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## Luca, Florian

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 Author ID: 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: 705 Publications since 1993, including 7 Books Reviewing Activity: 306 Reviews
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#### Serials

 50 Journal of Number Theory 42 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 13 Monatshefte für Mathematik 13 Boletín de la Sociedad Matemática Mexicana. Third Series 12 Glasnik Matematički. Serija III 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 The Ramanujan Journal 8 Uniform Distribution Theory 7 Mathematica Slovaca 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 Quaestiones Mathematicae 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 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 Publications de l’Institut Mathématique. Nouvelle Série 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 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 1 Acta Scientiarum Mathematicarum 1 Ars Combinatoria ...and 64 more Serials
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#### Fields

 689 Number theory (11-XX) 25 Combinatorics (05-XX) 9 Field theory and polynomials (12-XX) 9 Group theory and generalizations (20-XX) 8 Algebraic geometry (14-XX) 5 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 4 $$K$$-theory (19-XX) 3 History and biography (01-XX) 2 Functions of a complex variable (30-XX) 2 Sequences, series, summability (40-XX) 2 Geometry (51-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Algebraic topology (55-XX) 1 Probability theory and stochastic processes (60-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

462 Publications have been cited 1,740 times in 927 Documents Cited by Year
On a conjecture about repdigits in $$k$$-generalized Fibonacci sequences. Zbl 1274.11035
Bravo, Jhon J.; Luca, Florian
2013
Powers of two in generalized Fibonacci sequences. Zbl 1353.11020
Bravo, Jhon J.; Luca, Florian
2012
On the complexity of algebraic numbers. Zbl 1119.11019
Adamczewski, Boris; Bugeaud, Yann; Luca, Florian
2004
Fibonacci and Lucas numbers with only one distinct digit. Zbl 0958.11007
Luca, F.
2000
Linear combinations of factorials and $$S$$-units in a binary recurrence sequence. Zbl 1361.11007
Sanchez, Sergio Guzmán; Luca, Florian
2014
Analytic number theory. Exploring the anatomy of integers. Zbl 1247.11001
De Koninck, Jean-Marie; Luca, Florian
2012
Fibonacci numbers at most one away from a perfect power. Zbl 1156.11008
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
2008
Powers of two as sums of two $$k$$-Fibonacci numbers. Zbl 1389.11041
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
2016
On the equation $$x^2 + 2^a \cdot 3^b = y^n$$. Zbl 1085.11021
Luca, Florian
2002
Repdigits as sums of three Fibonacci numbers. Zbl 1305.11008
Luca, Florian
2012
On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions $$\varphi$$ and $$\sigma$$. Zbl 1027.11007
Luca, Florian; Pomerance, Carl
2002
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
2001
Distinct digits in base $$b$$ expansions of linear recurrence sequences. Zbl 1030.11004
Luca, Florian
2000
Coincidences in generalized Fibonacci sequences. Zbl 1272.11028
Bravo, Jhon J.; Luca, Florian
2013
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.
2012
Fibonacci numbers which are sums of two repdigits. Zbl 1287.11021
2011
A generalization of a classical zero-sum problem. Zbl 1123.11012
Luca, Florian
2007
Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers. Zbl 1289.11021
Komatsu, Takao; Luca, Florian
2013
On the largest prime factor of the $$k$$-Fibonacci numbers. Zbl 1292.11034
Bravo, Jhon J.; Luca, Florian
2013
Character sums and congruences with $$n!$$. Zbl 1060.11046
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2004
On a Diophantine equation. Zbl 0997.11027
Luca, Florian
2000
On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
2017
On the $$x$$-coordinates of Pell equations which are rep-digits. Zbl 1389.11076
Dossavi-Yovo, Appolinaire; Luca, Florian; Togbé, Alain
2016
On the Diophantine equation $$x^2+2^a\cdot 5^b=y^n$$. Zbl 1231.11041
Luca, Florian; Togbé, Alain
2008
Diophantine equations with products of consecutive terms in Lucas sequences. Zbl 1081.11023
Luca, F.; Shorey, T. N.
2005
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
2014
Irreducible radical extensions and Euler-function chains. Zbl 1172.11029
Luca, Florian; Pomerance, Carl
2007
On $$X$$-coordinates of Pell equations that are repdigits. Zbl 1459.11082
2018
On the $$x$$-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027
Luca, Florian; Togbé, Alain
2018
On the $$X$$-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007
Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain
2017
Functional graphs of polynomials over finite fields. Zbl 1327.05323
Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E.
2016
The distribution of self-Fibonacci divisors. Zbl 1390.11119
Luca, Florian; Tron, Emanuele
2015
On the exponential local-global principle. Zbl 1330.11019
Bartolome, Boris; Bilu, Yuri; Luca, Florian
2013
An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Zbl 1253.11046
Luca, Florian; Oyono, Roger
2011
Almost powers in the Lucas sequence. Zbl 1204.11030
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
2008
Fibonacci numbers of the form $$p^a\pm p^b+1$$. Zbl 1228.11021
Luca, Florian; Szalay, László
2007
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
2006
On Pillai’s Diophantine equation. Zbl 1136.11026
Bugeaud, Yann; Luca, Florian
2006
On the exponent of the group of points on elliptic curves in extension fields. Zbl 1082.11041
Luca, Florian; Shparlinski, Igor E.
2005
Divisibility of class numbers: enumerative approach. Zbl 1072.11084
Bilu, Yuri F.; Luca, Florian
2005
On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013
Bravo, Jhon J.; Luca, Florian; Yazán, Karina
2017
$$p$$-adic quotient sets. Zbl 1428.11023
Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam
2017
Quotients of Fibonacci numbers. Zbl 1391.11027
Garcia, Stephan Ramon; Luca, Florian
2016
Rational products of singular moduli. Zbl 1400.11113
Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia
2016
Pell and Pell-Lucas numbers with only one distinct digit. Zbl 1349.11023
2015
Generalized balancing numbers. Zbl 1239.11035
Liptai, Kálmán; Luca, Florian; Pintér, Ákos; Szalay, László
2009
Fibonacci Diophantine triples. Zbl 1218.11020
Luca, Florian; Szalay, László
2008
Catalan and Apéry numbers in residue classes. Zbl 1101.11010
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2006
The Diophantine equation $$P(x)=n!$$ and a result of M. Overholt. Zbl 1085.11023
Luca, Florian
2002
On shifted primes with large prime factors and their products. Zbl 1370.11110
Luca, Florian; Menares, Ricardo; Pizarro-Madariaga, Amalia
2015
On stable quadratic polynomials. Zbl 1241.11027
Ahmadi, Omran; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E.
2012
On composite integers $$n$$ for which $$\varphi(n)\mid n-1$$. Zbl 1294.11005
Luca, Florian; Pomerance, Carl
2011
Some additive combinatorics problems in matrix rings. Zbl 1208.11037
Ferguson, Ron; Hoffman, Corneliu; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E.
2010
Common values of the arithmetic functions $$\varphi$$ and $$\sigma$$. Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
2010
Some results on Oppenheim’s “factorisatio numerorum” function. Zbl 1213.11020
2010
On the Diophantine equation $$x^2 + 2^{\alpha}5^{\beta}13^{\gamma} = y^n$$. Zbl 1232.11130
Goins, Edray; Luca, Florian; Togbé, Alain
2008
On the Diophantine equation $$x^2 + 5^a 13^b = y^n$$. Zbl 1186.11016
Abu Muriefah, Fadwa S.; Luca, Florian; Togbé, Alain
2008
On a diophantine equation related to a conjecture of Erdös and Graham. Zbl 1132.11319
Luca, F.; Walsh, P. G.
2007
On factorials which are products of factorials. Zbl 1132.11017
Luca, Florian
2007
Fibonacci numbers with the Lehmer property. Zbl 1112.11007
Luca, Florian
2007
On the maximal order of numbers in the “factorisatio numerorum” problem. Zbl 1169.11043
Klazar, Martin; Luca, Florian
2007
Exponential sums and congruences with factorials. Zbl 1071.11051
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2005
Average order in cyclic groups. Zbl 1079.11003
von zur Gathen, Joachim; Knopfmacher, Arnold; Luca, Florian; Lucht, Lutz G.; Shparlinski, Igor E.
2004
MOV attack in various subgroups on elliptic curves. Zbl 1072.11094
Luca, Florian; Mireles, David Jose; Shparlinski, Igor E.
2004
On the largest prime factor of $$(ab+1)(ac+1)(bc+1)$$. Zbl 1108.11030
Hernández, Santos; Luca, Florian
2003
The number of non-zero digits of $$n$$! Zbl 1043.11008
Luca, Florian
2002
Some remarks on Heron triangles. Zbl 1062.11019
Kramer, Alpar-Vajk; Luca, Florian
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
2018
On perfect powers that are sums of two Fibonacci numbers. Zbl 06865878
Luca, Florian; Patel, Vandita
2018
Powers of two as sums of three Pell numbers. Zbl 1433.11032
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian
2017
On the $$x$$-coordinates of Pell equations which are Fibonacci numbers. II. Zbl 1420.11037
Kafle, Bir; Luca, Florian; Togbé, Alain
2017
Powers of two as sums of two Lucas numbers. Zbl 1358.11026
Bravo, Jhon J.; Luca, Florian
2014
Control of coupled parabolic systems and Diophantine approximations. Zbl 1272.93029
Luca, Florian; De Teresa, Luz
2013
On equal values of power sums of arithmetic progressions. Zbl 1330.11020
Bazsó, András; Kreso, Dijana; Luca, Florian; Pintér, Ákos
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.
2012
On the number of factorizations of an integer. Zbl 1245.11100
Balasubramanian, Ramachandran; Luca, Florian
2011
Fibonacci numbers which are sums of three factorials. Zbl 1259.11038
Bollman, Mark; Hernández Hernández, Santos; Luca, Florian
2010
On factorials expressible as sums of at most three Fibonacci numbers. Zbl 1253.11048
Luca, Florian; Siksek, Samir
2010
Fibonacci numbers of the form $$p^a\pm p^b$$. Zbl 1273.11030
Luca, Florian; Stănică, Pantelimon
2009
Non-holonomicity of sequences defined via elementary functions. Zbl 1189.11007
Bell, Jason P.; Gerhold, Stefan; Klazar, Martin; Luca, Florian
2008
On the Diophantine equation $$x^2+7^{2k}=y^n$$. Zbl 1221.11091
Luca, Florian; Togbé, Alain
2007
Composite integers $$n$$ for which $$\varphi (n)\mid n-1$$. Zbl 1215.11094
Banks, William D.; Luca, Florian
2007
Perfect powers from products of terms in Lucas sequences. Zbl 1137.11011
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
2007
Elliptic curves with low embedding degree. Zbl 1133.14303
Luca, Florian; Shparlinski, Igor E.
2006
Diophantine $$m$$-tuples for primes. Zbl 1085.11019
Dujella, Andrej; Luca, Florian
2005
On shifted products which are powers. Zbl 1123.11011
Luca, Florian
2005
Fibonacci numbers that are not sums of two prime powers. Zbl 1113.11011
Luca, Florian; Stănică, Pantelimon
2005
A quantitative lower bound for the greatest prime factor of $$(ab+1)(bc+1)(ca+1)$$. Zbl 1122.11060
Bugeaud, Yann; Luca, Florian
2004
The Diophantine equation $$x^2=p^a\pm p^b+1$$. Zbl 1067.11016
Luca, Florian
2004
On the prime power factorization of $$n$$! Zbl 1049.11092
Luca, Florian; Stănică, Pantelimon
2003
Palindromes in Lucas sequences. Zbl 1027.11012
Luca, Florian
2003
On the convergence of series of reciprocals of primes related to the Fermat numbers. Zbl 1026.11011
Křížek, Michal; Luca, Florian; Somer, Lawrence
2002
Squares in Lehmer sequences and some Diophantine applications. Zbl 1006.11011
Luca, Florian; Walsh, P. G.
2001
On the $$x$$-coordinates of Pell equations which are $$k$$-generalized Fibonacci numbers. Zbl 1447.11025
2020
Repdigits as sums of four Pell numbers. Zbl 1455.11019
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
2019
On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
2019
$$X$$-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian
2018
Repdigits as sums of three Pell numbers. Zbl 1413.11008
Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain
2018
Polynomial values of sums of products of consecutive integers. Zbl 1442.11055
Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F.
2018
Every positive integer is a sum of three palindromes. Zbl 1441.11016
Cilleruelo, Javier; Luca, Florian; Baxter, Lewis
2018
On the $$x$$-coordinates of Pell equations which are $$k$$-generalized Fibonacci numbers. Zbl 1447.11025
2020
Zeckendorf representations with at most two terms to $$x$$-coordinates of Pell equations. Zbl 1455.11031
Gómez, Carlos A.; Luca, Florian
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
2020
Products of $$k$$-Fibonacci numbers which are rep-digits. Zbl 07287377
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
2020
Trinomials with given roots. Zbl 07152833
Bilu, Yuri; Luca, Florian
2020
Multiplicative dependence between $$k$$-Fibonacci and $$k$$-Lucas numbers. Zbl 07301185
Gómez, Carlos A.; Gómez, Jhonny C.; Luca, Florian
2020
The $$x$$-coordinates of Pell equations and sums of two Fibonacci numbers. II. Zbl 07271355
2020
On members of Lucas sequences which are products of factorials. Zbl 07242544
Laishram, Shanta; Luca, Florian; Sias, Mark
2020
Lucas factoriangular numbers. Zbl 07217178
Kafle, Bir; Luca, Florian; Togbé, Alain
2020
On a Diophantine equation involving powers of Fibonacci numbers. Zbl 07192786
Gueth, Krisztián; Luca, Florian; Szalay, László
2020
Pell and Pell-Lucas numbers as sums of two repdigits. Zbl 1452.11020
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
2020
On $$Y$$-coordinates of Pell equations which are members of a fixed binary recurrence. Zbl 07179055
2020
On certain sums concerning the gcd’s and lcm’s of $$k$$ positive integers. Zbl 1452.11007
Hilberdink, Titus; Luca, Florian; Tóth, László
2020
Repdigits as sums of four Pell numbers. Zbl 1455.11019
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
2019
On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
2019
$$X$$-coordinates of Pell equations which are Lucas numbers. Zbl 07137965
Kafle, Bir; Luca, Florian; Togbé, Alain
2019
Primitive root bias for twin primes. Zbl 1450.11001
Garcia, Stephan Ramon; Kahoro, Elvis; Luca, Florian
2019
Repdigits as sums of three Lucas numbers. Zbl 1459.11041
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
2019
$$x$$-Coordinates of Pell equations which are Tribonacci numbers. II. Zbl 1449.11030
Kafle, Bir; Luca, Florian; Togbé, Alain
2019
Lucas numbers as sums of two repdigits. Zbl 1427.11013
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
2019
On Pillai’s problem with the Fibonacci and Pell sequences. Zbl 1440.11018
Hernández Hernández, Santos; Luca, Florian; Rivera, Luis Manuel
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
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
2019
Recurrence relations for polynomials obtained by arithmetic functions. Zbl 1435.11055
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
2019
On the discriminator of Lucas sequences. Zbl 1456.11021
Faye, Bernadette; Luca, Florian; Moree, Pieter
2019
On the zero-multiplicity of a fifth-order linear recurrence. Zbl 1450.11009
Gómez Ruiz, Carlos Alexis; Luca, Florian
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
2019
Product of consecutive tribonacci numbers with only one distinct digit. Zbl 1455.11027
Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian
2019
Diophantine equations with the Ramanujan $$\tau$$ function of factorials, Fibonacci numbers, and Catalan numbers. Zbl 1456.11031
Luca, Florian; Mabaso, Sibusiso
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
2019
On the typical size and cancellations among the coefficients of some modular forms. Zbl 1450.11100
Luca, Florian; Radziwiłł, Maksym; Shparlinski, Igor E.
2019
Linear independence of powers of singular moduli of degree three. Zbl 1451.11069
Luca, Florian; Riffaut, Antonin
2019
On $$X$$-coordinates of Pell equations that are repdigits. Zbl 1459.11082
2018
On the $$x$$-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027
Luca, Florian; Togbé, Alain
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
2018
On perfect powers that are sums of two Fibonacci numbers. Zbl 06865878
Luca, Florian; Patel, Vandita
2018
$$X$$-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian
2018
Repdigits as sums of three Pell numbers. Zbl 1413.11008
Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain
2018
Polynomial values of sums of products of consecutive integers. Zbl 1442.11055
Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F.
2018
Every positive integer is a sum of three palindromes. Zbl 1441.11016
Cilleruelo, Javier; Luca, Florian; Baxter, Lewis
2018
On the difference in values of the Euler totient function near prime arguments. Zbl 1455.11127
Garcia, Stephan Ramon; Luca, Florian
2018
Repdigits as sums of four Fibonacci or Lucas numbers. Zbl 1453.11006
Normenyo, Benedict Vasco; Luca, Florian; Togb, Alain
2018
Primitive root biases for prime pairs. I: Existence and non-totality of biases. Zbl 1431.11112
Garcia, Stephan Ramon; Luca, Florian; Schaaff, Timothy
2018
On Pillai’s problem with Pell numbers and powers of 2. Zbl 1448.11042
Ouamar Hernane, Mohand; Luca, Florian; Rihane, Salah; Togbé, Alain
2018
Diophantine triples and $$k$$-generalized Fibonacci sequences. Zbl 1447.11054
Fuchs, Clemens; Hutle, Christoph; Luca, Florian; Szalay, László
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
2018
Markov equation with Fibonacci components. Zbl 1458.11056
Luca, Florian; Srinivasan, Anitha
2018
A Diophantine equation in $$k$$-Fibonacci numbers and repdigits. Zbl 1407.11026
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
2018
Arithmetic properties of coefficients of $$L$$-functions of elliptic curves. Zbl 1423.11169
Güloğlu, Ahmet M.; Luca, Florian; Yalçiner, Aynur
2018
Denominators of Bernoulli polynomials. Zbl 1415.11121
Bordellès, Olivier; Luca, Florian; Moree, Pieter; Shparlinski, Igor E.
2018
A variation on the theme of Nicomachus. Zbl 1410.11079
Luca, Florian; Polanco, Geremías; Zudilin, Wadim
2018
On the error term of a lattice counting problem. Zbl 1380.11085
Bordellès, Olivier; Luca, Florian; Shparlinski, Igor E.
2018
On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
2017
On the $$X$$-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007
Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain
2017
On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013
Bravo, Jhon J.; Luca, Florian; Yazán, Karina
2017
$$p$$-adic quotient sets. Zbl 1428.11023
Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam
2017
Powers of two as sums of three Pell numbers. Zbl 1433.11032
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian
2017
On the $$x$$-coordinates of Pell equations which are Fibonacci numbers. II. Zbl 1420.11037
Kafle, Bir; Luca, Florian; Togbé, Alain
2017
On Diophantine quadruples of Fibonacci numbers. Zbl 1386.11065
Fujita, Yasutsugu; Luca, Florian
2017
On arithmetic lattices in the plane. Zbl 1358.11074
Fukshansky, Lenny; Guerzhoy, Pavel; Luca, Florian
2017
Diversity in parametric families of number fields. Zbl 1414.11150
Bilu, Yuri; Luca, Florian
2017
Only finitely many Tribonacci Diophantine triples exist. Zbl 1440.11042
Fuchs, Clemens; Hutle, Christoph; Irmak, Nurettin; Luca, Florian; Szalay, László
2017
Fibonacci factoriangular numbers. Zbl 1373.11011
Gómez Ruiz, Carlos Alexis; Luca, Florian
2017
The $$r$$th moment of the divisor function: an elementary approach. Zbl 1366.11103
Luca, Florian; Tóth, László
2017
Palindromes in several sequences. Zbl 1429.11018
Luca, Florian
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.
2017
Generalized incomplete poly-Bernoulli polynomials and generalized incomplete poly-Cauchy polynomials. Zbl 1409.11015
Komatsu, Takao; Luca, Florian
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
2017
Local behavior of the composition of the aliquot and co-totient functions. Zbl 1421.11076
Luca, Florian; Pomerance, Carl
2017
Number fields in fibers: the geometrically abelian case with rational critical values. Zbl 1413.12001
Bilu, Yuri; Luca, Florian
2017
Diophantine triples with values in the sequences of Fibonacci and Lucas numbers. Zbl 1417.11011
Luca, Florian; Munagi, Augustine O.
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
2017
Lucas numbers with the Lehmer property. Zbl 1389.11043
2017
On polynomials whose roots have rational quotient of differences. Zbl 1435.11061
Luca, Florian
2017
On two functions arising in the study of the Euler and Carmichael quotients. Zbl 1425.11009
Luca, Florian; Sha, Min; Shparlinski, Igor E.
2017
Collinear CM-points. Zbl 1432.11061
Bilu, Yuri; Luca, Florian; Masser, David
2017
Pell numbers with the Lehmer property. Zbl 1439.11015
2017
Monotonic phinomial coefficients. Zbl 1437.11006
Luca, Florian; Stănică, Pantelimon
2017
Powers of two as sums of two $$k$$-Fibonacci numbers. Zbl 1389.11041
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
2016
On the $$x$$-coordinates of Pell equations which are rep-digits. Zbl 1389.11076
Dossavi-Yovo, Appolinaire; Luca, Florian; Togbé, Alain
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.
2016
Quotients of Fibonacci numbers. Zbl 1391.11027
Garcia, Stephan Ramon; Luca, Florian
2016
Rational products of singular moduli. Zbl 1400.11113
Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia
2016
Fibonacci numbers which are products of two Pell numbers. Zbl 1400.11040
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
2016
An explicit bound for the number of partitions into roots. Zbl 1343.05031
Luca, Florian; Ralaivaosaona, Dimbinaina
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
2016
On the Diophantine equation $$F_n + F_m=2^a$$. Zbl 1419.11024
Bravo, Jhon J.; Luca, Florian
2016
Sylvester’s theorem and the non-integrality of a certain binomial sum. Zbl 1400.11061
López-Aguayo, Daniel; Luca, Florian
2016
Multiplicative independence in $$k$$-generalized Fibonacci sequences. Zbl 1355.11010
Gómez Ruiz, Carlos Alexis; Luca, Florian
2016
Diophantine triples of Fibonacci numbers. Zbl 1359.11028
He, Bo; Luca, Florian; Togbé, Alain
2016
Cyclotomic coefficients: gaps and jumps. Zbl 1405.11032
Camburu, Oana-Maria; Ciolan, Emil-Alexandru; Luca, Florian; Moree, Pieter; Shparlinski, Igor E.
2016
A note on odd perfect numbers. Zbl 1400.11010
Dris, Jose Arnaldo B.; Luca, Florian
2016
Repdigits as Euler functions of Lucas numbers. Zbl 1389.11040
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian; Tall, Amandou
2016
An elliptic sequence is not a sampled linear recurrence sequence. Zbl 1367.11020
Luca, F.; Ward, T.
2016
On a divisibility relation for Lucas sequences. Zbl 1402.11023
Bilu, Yuri F.; Komatsu, Takao; Luca, Florian; Pizarro-Madariaga, Amalia; Stănică, Pantelimon
2016
Carmichael numbers in the sequence $$(2^{n} k+1)_{n\geq 1}$$. Zbl 1400.11017
Cilleruelo, Javier; Luca, Florian; Pizarro-Madariaga, Amalia
2016
The distribution of self-Fibonacci divisors. Zbl 1390.11119
Luca, Florian; Tron, Emanuele
2015
Pell and Pell-Lucas numbers with only one distinct digit. Zbl 1349.11023
2015
On shifted primes with large prime factors and their products. Zbl 1370.11110
Luca, Florian; Menares, Ricardo; Pizarro-Madariaga, Amalia
2015
...and 362 more Documents
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#### Cited by 878 Authors

 210 Luca, Florian 46 Shparlinski, Igor E. 27 Togbé, Alain 22 Pollack, Paul 21 Hajdu, Lajos 19 Bugeaud, Yann 16 Sanna, Carlo 14 Bravo, Jhon Jairo 14 Marques, Diego 14 Pomerance, Carl Bernard 14 Szalay, László 13 Komatsu, Takao 12 De Koninck, Jean-Marie 12 Dubickas, Artūras 12 Dujella, Andrej 12 Gómez, Carlos Alexis 12 Stănică, Pantelimon 11 Chen, Yonggao 11 Garaev, Moubariz Z. 10 Adamczewski, Boris 10 Ddamulira, Mahadi 10 Keskin, Refik 10 Pink, István 10 Ziegler, Volker 9 Bennett, Michael A. 9 Bilu, Yuri F. 9 Cilleruelo, Javier 9 Gómez Ruiz, Carlos Alexis 9 Siksek, Samir 9 Soydan, Gokhan 8 Banks, William D. 8 Fuchs, Clemens 8 Garcia, Stephan Ramon 8 Moree, Pieter 8 Shorey, Tarlok Nath 7 Bérczes, Attila 7 Heim, Bernhard Ernst 7 Neuhauser, Markus 7 Sha, Min 7 Tengely, Szabolcs 7 Tijdeman, Robert 7 Ulas, Maciej 6 Bazsó, András 6 Faye, Bernadette 6 Ford, Kevin B. 6 Grau, José María 6 Laishram, Shanta 6 Mignotte, Maurice 6 Panda, Gopal Krishna 6 Somer, Lawrence E. 6 Winterhof, Arne 5 Adhikari, Sukumar Das 5 Broughan, Kevin A. 5 Erduvan, Fatih 5 Irmak, Nurettin 5 Kátai, Imre 5 Křížek, Michal 5 Le, Maohua 5 Leonetti, Paolo 5 Miska, Piotr 5 Pappalardi, Francesco 5 Rout, Sudhansu Sekhar 4 Abu Muriefah, Fadwa S. 4 Bell, Jason P. 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 Hernández, Santos 4 Hu, Su 4 Kafle, Bir 4 Kihel, Omar 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 Shallit, Jeffrey O. 4 Sun, Xuegong 4 Thangadurai, Ravindrananathan 4 Trojovský, Pavel 4 Wu, Jie 4 Zhu, Huilin 3 Altassan, Alaa 3 Balasubramanian, Ramachandran 3 Berend, Daniel 3 Brandstätter, Nina 3 Bridy, Andrew 3 Bubboloni, Daniela 3 Chakraborty, Kalyan 3 Dai, Lixia 3 Deshouillers, Jean-Marc 3 Freiberg, Tristan 3 Fu, Ruiqin 3 Fujita, Yasutsugu ...and 778 more Authors
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#### Cited in 190 Serials

 126 Journal of Number Theory 56 International Journal of Number Theory 28 Proceedings of the American Mathematical Society 25 Periodica Mathematica Hungarica 24 Mathematics of Computation 24 Monatshefte für Mathematik 22 Journal de Théorie des Nombres de Bordeaux 22 Journal of Integer Sequences 21 Bulletin of the Australian Mathematical Society 21 Indagationes Mathematicae. New Series 20 Integers 19 The Ramanujan Journal 18 Acta Arithmetica 15 Rocky Mountain Journal of Mathematics 15 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 14 Boletín de la Sociedad Matemática Mexicana. Third Series 13 Archiv der Mathematik 11 Lithuanian Mathematical Journal 11 Functiones et Approximatio. Commentarii Mathematici 11 Transactions of the American Mathematical Society 11 Research in Number Theory 10 Finite Fields and their Applications 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Acta Mathematica Hungarica 8 Turkish Journal of Mathematics 8 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 7 Mathematical Proceedings of the Cambridge Philosophical Society 7 Mathematica Slovaca 7 Experimental Mathematics 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 Quaestiones Mathematicae 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 Canadian Mathematical Bulletin 3 Czechoslovak Mathematical Journal 3 Manuscripta Mathematica 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 Mediterranean Journal of Mathematics 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 European Journal of Mathematics 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 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 Constructive Approximation 2 Forum Mathematicum 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 Expositiones Mathematicae 2 Applicable Algebra in Engineering, Communication and Computing 2 The Electronic Journal of Combinatorics 2 The New York Journal of Mathematics 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 Communications of the Korean Mathematical Society 2 RAIRO. Theoretical Informatics and Applications 2 Acta et Commentationes Universitatis Tartuensis de Mathematica 2 Journal of High Energy Physics 2 Journal of Mathematical Cryptology 2 Algebra & Number Theory 2 Afrika Matematika ...and 90 more Serials
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#### Cited in 38 Fields

 872 Number theory (11-XX) 60 Combinatorics (05-XX) 38 Algebraic geometry (14-XX) 26 Group theory and generalizations (20-XX) 23 Computer science (68-XX) 21 Information and communication theory, circuits (94-XX) 17 Dynamical systems and ergodic theory (37-XX) 13 Field theory and polynomials (12-XX) 9 Functions of a complex variable (30-XX) 8 Commutative algebra (13-XX) 8 $$K$$-theory (19-XX) 8 Special functions (33-XX) 8 Probability theory and stochastic processes (60-XX) 6 Systems theory; control (93-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Real functions (26-XX) 5 Partial differential equations (35-XX) 5 Numerical analysis (65-XX) 4 Measure and integration (28-XX) 4 Difference and functional equations (39-XX) 4 Approximations and expansions (41-XX) 3 Sequences, series, summability (40-XX) 3 Operator theory (47-XX) 3 Geometry (51-XX) 2 Ordinary differential equations (34-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Convex and discrete geometry (52-XX) 2 Statistics (62-XX) 2 Mechanics of deformable solids (74-XX) 2 Quantum theory (81-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Associative rings and algebras (16-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX)

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