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## Fuchs, Clemens

Compute Distance To:
 Author ID: fuchs.clemens Published as: Fuchs, Clemens; Fuchs, C. Homepage: http://fuchsc.sbg.ac.at/ External Links: MGP · ORCID · dblp · IdRef · theses.fr
 Documents Indexed: 53 Publications since 2002, including 3 Books
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#### Co-Authors

 6 single-authored 8 Dujella, Andrej 6 Heintze, Sebastian 6 Luca, Florian 6 Tichy, Robert Franz 5 Pethő, Attila 5 Wüstholz, Gisbert 3 Hutle, Christoph 3 Pham, Duc Hiep 3 Szalay, László 3 Ziegler, Volker 2 Karolus, Christina 2 Scremin, Amedeo 2 Shorey, Tarlok Nath 2 Zannier, Umberto M. 1 Bilu, Yuri F. 1 Filipin, Alan 1 Irmak, Nurettin 1 Jadrijević, Borka 1 Jurasić, Ana 1 Kreso, Dijana 1 Mantova, Vincenzo 1 Paulin, Roland 1 Pintér, Ákos 1 Tijdeman, Robert 1 Von Känel, Rafael 1 Walsh, Peter Gareth
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#### Serials

 5 Acta Arithmetica 4 Journal of Number Theory 4 Monatshefte für Mathematik 2 Manuscripta Mathematica 2 Mathematica Slovaca 2 Proceedings of the American Mathematical Society 2 Publicationes Mathematicae 2 Glasnik Matematički. Serija III 2 Indagationes Mathematicae. New Series 1 Bulletin of the Australian Mathematical Society 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Periodica Mathematica Hungarica 1 Rocky Mountain Journal of Mathematics 1 Annales de l’Institut Fourier 1 Archiv der Mathematik 1 Journal of the London Mathematical Society. Second Series 1 Studia Scientiarum Mathematicarum Hungarica 1 Transactions of the American Mathematical Society 1 Journal of the American Mathematical Society 1 Elemente der Mathematik 1 Journal de Théorie des Nombres de Bordeaux 1 Annales Mathématiques Blaise Pascal 1 Journal of the European Mathematical Society (JEMS) 1 The Quarterly Journal of Mathematics 1 Integers 1 Portugaliae Mathematica. Nova Série 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 International Journal of Number Theory 1 Annals of Mathematics Studies 1 Journal of Combinatorics and Number Theory 1 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 1 Research in Number Theory 1 Springer Studium Mathematik – Bachelor
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#### Fields

 52 Number theory (11-XX) 8 Algebraic geometry (14-XX) 6 Field theory and polynomials (12-XX) 3 General and overarching topics; collections (00-XX) 3 Group theory and generalizations (20-XX) 2 Combinatorics (05-XX) 2 Commutative algebra (13-XX) 2 Special functions (33-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Associative rings and algebras (16-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Computer science (68-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

36 Publications have been cited 163 times in 90 Documents Cited by Year
Complete solution of a problem of Diophantus and Euler. Zbl 1166.11309
Dujella, Andrej; Fuchs, Clemens
2005
Effective solution of the $$D(-1)$$-quadruple conjecture. Zbl 1137.11019
Dujella, Andrej; Filipin, Alan; Fuchs, Clemens
2007
Composite rational functions expressible with few terms. Zbl 1244.12001
Fuchs, Clemens; Zannier, Umberto
2012
A polynomial variant of a problem of Diophantus and Euler. Zbl 1074.11019
Dujella, Andrej; Fuchs, Clemens
2003
Perfect powers in linear recurring sequences. Zbl 1052.11022
Fuchs, Clemens; Tichy, Robert F.
2003
Diophantine $$m$$-tuples for linear polynomials. Zbl 1059.11027
Dujella, Andrej; Fuchs, Clemens; Tichy, Robert F.
2002
Polynomial-exponential equations and linear recurrences. Zbl 1056.11019
Fuchs, Clemens
2003
Complete solution of the polynomial version of a problem of Diophantus. Zbl 1047.11024
Dujella, Andrej; Fuchs, Clemens
2004
An upper bound for the G.C.D. of two linear recurring sequences. Zbl 1048.11025
Fuchs, Clemens
2003
On fewnomials, integral points, and a toric version of Bertini’s theorem. Zbl 1439.11091
Fuchs, Clemens; Mantova, Vincenzo; Zannier, Umberto
2018
On the Diophantine equation $$G_n(x)=G_m(P(x))$$: Higher-order recurrences. Zbl 1026.11040
Fuchs, Clemens; Pethő, Attila; Tichy, Robert F.
2003
Substitutions, abstract number systems and the space filling property. Zbl 1194.11023
Fuchs, Clemens; Tijdeman, Robert
2006
Diophantine triples with values in binary recurrences. Zbl 1193.11032
Fuchs, Clemens; Luca, Florian; Szalay, László
2008
Effective bounds for the zeros of linear recurrences in function fields. Zbl 1153.11303
Fuchs, Clemens; Pethő, Attila
2005
On a family of Thue equations over function fields. Zbl 1103.11009
Fuchs, Clemens; Ziegler, Volker
2006
On the Diophantine equation $$G_n(x)=G_m(P(x))$$ for third order linear recurring sequences. Zbl 1114.11030
Fuchs, Clemens
2004
On the Diophantine equation $$G_{n}(x) = G_{m}(P(x))$$. Zbl 1026.11039
Pethő, Attila; Fuchs, Clemens; Tichy, Robert F.
2002
Thomas’s family of Thue equations over functions fields. Zbl 1185.11020
Fuchs, Clemens; Ziegler, Volker
2006
Combinatorial Diophantine equations and a refinement of a theorem on separated variables equations. Zbl 1289.11035
Bilu, Yuri F.; Fuchs, Clemens; Luca, Florian; Pintér, Ákos
2013
Diophantine $$m$$-tuples for linear polynomials. II: Equal degrees. Zbl 1132.11014
Dujella, Andrej; Fuchs, Clemens; Walsh, Gary
2006
Decomposable polynomials in second order linear recurrence sequences. Zbl 1465.11060
Fuchs, Clemens; Karolus, Christina; Kreso, Dijana
2019
On the Diophantine equation $$G_n(x)=G_m(y)$$ with $$Q(x,y)=0$$. Zbl 1215.11031
Fuchs, Clemens; Pethő, Attila; Tichy, Robert F.
2008
On quantitative aspects of the unit sum number problem. Zbl 1250.11090
Fuchs, Clemens; Tichy, Robert; Ziegler, Volker
2009
Composite rational functions having a bounded number of zeros and poles. Zbl 1234.11156
Fuchs, Clemens; Pethő, Attila
2011
An effective Shafarevich theorem for elliptic curves. Zbl 1231.11061
Fuchs, Clemens; von Känel, Rafael; Wüstholz, Gisbert
2011
The $$p$$-adic analytic subgroup theorem revisited. Zbl 1327.11049
Fuchs, C.; Pham, D. H.
2015
Diophantine triples and $$k$$-generalized Fibonacci sequences. Zbl 1447.11054
Fuchs, Clemens; Hutle, Christoph; Luca, Florian; Szalay, László
2018
Only finitely many Tribonacci Diophantine triples exist. Zbl 1440.11042
Fuchs, Clemens; Hutle, Christoph; Irmak, Nurettin; Luca, Florian; Szalay, László
2017
Commutative algebraic groups and $$p$$-adic linear forms. Zbl 1391.11089
Fuchs, Clemens; Pham, Duc Hiep
2015
Polynomial-exponential equations involving several linear recurrences. Zbl 1064.11031
Fuchs, Clemens; Scremin, Amedeo
2004
Polynomial-exponential equations involving multi-recurrences. Zbl 1224.11060
Fuchs, Clemens
2009
On a problem of Diophantus for rationals. Zbl 1293.11052
Dujella, Andrej; Fuchs, Clemens
2012
Diophantine problems with linear recurrences via the subspace theorem. Zbl 1140.11337
Fuchs, Clemens
2005
On a parametric family of Thue inequalities over function fields. Zbl 1139.11017
2007
A polynomial variant of a problem of Diophantus for pure powers. Zbl 1218.11028
Dujella, Andrej; Fuchs, Clemens; Luca, Florian
2008
Divisibility properties of generalized Laguerre polynomials. Zbl 1208.11036
Fuchs, Clemens; Shorey, T. N.
2009
Decomposable polynomials in second order linear recurrence sequences. Zbl 1465.11060
Fuchs, Clemens; Karolus, Christina; Kreso, Dijana
2019
On fewnomials, integral points, and a toric version of Bertini’s theorem. Zbl 1439.11091
Fuchs, Clemens; Mantova, Vincenzo; Zannier, Umberto
2018
Diophantine triples and $$k$$-generalized Fibonacci sequences. Zbl 1447.11054
Fuchs, Clemens; Hutle, Christoph; Luca, Florian; Szalay, László
2018
Only finitely many Tribonacci Diophantine triples exist. Zbl 1440.11042
Fuchs, Clemens; Hutle, Christoph; Irmak, Nurettin; Luca, Florian; Szalay, László
2017
The $$p$$-adic analytic subgroup theorem revisited. Zbl 1327.11049
Fuchs, C.; Pham, D. H.
2015
Commutative algebraic groups and $$p$$-adic linear forms. Zbl 1391.11089
Fuchs, Clemens; Pham, Duc Hiep
2015
Combinatorial Diophantine equations and a refinement of a theorem on separated variables equations. Zbl 1289.11035
Bilu, Yuri F.; Fuchs, Clemens; Luca, Florian; Pintér, Ákos
2013
Composite rational functions expressible with few terms. Zbl 1244.12001
Fuchs, Clemens; Zannier, Umberto
2012
On a problem of Diophantus for rationals. Zbl 1293.11052
Dujella, Andrej; Fuchs, Clemens
2012
Composite rational functions having a bounded number of zeros and poles. Zbl 1234.11156
Fuchs, Clemens; Pethő, Attila
2011
An effective Shafarevich theorem for elliptic curves. Zbl 1231.11061
Fuchs, Clemens; von Känel, Rafael; Wüstholz, Gisbert
2011
On quantitative aspects of the unit sum number problem. Zbl 1250.11090
Fuchs, Clemens; Tichy, Robert; Ziegler, Volker
2009
Polynomial-exponential equations involving multi-recurrences. Zbl 1224.11060
Fuchs, Clemens
2009
Divisibility properties of generalized Laguerre polynomials. Zbl 1208.11036
Fuchs, Clemens; Shorey, T. N.
2009
Diophantine triples with values in binary recurrences. Zbl 1193.11032
Fuchs, Clemens; Luca, Florian; Szalay, László
2008
On the Diophantine equation $$G_n(x)=G_m(y)$$ with $$Q(x,y)=0$$. Zbl 1215.11031
Fuchs, Clemens; Pethő, Attila; Tichy, Robert F.
2008
A polynomial variant of a problem of Diophantus for pure powers. Zbl 1218.11028
Dujella, Andrej; Fuchs, Clemens; Luca, Florian
2008
Effective solution of the $$D(-1)$$-quadruple conjecture. Zbl 1137.11019
Dujella, Andrej; Filipin, Alan; Fuchs, Clemens
2007
On a parametric family of Thue inequalities over function fields. Zbl 1139.11017
2007
Substitutions, abstract number systems and the space filling property. Zbl 1194.11023
Fuchs, Clemens; Tijdeman, Robert
2006
On a family of Thue equations over function fields. Zbl 1103.11009
Fuchs, Clemens; Ziegler, Volker
2006
Thomas’s family of Thue equations over functions fields. Zbl 1185.11020
Fuchs, Clemens; Ziegler, Volker
2006
Diophantine $$m$$-tuples for linear polynomials. II: Equal degrees. Zbl 1132.11014
Dujella, Andrej; Fuchs, Clemens; Walsh, Gary
2006
Complete solution of a problem of Diophantus and Euler. Zbl 1166.11309
Dujella, Andrej; Fuchs, Clemens
2005
Effective bounds for the zeros of linear recurrences in function fields. Zbl 1153.11303
Fuchs, Clemens; Pethő, Attila
2005
Diophantine problems with linear recurrences via the subspace theorem. Zbl 1140.11337
Fuchs, Clemens
2005
Complete solution of the polynomial version of a problem of Diophantus. Zbl 1047.11024
Dujella, Andrej; Fuchs, Clemens
2004
On the Diophantine equation $$G_n(x)=G_m(P(x))$$ for third order linear recurring sequences. Zbl 1114.11030
Fuchs, Clemens
2004
Polynomial-exponential equations involving several linear recurrences. Zbl 1064.11031
Fuchs, Clemens; Scremin, Amedeo
2004
A polynomial variant of a problem of Diophantus and Euler. Zbl 1074.11019
Dujella, Andrej; Fuchs, Clemens
2003
Perfect powers in linear recurring sequences. Zbl 1052.11022
Fuchs, Clemens; Tichy, Robert F.
2003
Polynomial-exponential equations and linear recurrences. Zbl 1056.11019
Fuchs, Clemens
2003
An upper bound for the G.C.D. of two linear recurring sequences. Zbl 1048.11025
Fuchs, Clemens
2003
On the Diophantine equation $$G_n(x)=G_m(P(x))$$: Higher-order recurrences. Zbl 1026.11040
Fuchs, Clemens; Pethő, Attila; Tichy, Robert F.
2003
Diophantine $$m$$-tuples for linear polynomials. Zbl 1059.11027
Dujella, Andrej; Fuchs, Clemens; Tichy, Robert F.
2002
On the Diophantine equation $$G_{n}(x) = G_{m}(P(x))$$. Zbl 1026.11039
Pethő, Attila; Fuchs, Clemens; Tichy, Robert F.
2002
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#### Cited by 90 Authors

 23 Fuchs, Clemens 11 Dujella, Andrej 10 Luca, Florian 6 Ziegler, Volker 5 Heintze, Sebastian 4 Fujita, Yasutsugu Fujita 4 Kreso, Dijana 4 Ostafe, Alina 4 Szalay, László 4 Togbé, Alain 4 Zannier, Umberto M. 3 Filipin, Alan 3 He, Bo 3 Hutle, Christoph 3 Pethő, Attila 3 Sanna, Carlo 3 Tichy, Robert Franz 2 Berthé, Valérie 2 Franušić, Zrinka 2 Frei, Christopher 2 Irmak, Nurettin 2 Jurasić, Ana 2 Karolus, Christina 2 Pham, Duc Hiep 2 Rosema, Sierk W. 2 Shparlinski, Igor E. 2 Soldo, Ivan 2 Thuswaldner, Jörg Maximilian 2 Von Känel, Rafael 2 Walsh, Peter Gareth 2 Young, Marley 1 Adžaga, Nikola 1 Akiyama, Shigeki 1 Alp, Murat 1 Amoroso, Francesco 1 Barat, Guy 1 Bennett, Michael A. 1 Bérczes, Attila 1 Billerey, Nicolas 1 Bilu, Yuri F. 1 Bonciocat, Nicolae Ciprian 1 Borichev, Aleksandr Aleksandrovich 1 Bourdon, Jérémie 1 Bugeaud, Yann 1 Bujačić, Sanda 1 Chen, Evan 1 Chim, Kwok Chi 1 Cipu, Mihai 1 Ddamulira, Mahadi 1 Dogra, Netan 1 Dvornicich, Roberto 1 Elsholtz, Christian 1 Fried, Michael David 1 Gomez-Perez, Domingo 1 Guest, Simon D. 1 Hajdu, Lajos 1 Hu, Zhi 1 Jadrijević, Borka 1 Jolivet, Timo 1 Jukić Bokun, Mirela 1 Kaneko, Hajime 1 Kebli, Salima 1 Kihel, Omar 1 Larone, Jesse 1 Le Fourn, Samuel 1 Levin, Aaron 1 Liardet, Pierre 1 Mantova, Vincenzo 1 Mastrostefano, Daniele 1 Mignotte, Maurice 1 Miyazaki, Takafumi 1 Morris, Joy 1 Paganin, Matteo 1 Park, Jinseo 1 Paulin, Roland 1 Petričević, Vinko 1 Pink, István 1 Praeger, Cheryl Elisabeth 1 Ramasamy, A. M. S. 1 Sadek, Mohammad 1 Scremin, Amedeo 1 Sha, Min 1 Shorey, Tarlok Nath 1 Siegel, Anne 1 Sombra, Martín 1 Spiga, Pablo 1 Tadić, Petra 1 Tijdeman, Robert 1 Zaïmi, Toufik Mostepha 1 Ziegler, Konstantin
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#### Cited in 42 Serials

 10 Journal of Number Theory 7 Monatshefte für Mathematik 5 Periodica Mathematica Hungarica 5 Rocky Mountain Journal of Mathematics 5 International Journal of Number Theory 4 Proceedings of the American Mathematical Society 4 Indagationes Mathematicae. New Series 4 Journal de Théorie des Nombres de Bordeaux 3 Bulletin of the Australian Mathematical Society 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Acta Arithmetica 2 Annales de l’Institut Fourier 2 Manuscripta Mathematica 2 Transactions of the American Mathematical Society 2 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 2 Research in Number Theory 1 Israel Journal of Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematics of Computation 1 Inventiones Mathematicae 1 Journal of Algebra 1 Mathematische Annalen 1 Mathematica Slovaca 1 Michigan Mathematical Journal 1 Tokyo Journal of Mathematics 1 Ergodic Theory and Dynamical Systems 1 Acta Mathematica Hungarica 1 Journal of Symbolic Computation 1 Revista Matemática Iberoamericana 1 Journal of the American Mathematical Society 1 Publicacions Matemàtiques 1 Glasnik Matematički. Serija III 1 Annales Mathématiques Blaise Pascal 1 Kyushu Journal of Mathematics 1 Finite Fields and their Applications 1 The Ramanujan Journal 1 Journal of the Australian Mathematical Society 1 Cryptography and Communications 1 Science China. Mathematics 1 Forum of Mathematics, Sigma 1 Korean Journal of Mathematics 1 Journal of Ramanujan Society of Mathematics and Mathematical Sciences
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#### Cited in 12 Fields

 87 Number theory (11-XX) 10 Field theory and polynomials (12-XX) 8 Algebraic geometry (14-XX) 7 Dynamical systems and ergodic theory (37-XX) 3 Group theory and generalizations (20-XX) 3 Computer science (68-XX) 2 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 Information and communication theory, circuits (94-XX)