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Author ID: luca.florian Recent zbMATH articles by "Luca, Florian"
Published as: Luca, Florian; Luca, F.
Homepage: https://www.wits.ac.za/staff/academic-a-z-listing/l/florianlucawitsacza/
External Links: MGP · ORCID · Wikidata · Math-Net.Ru · dblp · GND · IdRef · theses.fr
Documents Indexed: 724 Publications since 1993, including 3 Books
5 Contributions as Editor
Reviewing Activity: 331 Reviews
Co-Authors: 321 Co-Authors with 630 Joint Publications
5,222 Co-Co-Authors
all top 5

Co-Authors

99 single-authored
77 Shparlinski, Igor E.
42 Togbé, Alain
38 Stănică, Pantelimon
37 Gómez, Carlos Alexis
29 De Koninck, Jean-Marie
25 Banks, William D.
24 Pomerance, Carl Bernard
23 Bravo, Jhon Jairo
20 Szalay, László
17 Faye, Bernadette
13 Bilu, Yuri F.
13 Garaev, Moubariz Z.
12 Cilleruelo, Javier
11 Mignotte, Maurice
10 Bugeaud, Yann
10 Ford, Kevin B.
9 Mejía-Huguet, V. Janitzio
9 Pappalardi, Francesco
9 Walsh, Peter Gareth
8 Ddamulira, Mahadi
8 Dujella, Andrej
8 Garcia, Stephan Ramon
8 Kafle, Bir
8 Moree, Pieter
7 Bérczes, Attila
7 Hajdu, Lajos
7 Hernández Hernández, Santos
7 Komatsu, Takao
7 Siksek, Samir
7 Somer, Lawrence E.
7 Tachiya, Yohei
6 Altassan, Alaa
6 Bravo, Eric F.
6 Broughan, Kevin A.
6 Friedlander, John Benjamin
6 Fuchs, Clemens
6 Gómez, Jhonny C.
6 Křížek, Michal
6 Pizarro-Madariaga, Amalia
5 Berrizbeitia, Pedro
5 Grytczuk, Aleksander
5 Klazar, Martin
5 Knopfmacher, Arnold
5 Rihane, Salah Eddine
5 Shorey, Tarlok Nath
5 Thangadurai, Ravindranathan
5 Wójtowicz, Marek
5 Yalçiner, Aynur
5 Young, Paul Thomas
4 Alahmadi, Adel N.
4 Balasubramanian, Ramachandran
4 Ballot, Christian
4 Cipu, Mihai
4 Deshouillers, Jean-Marc
4 Doyon, Nicolas
4 González, Marcos José
4 Hernández, Santos
4 Kihel, Omar
4 Konyagin, Sergeĭ Vladimirovich
4 Laishram, Shanta
4 Normenyo, Benedict Vasco
4 Pintér, Ákos
4 Pollack, Paul
4 Sankaranarayanan, Ayyadurai
4 Ziegler, Volker
3 Adegbindin, Chèfiath Awero
3 Alba González, Juan José
3 Chakraborty, Kalyan
3 Dress, Andreas W. M.
3 Erazo, Harold S.
3 Filaseta, Michael A.
3 Grau, José María
3 Hutle, Christoph
3 Iannucci, Douglas E.
3 Ionaşcu, Eugen Julien
3 Mabaso, Sibusiso
3 Mukhopadhyay, Anirban
3 Munagi, Augustine O.
3 Nicolae, Florin
3 Nowak, Werner Georg
3 Oyono, Roger
3 Porubsky, Stefan
3 Ralaivaosaona, Dimbinaina
3 Shoaib, Hatoon
3 Soydan, Gokhan
3 Tall, Amadou Makhtar
2 Abu Muriefah, Fadwa S.
2 Adamczewski, Boris
2 Alvarado, Saúl Díaz
2 Ayad, Mohamed
2 Balasuriya, Sanka
2 Banderier, Cyril
2 Bazsó, András
2 Bordellès, Olivier
2 Bubboloni, Daniela
2 Cangul, Ismail Naci
2 Ciolan, Alexandru
2 de Weger, Benne
2 Demirci, Musa
2 Flammenkamp, Achim
...and 223 more Co-Authors
all top 5

Serials

51 Journal of Number Theory
42 Acta Arithmetica
29 International Journal of Number Theory
28 The Fibonacci Quarterly
22 Journal of Integer Sequences
21 Colloquium Mathematicum
18 Publicationes Mathematicae
18 Integers
15 Indagationes Mathematicae. New Series
13 Periodica Mathematica Hungarica
13 Monatshefte für Mathematik
13 Glasnik Matematički. Serija III
13 Boletín de la Sociedad Matemática Mexicana. Third Series
12 Annales Mathematicae et Informaticae
11 Bulletin of the Australian Mathematical Society
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
9 The Ramanujan 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 Functiones et Approximatio. Commentarii Mathematici
7 Mathematica Slovaca
7 The New York Journal of Mathematics
6 American Mathematical Monthly
6 Proceedings of the Edinburgh Mathematical Society. Series II
6 Journal of Combinatorics and Number Theory
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 Mathematica Bohemica
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 Quaestiones Mathematicae
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
4 Communications in Mathematics
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 Publications de l’Institut Mathématique. Nouvelle Série
3 Results in Mathematics
3 Studia Scientiarum Mathematicarum Hungarica
3 Transactions of the American Mathematical Society
3 Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica
3 Acta Mathematica Hungarica
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 Afrika Matematika
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 Revista de la Unión Matemática Argentina
2 Bulletin of the Greek Mathematical Society
2 Bulletin of the Korean Mathematical Society
2 Forum Mathematicum
2 Journal of the Ramanujan Mathematical Society
2 Elemente der Mathematik
2 Analele Științifice ale Universității Al. I. Cuza din Iași. 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 Științifice ale Universității “Ovidius” Constanța. 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 Mediterranean Journal of Mathematics
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
...and 66 more Serials

Publications by Year

Citations contained in zbMATH Open

492 Publications have been cited 2,109 times in 1,071 Documents Cited by Year
On a conjecture about repdigits in \(k\)-generalized Fibonacci sequences. Zbl 1274.11035
Bravo, Jhon J.; Luca, Florian
44
2013
Fibonacci and Lucas numbers with only one distinct digit. Zbl 0958.11007
Luca, F.
41
2000
Powers of two in generalized Fibonacci sequences. Zbl 1353.11020
Bravo, Jhon J.; Luca, Florian
33
2012
Linear combinations of factorials and \(S\)-units in a binary recurrence sequence. Zbl 1361.11007
Sanchez, Sergio Guzmán; Luca, Florian
32
2014
Powers of two as sums of two \(k\)-Fibonacci numbers. Zbl 1389.11041
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
31
2016
On the complexity of algebraic numbers. (Sur la complexité des nombres algébriques.) Zbl 1119.11019
Adamczewski, Boris; Bugeaud, Yann; Luca, Florian
30
2004
Fibonacci numbers at most one away from a perfect power. Zbl 1156.11008
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
28
2008
Analytic number theory. Exploring the anatomy of integers. Zbl 1247.11001
De Koninck, Jean-Marie; Luca, Florian
27
2012
Repdigits as sums of three Fibonacci numbers. Zbl 1305.11008
Luca, Florian
21
2012
Fibonacci numbers which are sums of two repdigits. Zbl 1287.11021
Díaz Alvarado, Saúl; Luca, Florian
20
2011
A generalization of a classical zero-sum problem. Zbl 1123.11012
Luca, Florian
19
2007
On the equation \(x^2 + 2^a \cdot 3^b = y^n\). Zbl 1085.11021
Luca, Florian
18
2002
Pell and Pell-Lucas numbers with only one distinct digit. Zbl 1349.11023
Faye, Bernadette; Luca, Florian
18
2015
Distinct digits in base \(b\) expansions of linear recurrence sequences. Zbl 1030.11004
Luca, Florian
16
2000
On the largest prime factor of the \(k\)-Fibonacci numbers. Zbl 1292.11034
Bravo, Jhon J.; Luca, Florian
16
2013
Coincidences in generalized Fibonacci sequences. Zbl 1272.11028
Bravo, Jhon J.; Luca, Florian
15
2013
On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
14
2017
On the Diophantine equation \(x^2+2^a\cdot 5^b=y^n\). Zbl 1231.11041
Luca, Florian; Togbé, Alain
14
2008
On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions \(\varphi\) and \(\sigma\). Zbl 1027.11007
Luca, Florian; Pomerance, Carl
14
2002
Character sums and congruences with \(n!\). Zbl 1060.11046
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
13
2004
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
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
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
13
2014
On a Diophantine equation. Zbl 0997.11027
Luca, Florian
12
2000
On the \(x\)-coordinates of Pell equations which are rep-digits. Zbl 1389.11076
Dossavi-Yovo, Appolinaire; Luca, Florian; Togbé, Alain
12
2016
Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers. Zbl 1289.11021
Komatsu, Takao; Luca, Florian
12
2013
An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Zbl 1253.11046
Luca, Florian; Oyono, Roger
12
2011
On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013
Bravo, Jhon J.; Luca, Florian; Yazán, Karina
11
2017
Diophantine equations with products of consecutive terms in Lucas sequences. Zbl 1081.11023
Luca, F.; Shorey, T. N.
11
2005
On \(X\)-coordinates of Pell equations that are repdigits. Zbl 1459.11082
Faye, Bernadette; Luca, Florian
10
2018
Repdigits as sums of four Pell numbers. Zbl 1455.11019
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
10
2019
Rational products of singular moduli. Zbl 1400.11113
Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia
10
2016
Almost powers in the Lucas sequence. Zbl 1204.11030
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
10
2008
On the exponential local-global principle. Zbl 1330.11019
Bartolome, Boris; Bilu, Yuri; Luca, Florian
10
2013
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
10
2006
Functional graphs of polynomials over finite fields. Zbl 1327.05323
Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E.
10
2016
Quotients of Fibonacci numbers. Zbl 1391.11027
Garcia, Stephan Ramon; Luca, Florian
9
2016
On a problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of 2. Zbl 1437.11051
Ddamulira, Mahadi; Gómez, Carlos A.; Luca, Florian
9
2018
Repdigits as sums of three Pell numbers. Zbl 1413.11008
Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain
9
2018
On perfect powers that are sums of two Fibonacci numbers. Zbl 1467.11038
Luca, Florian; Patel, Vandita
9
2018
Divisibility of class numbers: enumerative approach. Zbl 1072.11084
Bilu, Yuri F.; Luca, Florian
9
2005
Some results on Oppenheim’s “factorisatio numerorum” function. Zbl 1213.11020
Luca, Florian; Mukhopadhyay, Anirban; Srinivas, Kotyada
9
2010
Fibonacci numbers of the form \(p^a\pm p^b+1\). Zbl 1228.11021
Luca, Florian; Szalay, László
9
2007
Irreducible radical extensions and Euler-function chains. Zbl 1172.11029
Luca, Florian; Pomerance, Carl
9
2007
The Diophantine equation \(P(x)=n!\) and a result of M. Overholt. Zbl 1085.11023
Luca, Florian
9
2002
Generalized balancing numbers. Zbl 1239.11035
Liptai, Kálmán; Luca, Florian; Pintér, Ákos; Szalay, László
9
2009
On the Diophantine equation \(x^2 + 2^{\alpha}5^{\beta}13^{\gamma} = y^n\). Zbl 1232.11130
Goins, Edray; Luca, Florian; Togbé, Alain
9
2008
On Pillai’s Diophantine equation. Zbl 1136.11026
Bugeaud, Yann; Luca, Florian
9
2006
On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027
Luca, Florian; Togbé, Alain
9
2018
On a diophantine equation related to a conjecture of Erdös and Graham. Zbl 1132.11319
Luca, F.; Walsh, P. G.
9
2007
On the \(X\)-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007
Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain
9
2017
\(p\)-adic quotient sets. Zbl 1428.11023
Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam
9
2017
Every positive integer is a sum of three palindromes. Zbl 1441.11016
Cilleruelo, Javier; Luca, Florian; Baxter, Lewis
8
2018
Powers of two as sums of three Pell numbers. Zbl 1433.11032
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian
8
2017
Average order in cyclic groups. Zbl 1079.11003
von zur Gathen, Joachim; Knopfmacher, Arnold; Luca, Florian; Lucht, Lutz G.; Shparlinski, Igor E.
8
2004
Some remarks on Heron triangles. Zbl 1062.11019
Kramer, Alpar-Vajk; Luca, Florian
8
2000
Squares in Lehmer sequences and some Diophantine applications. Zbl 1006.11011
Luca, Florian; Walsh, P. G.
8
2001
MOV attack in various subgroups on elliptic curves. Zbl 1072.11094
Luca, Florian; Mireles, David Jose; Shparlinski, Igor E.
8
2004
Some additive combinatorics problems in matrix rings. Zbl 1208.11037
Ferguson, Ron; Hoffman, Corneliu; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E.
8
2010
On factorials expressible as sums of at most three Fibonacci numbers. Zbl 1253.11048
Luca, Florian; Siksek, Samir
8
2010
Common values of the arithmetic functions \(\varphi\) and \(\sigma\). Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
8
2010
On the maximal order of numbers in the “factorisatio numerorum” problem. Zbl 1169.11043
Klazar, Martin; Luca, Florian
8
2007
Fibonacci numbers with the Lehmer property. Zbl 1112.11007
Luca, Florian
8
2007
On the exponent of the group of points on elliptic curves in extension fields. Zbl 1082.11041
Luca, Florian; Shparlinski, Igor E.
8
2005
On stable quadratic polynomials. Zbl 1241.11027
Ahmadi, Omran; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E.
8
2012
On the Diophantine equation \(x^2 + C = 2y^n\). Zbl 1233.11037
Abu Muriefah, Fadwa S.; Luca, Florian; Siksek, Samir; Tengely, Szabolcs
8
2009
The distribution of self-Fibonacci divisors. Zbl 1390.11119
Luca, Florian; Tron, Emanuele
8
2015
Perfect powers from products of terms in Lucas sequences. Zbl 1137.11011
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
8
2007
Catalan and Apéry numbers in residue classes. Zbl 1101.11010
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
8
2006
Fibonacci Diophantine triples. Zbl 1218.11020
Luca, Florian; Szalay, László
8
2008
On the Diophantine equation \(x^2 + 5^a 13^b = y^n\). Zbl 1186.11016
Abu Muriefah, Fadwa S.; Luca, Florian; Togbé, Alain
8
2008
Powers of two as sums of two Lucas numbers. Zbl 1358.11026
Bravo, Jhon J.; Luca, Florian
8
2014
Polynomial values of sums of products of consecutive integers. Zbl 1442.11055
Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F.
7
2018
On the Diophantine equation \(F_n + F_m=2^a\). Zbl 1419.11024
Bravo, Jhon J.; Luca, Florian
7
2016
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
7
2010
Exponential sums and congruences with factorials. Zbl 1071.11051
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
7
2005
The number of non-zero digits of \(n\)! Zbl 1043.11008
Luca, Florian
7
2002
Fibonacci numbers which are sums of three factorials. Zbl 1259.11038
Bollman, Mark; Hernández Hernández, Santos; Luca, Florian
7
2010
On the Diophantine equation \(x^2+7^{2k}=y^n\). Zbl 1221.11091
Luca, Florian; Togbé, Alain
7
2007
On shifted primes with large prime factors and their products. Zbl 1370.11110
Luca, Florian; Menares, Ricardo; Pizarro-Madariaga, Amalia
7
2015
On the Diophantine equation \(x^2+2^a\cdot 3^b \cdot 11^c = y^n\). Zbl 1349.11069
Cangül, İsmail Naci; Demirci, Musa; İnam, İlker; Luca, Florian; Soydan, Gökhan
7
2013
On the largest prime factor of \((ab+1)(ac+1)(bc+1)\). Zbl 1108.11030
Hernández, Santos; Luca, Florian
7
2003
On composite integers \(n\) for which \(\varphi(n)\mid n-1\). Zbl 1294.11005
Luca, Florian; Pomerance, Carl
7
2011
Repdigits as sums of four Fibonacci or Lucas numbers. Zbl 1453.11006
Normenyo, Benedict Vasco; Luca, Florian; Togb, Alain
7
2018
On the number of factorizations of an integer. Zbl 1245.11100
Balasubramanian, Ramachandran; Luca, Florian
7
2011
On factorials which are products of factorials. Zbl 1132.11017
Luca, Florian
7
2007
Fibonacci numbers which are products of two Pell numbers. Zbl 1400.11040
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
6
2016
An exponential Diophantine equation related to the sum of powers of two consecutive \(k\)-generalized Fibonacci numbers. Zbl 1338.11016
Gómez Ruiz, Carlos Alexis; Luca, Florian
6
2014
Recurrence relations for polynomials obtained by arithmetic functions. Zbl 1435.11055
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
6
2019
On Pillai’s problem with Pell numbers and powers of 2. Zbl 1448.11042
Ouamar Hernane, Mohand; Luca, Florian; Rihane, Salah; Togbé, Alain
6
2018
On shifted products which are powers. Zbl 1123.11011
Luca, Florian
6
2005
The Diophantine equation \(x^2=p^a\pm p^b+1\). Zbl 1067.11016
Luca, Florian
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
Fibonacci numbers of the form \(k^2+k+2\). Zbl 0979.11012
Luca, Florian
6
1999
Fibonacci numbers that are not sums of two prime powers. Zbl 1113.11011
Luca, Florian; Stănică, Pantelimon
6
2005
On Fibonacci numbers with few prime divisors. Zbl 1087.11009
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
6
2005
On the convergence of series of reciprocals of primes related to the Fermat numbers. Zbl 1026.11011
Křížek, Michal; Luca, Florian; Somer, Lawrence
6
2002
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
Fibonacci numbers of the form \(p^a\pm p^b\). Zbl 1273.11030
Luca, Florian; Stănică, Pantelimon
6
2009
Control of coupled parabolic systems and Diophantine approximations. Zbl 1272.93029
Luca, Florian; De Teresa, Luz
6
2013
Fibonacci numbers which are concatenations of two repdigits. Zbl 1472.11067
Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon
6
2021
On a generalization of the Pell sequence. Zbl 07361099
Bravo, Jhon J.; Herrera, Jose L.; Luca, Florian
5
2021
Common values of generalized Fibonacci and Pell sequences. Zbl 1471.11049
Bravo, Jhon J.; Herrera, Jose L.; Luca, Florian
3
2021
\(k\)-generalized Fibonacci numbers which are concatenations of two repdigits. Zbl 07414938
Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon
1
2021
On the nonnegative integer solutions to the equation \(F_n \pm F_m = y^a\). Zbl 07276978
Kebli, Salima; Kihel, Omar; Larone, Jesse; Luca, Florian
1
2021
Pell and Pell-Lucas numbers as sums of two repdigits. Zbl 1452.11020
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
6
2020
On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers. Zbl 1447.11025
Ddamulira, Mahadi; Luca, Florian
5
2020
Products of \(k\)-Fibonacci numbers which are rep-digits. Zbl 1463.11032
Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon
4
2020
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 certain sums concerning the gcd’s and lcm’s of \(k\) positive integers. Zbl 1452.11007
Hilberdink, Titus; Luca, Florian; Tóth, László
3
2020
On the problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of \(3\). Zbl 1446.11025
Ddamulira, Mahadi; Luca, Florian
3
2020
Zeckendorf representations with at most two terms to \(x\)-coordinates of Pell equations. Zbl 1455.11031
Gómez, Carlos A.; Luca, Florian
3
2020
Trinomials with given roots. Zbl 1479.11052
Bilu, Yuri; Luca, Florian
2
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
2
2020
On members of Lucas sequences which are products of factorials. Zbl 1478.11018
Laishram, Shanta; Luca, Florian; Sias, Mark
2
2020
On a conjecture concerning the multiplicity of the Tribonacci sequence. Zbl 1459.11036
Bravo, Eric F.; Gómez, Carlos A.; Kafle, Bir; Luca, Florian; Togbé, Alain
1
2020
Total multiplicity of the Tribonacci sequence. Zbl 1459.11037
Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian
1
2020
Lucas factoriangular numbers. Zbl 07217178
Kafle, Bir; Luca, Florian; Togbé, Alain
1
2020
On the equation \(\sum_{j = 1}^k j F_j^p = F_n^q\). Zbl 1471.11043
Altassan, Alaa; Luca, Florian
1
2020
Composite positive integers whose sum of prime factors is prime. Zbl 07177880
Luca, Florian; Moodley, Damon
1
2020
On \(Y\)-coordinates of Pell equations which are members of a fixed binary recurrence. Zbl 1477.11060
Faye, Bernadette; Luca, Florian
1
2020
On a Diophantine equation involving powers of Fibonacci numbers. Zbl 1478.11017
Gueth, Krisztián; Luca, Florian; Szalay, László
1
2020
The \(x\)-coordinates of Pell equations and sums of two Fibonacci numbers. II. Zbl 1471.11065
Ddamulira, Mahadi; Luca, Florian
1
2020
Binary recurrences for which powers of two are discriminating moduli. Zbl 1471.11086
de Clercq, Adriaan A.; Luca, Florian; Martirosyan, Lilit; Matthis, Maria; Moree, Pieter; Stoumen, Max A.; Weiß, Melvin
1
2020
On the prime factors of the iterates of the Ramanujan \(\tau\)-function. Zbl 1472.11036
Luca, Florian; Mabaso, Sibusiso; Stănică, Pantelimon
1
2020
Multiplicative dependence between \(k\)-Fibonacci and \(k\)-Lucas numbers. Zbl 1474.11047
Gómez, Carlos A.; Gómez, Jhonny C.; Luca, Florian
1
2020
On the zero-multiplicity of the \(k\)-generalized Fibonacci sequence. Zbl 1464.11024
García, Jonathan; Gómez, Carlos A.; Luca, Florian
1
2020
Repdigits as sums of four Pell numbers. Zbl 1455.11019
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
10
2019
Recurrence relations for polynomials obtained by arithmetic functions. Zbl 1435.11055
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
6
2019
Repdigits as sums of three Lucas numbers. Zbl 1459.11041
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
5
2019
On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
5
2019
Lucas numbers as sums of two repdigits. Zbl 1427.11013
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
5
2019
On Pillai’s problem with the Fibonacci and Pell sequences. Zbl 1440.11018
Hernández Hernández, Santos; Luca, Florian; Rivera, Luis Manuel
5
2019
Primitive root bias for twin primes. Zbl 1450.11001
Garcia, Stephan Ramon; Kahoro, Elvis; Luca, Florian
4
2019
On Pillai’s problem with \(X\)-coordinates of Pell equations and powers of 2. Zbl 1465.11086
Erazo, Harold S.; Gómez, Carlos A.; Luca, Florian
4
2019
\(X\)-coordinates of Pell equations which are Lucas numbers. Zbl 07137965
Kafle, Bir; Luca, Florian; Togbé, Alain
4
2019
On the zero-multiplicity of a fifth-order linear recurrence. Zbl 1450.11009
Gómez Ruiz, Carlos Alexis; Luca, Florian
3
2019
On the exponential Diophantine equation \(P_n^x+P_{n+1}^x=P_m\). Zbl 1455.11056
Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain
3
2019
\(x\)-Coordinates of Pell equations which are Tribonacci numbers. II. Zbl 1449.11030
Kafle, Bir; Luca, Florian; Togbé, Alain
3
2019
An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers. Zbl 1449.11036
Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain
3
2019
On the discriminator of Lucas sequences. Zbl 1456.11021
Faye, Bernadette; Luca, Florian; Moree, Pieter
2
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
2
2019
Diophantine equations with the Ramanujan \(\tau\) function of factorials, Fibonacci numbers, and Catalan numbers. Zbl 1456.11031
Luca, Florian; Mabaso, Sibusiso
2
2019
On ternary Egyptian fractions with prime denominator. Zbl 1455.11057
Luca, Florian; Pappalardi, Francesco
2
2019
Product of consecutive tribonacci numbers with only one distinct digit. Zbl 1455.11027
Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian
2
2019
Linear independence of powers of singular moduli of degree three. Zbl 1451.11069
Luca, Florian; Riffaut, Antonin
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
Diophantine \(S\)-quadruples with two primes which are twin. Zbl 1449.11067
Luca, F.
1
2019
Perfect Pell and Pell-Lucas numbers. Zbl 1449.11026
Bravo, Jhon J.; Luca, Florian
1
2019
Consecutive integers with close kernels. Zbl 1478.11008
De Koninck, Jean-Marie; Luca, Florian
1
2019
On \(X\)-coordinates of Pell equations that are repdigits. Zbl 1459.11082
Faye, Bernadette; Luca, Florian
10
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
9
2018
Repdigits as sums of three Pell numbers. Zbl 1413.11008
Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain
9
2018
On perfect powers that are sums of two Fibonacci numbers. Zbl 1467.11038
Luca, Florian; Patel, Vandita
9
2018
On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027
Luca, Florian; Togbé, Alain
9
2018
Every positive integer is a sum of three palindromes. Zbl 1441.11016
Cilleruelo, Javier; Luca, Florian; Baxter, Lewis
8
2018
Polynomial values of sums of products of consecutive integers. Zbl 1442.11055
Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F.
7
2018
Repdigits as sums of four Fibonacci or Lucas numbers. Zbl 1453.11006
Normenyo, Benedict Vasco; Luca, Florian; Togb, Alain
7
2018
On Pillai’s problem with Pell numbers and powers of 2. Zbl 1448.11042
Ouamar Hernane, Mohand; Luca, Florian; Rihane, Salah; Togbé, Alain
6
2018
\(X\)-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian
5
2018
A Diophantine equation in \(k\)-Fibonacci numbers and repdigits. Zbl 1407.11026
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
5
2018
Diophantine triples and \(k\)-generalized Fibonacci sequences. Zbl 1447.11054
Fuchs, Clemens; Hutle, Christoph; Luca, Florian; Szalay, László
4
2018
On the difference in values of the Euler totient function near prime arguments. Zbl 1455.11127
Garcia, Stephan Ramon; Luca, Florian
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
Markov equation with Fibonacci components. Zbl 1458.11056
Luca, Florian; Srinivasan, Anitha
3
2018
Arithmetic properties of coefficients of \(L\)-functions of elliptic curves. Zbl 1423.11169
Güloğlu, Ahmet M.; Luca, Florian; Yalçiner, Aynur
2
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
Denominators of Bernoulli polynomials. Zbl 1415.11121
Bordellès, Olivier; Luca, Florian; Moree, Pieter; Shparlinski, Igor E.
1
2018
There are no Diophantine quadruples of Fibonacci numbers. Zbl 1441.11058
Fujita, Yasutsugu; Luca, Florian
1
2018
A variation on the theme of Nicomachus. Zbl 1410.11079
Luca, Florian; Polanco, Geremías; Zudilin, Wadim
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
14
2017
On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013
Bravo, Jhon J.; Luca, Florian; Yazán, Karina
11
2017
On the \(X\)-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007
Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain
9
2017
\(p\)-adic quotient sets. Zbl 1428.11023
Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam
9
2017
Powers of two as sums of three Pell numbers. Zbl 1433.11032
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian
8
2017
On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. II. Zbl 1420.11037
Kafle, Bir; Luca, Florian; Togbé, Alain
6
2017
On Diophantine quadruples of Fibonacci numbers. Zbl 1386.11065
Fujita, Yasutsugu; Luca, Florian
3
2017
On arithmetic lattices in the plane. Zbl 1358.11074
Fukshansky, Lenny; Guerzhoy, Pavel; Luca, Florian
3
2017
Diversity in parametric families of number fields. Zbl 1414.11150
Bilu, Yuri; Luca, Florian
2
2017
Lucas numbers with the Lehmer property. Zbl 1389.11043
Faye, Bernadette; Luca, Florian
2
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
2
2017
Generalized incomplete poly-Bernoulli polynomials and generalized incomplete poly-Cauchy polynomials. Zbl 1409.11015
Komatsu, Takao; 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
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
Palindromes in several sequences. Zbl 1429.11018
Luca, Florian
2
2017
Monotonic phinomial coefficients. Zbl 1437.11006
Luca, Florian; Stănică, Pantelimon
2
2017
The \(r\)th moment of the divisor function: an elementary approach. Zbl 1366.11103
Luca, Florian; Tóth, László
2
2017
Collinear CM-points. Zbl 1432.11061
Bilu, Yuri; Luca, Florian; Masser, David
2
2017
Fibonacci factoriangular numbers. Zbl 1373.11011
Gómez Ruiz, Carlos Alexis; Luca, Florian
2
2017
Local behavior of the composition of the aliquot and co-totient functions. Zbl 1421.11076
Luca, Florian; Pomerance, Carl
1
2017
Diophantine triples with values in the sequences of Fibonacci and Lucas numbers. Zbl 1417.11011
Luca, Florian; Munagi, Augustine O.
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
On polynomials whose roots have rational quotient of differences. Zbl 1435.11061
Luca, Florian
1
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
Number fields in fibers: the geometrically abelian case with rational critical values. Zbl 1413.12001
Bilu, Yuri; Luca, Florian
1
2017
Linear independence results for the reciprocal sums of Fibbonacci numbers associated with Dirichlet characters. Zbl 1399.11122
Ei, Hiromi; Luca, Florian; Tachiya, Yohei
1
2017
Pell numbers with the Lehmer property. Zbl 1439.11015
Faye, Bernadette; Luca, Florian
1
2017
Powers of two as sums of two \(k\)-Fibonacci numbers. Zbl 1389.11041
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
31
2016
On the \(x\)-coordinates of Pell equations which are rep-digits. Zbl 1389.11076
Dossavi-Yovo, Appolinaire; Luca, Florian; Togbé, Alain
12
2016
...and 392 more Documents
all top 5

Cited by 964 Authors

226 Luca, Florian
46 Shparlinski, Igor E.
35 Togbé, Alain
28 Gómez, Carlos Alexis
24 Pollack, Paul
22 Bravo, Jhon Jairo
22 Hajdu, Lajos
19 Sanna, Carlo
18 Bugeaud, Yann
17 Keskin, Refik
15 Marques, Diego
15 Szalay, László
14 De Koninck, Jean-Marie
14 Pomerance, Carl Bernard
13 Ddamulira, Mahadi
13 Komatsu, Takao
12 Dubickas, Artūras
12 Dujella, Andrej
12 Rihane, Salah Eddine
12 Stănică, Pantelimon
11 Garaev, Moubariz Z.
10 Adamczewski, Boris
10 Bennett, Michael A.
10 Chen, Yonggao
10 Erduvan, Fatih
10 Heim, Bernhard Ernst
10 Neuhauser, Markus
10 Pink, István
10 Siksek, Samir
10 Ziegler, Volker
9 Bilu, Yuri F.
9 Cilleruelo, Javier
9 Fuchs, Clemens
9 Moree, Pieter
9 Soydan, Gokhan
8 Banks, William D.
8 Bérczes, Attila
8 Garcia, Stephan Ramon
8 Shorey, Tarlok Nath
8 Tengely, Szabolcs
8 Tijdeman, Robert
7 Bazsó, András
7 Faye, Bernadette
7 Kihel, Omar
7 Laishram, Shanta
7 Panda, Gopal Krishna
7 Pappalardi, Francesco
7 Sha, Min
7 Shallit, Jeffrey O.
7 Şiar, Zafer
7 Ulas, Maciej
7 Winterhof, Arne
6 Adhikari, Sukumar Das
6 Ford, Kevin B.
6 Grau, José María
6 Hernández Hernández, Santos
6 Herrera, José L.
6 Kátai, Imre
6 Mignotte, Maurice
6 Patel, Vandita
6 Rout, Sudhansu Sekhar
6 Trojovský, Pavel
5 Bravo, Eric F.
5 Broughan, Kevin A.
5 Chakraborty, Kalyan
5 Hernane, Mohand-Ouamar
5 Irmak, Nurettin
5 Le, Maohua
5 Leonetti, Paolo
5 Miska, Piotr
5 Sarkar, Subha
5 Zhang, Yong
5 Zhu, Huilin
4 Altassan, Alaa
4 Balasubramanian, Ramachandran
4 Bell, Jason P.
4 Berrizbeitia, Pedro
4 Bertók, Csanád
4 Bordellès, Olivier
4 Bubboloni, Daniela
4 Chattopadhyay, Jaitra
4 Chim, Kwok Chi
4 Coons, Michael
4 Deshouillers, Jean-Marc
4 Drungilas, Paulius
4 Elsholtz, Christian
4 Fu, Ruiqin
4 García Lomelí, Ana Cecilia
4 Gómez, Jhonny C.
4 Hu, Su
4 Jones, Rafe
4 Kafle, Bir
4 Kumar, Veekesh
4 Lebowitz-Lockard, Noah
4 Normenyo, Benedict Vasco
4 Öğüt, Ümmügülsüm
4 Oller-Marcén, Antonio M.
4 Pizarro-Madariaga, Amalia
4 Pongsriiam, Prapanpong
4 Raggi-Cárdenas, Alberto Gerardo
...and 864 more Authors
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Cited in 207 Serials

125 Journal of Number Theory
67 International Journal of Number Theory
29 Periodica Mathematica Hungarica
29 Proceedings of the American Mathematical Society
26 Journal of Integer Sequences
25 Mathematics of Computation
25 Monatshefte für Mathematik
25 Integers
24 Bulletin of the Australian Mathematical Society
24 Journal de Théorie des Nombres de Bordeaux
24 The Ramanujan Journal
19 Rocky Mountain Journal of Mathematics
19 Acta Arithmetica
19 Indagationes Mathematicae. New Series
18 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
18 Boletín de la Sociedad Matemática Mexicana. Third Series
14 Archiv der Mathematik
13 Lithuanian Mathematical Journal
13 Functiones et Approximatio. Commentarii Mathematici
13 Acta Mathematica Hungarica
13 Research in Number Theory
11 Mathematica Slovaca
11 Transactions of the American Mathematical Society
10 Results in Mathematics
10 Finite Fields and their Applications
10 Comptes Rendus. Mathématique. Académie des Sciences, Paris
9 Experimental Mathematics
8 Colloquium Mathematicum
8 Quaestiones Mathematicae
8 Turkish Journal of Mathematics
8 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
7 Mathematical Proceedings of the Cambridge Philosophical Society
7 Bulletin of the Brazilian Mathematical Society. New Series
7 Mediterranean Journal of Mathematics
7 Science China. Mathematics
7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
6 Journal of Algebra
6 Mathematika
6 Proceedings of the Japan Academy. Series A
6 Journal of the Australian Mathematical Society
6 Communications in Mathematics
5 Discrete Mathematics
5 Indian Journal of Pure & Applied Mathematics
5 Mathematische Zeitschrift
5 Proceedings of the Edinburgh Mathematical Society. Series II
5 European Journal of Combinatorics
5 Journal of the Ramanujan Mathematical Society
5 Glasnik Matematički. Serija III
5 The Electronic Journal of Combinatorics
5 Research in the Mathematical Sciences
4 Information Processing Letters
4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
4 Glasgow Mathematical Journal
4 Journal of Combinatorial Theory. Series A
4 Revista Matemática Iberoamericana
4 Forum Mathematicum
4 Journal of Inequalities and Applications
4 Afrika Matematika
3 Israel Journal of Mathematics
3 Mathematical Notes
3 Ukrainian Mathematical Journal
3 Chaos, Solitons and Fractals
3 Archivum Mathematicum
3 Canadian Mathematical Bulletin
3 Czechoslovak Mathematical Journal
3 Manuscripta Mathematica
3 Mathematische Annalen
3 Publications de l’Institut Mathématique. Nouvelle Série
3 Elemente der Mathematik
3 Expositiones Mathematicae
3 Applicable Algebra in Engineering, Communication and Computing
3 The New York Journal of Mathematics
3 Journal of Difference Equations and Applications
3 Abstract and Applied Analysis
3 Acta Mathematica Sinica. English Series
3 Acta et Commentationes Universitatis Tartuensis de Mathematica
3 Portugaliae Mathematica. Nova Série
3 JP Journal of Algebra, Number Theory and Applications
3 European Journal of Mathematics
2 American Mathematical Monthly
2 Discrete Applied Mathematics
2 Journal of Mathematical Analysis and Applications
2 Applied Mathematics and Computation
2 Bulletin of the London Mathematical Society
2 Illinois Journal of Mathematics
2 Inventiones Mathematicae
2 Rendiconti del Circolo Matemàtico di Palermo. Serie II
2 Advances in Applied Mathematics
2 Constructive Approximation
2 Mathematica Bohemica
2 International Journal of Foundations of Computer Science
2 Designs, Codes and Cryptography
2 Geometric and Functional Analysis. GAFA
2 Aequationes Mathematicae
2 Bulletin of the American Mathematical Society. New Series
2 Integral Transforms and Special Functions
2 Matematychni Studiï
2 Annals of Combinatorics
2 LMS Journal of Computation and Mathematics
2 Journal of the European Mathematical Society (JEMS)
...and 107 more Serials

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