Edit Profile (opens in new tab) Luca, Florian Co-Author Distance 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: 763 Publications since 1993, including 3 Books 6 Contributions as Editor Reviewing Activity: 372 Reviews Co-Authors: 347 Co-Authors with 666 Joint Publications 5,770 Co-Co-Authors all top 5 Co-Authors 102 single-authored 77 Shparlinski, Igor E. 49 Togbé, Alain 41 Gómez, Carlos Alexis 38 Stănică, Pantelimon 29 De Koninck, Jean-Marie 25 Banks, William David 25 Pomerance, Carl Bernard 24 Bravo, Jhon Jairo 20 Faye, Bernadette 20 Szalay, László 15 Bilu, Yuri F. 13 Garaev, Moubariz Z. 12 Alahmadi, Adel N. 12 Cilleruelo, Javier 11 Mignotte, Maurice 10 Bugeaud, Yann 10 Ford, Kevin B. 9 Ddamulira, Mahadi 9 Mejía-Huguet, V. Janitzio 9 Moree, Pieter 9 Pappalardi, Francesco 9 Walsh, Peter Gareth 8 Bérczes, Attila 8 Dujella, Andrej 8 Garcia, Stephan Ramon 8 Gómez, Jhonny Carpediem 8 Hajdu, Lajos 8 Kafle, Bir 7 Bravo, Eric Fernando 7 Hernández Hernández, Santos 7 Komatsu, Takao 7 Pizarro-Madariaga, Amalia 7 Rihane, Salah Eddine 7 Siksek, Samir 7 Somer, Lawrence E. 7 Tachiya, Yohei 6 Altassan, Alaa 6 Broughan, Kevin A. 6 Friedlander, John Benjamin 6 Fuchs, Clemens 6 Křížek, Michal 5 Berrizbeitia, Pedro 5 Grytczuk, Aleksander 5 Klazar, Martin 5 Knopfmacher, Arnold 5 Shorey, Tarlok Nath 5 Thangadurai, Ravindranathan 5 Wójtowicz, Marek 5 Yalçiner, Aynur 5 Young, Paul Thomas 4 Balasubramanian, Ramachandran 4 Ballot, Christian 4 Cipu, Mihai 4 Deshouillers, Jean-Marc 4 Doyon, Nicolas 4 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 Landman, Bruce M. 3 Mabaso, Sibusiso 3 Mukhopadhyay, Anirban 3 Munagi, Augustine O. 3 Nathanson, Melvyn Bernard 3 Nešetřil, Jaroslav 3 Nicolae, Florin 3 Nowak, Werner Georg 3 Ouaknine, Joel O. 3 Oyono, Roger 3 Pink, István 3 Porubsky, Stefan 3 Ralaivaosaona, Dimbinaina 3 Robertson, Aaron 3 Shoaib, Hatoon 3 Soydan, Gokhan 3 Tall, Amadou Makhtar 3 Tchammou, Euloge B. 3 Worrell, James B. 2 Abu Muriefah, Fadwa S. 2 Adamczewski, Boris 2 Adédji, Kouèssi Norbert 2 Alvarado, Saúl Díaz 2 Alzer, Horst 2 Ayad, Mohamed ...and 253 more Co-Authors all top 5 Serials 52 Journal of Number Theory 42 Acta Arithmetica 31 International Journal of Number Theory 29 The Fibonacci Quarterly 24 Journal of Integer Sequences 21 Colloquium Mathematicum 20 Publicationes Mathematicae Debrecen 18 Integers 15 Indagationes Mathematicae. New Series 14 Periodica Mathematica Hungarica 14 Glasnik Matematički. Serija III 14 Boletín de la Sociedad Matemática Mexicana. Third Series 13 Monatshefte für Mathematik 12 Bulletin of the Australian Mathematical Society 12 Annales Mathematicae et Informaticae 11 Rocky Mountain Journal of Mathematics 10 Proceedings of the American Mathematical Society 10 Journal de Théorie des Nombres de Bordeaux 10 The Ramanujan Journal 9 Functiones et Approximatio. Commentarii Mathematici 9 Glasgow Mathematical Journal 9 Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. Nouvelle Série 8 Mathematics of Computation 8 Archiv der Mathematik 8 Uniform Distribution Theory 7 Mathematica Slovaca 7 The New York Journal of Mathematics 6 American Mathematical Monthly 6 Canadian Mathematical Bulletin 6 Proceedings of the Edinburgh Mathematical Society. Series II 6 Mathematica Bohemica 6 Journal of Combinatorics and Number Theory 5 Annales des Sciences Mathématiques du Québec 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 Results in Mathematics 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Mathematical Communications 4 Acta Academiae Paedagogicae Agriensis. Nova Series. Sectio Matematicae 4 Journal of the Australian Mathematical Society 4 Portugaliae Mathematica. Nova Série 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Afrika Matematika 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 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 Analele Științifice ale Universității “Ovidius” Constanța. Seria: Matematică 3 Revista Matemática Complutense 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Moscow Journal of Combinatorics and Number Theory 3 Research in Number Theory 2 Houston Journal of Mathematics 2 Acta Scientiarum Mathematicarum 2 Archivum Mathematicum 2 Journal of Algebra 2 Michigan Mathematical Journal 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 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 Taiwanese Journal of Mathematics 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 JP Journal of Algebra, Number Theory and Applications 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Missouri Journal of Mathematical Sciences 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Mediterranean Journal of Mathematics 2 Algebra & Number Theory 2 Albanian Journal of Mathematics 2 Annales Mathématiques du Québec ...and 70 more Serials all top 5 Fields 749 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) 6 General and overarching topics; collections (00-XX) 5 Information and communication theory, circuits (94-XX) 4 History and biography (01-XX) 4 \(K\)-theory (19-XX) 3 Computer science (68-XX) 2 Commutative algebra (13-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Dynamical systems and ergodic theory (37-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 Difference and functional equations (39-XX) 1 Algebraic topology (55-XX) 1 Probability theory and stochastic processes (60-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 531 Publications have been cited 2,642 times in 1,287 Documents Cited by ▼ Year ▼ On a conjecture about repdigits in \(k\)-generalized Fibonacci sequences. Zbl 1274.11035Bravo, Jhon J.; Luca, Florian 57 2013 Fibonacci and Lucas numbers with only one distinct digit. Zbl 0958.11007Luca, F. 56 2000 Powers of two as sums of two \(k\)-Fibonacci numbers. Zbl 1389.11041Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian 46 2016 Linear combinations of factorials and \(S\)-units in a binary recurrence sequence. Zbl 1361.11007Sanchez, Sergio Guzmán; Luca, Florian 46 2014 Powers of two in generalized Fibonacci sequences. Zbl 1353.11020Bravo, Jhon J.; Luca, Florian 43 2012 On the complexity of algebraic numbers. (Sur la complexité des nombres algébriques.) Zbl 1119.11019Adamczewski, Boris; Bugeaud, Yann; Luca, Florian 34 2004 Analytic number theory. Exploring the anatomy of integers. Zbl 1247.11001De Koninck, Jean-Marie; Luca, Florian 33 2012 Fibonacci numbers at most one away from a perfect power. Zbl 1156.11008Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 31 2008 On the equation \(x^2 + 2^a \cdot 3^b = y^n\). Zbl 1085.11021Luca, Florian 26 2002 Repdigits as sums of three Fibonacci numbers. Zbl 1305.11008Luca, Florian 25 2012 Pell and Pell-Lucas numbers with only one distinct digit. Zbl 1349.11023Faye, Bernadette; Luca, Florian 25 2015 Fibonacci numbers which are sums of two repdigits. Zbl 1287.11021Díaz Alvarado, Saúl; Luca, Florian 23 2011 Coincidences in generalized Fibonacci sequences. Zbl 1272.11028Bravo, Jhon J.; Luca, Florian 22 2013 A generalization of a classical zero-sum problem. Zbl 1123.11012Luca, Florian 21 2007 An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Zbl 1253.11046Luca, Florian; Oyono, Roger 19 2011 On the \(x\)-coordinates of Pell equations which are rep-digits. Zbl 1389.11076Dossavi-Yovo, Appolinaire; Luca, Florian; Togbé, Alain 18 2016 Distinct digits in base \(b\) expansions of linear recurrence sequences. Zbl 1030.11004Luca, Florian 17 2000 On the largest prime factor of the \(k\)-Fibonacci numbers. Zbl 1292.11034Bravo, Jhon J.; Luca, Florian 17 2013 On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja 17 2017 17 lectures on Fermat numbers. From number theory to geometry. With a foreword by Alena Šolcová. Zbl 1010.11002Křížek, Michal; Luca, Florian; Somer, Lawrence 17 2001 On the Diophantine equation \(x^2+2^a\cdot 5^b=y^n\). Zbl 1231.11041Luca, Florian; Togbé, Alain 16 2008 On the Diophantine equation \(F_n + F_m=2^a\). Zbl 1419.11024Bravo, Jhon J.; Luca, Florian 16 2016 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. 16 2012 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 16 2014 On \(X\)-coordinates of Pell equations that are repdigits. Zbl 1459.11082Faye, Bernadette; Luca, Florian 15 2018 On a Diophantine equation. Zbl 0997.11027Luca, Florian 15 2000 Generalized balancing numbers. Zbl 1239.11035Liptai, Kálmán; Luca, Florian; Pintér, Ákos; Szalay, László 14 2009 Character sums and congruences with \(n!\). Zbl 1060.11046Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. 14 2004 Powers of two as sums of two Lucas numbers. Zbl 1358.11026Bravo, Jhon J.; Luca, Florian 14 2014 On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027Luca, Florian; Togbé, Alain 14 2018 On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions \(\varphi\) and \(\sigma\). Zbl 1027.11007Luca, Florian; Pomerance, Carl 14 2002 On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013Bravo, Jhon J.; Luca, Florian; Yazán, Karina 13 2017 Functional graphs of polynomials over finite fields. Zbl 1327.05323Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E. 13 2016 Almost powers in the Lucas sequence. Zbl 1204.11030Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 12 2008 Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers. Zbl 1289.11021Komatsu, Takao; Luca, Florian 12 2013 The distribution of self-Fibonacci divisors. Zbl 1390.11119Luca, Florian; Tron, Emanuele 12 2015 \(p\)-adic quotient sets. Zbl 1428.11023Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam 12 2017 Quotients of Fibonacci numbers. Zbl 1391.11027Garcia, Stephan Ramon; Luca, Florian 12 2016 Fibonacci numbers which are concatenations of two repdigits. Zbl 1472.11067Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon 12 2021 Every positive integer is a sum of three palindromes. Zbl 1441.11016Cilleruelo, Javier; Luca, Florian; Baxter, Lewis 12 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 12 2006 Repdigits as sums of three Pell numbers. Zbl 1413.11008Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain 11 2018 Repdigits as sums of four Pell numbers. Zbl 1455.11019Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain 11 2019 On a problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of 2. Zbl 1437.11051Ddamulira, Mahadi; Gómez, Carlos A.; Luca, Florian 11 2018 On the \(X\)-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain 11 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 11 2014 Divisibility of class numbers: enumerative approach. Zbl 1072.11084Bilu, Yuri F.; Luca, Florian 11 2005 Irreducible radical extensions and Euler-function chains. Zbl 1172.11029Luca, Florian; Pomerance, Carl 11 2007 Diophantine equations with products of consecutive terms in Lucas sequences. Zbl 1081.11023Luca, F.; Shorey, T. N. 11 2005 Fibonacci numbers of the form \(p^a\pm p^b+1\). Zbl 1228.11021Luca, Florian; Szalay, László 11 2007 Pell and Pell-Lucas numbers as sums of two repdigits. Zbl 1452.11020Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain 11 2020 Rational products of singular moduli. Zbl 1400.11113Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia 11 2016 On perfect powers that are sums of two Fibonacci numbers. Zbl 1467.11038Luca, Florian; Patel, Vandita 11 2018 On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers. Zbl 1447.11025Ddamulira, Mahadi; Luca, Florian 10 2020 Fibonacci numbers which are products of two Pell numbers. Zbl 1400.11040Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja 10 2016 On Pillai’s Diophantine equation. Zbl 1136.11026Bugeaud, Yann; Luca, Florian 10 2006 On the exponential local-global principle. Zbl 1330.11019Bartolome, Boris; Bilu, Yuri; Luca, Florian 10 2013 On the Diophantine equation \(x^2 + 2^{\alpha}5^{\beta}13^{\gamma} = y^n\). Zbl 1232.11130Goins, Edray; Luca, Florian; Togbé, Alain 10 2008 On factorials which are products of factorials. Zbl 1132.11017Luca, Florian 10 2007 The Diophantine equation \(P(x)=n!\) and a result of M. Overholt. Zbl 1085.11023Luca, Florian 10 2002 Some remarks on Heron triangles. Zbl 1062.11019Kramer, Alpar-Vajk; Luca, Florian 10 2000 On the Diophantine equation \(x^2 + 5^a 13^b = y^n\). Zbl 1186.11016Abu Muriefah, Fadwa S.; Luca, Florian; Togbé, Alain 10 2008 Powers of two as sums of three Pell numbers. Zbl 1433.11032Bravo, Jhon J.; Faye, Bernadette; Luca, Florian 10 2017 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 9 2019 On the number of factorizations of an integer. Zbl 1245.11100Balasubramanian, Ramachandran; Luca, Florian 9 2011 On shifted primes with large prime factors and their products. Zbl 1370.11110Luca, Florian; Menares, Ricardo; Pizarro-Madariaga, Amalia 9 2015 On a diophantine equation related to a conjecture of Erdös and Graham. Zbl 1132.11319Luca, F.; Walsh, P. G. 9 2007 Some results on Oppenheim’s “factorisatio numerorum” function. Zbl 1213.11020Luca, Florian; Mukhopadhyay, Anirban; Srinivas, Kotyada 9 2010 Members of Lucas sequences whose Euler function is a power of 2. Zbl 1351.11015Taoufiq Damir, Mohamed; Faye, Bernadette; Luca, Florian; Tall, Amadou 9 2014 Lucas numbers as sums of two repdigits. Zbl 1427.11013Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain 8 2019 \(X\)-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian 8 2018 On Pillai’s problem with Pell numbers and powers of 2. Zbl 1448.11042Ouamar Hernane, Mohand; Luca, Florian; Rihane, Salah; Togbé, Alain 8 2018 Repdigits in \(k\)-Lucas sequences. Zbl 1382.11019Bravo, Jhon J.; Luca, Florian 8 2013 Sets with prescribed arithmetic densities. Zbl 1212.11018Luca, Florian; Pomerance, Carl; Porubský, Štefan 8 2008 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 largest prime factor of \(x^2-1\). Zbl 1221.11080Luca, Florian; Najman, Filip 8 2011 On stable quadratic polynomials. Zbl 1241.11027Ahmadi, Omran; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E. 8 2012 The Diophantine equation \(x^2=p^a\pm p^b+1\). Zbl 1067.11016Luca, Florian 8 2004 MOV attack in various subgroups on elliptic curves. Zbl 1072.11094Luca, Florian; Mireles, David Jose; Shparlinski, Igor E. 8 2004 Average order in cyclic groups. Zbl 1079.11003von zur Gathen, Joachim; Knopfmacher, Arnold; Luca, Florian; Lucht, Lutz G.; Shparlinski, Igor E. 8 2004 Catalan and Apéry numbers in residue classes. Zbl 1101.11010Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. 8 2006 Common values of the arithmetic functions \(\varphi\) and \(\sigma\). Zbl 1205.11010Ford, Kevin; Luca, Florian; Pomerance, Carl 8 2010 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 Perfect powers from products of terms in Lucas sequences. Zbl 1137.11011Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 8 2007 On the exponent of the group of points on elliptic curves in extension fields. Zbl 1082.11041Luca, Florian; Shparlinski, Igor E. 8 2005 Fibonacci Diophantine triples. Zbl 1218.11020Luca, Florian; Szalay, László 8 2008 Fibonacci numbers of the form \(k^2+k+2\). Zbl 0979.11012Luca, Florian 8 1999 On the Diophantine equation \(x^2+7^{2k}=y^n\). Zbl 1221.11091Luca, Florian; Togbé, Alain 8 2007 Squares in Lehmer sequences and some Diophantine applications. Zbl 1006.11011Luca, Florian; Walsh, P. G. 8 2001 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 the largest prime factor of \((ab+1)(ac+1)(bc+1)\). Zbl 1108.11030Hernández, Santos; Luca, Florian 8 2003 Exponential sums and congruences with factorials. Zbl 1071.11051Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. 8 2005 Fibonacci numbers of the form \(p^a\pm p^b\). Zbl 1273.11030Luca, Florian; Stănică, Pantelimon 7 2009 On the largest prime factor of the Mersenne numbers. Zbl 1178.11061Ford, Kevin; Luca, Florian; Shparlinski, Igor E. 7 2009 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; Togbé, Alain 7 2018 On Pillai’s problem with the Fibonacci and Pell sequences. Zbl 1440.11018Hernández Hernández, Santos; Luca, Florian; Rivera, Luis Manuel 7 2019 On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041Heim, Bernhard; Luca, Florian; Neuhauser, Markus 7 2019 On a Diophantine equation involving Fibonacci numbers and the Ramanujan \(\tau\)-function of factorials. Zbl 1499.11069Luca, Florian; Mabaso, Sibusiso 2 2022 Trinomials, singular moduli and Riffaut’s conjecture. Zbl 07644998Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia 1 2022 An inequality for Fibonacci numbers. Zbl 07655828Alzer, Horst; Luca, Florian 1 2022 On the multiplicities of Padovan-type sequences. Zbl 1502.11023Bravo, Eric F.; Bravo, Jhon J.; Luca, Florian 1 2022 On the multiplicity in Pillai’s problem with Fibonacci numbers and powers of a fixed prime. Zbl 07644252Batte, Herbert; Ddamulira, Mahadi; Kasozi, Juma; Luca, Florian 1 2022 Fibonacci numbers which are concatenations of two repdigits. Zbl 1472.11067Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon 12 2021 Common values of generalized Fibonacci and Pell sequences. Zbl 1471.11049Bravo, Jhon J.; Herrera, Jose L.; Luca, Florian 6 2021 On a generalization of the Pell sequence. Zbl 1499.11049Bravo, Jhon J.; Herrera, Jose L.; Luca, Florian 6 2021 Binary polynomial power sums vanishing at roots of unity. Zbl 1475.11042Bilu, Yuri; Luca, Florian 4 2021 \(k\)-generalized Fibonacci numbers which are concatenations of two repdigits. Zbl 1515.11013Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon 3 2021 On the nonnegative integer solutions to the equation \(F_n \pm F_m = y^a\). Zbl 1486.11018Kebli, Salima; Kihel, Omar; Larone, Jesse; Luca, Florian 3 2021 On Pillai’s problem with \(X\)-coordinates of Pell equations and powers of 2. II. Zbl 1493.11074Erazo, Harold S.; Gómez, Carlos A.; Luca, Florian 2 2021 On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. Zbl 1481.11020Ddamulira, Mahadi; Luca, Florian 2 2021 On Egyptian fractions of length 3. Zbl 1482.11057Banderier, Cyril; Gómez Ruiz, Carlos Alexis; Luca, Florian; Pappalardi, Francesco; Treviño, Enrique 1 2021 Markov type equations with solutions in Lucas sequences. Zbl 1472.11068Altassan, Alaa; Luca, Florian 1 2021 Pell and Pell-Lucas numbers as sums of two repdigits. Zbl 1452.11020Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain 11 2020 On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers. Zbl 1447.11025Ddamulira, Mahadi; Luca, Florian 10 2020 On certain sums concerning the gcd’s and lcm’s of \(k\) positive integers. Zbl 1452.11007Hilberdink, Titus; Luca, Florian; Tóth, László 6 2020 On \(Y\)-coordinates of Pell equations which are base 2 rep-digits. Zbl 1478.11016Faye-Fall, Bernadette; Luca, Florian 6 2020 On the problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of \(3\). Zbl 1446.11025Ddamulira, Mahadi; Luca, Florian 6 2020 Zeckendorf representations with at most two terms to \(x\)-coordinates of Pell equations. Zbl 1455.11031Gómez, Carlos A.; Luca, Florian 6 2020 On members of Lucas sequences which are products of factorials. Zbl 1478.11018Laishram, Shanta; Luca, Florian; Sias, Mark 5 2020 On \(Y\)-coordinates of Pell equations which are members of a fixed binary recurrence. Zbl 1477.11060Faye, Bernadette; Luca, Florian 5 2020 Products of \(k\)-Fibonacci numbers which are rep-digits. Zbl 1463.11032Alahmadi, Adel; Altassan, Alaa; Luca, Florian; Shoaib, Hatoon 5 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 4 2020 Total multiplicity of the Tribonacci sequence. Zbl 1459.11037Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian 4 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 4 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 Trinomials with given roots. Zbl 1479.11052Bilu, Yuri; Luca, Florian 3 2020 On \(X\)-coordinates of Pell equations which are repdigits. Zbl 1470.11026Gómez, Carlos A.; Luca, Florian; Zottor, Faith Shadow 3 2020 On the zero-multiplicity of the \(k\)-generalized Fibonacci sequence. Zbl 1464.11024García, Jonathan; Gómez, Carlos A.; Luca, Florian 3 2020 Lucas factoriangular numbers. Zbl 1499.11016Kafle, Bir; Luca, Florian; Togbé, Alain 2 2020 The \(x\)-coordinates of Pell equations and sums of two Fibonacci numbers. II. Zbl 1471.11065Ddamulira, Mahadi; Luca, Florian 2 2020 On the equation \(\sum_{j = 1}^k j F_j^p = F_n^q\). Zbl 1471.11043Altassan, Alaa; Luca, Florian 2 2020 On the exponential Diophantine equation \(P_n^x+P_{n+1}^x+\cdots +P_{n+k-1}^x=P_m\). Zbl 1472.11105Luca, Florian; Tchammou, Euloge; Togbé, Alain 2 2020 Linear combinations of prime powers in \(X\)-coordinates of Pell equations. Zbl 1485.11027Erazo, Harold; Gómez, Carlos A.; Luca, Florian 2 2020 On a Diophantine equation involving powers of Fibonacci numbers. Zbl 1478.11017Gueth, Krisztián; Luca, Florian; Szalay, László 2 2020 Ratios of sums of two Fibonacci numbers equal to powers of 2. Zbl 1471.11047Bravo, Jhon J.; Díaz, Maribel; Luca, Florian 1 2020 Elliptic curves over finite fields with Fibonacci numbers of points. Zbl 1456.11116Bilu, Yuri; Gómez, Carlos A.; Gómez, Jhonny C.; 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 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 Powers of two in generalized Lucas sequences. Zbl 1468.11060Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain 1 2020 Perfect squares representing the number of rational points on elliptic curves over finite field extensions. Zbl 1455.11053Chim, Kwok Chi; Luca, Florian 1 2020 Composite positive integers whose sum of prime factors is prime. Zbl 1513.11160Luca, Florian; Moodley, Damon 1 2020 Repdigits as sums of four Pell numbers. Zbl 1455.11019Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain 11 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 9 2019 Lucas numbers as sums of two repdigits. Zbl 1427.11013Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain 8 2019 On Pillai’s problem with the Fibonacci and Pell sequences. Zbl 1440.11018Hernández Hernández, Santos; Luca, Florian; Rivera, Luis Manuel 7 2019 On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041Heim, Bernhard; Luca, Florian; Neuhauser, Markus 7 2019 \(X\)-coordinates of Pell equations which are Lucas numbers. Zbl 1496.11051Kafle, Bir; Luca, Florian; Togbé, Alain 6 2019 Recurrence relations for polynomials obtained by arithmetic functions. Zbl 1435.11055Heim, Bernhard; Luca, Florian; Neuhauser, Markus 6 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 6 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 6 2019 Repdigits as sums of three Lucas numbers. Zbl 1459.11041Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain 5 2019 Primitive root bias for twin primes. Zbl 1450.11001Garcia, Stephan Ramon; Kahoro, Elvis; Luca, Florian 5 2019 On the zero-multiplicity of a fifth-order linear recurrence. Zbl 1450.11009Gómez Ruiz, Carlos Alexis; Luca, Florian 4 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 ternary Egyptian fractions with prime denominator. Zbl 1455.11057Luca, Florian; Pappalardi, Francesco 3 2019 \(x\)-Coordinates of Pell equations which are Tribonacci numbers. II. Zbl 1449.11030Kafle, Bir; Luca, Florian; Togbé, Alain 3 2019 Product of consecutive tribonacci numbers with only one distinct digit. Zbl 1455.11027Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian 2 2019 On the typical size and cancellations among the coefficients of some modular forms. Zbl 1450.11100Luca, Florian; Radziwiłł, Maksym; Shparlinski, Igor E. 2 2019 On the discriminator of Lucas sequences. Zbl 1456.11021Faye, Bernadette; Luca, Florian; Moree, Pieter 2 2019 Diophantine equations with the Ramanujan \(\tau\) function of factorials, Fibonacci numbers, and Catalan numbers. Zbl 1456.11031Luca, Florian; Mabaso, Sibusiso 2 2019 Linear independence of powers of singular moduli of degree three. Zbl 1451.11069Luca, Florian; Riffaut, Antonin 2 2019 Pillai’s problem with the Padovan and Tribonacci sequences. Zbl 1436.11090García Lomelí, Ana Cecilia; Hernández Hernández, Santos; Luca, Florian 1 2019 On the period mod \(m\) of polynomially-recursive sequences: a case study. Zbl 1460.11025Banderier, Cyril; Luca, Florian 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 The zero-multiplicity of Berstel type sequences. Zbl 1463.11036Gómez, Carlos A.; Luca, Florian; Orozco, Jose L. 1 2019 Constrained ternary integers. Zbl 1437.11148Luca, Florian; Moree, Pieter; Osburn, Robert; Eddin, Sumaia Saad; Sedunova, Alisa 1 2019 Algebraic results for the values \(\vartheta_3(m\tau)\) and \(\vartheta_3(n\tau)\) of the Jacobi theta-constant. Zbl 1456.11131Elsner, Carsten; Luca, Florian; Tachiya, Yohei 1 2019 Pell factoriangular numbers. Zbl 1474.11092Luca, Florian; Odjoumani, Japhet; Togbé, Alain 1 2019 On \(X\)-coordinates of Pell equations that are repdigits. Zbl 1459.11082Faye, Bernadette; Luca, Florian 15 2018 On the \(x\)-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027Luca, Florian; Togbé, Alain 14 2018 Every positive integer is a sum of three palindromes. Zbl 1441.11016Cilleruelo, Javier; Luca, Florian; Baxter, Lewis 12 2018 Repdigits as sums of three Pell numbers. Zbl 1413.11008Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain 11 2018 On a problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of 2. Zbl 1437.11051Ddamulira, Mahadi; Gómez, Carlos A.; Luca, Florian 11 2018 On perfect powers that are sums of two Fibonacci numbers. Zbl 1467.11038Luca, Florian; Patel, Vandita 11 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 On Pillai’s problem with Pell numbers and powers of 2. Zbl 1448.11042Ouamar Hernane, Mohand; Luca, Florian; Rihane, Salah; Togbé, Alain 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; Togbé, Alain 7 2018 A Diophantine equation in \(k\)-Fibonacci numbers and repdigits. Zbl 1407.11026Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian 7 2018 On the difference in values of the Euler totient function near prime arguments. Zbl 1455.11127Garcia, Stephan Ramon; Luca, Florian 5 2018 Diophantine triples and \(k\)-generalized Fibonacci sequences. Zbl 1447.11054Fuchs, Clemens; Hutle, Christoph; Luca, Florian; Szalay, László 5 2018 Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms. Zbl 1444.11071Bilu, Yuri F.; Deshouillers, Jean-Marc; Gun, Sanoli; Luca, Florian 4 2018 Markov equation with Fibonacci components. Zbl 1458.11056Luca, Florian; Srinivasan, Anitha 4 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 Arithmetic properties of coefficients of \(L\)-functions of elliptic curves. Zbl 1423.11169Güloğlu, Ahmet M.; Luca, Florian; Yalçiner, Aynur 2 2018 Denominators of Bernoulli polynomials. Zbl 1415.11121Bordellès, Olivier; Luca, Florian; Moree, Pieter; Shparlinski, Igor E. 2 2018 On the error term of a lattice counting problem. Zbl 1380.11085Bordellès, Olivier; Luca, Florian; Shparlinski, Igor E. 2 2018 There are no Diophantine quadruples of Fibonacci numbers. Zbl 1441.11058Fujita, Yasutsugu; Luca, Florian 1 2018 Romanov type problems. Zbl 1451.11106Elsholtz, Christian; Luca, Florian; Planitzer, Stefan 1 2018 A variation on the theme of Nicomachus. Zbl 1410.11079Luca, Florian; Polanco, Geremías; Zudilin, Wadim 1 2018 On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja 17 2017 On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013Bravo, Jhon J.; Luca, Florian; Yazán, Karina 13 2017 \(p\)-adic quotient sets. Zbl 1428.11023Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam 12 2017 On the \(X\)-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain 11 2017 ...and 431 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,125 Authors 255 Luca, Florian 55 Togbé, Alain 51 Shparlinski, Igor E. 33 Gómez, Carlos Alexis 28 Bravo, Jhon Jairo 27 Pollack, Paul 24 Keskin, Refik 24 Sanna, Carlo 23 Hajdu, Lajos 21 Rihane, Salah Eddine 20 Bugeaud, Yann 17 De Koninck, Jean-Marie 17 Szalay, László 16 Marques, Diego 16 Pomerance, Carl Bernard 15 Erduvan, Fatih 14 Ddamulira, Mahadi 14 Ziegler, Volker 13 Chen, Yonggao 13 Dubickas, Artūras 13 Komatsu, Takao 13 Moree, Pieter 13 Stănică, Pantelimon 12 Dujella, Andrej 12 Garaev, Moubariz Z. 12 Heim, Bernhard Ernst 12 Neuhauser, Markus 11 Bennett, Michael A. 11 Rout, Sudhansu Sekhar 11 Şiar, Zafer 11 Siksek, Samir 10 Adamczewski, Boris 10 Bilu, Yuri F. 10 Faye, Bernadette 10 Fuchs, Clemens 10 Pink, István 10 Soydan, Gokhan 9 Cilleruelo, Javier 9 Herrera, José L. 9 Panda, Gopal Krishna 9 Ray, Prasanta Kumar 9 Shallit, Jeffrey Outlaw 9 Shorey, Tarlok Nath 9 Tengely, Szabolcs 9 Ulas, Maciej 8 Adhikari, Sukumar Das 8 Banks, William David 8 Bérczes, Attila 8 Garcia, Stephan Ramon 8 Kátai, Imre 8 Laishram, Shanta 8 Pappalardi, Francesco 8 Sha, Min 8 Thangadurai, Ravindranathan 8 Tijdeman, Robert 7 Alahmadi, Adel N. 7 Bazsó, András 7 Bravo, Eric Fernando 7 Chattopadhyay, Jaitra 7 Kihel, Omar 7 Le, Maohua 7 Trojovský, Pavel 7 Winterhof, Arne 6 Bordellès, Olivier 6 Ford, Kevin B. 6 Gómez, Jhonny Carpediem 6 Grau, José María 6 Hernández Hernández, Santos 6 Irmak, Nurettin 6 Mignotte, Maurice 6 Miska, Piotr 6 Patel, Vandita 6 Rayaguru, Sai Gopal 6 Tóth, László 6 Wu, Jie 6 Zhang, Yong 5 Abu Muriefah, Fadwa S. 5 Broughan, Kevin A. 5 Chakraborty, Kalyan 5 Coons, Michael 5 Heintze, Sebastian 5 Hernane, Mohand-Ouamar 5 Jha, Abhishek Kumar 5 Kafle, Bir 5 Languasco, Alessandro 5 Leonetti, Paolo 5 Meher, Nabin Kumar 5 Mukhopadhyay, Anirban 5 Patel, Bijan Kumar 5 Pongsriiam, Prapanpong 5 Sarkar, Subha 5 Somer, Lawrence E. 5 Stoll, Thomas 5 Tchammou, Euloge B. 5 Zhu, Huilin 4 Adédji, Kouèssi Norbert 4 Adegbindin, Chèfiath Awero 4 Alan, Murat 4 Altassan, Alaa 4 Antony, Deepa ...and 1,025 more Authors all top 5 Cited in 234 Serials 132 Journal of Number Theory 82 International Journal of Number Theory 38 Periodica Mathematica Hungarica 34 Integers 31 Proceedings of the American Mathematical Society 31 The Ramanujan Journal 31 Journal of Integer Sequences 28 Bulletin of the Australian Mathematical Society 27 Mathematics of Computation 27 Monatshefte für Mathematik 25 Journal de Théorie des Nombres de Bordeaux 24 Acta Arithmetica 23 Indagationes Mathematicae. 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Second Series 2 Advances in Applied Mathematics 2 Constructive Approximation ...and 134 more Serials all top 5 Cited in 41 Fields 1,223 Number theory (11-XX) 80 Combinatorics (05-XX) 45 Algebraic geometry (14-XX) 37 Group theory and generalizations (20-XX) 29 Computer science (68-XX) 26 Information and communication theory, circuits (94-XX) 21 Dynamical systems and ergodic theory (37-XX) 16 Field theory and polynomials (12-XX) 12 Special functions (33-XX) 11 Functions of a complex variable (30-XX) 10 Commutative algebra (13-XX) 9 \(K\)-theory (19-XX) 9 Probability theory and stochastic processes (60-XX) 8 Real functions (26-XX) 8 Geometry (51-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Numerical analysis (65-XX) 6 Systems theory; control (93-XX) 5 History and biography (01-XX) 5 Mathematical logic and foundations (03-XX) 5 Difference and functional equations (39-XX) 4 Measure and integration (28-XX) 4 Partial differential equations (35-XX) 4 Sequences, series, summability (40-XX) 4 Approximations and expansions (41-XX) 3 Operator theory (47-XX) 2 General and overarching topics; collections (00-XX) 2 Associative rings and algebras (16-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 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Algebraic topology (55-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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