Edit Profile (opens in new tab) Luca, Florian Compute Distance To: Compute 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 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. 25 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 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 1274.11035Bravo, Jhon J.; Luca, Florian 47 2013 Fibonacci and Lucas numbers with only one distinct digit. Zbl 0958.11007Luca, F. 43 2000 Powers of two in generalized Fibonacci sequences. Zbl 1353.11020Bravo, Jhon J.; Luca, Florian 36 2012 Powers of two as sums of two \(k\)-Fibonacci numbers. Zbl 1389.11041Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian 34 2016 Linear combinations of factorials and \(S\)-units in a binary recurrence sequence. Zbl 1361.11007Sanchez, Sergio Guzmán; Luca, Florian 33 2014 On the complexity of algebraic numbers. (Sur la complexité des nombres algébriques.) Zbl 1119.11019Adamczewski, Boris; Bugeaud, Yann; Luca, Florian 30 2004 Fibonacci numbers at most one away from a perfect power. Zbl 1156.11008Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 29 2008 Analytic number theory. Exploring the anatomy of integers. Zbl 1247.11001De Koninck, Jean-Marie; Luca, Florian 28 2012 Repdigits as sums of three Fibonacci numbers. Zbl 1305.11008Luca, Florian 23 2012 Fibonacci numbers which are sums of two repdigits. Zbl 1287.11021Díaz Alvarado, Saúl; Luca, Florian 20 2011 A generalization of a classical zero-sum problem. Zbl 1123.11012Luca, Florian 19 2007 On the equation \(x^2 + 2^a \cdot 3^b = y^n\). Zbl 1085.11021Luca, Florian 18 2002 Pell and Pell-Lucas numbers with only one distinct digit. Zbl 1349.11023Faye, Bernadette; Luca, Florian 18 2015 Distinct digits in base \(b\) expansions of linear recurrence sequences. Zbl 1030.11004Luca, Florian 16 2000 An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Zbl 1253.11046Luca, Florian; Oyono, Roger 16 2011 Coincidences in generalized Fibonacci sequences. Zbl 1272.11028Bravo, Jhon J.; Luca, Florian 16 2013 On the largest prime factor of the \(k\)-Fibonacci numbers. Zbl 1292.11034Bravo, Jhon J.; Luca, Florian 16 2013 On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions \(\varphi\) and \(\sigma\). Zbl 1027.11007Luca, Florian; Pomerance, Carl 14 2002 17 lectures on Fermat numbers. From number theory to geometry. With a foreword by Alena Šolcová. Zbl 1010.11002Křížek, Michal; Luca, Florian; Somer, Lawrence 14 2001 Character sums and congruences with \(n!\). Zbl 1060.11046Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. 14 2004 On the Diophantine equation \(x^2+2^a\cdot 5^b=y^n\). Zbl 1231.11041Luca, Florian; Togbé, Alain 14 2008 On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja 14 2017 On the \(x\)-coordinates of Pell equations which are rep-digits. Zbl 1389.11076Dossavi-Yovo, Appolinaire; Luca, Florian; Togbé, Alain 13 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 1294.11164Ford, Kevin; Luca, Florian; Moree, Pieter 13 2014 On numbers \(n\) dividing the \(n\)th term of a linear recurrence. Zbl 1262.11015Alba González, Juan José; Luca, Florian; Pomerance, Carl; Shparlinski, Igor E. 13 2012 On a Diophantine equation. Zbl 0997.11027Luca, Florian 12 2000 Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers. Zbl 1289.11021Komatsu, Takao; Luca, Florian 12 2013 On \(X\)-coordinates of Pell equations that are repdigits. Zbl 1459.11082Faye, Bernadette; Luca, Florian 12 2018 On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013Bravo, Jhon J.; Luca, Florian; Yazán, Karina 11 2017 Functional graphs of polynomials over finite fields. Zbl 1327.05323Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E. 11 2016 Diophantine equations with products of consecutive terms in Lucas sequences. Zbl 1081.11023Luca, F.; Shorey, T. N. 11 2005 Rational products of singular moduli. Zbl 1400.11113Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia 10 2016 On Pillai’s Diophantine equation. Zbl 1136.11026Bugeaud, Yann; Luca, Florian 10 2006 Almost powers in the Lucas sequence. Zbl 1204.11030Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 10 2008 On the exponential local-global principle. Zbl 1330.11019Bartolome, Boris; Bilu, Yuri; Luca, Florian 10 2013 Repdigits as sums of four Pell numbers. Zbl 1455.11019Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain 10 2019 Repdigits as sums of three Pell numbers. Zbl 1413.11008Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain 10 2018 On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027Luca, Florian; Togbé, Alain 10 2018 On perfect powers that are sums of two Fibonacci numbers. Zbl 1467.11038Luca, Florian; Patel, Vandita 10 2018 On the lower bound of the linear complexity over \(\mathbb F_p\) of Sidelnikov sequences. Zbl 1296.94073Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor; Winterhof, Arne 10 2006 Divisibility of class numbers: enumerative approach. Zbl 1072.11084Bilu, Yuri F.; Luca, Florian 9 2005 The Diophantine equation \(P(x)=n!\) and a result of M. Overholt. Zbl 1085.11023Luca, Florian 9 2002 On the \(X\)-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain 9 2017 An exponential Diophantine equation related to the sum of powers of two consecutive \(k\)-generalized Fibonacci numbers. Zbl 1338.11016Gómez Ruiz, Carlos Alexis; Luca, Florian 9 2014 Some remarks on Heron triangles. Zbl 1062.11019Kramer, Alpar-Vajk; Luca, Florian 9 2000 \(p\)-adic quotient sets. Zbl 1428.11023Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam 9 2017 Generalized balancing numbers. Zbl 1239.11035Liptai, Kálmán; Luca, Florian; Pintér, Ákos; Szalay, László 9 2009 Irreducible radical extensions and Euler-function chains. Zbl 1172.11029Luca, Florian; Pomerance, Carl 9 2007 On a diophantine equation related to a conjecture of Erdös and Graham. Zbl 1132.11319Luca, F.; Walsh, P. G. 9 2007 Powers of two as sums of two Lucas numbers. Zbl 1358.11026Bravo, Jhon J.; Luca, Florian 9 2014 On the Diophantine equation \(x^2 + 2^{\alpha}5^{\beta}13^{\gamma} = y^n\). Zbl 1232.11130Goins, Edray; Luca, Florian; Togbé, Alain 9 2008 Some results on Oppenheim’s “factorisatio numerorum” function. Zbl 1213.11020Luca, Florian; Mukhopadhyay, Anirban; Srinivas, Kotyada 9 2010 Fibonacci numbers of the form \(p^a\pm p^b+1\). Zbl 1228.11021Luca, Florian; Szalay, László 9 2007 Quotients of Fibonacci numbers. Zbl 1391.11027Garcia, Stephan Ramon; Luca, Florian 9 2016 Powers of two as sums of three Pell numbers. Zbl 1433.11032Bravo, Jhon J.; Faye, Bernadette; Luca, Florian 9 2017 On a problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of 2. Zbl 1437.11051Ddamulira, Mahadi; Gómez, Carlos A.; Luca, Florian 9 2018 MOV attack in various subgroups on elliptic curves. Zbl 1072.11094Luca, Florian; Mireles, David Jose; Shparlinski, Igor E. 8 2004 Catalan and Apéry numbers in residue classes. Zbl 1101.11010Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. 8 2006 Average order in cyclic groups. Zbl 1079.11003von zur Gathen, Joachim; Knopfmacher, Arnold; Luca, Florian; Lucht, Lutz G.; Shparlinski, Igor E. 8 2004 Exponential sums and congruences with factorials. Zbl 1071.11051Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. 8 2005 The distribution of self-Fibonacci divisors. Zbl 1390.11119Luca, Florian; Tron, Emanuele 8 2015 Perfect powers from products of terms in Lucas sequences. Zbl 1137.11011Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 8 2007 On shifted primes with large prime factors and their products. Zbl 1370.11110Luca, Florian; Menares, Ricardo; Pizarro-Madariaga, Amalia 8 2015 Members of Lucas sequences whose Euler function is a power of 2. Zbl 1351.11015Taoufiq Damir, Mohamed; Faye, Bernadette; Luca, Florian; Tall, Amadou 8 2014 Squares in Lehmer sequences and some Diophantine applications. Zbl 1006.11011Luca, Florian; Walsh, P. G. 8 2001 On the largest prime factor of \((ab+1)(ac+1)(bc+1)\). Zbl 1108.11030Hernández, Santos; Luca, Florian 8 2003 On the exponent of the group of points on elliptic curves in extension fields. Zbl 1082.11041Luca, Florian; Shparlinski, Igor E. 8 2005 Common values of the arithmetic functions \(\varphi\) and \(\sigma\). Zbl 1205.11010Ford, Kevin; Luca, Florian; Pomerance, Carl 8 2010 On the maximal order of numbers in the “factorisatio numerorum” problem. Zbl 1169.11043Klazar, Martin; Luca, Florian 8 2007 Fibonacci numbers with the Lehmer property. Zbl 1112.11007Luca, Florian 8 2007 On stable quadratic polynomials. Zbl 1241.11027Ahmadi, Omran; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E. 8 2012 Some additive combinatorics problems in matrix rings. Zbl 1208.11037Ferguson, Ron; Hoffman, Corneliu; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E. 8 2010 On factorials expressible as sums of at most three Fibonacci numbers. Zbl 1253.11048Luca, Florian; Siksek, Samir 8 2010 On the Diophantine equation \(x^2 + C = 2y^n\). Zbl 1233.11037Abu Muriefah, Fadwa S.; Luca, Florian; Siksek, Samir; Tengely, Szabolcs 8 2009 On the Diophantine equation \(F_n + F_m=2^a\). Zbl 1419.11024Bravo, Jhon J.; Luca, Florian 8 2016 \(X\)-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian 8 2018 Fibonacci Diophantine triples. Zbl 1218.11020Luca, Florian; Szalay, László 8 2008 On the Diophantine equation \(x^2 + 5^a 13^b = y^n\). Zbl 1186.11016Abu Muriefah, Fadwa S.; Luca, Florian; Togbé, Alain 8 2008 Every positive integer is a sum of three palindromes. Zbl 1441.11016Cilleruelo, Javier; Luca, Florian; Baxter, Lewis 8 2018 On the largest prime factor of \(x^2-1\). Zbl 1221.11080Luca, Florian; Najman, Filip 7 2011 On the number of factorizations of an integer. Zbl 1245.11100Balasubramanian, Ramachandran; Luca, Florian 7 2011 The number of non-zero digits of \(n\)! Zbl 1043.11008Luca, Florian 7 2002 On the Diophantine equation \(x^2 + 2^a \cdot 11^b = y^n\). Zbl 1219.11056Cangül, Ismail Naci; Demirci, Musa; Luca, Florian; Pintér, Ákos; Soydan, Gökhan 7 2010 The Diophantine equation \(x^2=p^a\pm p^b+1\). Zbl 1067.11016Luca, Florian 7 2004 On the Diophantine equation \(x^2+7^{2k}=y^n\). Zbl 1221.11091Luca, Florian; Togbé, Alain 7 2007 Fibonacci numbers which are sums of three factorials. Zbl 1259.11038Bollman, Mark; Hernández Hernández, Santos; Luca, Florian 7 2010 On the Diophantine equation \(x^2+2^a\cdot 3^b \cdot 11^c = y^n\). Zbl 1349.11069Cangül, İsmail Naci; Demirci, Musa; İnam, İlker; Luca, Florian; Soydan, Gökhan 7 2013 On composite integers \(n\) for which \(\varphi(n)\mid n-1\). Zbl 1294.11005Luca, Florian; Pomerance, Carl 7 2011 On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers. Zbl 1447.11025Ddamulira, Mahadi; Luca, Florian 7 2020 Fibonacci numbers which are products of two Pell numbers. Zbl 1400.11040Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja 7 2016 On factorials which are products of factorials. Zbl 1132.11017Luca, Florian 7 2007 Polynomial values of sums of products of consecutive integers. Zbl 1442.11055Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F. 7 2018 Repdigits as sums of four Fibonacci or Lucas numbers. Zbl 1453.11006Normenyo, Benedict Vasco; Luca, Florian; Togb, Alain 7 2018 Pell and Pell-Lucas numbers as sums of two repdigits. Zbl 1452.11020Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain 7 2020 Fibonacci numbers which are concatenations of two repdigits. Zbl 1472.11067Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon 6 2021 On shifted products which are powers. Zbl 1123.11011Luca, Florian 6 2005 On the value set of \(n!\) modulo a prime. Zbl 1161.11386Banks, William D.; Luca, Florian; Shparlinski, Igor E.; Stichtenoth, Henning 6 2005 On the convergence of series of reciprocals of primes related to the Fermat numbers. Zbl 1026.11011Křížek, Michal; Luca, Florian; Somer, Lawrence 6 2002 On the counting function of irregular primes. Zbl 1356.11067Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl 6 2015 Fibonacci numbers of the form \(k^2+k+2\). Zbl 0979.11012Luca, Florian 6 1999 Fibonacci numbers which are concatenations of two repdigits. Zbl 1472.11067Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon 6 2021 On a generalization of the Pell sequence. Zbl 07361099Bravo, Jhon J.; Herrera, Jose L.; Luca, Florian 5 2021 Common values of generalized Fibonacci and Pell sequences. Zbl 1471.11049Bravo, Jhon J.; Herrera, Jose L.; Luca, Florian 3 2021 On Pillai’s problem with \(X\)-coordinates of Pell equations and powers of 2. II. Zbl 07410933Erazo, Harold S.; Gómez, Carlos A.; Luca, Florian 1 2021 \(k\)-generalized Fibonacci numbers which are concatenations of two repdigits. Zbl 07414938Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon 1 2021 On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. Zbl 1481.11020Ddamulira, Mahadi; Luca, Florian 1 2021 Binary polynomial power sums vanishing at roots of unity. Zbl 1475.11042Bilu, Yuri; Luca, Florian 1 2021 On the nonnegative integer solutions to the equation \(F_n \pm F_m = y^a\). Zbl 07276978Kebli, Salima; Kihel, Omar; Larone, Jesse; Luca, Florian 1 2021 On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers. Zbl 1447.11025Ddamulira, Mahadi; Luca, Florian 7 2020 Pell and Pell-Lucas numbers as sums of two repdigits. Zbl 1452.11020Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain 7 2020 Zeckendorf representations with at most two terms to \(x\)-coordinates of Pell equations. Zbl 1455.11031Gómez, Carlos A.; Luca, Florian 5 2020 On certain sums concerning the gcd’s and lcm’s of \(k\) positive integers. Zbl 1452.11007Hilberdink, Titus; Luca, Florian; Tóth, László 5 2020 Products of \(k\)-Fibonacci numbers which are rep-digits. Zbl 1463.11032Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon 4 2020 On the problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of \(3\). Zbl 1446.11025Ddamulira, Mahadi; Luca, Florian 3 2020 Primitive root bias for twin primes. II: Schinzel-type theorems for totient quotients and the sum-of-divisors function. Zbl 1450.11002Garcia, Stephan Ramon; Luca, Florian; Shi, Kye; Udell, Gabe 3 2020 Correction to: \(X\)-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1449.11051Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian 3 2020 Trinomials with given roots. Zbl 1479.11052Bilu, Yuri; Luca, Florian 2 2020 On \(Y\)-coordinates of Pell equations which are members of a fixed binary recurrence. Zbl 1477.11060Faye, Bernadette; Luca, Florian 2 2020 On \(Y\)-coordinates of Pell equations which are base 2 rep-digits. Zbl 1478.11016Faye-Fall, Bernadette; Luca, Florian 2 2020 On members of Lucas sequences which are products of factorials. Zbl 1478.11018Laishram, Shanta; Luca, Florian; Sias, Mark 2 2020 The \(x\)-coordinates of Pell equations and sums of two Fibonacci numbers. II. Zbl 1471.11065Ddamulira, Mahadi; Luca, Florian 2 2020 Linear combinations of prime powers in \(X\)-coordinates of Pell equations. Zbl 1485.11027Erazo, Harold; Gómez, Carlos A.; Luca, Florian 1 2020 On the prime factors of the iterates of the Ramanujan \(\tau\)-function. Zbl 1472.11036Luca, Florian; Mabaso, Sibusiso; Stănică, Pantelimon 1 2020 Multiplicative dependence between \(k\)-Fibonacci and \(k\)-Lucas numbers. Zbl 1474.11047Gómez, Carlos A.; Gómez, Jhonny C.; Luca, Florian 1 2020 On \(X\)-coordinates of Pell equations which are repdigits. Zbl 1470.11026Gómez, Carlos A.; Luca, Florian; Zottor, Faith Shadow 1 2020 On a conjecture concerning the multiplicity of the Tribonacci sequence. Zbl 1459.11036Bravo, Eric F.; Gómez, Carlos A.; Kafle, Bir; Luca, Florian; Togbé, Alain 1 2020 Total multiplicity of the Tribonacci sequence. Zbl 1459.11037Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian 1 2020 Composite positive integers whose sum of prime factors is prime. Zbl 07177880Luca, Florian; Moodley, Damon 1 2020 On a Diophantine equation involving powers of Fibonacci numbers. Zbl 1478.11017Gueth, Krisztián; Luca, Florian; Szalay, László 1 2020 Lucas factoriangular numbers. Zbl 07217178Kafle, Bir; Luca, Florian; Togbé, Alain 1 2020 On the equation \(\sum_{j = 1}^k j F_j^p = F_n^q\). Zbl 1471.11043Altassan, Alaa; Luca, Florian 1 2020 Ratios of sums of two Fibonacci numbers equal to powers of 2. Zbl 1471.11047Bravo, Jhon J.; Díaz, Maribel; Luca, Florian 1 2020 Binary recurrences for which powers of two are discriminating moduli. Zbl 1471.11086de Clercq, Adriaan A.; Luca, Florian; Martirosyan, Lilit; Matthis, Maria; Moree, Pieter; Stoumen, Max A.; Weiß, Melvin 1 2020 On the zero-multiplicity of the \(k\)-generalized Fibonacci sequence. Zbl 1464.11024García, Jonathan; Gómez, Carlos A.; Luca, Florian 1 2020 Powers of two in generalized Lucas sequences. Zbl 1468.11060Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain 1 2020 Repdigits as sums of four Pell numbers. Zbl 1455.11019Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain 10 2019 Recurrence relations for polynomials obtained by arithmetic functions. Zbl 1435.11055Heim, Bernhard; Luca, Florian; Neuhauser, Markus 6 2019 On the exponential Diophantine equation \(P_n^x+P_{n+1}^x=P_m\). Zbl 1455.11056Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain 6 2019 Lucas numbers as sums of two repdigits. Zbl 1427.11013Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain 6 2019 Repdigits as sums of three Lucas numbers. Zbl 1459.11041Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain 5 2019 On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041Heim, Bernhard; Luca, Florian; Neuhauser, Markus 5 2019 \(X\)-coordinates of Pell equations which are Lucas numbers. Zbl 07137965Kafle, Bir; Luca, Florian; Togbé, Alain 5 2019 On Pillai’s problem with the Fibonacci and Pell sequences. Zbl 1440.11018Hernández Hernández, Santos; Luca, Florian; Rivera, Luis Manuel 5 2019 An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers. Zbl 1449.11036Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain 5 2019 On Pillai’s problem with \(X\)-coordinates of Pell equations and powers of 2. Zbl 1465.11086Erazo, Harold S.; Gómez, Carlos A.; Luca, Florian 4 2019 On the \(x\)-coordinates of Pell equations which are products of two Fibonacci numbers. Zbl 1420.11061Kafle, Bir; Luca, Florian; Montejano, Amanda; Szalay, László; Togbé, Alain 4 2019 Primitive root bias for twin primes. Zbl 1450.11001Garcia, Stephan Ramon; Kahoro, Elvis; Luca, Florian 4 2019 On the zero-multiplicity of a fifth-order linear recurrence. Zbl 1450.11009Gómez Ruiz, Carlos Alexis; Luca, Florian 3 2019 \(x\)-Coordinates of Pell equations which are Tribonacci numbers. II. Zbl 1449.11030Kafle, Bir; Luca, Florian; Togbé, Alain 3 2019 Diophantine equations with the Ramanujan \(\tau\) function of factorials, Fibonacci numbers, and Catalan numbers. Zbl 1456.11031Luca, Florian; Mabaso, Sibusiso 2 2019 Product of consecutive tribonacci numbers with only one distinct digit. Zbl 1455.11027Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian 2 2019 On ternary Egyptian fractions with prime denominator. Zbl 1455.11057Luca, Florian; Pappalardi, Francesco 2 2019 On the discriminator of Lucas sequences. Zbl 1456.11021Faye, Bernadette; Luca, Florian; Moree, Pieter 2 2019 Linear independence of powers of singular moduli of degree three. Zbl 1451.11069Luca, Florian; Riffaut, Antonin 1 2019 On the typical size and cancellations among the coefficients of some modular forms. Zbl 1450.11100Luca, Florian; Radziwiłł, Maksym; Shparlinski, Igor E. 1 2019 Consecutive integers with close kernels. Zbl 1478.11008De Koninck, Jean-Marie; Luca, Florian 1 2019 Diophantine \(S\)-quadruples with two primes which are twin. Zbl 1449.11067Luca, F. 1 2019 Perfect Pell and Pell-Lucas numbers. Zbl 1449.11026Bravo, Jhon J.; Luca, Florian 1 2019 On \(X\)-coordinates of Pell equations that are repdigits. Zbl 1459.11082Faye, Bernadette; Luca, Florian 12 2018 Repdigits as sums of three Pell numbers. Zbl 1413.11008Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain 10 2018 On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027Luca, Florian; Togbé, Alain 10 2018 On perfect powers that are sums of two Fibonacci numbers. Zbl 1467.11038Luca, Florian; Patel, Vandita 10 2018 On a problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of 2. Zbl 1437.11051Ddamulira, Mahadi; Gómez, Carlos A.; Luca, Florian 9 2018 \(X\)-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian 8 2018 Every positive integer is a sum of three palindromes. Zbl 1441.11016Cilleruelo, Javier; Luca, Florian; Baxter, Lewis 8 2018 Polynomial values of sums of products of consecutive integers. Zbl 1442.11055Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F. 7 2018 Repdigits as sums of four Fibonacci or Lucas numbers. Zbl 1453.11006Normenyo, Benedict Vasco; Luca, Florian; Togb, Alain 7 2018 On Pillai’s problem with Pell numbers and powers of 2. Zbl 1448.11042Ouamar Hernane, Mohand; Luca, Florian; Rihane, Salah; Togbé, Alain 6 2018 A Diophantine equation in \(k\)-Fibonacci numbers and repdigits. Zbl 1407.11026Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian 6 2018 Primitive root biases for prime pairs. I: Existence and non-totality of biases. Zbl 1431.11112Garcia, Stephan Ramon; Luca, Florian; Schaaff, Timothy 4 2018 Diophantine triples and \(k\)-generalized Fibonacci sequences. Zbl 1447.11054Fuchs, Clemens; Hutle, Christoph; Luca, Florian; Szalay, László 4 2018 On the difference in values of the Euler totient function near prime arguments. Zbl 1455.11127Garcia, Stephan Ramon; Luca, Florian 4 2018 Markov equation with Fibonacci components. Zbl 1458.11056Luca, Florian; Srinivasan, Anitha 3 2018 Arithmetic properties of coefficients of \(L\)-functions of elliptic curves. Zbl 1423.11169Güloğlu, Ahmet M.; Luca, Florian; Yalçiner, Aynur 2 2018 Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms. Zbl 1444.11071Bilu, Yuri F.; Deshouillers, Jean-Marc; Gun, Sanoli; Luca, Florian 2 2018 On the error term of a lattice counting problem. Zbl 1380.11085Bordellès, Olivier; Luca, Florian; Shparlinski, Igor E. 1 2018 There are no Diophantine quadruples of Fibonacci numbers. Zbl 1441.11058Fujita, Yasutsugu; Luca, Florian 1 2018 A variation on the theme of Nicomachus. Zbl 1410.11079Luca, Florian; Polanco, Geremías; Zudilin, Wadim 1 2018 Denominators of Bernoulli polynomials. Zbl 1415.11121Bordellès, Olivier; Luca, Florian; Moree, Pieter; Shparlinski, Igor E. 1 2018 On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja 14 2017 On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013Bravo, Jhon J.; Luca, Florian; Yazán, Karina 11 2017 On the \(X\)-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain 9 2017 \(p\)-adic quotient sets. Zbl 1428.11023Garcia, 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 1433.11032Bravo, Jhon J.; Faye, Bernadette; Luca, Florian 9 2017 On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. II. Zbl 1420.11037Kafle, Bir; Luca, Florian; Togbé, Alain 6 2017 On arithmetic lattices in the plane. Zbl 1358.11074Fukshansky, Lenny; Guerzhoy, Pavel; Luca, Florian 3 2017 On Diophantine quadruples of Fibonacci numbers. Zbl 1386.11065Fujita, Yasutsugu; Luca, Florian 3 2017 Diversity in parametric families of number fields. Zbl 1414.11150Bilu, Yuri; Luca, Florian 3 2017 Corrigendum to “Positive integers divisible by the product of their nonzero digits”, portugaliae math. 64 (2007), 1: 75 – 85. Zbl 1434.11195De Koninck, Jean-Marie; Luca, Florian 2 2017 The \(r\)th moment of the divisor function: an elementary approach. Zbl 1366.11103Luca, Florian; Tóth, László 2 2017 Collinear CM-points. Zbl 1432.11061Bilu, Yuri; Luca, Florian; Masser, David 2 2017 On the number of non-zero digits of integers in multi-base representations. Zbl 1399.11027Bertók, Cs.; Hajdu, L.; Luca, F.; Sharma, D. 2 2017 Palindromes in several sequences. Zbl 1429.11018Luca, Florian 2 2017 Monotonic phinomial coefficients. Zbl 1437.11006Luca, Florian; Stănică, Pantelimon 2 2017 Lucas numbers with the Lehmer property. Zbl 1389.11043Faye, Bernadette; Luca, Florian 2 2017 Generalized incomplete poly-Bernoulli polynomials and generalized incomplete poly-Cauchy polynomials. Zbl 1409.11015Komatsu, Takao; Luca, Florian 2 2017 Fibonacci factoriangular numbers. Zbl 1373.11011Gómez Ruiz, Carlos Alexis; Luca, Florian 2 2017 Only finitely many Tribonacci Diophantine triples exist. Zbl 1440.11042Fuchs, Clemens; Hutle, Christoph; Irmak, Nurettin; Luca, Florian; Szalay, László 2 2017 Diophantine triples with values in the sequences of Fibonacci and Lucas numbers. Zbl 1417.11011Luca, Florian; Munagi, Augustine O. 1 2017 Pell numbers with the Lehmer property. Zbl 1439.11015Faye, Bernadette; Luca, Florian 1 2017 ...and 404 more Documents all cited Publications top 5 cited Publications 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 all top 5 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. 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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 all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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