 Integers
16 Acta Arithmetica
16 The Ramanujan Journal
15 Rocky Mountain Journal of Mathematics
15 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
13 Archiv der Mathematik
11 Lithuanian Mathematical Journal
11 Transactions of the American Mathematical Society
11 Boletín de la Sociedad Matemática Mexicana. Third Series
10 Functiones et Approximatio. Commentarii Mathematici
10 Finite Fields and their Applications
10 Comptes Rendus. Mathématique. Académie des Sciences, Paris
9 Acta Mathematica Hungarica
9 Research in Number Theory
8 Turkish Journal of Mathematics
7 Mathematical Proceedings of the Cambridge Philosophical Society
7 Mathematica Slovaca
7 Experimental Mathematics
7 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
7 Science China. Mathematics
6 Colloquium Mathematicum
6 Journal of Algebra
6 Mathematika
6 Proceedings of the Japan Academy. Series A
6 Journal of the Australian Mathematical Society
6 Bulletin of the Brazilian Mathematical Society. New Series
5 Discrete Mathematics
5 Proceedings of the Edinburgh Mathematical Society. Series II
5 European Journal of Combinatorics
5 Communications in Mathematics
5 Research in the Mathematical Sciences
4 Information Processing Letters
4 Glasgow Mathematical Journal
4 Journal of Combinatorial Theory. Series A
4 Mathematische Zeitschrift
4 Journal of Inequalities and Applications
3 Indian Journal of Pure & Applied Mathematics
3 Israel Journal of Mathematics
3 Mathematical Notes
3 Ukrainian Mathematical Journal
3 Chaos, Solitons and Fractals
3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
3 Czechoslovak Mathematical Journal
3 Manuscripta Mathematica
3 Quaestiones Mathematicae
3 Revista Matemática Iberoamericana
3 Journal of the Ramanujan Mathematical Society
3 Elemente der Mathematik
3 Glasnik Matematički. Serija III
3 Abstract and Applied Analysis
3 Acta Mathematica Sinica. English Series
3 Portugaliae Mathematica. Nova Série
3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
2 Discrete Applied Mathematics
2 Journal of Mathematical Analysis and Applications
2 Applied Mathematics and Computation
2 Archivum Mathematicum
2 Bulletin of the London Mathematical Society
2 Canadian Mathematical Bulletin
2 Illinois Journal of Mathematics
2 Inventiones Mathematicae
2 Mathematische Annalen
2 Rendiconti del Circolo Matemàtico di Palermo. Serie II
2 Results in Mathematics
2 Advances in Applied Mathematics
2 Forum Mathematicum
2 Designs, Codes and Cryptography
2 Geometric and Functional Analysis. GAFA
2 Aequationes Mathematicae
2 Bulletin of the American Mathematical Society. New Series
2 Expositiones Mathematicae
2 Applicable Algebra in Engineering, Communication and Computing
2 The Electronic Journal of Combinatorics
2 Integral Transforms and Special Functions
2 Journal of Difference Equations and Applications
2 Annals of Combinatorics
2 LMS Journal of Computation and Mathematics
2 Journal of the European Mathematical Society (JEMS)
2 RAIRO. Theoretical Informatics and Applications
2 Acta et Commentationes Universitatis Tartuensis de Mathematica
2 Journal of High Energy Physics
2 Mediterranean Journal of Mathematics
2 Journal of Mathematical Cryptology
2 Algebra & Number Theory
2 Afrika Matematika
2 European Journal of Mathematics
2 Bulletin of the Hellenic Mathematical Society
1 American Mathematical Monthly
1 Communications in Algebra
1 Computers & Mathematics with Applications
...and 82 more Serials

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