Luca, Florian

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 Author ID: 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: 725 Publications since 1993, including 3 Books 5 Contributions as Editor Reviewing Activity: 338 Reviews Co-Authors: 321 Co-Authors with 631 Joint Publications 5,217 Co-Co-Authors
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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 Debrecen 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 67 more Serials
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Fields

 714 Number theory (11-XX) 27 Combinatorics (05-XX) 10 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 History and biography (01-XX) 4 $$K$$-theory (19-XX) 2 Commutative algebra (13-XX) 2 Linear and multilinear algebra; matrix theory (15-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 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

504 Publications have been cited 2,206 times in 1,104 Documents Cited by Year
On a conjecture about repdigits in $$k$$-generalized Fibonacci sequences. Zbl 1274.11035
Bravo, Jhon J.; Luca, Florian
2013
Fibonacci and Lucas numbers with only one distinct digit. Zbl 0958.11007
Luca, F.
2000
Powers of two in generalized Fibonacci sequences. Zbl 1353.11020
Bravo, Jhon J.; Luca, Florian
2012
Powers of two as sums of two $$k$$-Fibonacci numbers. Zbl 1389.11041
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
2016
Linear combinations of factorials and $$S$$-units in a binary recurrence sequence. Zbl 1361.11007
Sanchez, Sergio Guzmán; Luca, Florian
2014
On the complexity of algebraic numbers. (Sur la complexité des nombres algébriques.) Zbl 1119.11019
Adamczewski, Boris; Bugeaud, Yann; Luca, Florian
2004
Fibonacci numbers at most one away from a perfect power. Zbl 1156.11008
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
2008
Analytic number theory. Exploring the anatomy of integers. Zbl 1247.11001
De Koninck, Jean-Marie; Luca, Florian
2012
Repdigits as sums of three Fibonacci numbers. Zbl 1305.11008
Luca, Florian
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
On the equation $$x^2 + 2^a \cdot 3^b = y^n$$. Zbl 1085.11021
Luca, Florian
2002
Pell and Pell-Lucas numbers with only one distinct digit. Zbl 1349.11023
2015
Distinct digits in base $$b$$ expansions of linear recurrence sequences. Zbl 1030.11004
Luca, Florian
2000
An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Zbl 1253.11046
Luca, Florian; Oyono, Roger
2011
Coincidences in generalized Fibonacci sequences. Zbl 1272.11028
Bravo, Jhon J.; Luca, Florian
2013
On the largest prime factor of the $$k$$-Fibonacci numbers. Zbl 1292.11034
Bravo, Jhon J.; Luca, Florian
2013
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
Character sums and congruences with $$n!$$. Zbl 1060.11046
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2004
On the Diophantine equation $$x^2+2^a\cdot 5^b=y^n$$. Zbl 1231.11041
Luca, Florian; Togbé, Alain
2008
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
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
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
On a Diophantine equation. Zbl 0997.11027
Luca, Florian
2000
Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers. Zbl 1289.11021
Komatsu, Takao; Luca, Florian
2013
On $$X$$-coordinates of Pell equations that are repdigits. Zbl 1459.11082
2018
On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013
Bravo, Jhon J.; Luca, Florian; Yazán, Karina
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
Diophantine equations with products of consecutive terms in Lucas sequences. Zbl 1081.11023
Luca, F.; Shorey, T. N.
2005
Rational products of singular moduli. Zbl 1400.11113
Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia
2016
On Pillai’s Diophantine equation. Zbl 1136.11026
Bugeaud, Yann; Luca, Florian
2006
Almost powers in the Lucas sequence. Zbl 1204.11030
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
2008
On the exponential local-global principle. Zbl 1330.11019
Bartolome, Boris; Bilu, Yuri; Luca, Florian
2013
Repdigits as sums of four Pell numbers. Zbl 1455.11019
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
2019
Repdigits as sums of three Pell numbers. Zbl 1413.11008
Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain
2018
On the $$x$$-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027
Luca, Florian; Togbé, Alain
2018
On perfect powers that are sums of two Fibonacci numbers. Zbl 1467.11038
Luca, Florian; Patel, Vandita
2018
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
Divisibility of class numbers: enumerative approach. Zbl 1072.11084
Bilu, Yuri F.; Luca, Florian
2005
The Diophantine equation $$P(x)=n!$$ and a result of M. Overholt. Zbl 1085.11023
Luca, Florian
2002
On the $$X$$-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007
Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain
2017
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
2014
Some remarks on Heron triangles. Zbl 1062.11019
Kramer, Alpar-Vajk; Luca, Florian
2000
$$p$$-adic quotient sets. Zbl 1428.11023
Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam
2017
Generalized balancing numbers. Zbl 1239.11035
Liptai, Kálmán; Luca, Florian; Pintér, Ákos; Szalay, László
2009
Irreducible radical extensions and Euler-function chains. Zbl 1172.11029
Luca, Florian; Pomerance, Carl
2007
On a diophantine equation related to a conjecture of Erdös and Graham. Zbl 1132.11319
Luca, F.; Walsh, P. G.
2007
Powers of two as sums of two Lucas numbers. Zbl 1358.11026
Bravo, Jhon J.; Luca, Florian
2014
On the Diophantine equation $$x^2 + 2^{\alpha}5^{\beta}13^{\gamma} = y^n$$. Zbl 1232.11130
Goins, Edray; Luca, Florian; Togbé, Alain
2008
Some results on Oppenheim’s “factorisatio numerorum” function. Zbl 1213.11020
2010
Fibonacci numbers of the form $$p^a\pm p^b+1$$. Zbl 1228.11021
Luca, Florian; Szalay, László
2007
Quotients of Fibonacci numbers. Zbl 1391.11027
Garcia, Stephan Ramon; Luca, Florian
2016
Powers of two as sums of three Pell numbers. Zbl 1433.11032
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian
2017
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
MOV attack in various subgroups on elliptic curves. Zbl 1072.11094
Luca, Florian; Mireles, David Jose; Shparlinski, Igor E.
2004
Catalan and Apéry numbers in residue classes. Zbl 1101.11010
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2006
Average order in cyclic groups. Zbl 1079.11003
von zur Gathen, Joachim; Knopfmacher, Arnold; Luca, Florian; Lucht, Lutz G.; Shparlinski, Igor E.
2004
Exponential sums and congruences with factorials. Zbl 1071.11051
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2005
The distribution of self-Fibonacci divisors. Zbl 1390.11119
Luca, Florian; Tron, Emanuele
2015
Perfect powers from products of terms in Lucas sequences. Zbl 1137.11011
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
2007
On shifted primes with large prime factors and their products. Zbl 1370.11110
Luca, Florian; Menares, Ricardo; Pizarro-Madariaga, Amalia
2015
Members of Lucas sequences whose Euler function is a power of 2. Zbl 1351.11015
2014
Squares in Lehmer sequences and some Diophantine applications. Zbl 1006.11011
Luca, Florian; Walsh, P. G.
2001
On the largest prime factor of $$(ab+1)(ac+1)(bc+1)$$. Zbl 1108.11030
Hernández, Santos; Luca, Florian
2003
On the exponent of the group of points on elliptic curves in extension fields. Zbl 1082.11041
Luca, Florian; Shparlinski, Igor E.
2005
Common values of the arithmetic functions $$\varphi$$ and $$\sigma$$. Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
2010
On the maximal order of numbers in the “factorisatio numerorum” problem. Zbl 1169.11043
Klazar, Martin; Luca, Florian
2007
Fibonacci numbers with the Lehmer property. Zbl 1112.11007
Luca, Florian
2007
On stable quadratic polynomials. Zbl 1241.11027
Ahmadi, Omran; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E.
2012
Some additive combinatorics problems in matrix rings. Zbl 1208.11037
Ferguson, Ron; Hoffman, Corneliu; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E.
2010
On factorials expressible as sums of at most three Fibonacci numbers. Zbl 1253.11048
Luca, Florian; Siksek, Samir
2010
On the Diophantine equation $$x^2 + C = 2y^n$$. Zbl 1233.11037
Abu Muriefah, Fadwa S.; Luca, Florian; Siksek, Samir; Tengely, Szabolcs
2009
On the Diophantine equation $$F_n + F_m=2^a$$. Zbl 1419.11024
Bravo, Jhon J.; Luca, Florian
2016
$$X$$-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian
2018
Fibonacci Diophantine triples. Zbl 1218.11020
Luca, Florian; Szalay, László
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
Every positive integer is a sum of three palindromes. Zbl 1441.11016
Cilleruelo, Javier; Luca, Florian; Baxter, Lewis
2018
On the largest prime factor of $$x^2-1$$. Zbl 1221.11080
Luca, Florian; Najman, Filip
2011
On the number of factorizations of an integer. Zbl 1245.11100
Balasubramanian, Ramachandran; Luca, Florian
2011
The number of non-zero digits of $$n$$! Zbl 1043.11008
Luca, Florian
2002
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
2010
The Diophantine equation $$x^2=p^a\pm p^b+1$$. Zbl 1067.11016
Luca, Florian
2004
On the Diophantine equation $$x^2+7^{2k}=y^n$$. Zbl 1221.11091
Luca, Florian; Togbé, Alain
2007
Fibonacci numbers which are sums of three factorials. Zbl 1259.11038
Bollman, Mark; Hernández Hernández, Santos; Luca, Florian
2010
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
2013
On composite integers $$n$$ for which $$\varphi(n)\mid n-1$$. Zbl 1294.11005
Luca, Florian; Pomerance, Carl
2011
On the $$x$$-coordinates of Pell equations which are $$k$$-generalized Fibonacci numbers. Zbl 1447.11025
2020
Fibonacci numbers which are products of two Pell numbers. Zbl 1400.11040
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
2016
On factorials which are products of factorials. Zbl 1132.11017
Luca, Florian
2007
Polynomial values of sums of products of consecutive integers. Zbl 1442.11055
Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F.
2018
Repdigits as sums of four Fibonacci or Lucas numbers. Zbl 1453.11006
Normenyo, Benedict Vasco; Luca, Florian; Togb, Alain
2018
Pell and Pell-Lucas numbers as sums of two repdigits. Zbl 1452.11020
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
2020
Fibonacci numbers which are concatenations of two repdigits. Zbl 1472.11067
2021
On shifted products which are powers. Zbl 1123.11011
Luca, Florian
2005
On the value set of $$n!$$ modulo a prime. Zbl 1161.11386
Banks, William D.; Luca, Florian; Shparlinski, Igor E.; Stichtenoth, Henning
2005
On the convergence of series of reciprocals of primes related to the Fermat numbers. Zbl 1026.11011
Křížek, Michal; Luca, Florian; Somer, Lawrence
2002
On the counting function of irregular primes. Zbl 1356.11067
Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl
2015
Fibonacci numbers of the form $$k^2+k+2$$. Zbl 0979.11012
Luca, Florian
1999
Fibonacci numbers which are concatenations of two repdigits. Zbl 1472.11067
2021
On a generalization of the Pell sequence. Zbl 07361099
Bravo, Jhon J.; Herrera, Jose L.; Luca, Florian
2021
Common values of generalized Fibonacci and Pell sequences. Zbl 1471.11049
Bravo, Jhon J.; Herrera, Jose L.; Luca, Florian
2021
On Pillai’s problem with $$X$$-coordinates of Pell equations and powers of 2. II. Zbl 07410933
Erazo, Harold S.; Gómez, Carlos A.; Luca, Florian
2021
$$k$$-generalized Fibonacci numbers which are concatenations of two repdigits. Zbl 07414938
2021
On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. Zbl 1481.11020
2021
Binary polynomial power sums vanishing at roots of unity. Zbl 1475.11042
Bilu, Yuri; Luca, Florian
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
2021
On the $$x$$-coordinates of Pell equations which are $$k$$-generalized Fibonacci numbers. Zbl 1447.11025
2020
Pell and Pell-Lucas numbers as sums of two repdigits. Zbl 1452.11020
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
2020
Zeckendorf representations with at most two terms to $$x$$-coordinates of Pell equations. Zbl 1455.11031
Gómez, Carlos A.; Luca, Florian
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
Products of $$k$$-Fibonacci numbers which are rep-digits. Zbl 1463.11032
2020
On the problem of Pillai with $$k$$-generalized Fibonacci numbers and powers of $$3$$. Zbl 1446.11025
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
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 1479.11052
Bilu, Yuri; Luca, Florian
2020
On $$Y$$-coordinates of Pell equations which are members of a fixed binary recurrence. Zbl 1477.11060
2020
On $$Y$$-coordinates of Pell equations which are base 2 rep-digits. Zbl 1478.11016
2020
On members of Lucas sequences which are products of factorials. Zbl 1478.11018
Laishram, Shanta; Luca, Florian; Sias, Mark
2020
The $$x$$-coordinates of Pell equations and sums of two Fibonacci numbers. II. Zbl 1471.11065
2020
Linear combinations of prime powers in $$X$$-coordinates of Pell equations. Zbl 1485.11027
Erazo, Harold; Gómez, Carlos A.; Luca, Florian
2020
On the prime factors of the iterates of the Ramanujan $$\tau$$-function. Zbl 1472.11036
Luca, Florian; Mabaso, Sibusiso; Stănică, Pantelimon
2020
Multiplicative dependence between $$k$$-Fibonacci and $$k$$-Lucas numbers. Zbl 1474.11047
Gómez, Carlos A.; Gómez, Jhonny C.; Luca, Florian
2020
On $$X$$-coordinates of Pell equations which are repdigits. Zbl 1470.11026
Gómez, Carlos A.; Luca, Florian; Zottor, Faith Shadow
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
2020
Total multiplicity of the Tribonacci sequence. Zbl 1459.11037
Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian
2020
Composite positive integers whose sum of prime factors is prime. Zbl 07177880
Luca, Florian; Moodley, Damon
2020
On a Diophantine equation involving powers of Fibonacci numbers. Zbl 1478.11017
Gueth, Krisztián; Luca, Florian; Szalay, László
2020
Lucas factoriangular numbers. Zbl 07217178
Kafle, Bir; Luca, Florian; Togbé, Alain
2020
On the equation $$\sum_{j = 1}^k j F_j^p = F_n^q$$. Zbl 1471.11043
Altassan, Alaa; Luca, Florian
2020
Ratios of sums of two Fibonacci numbers equal to powers of 2. Zbl 1471.11047
Bravo, Jhon J.; Díaz, Maribel; Luca, Florian
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
2020
On the zero-multiplicity of the $$k$$-generalized Fibonacci sequence. Zbl 1464.11024
García, Jonathan; Gómez, Carlos A.; Luca, Florian
2020
Powers of two in generalized Lucas sequences. Zbl 1468.11060
Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain
2020
Repdigits as sums of four Pell numbers. Zbl 1455.11019
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
2019
Recurrence relations for polynomials obtained by arithmetic functions. Zbl 1435.11055
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
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
Lucas numbers as sums of two repdigits. Zbl 1427.11013
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
2019
Repdigits as sums of three Lucas numbers. Zbl 1459.11041
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
On Pillai’s problem with the Fibonacci and Pell sequences. Zbl 1440.11018
Hernández Hernández, Santos; Luca, Florian; Rivera, Luis Manuel
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
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
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
Primitive root bias for twin primes. Zbl 1450.11001
Garcia, Stephan Ramon; Kahoro, Elvis; Luca, Florian
2019
On the zero-multiplicity of a fifth-order linear recurrence. Zbl 1450.11009
Gómez Ruiz, Carlos Alexis; Luca, Florian
2019
$$x$$-Coordinates of Pell equations which are Tribonacci numbers. II. Zbl 1449.11030
Kafle, Bir; Luca, Florian; Togbé, Alain
2019
Diophantine equations with the Ramanujan $$\tau$$ function of factorials, Fibonacci numbers, and Catalan numbers. Zbl 1456.11031
Luca, Florian; Mabaso, Sibusiso
2019
Product of consecutive tribonacci numbers with only one distinct digit. Zbl 1455.11027
Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian
2019
On ternary Egyptian fractions with prime denominator. Zbl 1455.11057
Luca, Florian; Pappalardi, Francesco
2019
On the discriminator of Lucas sequences. Zbl 1456.11021
Faye, Bernadette; Luca, Florian; Moree, Pieter
2019
Linear independence of powers of singular moduli of degree three. Zbl 1451.11069
Luca, Florian; Riffaut, Antonin
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
Consecutive integers with close kernels. Zbl 1478.11008
De Koninck, Jean-Marie; Luca, Florian
2019
Diophantine $$S$$-quadruples with two primes which are twin. Zbl 1449.11067
Luca, F.
2019
Perfect Pell and Pell-Lucas numbers. Zbl 1449.11026
Bravo, Jhon J.; Luca, Florian
2019
On $$X$$-coordinates of Pell equations that are repdigits. Zbl 1459.11082
2018
Repdigits as sums of three Pell numbers. Zbl 1413.11008
Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain
2018
On the $$x$$-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027
Luca, Florian; Togbé, Alain
2018
On perfect powers that are sums of two Fibonacci numbers. Zbl 1467.11038
Luca, Florian; Patel, Vandita
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
$$X$$-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian
2018
Every positive integer is a sum of three palindromes. Zbl 1441.11016
Cilleruelo, Javier; Luca, Florian; Baxter, Lewis
2018
Polynomial values of sums of products of consecutive integers. Zbl 1442.11055
Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F.
2018
Repdigits as sums of four Fibonacci or Lucas numbers. Zbl 1453.11006
Normenyo, Benedict Vasco; Luca, Florian; Togb, Alain
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
A Diophantine equation in $$k$$-Fibonacci numbers and repdigits. Zbl 1407.11026
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
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
Diophantine triples and $$k$$-generalized Fibonacci sequences. Zbl 1447.11054
Fuchs, Clemens; Hutle, Christoph; Luca, Florian; Szalay, László
2018
On the difference in values of the Euler totient function near prime arguments. Zbl 1455.11127
Garcia, Stephan Ramon; Luca, Florian
2018
Markov equation with Fibonacci components. Zbl 1458.11056
Luca, Florian; Srinivasan, Anitha
2018
Arithmetic properties of coefficients of $$L$$-functions of elliptic curves. Zbl 1423.11169
Güloğlu, Ahmet M.; Luca, Florian; Yalçiner, Aynur
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
On the error term of a lattice counting problem. Zbl 1380.11085
Bordellès, Olivier; Luca, Florian; Shparlinski, Igor E.
2018
There are no Diophantine quadruples of Fibonacci numbers. Zbl 1441.11058
Fujita, Yasutsugu; Luca, Florian
2018
A variation on the theme of Nicomachus. Zbl 1410.11079
Luca, Florian; Polanco, Geremías; Zudilin, Wadim
2018
Denominators of Bernoulli polynomials. Zbl 1415.11121
Bordellès, Olivier; Luca, Florian; Moree, Pieter; 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 Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013
Bravo, Jhon J.; Luca, Florian; Yazán, Karina
2017
On the $$X$$-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007
Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain
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 arithmetic lattices in the plane. Zbl 1358.11074
Fukshansky, Lenny; Guerzhoy, Pavel; Luca, Florian
2017
On Diophantine quadruples of Fibonacci numbers. Zbl 1386.11065
Fujita, Yasutsugu; Luca, Florian
2017
Diversity in parametric families of number fields. Zbl 1414.11150
Bilu, Yuri; Luca, Florian
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
The $$r$$th moment of the divisor function: an elementary approach. Zbl 1366.11103
Luca, Florian; Tóth, László
2017
Collinear CM-points. Zbl 1432.11061
Bilu, Yuri; Luca, Florian; Masser, David
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
Palindromes in several sequences. Zbl 1429.11018
Luca, Florian
2017
Monotonic phinomial coefficients. Zbl 1437.11006
Luca, Florian; Stănică, Pantelimon
2017
Lucas numbers with the Lehmer property. Zbl 1389.11043
2017
Generalized incomplete poly-Bernoulli polynomials and generalized incomplete poly-Cauchy polynomials. Zbl 1409.11015
Komatsu, Takao; Luca, Florian
2017
Fibonacci factoriangular numbers. Zbl 1373.11011
Gómez Ruiz, Carlos Alexis; Luca, Florian
2017
Only finitely many Tribonacci Diophantine triples exist. Zbl 1440.11042
Fuchs, Clemens; Hutle, Christoph; Irmak, Nurettin; Luca, Florian; Szalay, László
2017
Diophantine triples with values in the sequences of Fibonacci and Lucas numbers. Zbl 1417.11011
Luca, Florian; Munagi, Augustine O.
2017
Pell numbers with the Lehmer property. Zbl 1439.11015
2017
...and 404 more Documents
all top 5

Cited by 981 Authors

 229 Luca, Florian 48 Shparlinski, Igor E. 38 Togbé, Alain 29 Gómez, Carlos Alexis 24 Pollack, Paul 22 Bravo, Jhon Jairo 22 Hajdu, Lajos 19 Keskin, Refik 19 Sanna, Carlo 18 Bugeaud, Yann 16 Marques, Diego 15 Pomerance, Carl Bernard 15 Rihane, Salah Eddine 15 Szalay, László 14 De Koninck, Jean-Marie 13 Ddamulira, Mahadi 13 Komatsu, Takao 12 Dubickas, Artūras 12 Dujella, Andrej 12 Garaev, Moubariz Z. 12 Stănică, Pantelimon 11 Chen, Yonggao 11 Erduvan, Fatih 10 Adamczewski, Boris 10 Bennett, Michael A. 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 Shorey, Tarlok Nath 9 Şiar, Zafer 9 Soydan, Gokhan 8 Banks, William D. 8 Bérczes, Attila 8 Garcia, Stephan Ramon 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 Trojovský, Pavel 7 Ulas, Maciej 7 Winterhof, Arne 7 Zhang, Yong 6 Adhikari, Sukumar Das 6 Ford, Kevin B. 6 Grau, José María 6 Hernández Hernández, Santos 6 Herrera, José L. 6 Kátai, Imre 6 Le, Maohua 6 Mignotte, Maurice 6 Patel, Vandita 6 Rout, Sudhansu Sekhar 5 Bordellès, Olivier 5 Bravo, Eric F. 5 Broughan, Kevin A. 5 Chakraborty, Kalyan 5 Chattopadhyay, Jaitra 5 Hernane, Mohand-Ouamar 5 Irmak, Nurettin 5 Leonetti, Paolo 5 Miska, Piotr 5 Ray, Prasanta Kumar 5 Sarkar, Subha 5 Zhu, Huilin 4 Altassan, Alaa 4 Balasubramanian, Ramachandran 4 Bell, Jason P. 4 Berrizbeitia, Pedro 4 Bertók, Csanád 4 Bubboloni, Daniela 4 Chim, Kwok Chi 4 Coons, Michael 4 Deshouillers, Jean-Marc 4 Drungilas, Paulius 4 Elsholtz, Christian 4 Erazo, Harold S. 4 Fu, Ruiqin 4 Fujita, Yasutsugu Fujita 4 García Lomelí, Ana Cecilia 4 Gillibert, Jean 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 ...and 881 more Authors
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Cited in 211 Serials

 126 Journal of Number Theory 73 International Journal of Number Theory 33 Periodica Mathematica Hungarica 29 Proceedings of the American Mathematical Society 27 The Ramanujan Journal 26 Monatshefte für Mathematik 26 Journal of Integer Sequences 25 Mathematics of Computation 25 Integers 24 Bulletin of the Australian Mathematical Society 24 Journal de Théorie des Nombres de Bordeaux 20 Acta Arithmetica 20 Indagationes Mathematicae. New Series 19 Rocky Mountain Journal of Mathematics 19 Boletín de la Sociedad Matemática Mexicana. Third Series 18 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 14 Lithuanian Mathematical Journal 14 Archiv der Mathematik 14 Acta Mathematica Hungarica 13 Functiones et Approximatio. Commentarii Mathematici 13 Mathematica Slovaca 13 Research in Number Theory 12 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 8 Bulletin of the Brazilian Mathematical Society. New Series 8 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 Mathematical Proceedings of the Cambridge Philosophical Society 7 Mediterranean Journal of Mathematics 7 Science China. Mathematics 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 Mathematical Notes 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 4 European Journal of Mathematics 3 Israel Journal of Mathematics 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 AIMS 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 ...and 111 more Serials
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Cited in 39 Fields

 1,042 Number theory (11-XX) 74 Combinatorics (05-XX) 41 Algebraic geometry (14-XX) 33 Group theory and generalizations (20-XX) 26 Computer science (68-XX) 22 Information and communication theory, circuits (94-XX) 19 Dynamical systems and ergodic theory (37-XX) 13 Field theory and polynomials (12-XX) 11 Functions of a complex variable (30-XX) 9 Commutative algebra (13-XX) 9 Special functions (33-XX) 9 Probability theory and stochastic processes (60-XX) 8 $$K$$-theory (19-XX) 6 Geometry (51-XX) 6 Numerical analysis (65-XX) 6 Systems theory; control (93-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Real functions (26-XX) 4 Measure and integration (28-XX) 4 Partial differential equations (35-XX) 4 Difference and functional equations (39-XX) 4 Approximations and expansions (41-XX) 3 History and biography (01-XX) 3 Sequences, series, summability (40-XX) 3 Operator theory (47-XX) 2 Mathematical logic and foundations (03-XX) 2 Ordinary differential equations (34-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Convex and discrete geometry (52-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistics (62-XX) 2 Mechanics of deformable solids (74-XX) 2 Quantum theory (81-XX) 2 Mathematics education (97-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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