Edit Profile (opens in new tab) Mignotte, Maurice Co-Author Distance Author ID: mignotte.maurice Published as: Mignotte, Maurice; Mignotte, M. External Links: MGP Documents Indexed: 218 Publications since 1971, including 6 Books and 1 Additional arXiv Preprint 2 Further Contributions Reviewing Activity: 344 Reviews Co-Authors: 76 Co-Authors with 121 Joint Publications 2,009 Co-Co-Authors all top 5 Co-Authors 98 single-authored 34 Bugeaud, Yann 21 Cipu, Mihai 12 Siksek, Samir 11 Luca, Florian 10 Waldschmidt, Michel 9 Bonciocat, Nicolae Ciprian 7 Tzanakis, Nikos 6 Pethő, Attila 6 Roy, Yves 6 Ştefănescu, Doru 5 Bennett, Michael A. 4 Glesser, Philippe 3 Fujita, Yasutsugu 3 Gramain, Francois 3 Győry, Kálmán 3 Hanrot, Guillaume 3 Laurent, Michel 3 Petković, Miodrag S. 3 Shorey, Tarlok Nath 2 Amoroso, Francesco Antonio 2 Belaga, Edward G. 2 Bilu, Yuri F. 2 Bonciocat, Anca Iuliana 2 Cerlienco, Luigi 2 Diankha, Oumar 2 Diouf, Ismaïla 2 Fall, Oumar 2 Laradji, Abdallah 2 Piras, Francesco 2 Sanghare, Mamadou 2 Voutier, Paul M. 1 Arnon, Dennis S. 1 Avanissian, Vazgain 1 Batra, Prashant 1 Berstel, Jean 1 Bertrand, Daniel 1 Bonciocat, Ciprian Mircea 1 Boulagouaz, M’hammed 1 Buchmann, Johannes A. 1 Cao, Zhenfu 1 Cohen, Henri 1 Collins, George E. 1 Dahmen, Sander R. 1 Davenport, James Harold 1 de Weger, Benjamin M. M. 1 Diakhate, Babacar 1 Diaz, Guy 1 Dujella, Andrej 1 Duquesne, Sylvain 1 Emsalem, Michel 1 Filipin, Alan 1 Huttner, Marc 1 Kientega, Gérard 1 Langevin, Michel 1 Lemmermeyer, Franz 1 Loxton, John H. 1 Moreau, Jean-Charles 1 Nesterenko, Yuriĭ Valentinovich 1 Nicolas, Jean-Louis 1 Nikiema, Salifou 1 Normandin, Frédéric 1 Okazaki, Ryotaro 1 Payafar, M. 1 Philippon, Patrice 1 Pintér, Ákos 1 Reyssat, Eric 1 Roth, Ralf 1 Schnorr, Claus Peter 1 Shparlinski, Igor E. 1 Stoll, Michael 1 Tall, Amadou Makhtar 1 Tengely, Szabolcs 1 Tijdeman, Robert 1 Togbé, Alain 1 Trajković, Miroslav 1 van der Poorten, Alfred J. 1 von zur Gathen, Joachim 1 Winkler, Franz all top 5 Serials 11 Acta Arithmetica 9 Journal of Number Theory 9 Journal of Symbolic Computation 7 Comptes Rendus de l’Académie des Sciences. Série I 5 Publicationes Mathematicae Debrecen 5 Theoretical Computer Science 5 Comptes Rendus Mathématiques de l’Académie des Sciences 4 Mathematics of Computation 4 Glasgow Mathematical Journal 4 Journal für die Reine und Angewandte Mathematik 4 SIGSAM Bulletin 4 L’Enseignement Mathématique. 2e Série 4 Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. Nouvelle Série 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Compositio Mathematica 3 Elemente der Mathematik 3 Applicable Algebra in Engineering, Communication and Computing 3 International Journal of Number Theory 3 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 2 Gazette des Mathématiciens 2 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 2 Publicacions Matemàtiques 2 Rendiconti del Seminario della Facoltà di Scienze dell’ Università di Cagliari 2 Experimental Mathematics 2 Journal de Théorie des Nombres de Bordeaux 2 Bulletin de la Société Mathématique de France. Supplément. Mémoires 2 Science China. Mathematics 2 Africa Mathematics Annals (AFMA) 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 American Mathematical Monthly 1 Communications in Algebra 1 Mathematical Notes 1 Mathematische Semesterberichte 1 Rocky Mountain Journal of Mathematics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Arkiv för Matematik 1 Annales de l’Institut Fourier 1 Annales des Sciences Mathématiques du Québec 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Bulletin des Sciences Mathématiques. Deuxième Série 1 Bulletin de la Société Mathématique de France 1 Canadian Journal of Mathematics 1 Colloquium Mathematicum 1 The Fibonacci Quarterly 1 Journal of Algebra 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Annalen 1 Mathematica Scandinavica 1 Mathematika 1 Monatshefte für Mathematik 1 Numerische Mathematik 1 Pacific Journal of Mathematics 1 Portugaliae Mathematica 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the Japan Academy. Series A 1 Proceedings of the London Mathematical Society. Third Series 1 RAIRO. Analyse Numérique 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Bulletin of the Greek Mathematical Society 1 Journal of Algorithms 1 European Journal of Combinatorics 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Facta Universitatis. Series Mathematics and Informatics 1 Mathematica Pannonica 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 1 Glasnik Matematički. Serija III 1 Journal of the Australian Mathematical Society. Series A 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Indagationes Mathematicae. New Series 1 Divulgaciones Matemáticas 1 Revue d’Histoire des Mathématiques 1 The Ramanujan Journal 1 Acta Academiae Paedagogicae Agriensis. Nova Series. Sectio Matematicae 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Mathematical Inequalities & Applications 1 Annals of Mathematics. Second Series 1 The Quarterly Journal of Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 JP Journal of Algebra, Number Theory and Applications 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Bulletin de la Société Mathématique de Belgique 1 Graduate Texts in Mathematics 1 International Mathematical Forum 1 International Journal of Algebra 1 Algebra & Number Theory 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae 1 Annales Mathématiques du Québec 1 Mathematica 1 Research in Number Theory all top 5 Fields 195 Number theory (11-XX) 37 Field theory and polynomials (12-XX) 17 Functions of a complex variable (30-XX) 16 Computer science (68-XX) 11 Numerical analysis (65-XX) 6 Real functions (26-XX) 5 Commutative algebra (13-XX) 3 Mathematical logic and foundations (03-XX) 3 Information and communication theory, circuits (94-XX) 2 Potential theory (31-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 154 Publications have been cited 1,736 times in 1,222 Documents Cited by ▼ Year ▼ Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers. Zbl 1113.11021 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir 231 2006 Number theory. Volume II: Analytic and modern tools. Zbl 1119.11002 Cohen, Henri 216 2007 Existence of primitive divisors of Lucas and Lehmer numbers (with an appendix by M. Mignotte). Zbl 0995.11010 Bilu, Yu.; Hanrot, G.; Voutier, P. M. 209 2001 Linear forms in two logarithms and interpolation determinants. (Formes linéaires en deux logarithmes et déterminants d’interpolation.) Zbl 0843.11036 Laurent, Michel; Mignotte, Maurice; Nesterenko, Yuri 112 1995 Mathematics for computer algebra. Transl. from the French by Catherine Mignotte. Zbl 0741.11002 Mignotte, Maurice 71 1992 Classical and modular approaches to exponential Diophantine equations. II: The Lebesgue-Nagell equation. Zbl 1128.11013 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir 52 2006 An inequality about factors of polynomials. Zbl 0299.12101 Mignotte, M. 48 1974 Polynomials: an algorithmic approach. Zbl 0927.12004 Mignotte, Maurice; Ştefănescu, Doru 46 1999 Deux propriétés décidables des suites récurrentes linéaires. Zbl 0329.10009 Berstel, Jean; Mignotte, Maurice 44 1976 Some useful bounds. Zbl 0498.12019 Mignotte, M. 36 1982 The distance between terms of an algebraic recurrence sequence. Zbl 0521.10011 Mignotte, M.; Shorey, T. N.; Tijdeman, R. 35 1984 How to share a secret. Zbl 1447.94064 Mignotte, Maurice 33 1983 Fibonacci numbers at most one away from a perfect power. Zbl 1156.11008 Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 32 2008 On simple \(K_4\)-groups. Zbl 0989.20017 Bugeaud, Yann; Cao, Zhenfu; Mignotte, Maurice 31 2001 Verification of a conjecture of E. Thomas. Zbl 0780.11013 Mignotte, Maurice 30 1993 Linear forms in two logarithms and Schneider’s method. Zbl 0349.10029 Mignotte, Maurice; Waldschmidt, Michel 25 1978 Integral points on hyperelliptic curves. Zbl 1168.11026 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir; Stoll, Michael; Tengely, Szabolcs 24 2008 On the family of Diophantine triples \(\{k-1, k+1, 16k^3 - 4k\}\). Zbl 1168.11007 Bugeaud, Yann; Dujella, Andrej; Mignotte, Maurice 22 2007 Suites récurrentes linéaires. Propriétés algébriques et arithmétiques. (Linear recurrent sequences. Algebraic and arithmetic properties). Zbl 0626.10008 Cerlienco, L.; Mignotte, M.; Piras, F. 21 1987 Polynomial root separation. Zbl 1205.11032 Bugeaud, Yann; Mignotte, Maurice 21 2010 On the distance between roots of integer polynomials. Zbl 1071.11016 Bugeaud, Yann; Mignotte, Maurice 20 2004 On the distance between the roots of a polynomial. Zbl 0835.12002 Mignotte, Maurice 19 1995 On the number of solutions to systems of Pell equations. Zbl 1137.11018 Cipu, Mihai; Mignotte, Maurice 18 2007 Complete solutions of a family of quartic Thue and index form equations. Zbl 0853.11022 Mignotte, Maurice; Pethö, Attila; Roth, Ralf 17 1996 Linear forms in two logarithms and Schneider’s method. III. Zbl 0702.11044 Mignotte, Maurice; Waldschmidt, Michel 17 1989 Intersection des images de certaines suites recurrentes linéaires. Zbl 0393.10009 Mignotte, M. 16 1978 A corollary to a theorem of Laurent-Mignotte-Nesterenko. Zbl 0919.11051 Mignotte, M. 16 1998 On the diophantine equations \(x^ 2+ 74= y^ 5\) and \(x^ 2+ 86= y^ 5\). Zbl 0847.11011 Mignotte, Maurice; de Weger, Benjamin M. M. 16 1996 A multi-Frey approach to some multi-parameter families of Diophantine equations. Zbl 1156.11014 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir 16 2008 Linear forms in two and three logarithms and interpolation determinants. Zbl 1198.11071 Mignotte, M. 16 2008 On integers with identical digits. Zbl 1033.11012 Bugeaud, Yann; Mignotte, Maurice 16 1999 On the number of solutions of simultaneous Pell equations. II. Zbl 1165.11034 Bennett, Michael A.; Cipu, Mihai; Mignotte, Maurice; Okazaki, Ryotaro 16 2006 On the family of Thue equations \(x^ 3 - (n-1)x^ 2y - (n+2)xy^ 2 - y^ 3 = k\). Zbl 0862.11028 Mignotte, M.; Pethö, A.; Lemmermeyer, F. 15 1996 Sur les conjugués des nombres de Pisot. Zbl 0562.12001 Mignotte, Maurice 15 1984 Mathématiques pour le calcul formel. (Mathematics for computer algebra). Zbl 0679.12001 Mignotte, Maurice 14 1989 On a family of cubics. Zbl 0734.11025 Mignotte, M.; Tzanakis, N. 14 1991 Perfect powers with few binary digits and related Diophantine problems. II. Zbl 1291.11016 Bennett, Michael A.; Bugeaud, Yann; Mignotte, Maurice 14 2012 A note on the equation \(ax^ n-by^ n=c\). Zbl 0861.11025 Mignotte, Maurice 13 1996 Binomial Thue equations and polynomial powers. Zbl 1126.11018 Bennett, M. A.; Győry, K.; Mignotte, M.; Pintér, Á. 13 2006 On mechanical quantifier elimination for elementary algebra and geometry. Zbl 0644.68051 Arnon, Dennis S.; Mignotte, Maurice 13 1988 An inequality about irreducible factors of integer polynomials. Zbl 0648.12002 Mignotte, Maurice 13 1988 Almost powers in the Lucas sequence. Zbl 1204.11030 Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 13 2008 On algebraic numbers of small height: Linear forms in one logarithm. Zbl 0801.11033 Mignotte, Maurice; Waldschmidt, Michel 11 1994 Approximations rationnelles de \(\pi\) et quelques autres nombres. Zbl 0286.10017 Mignotte, Maurice 11 1974 The Nagell-Ljunggren equation \(\frac{x^n-1}{x-1}=y^q\). (L’équation de Nagell-Ljunggren \(\frac{x^n-1}{x-1}=y^q\).) Zbl 1040.11015 Bugeaud, Yann; Mignotte, Maurice 11 2002 Two-parameter families of uniquely extendable Diophantine triples. Zbl 1419.11054 Cipu, Mihai; Fujita, Yasutsugu; Mignotte, Maurice 11 2018 There is no Diophantine \(D(-1)\)-quadruple. Zbl 1531.11032 Bonciocat, Nicolae Ciprian; Cipu, Mihai; Mignotte, Maurice 11 2022 Approximation des nombres algébriques par des nombres algébriques de grand degré. Zbl 0421.10022 Mignotte, Maurice 10 1979 On Fibonacci numbers of the form \(q^ky^k\). (Sur les nombres de Fibonacci de la forme \(q^ky^p\).) Zbl 1113.11010 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir 10 2004 On \(D(-1)\)-quadruples. Zbl 1354.11024 Bonciocat, Nicolae Ciprian; Cipu, Mihai; Mignotte, Maurice 10 2012 Identification of algebraic numbers. Zbl 0498.12004 Mignotte, Maurice 10 1982 On the Diophantine equation \({x^ n-1\over x-1}=y^ q\). Zbl 1064.11030 Bugeaud, Yann; Mignotte, Maurice; Roy, Yves 10 2000 Remarque sur une question relative à des fonctions conjuguées. (Remark on a question on conjugate functions). Zbl 0773.31002 Mignotte, Maurice 9 1992 On squares in certain Lucas sequences. (Sur les carrés dans certaines suites de Lucas.) Zbl 0795.11007 Mignotte, Maurice; Pethö, Attila 9 1993 Perfect powers from products of terms in Lucas sequences. Zbl 1137.11011 Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 9 2007 Perfect powers with few binary digits and related Diophantine problems. Zbl 1303.11084 Bennett, Michael A.; Bugeaud, Yann; Mignotte, Maurice 9 2013 Computing the measure of a polynomial. Zbl 0629.12002 Cerlienco, L.; Mignotte, M.; Piras, F. 9 1987 Sur un théorème de M. Langevin. (On a theorem of M. Langevin). Zbl 0641.12003 Mignotte, Maurice 9 1989 Some inequalities about univariate polynomials. Zbl 0477.68040 Mignotte, Maurice 9 1981 On the Diophantine equation \((x^ n-1)/(x-1)=y^ q\). III. (Sur l’équation diophantienne \((x^ n-1)/(x-1)=y^ q\). III.) Zbl 1102.11305 Bugeaud, Yann; Hanrot, Guillaume; Mignotte, Maurice 8 2002 Shifted powers in binary recurrence sequences. Zbl 1371.11081 Bennett, Michael A.; Dahmen, Sander R.; Mignotte, Maurice; Siksek, Samir 8 2015 A note on linear recursive sequences. Zbl 0305.10009 Mignotte, M. 8 1975 On a conjecture on exponential Diophantine equations. Zbl 1235.11031 Cipu, Mihai; Mignotte, Maurice 8 2009 On the distribution of the roots of polynomials. Zbl 0867.26009 Amoroso, Francesco; Mignotte, Maurice 7 1996 Calcul déterministe des racines d’un polynôme dans un corps fini. (Deterministic computation of the roots of a polynomial over a finite field). Zbl 0653.12011 Mignotte, Maurice; Schnorr, Claus 7 1988 Arithmetical study of recurrence sequences. Zbl 0683.10010 Mignotte, M.; Tzanakis, N. 7 1991 Catalan’s equation just before 2000. Zbl 1065.11019 Mignotte, Maurice 7 2001 Valeurs algébriques de fonctions analytiques. (Algebraic values of analytic functions). Zbl 0553.10026 Gramain, François; Mignotte, Maurice; Waldschmidt, Michel 7 1986 Catalan’s equation has no new solution with either exponent less than 10651. Zbl 0857.11012 Mignotte, Maurice; Roy, Yves 6 1995 An application of W. Schmidt’s theorem. Transcendental numbers and golden number. Zbl 0353.10025 Mignotte, Maurice 6 1977 On Fibonacci numbers with few prime divisors. Zbl 1087.11009 Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 6 2005 The non-extendibility of some parametric families of \(D(-1)\)-triples. Zbl 1255.11015 Filipin, Alan; Fujita, Yasutsugu; Mignotte, Maurice 6 2012 On finding the largest root of a polynomial. Zbl 0715.65033 Davenport, J. H.; Mignotte, M. 6 1990 Improvements of Lagrange’s bound for polynomial roots. Zbl 1358.65028 Batra, Prashant; Mignotte, Maurice; Ştefănescu, Doru 6 2017 Linear forms in two logarithms and Schneider’s method. II. Zbl 0642.10034 Mignotte, Maurice; Waldschmidt, Michel 6 1989 Approximate polynomial GCD: small degree and small height perturbations. Zbl 1248.11106 von zur Gathen, Joachim; Mignotte, Maurice; Shparlinski, Igor E. 6 2010 Irreducibility criteria for sums of two relatively prime polynomials. Zbl 1303.11119 Bonciocat, Nicolae Ciprian; Bugeaud, Yann; Cipu, Mihai; Mignotte, Maurice 6 2013 Entiers algébriques dont les conjugues sont proches du cercle unite. Zbl 0424.12002 Mignotte, Maurice 5 1978 A criterion on Catalan’s equation. Zbl 0829.11016 Mignotte, Maurice 5 1995 On the Diophantine equation \(D_1x^2+D_2^m=4y^n\). Zbl 1028.11019 Mignotte, M. 5 1997 On the diophantine equation \(x^p-x=y^q-y\). Zbl 0949.11022 Mignotte, M.; Pethő, A. 5 1999 Distance entre les racines d’un polynôme. Zbl 0409.65025 Mignotte, M.; Payafar, M. 5 1979 Pethő’s cubics. Zbl 0960.11020 Mignotte, Maurice 5 2000 Quelques remarques sur l’approximation rationnelle des nombres algébriques. Zbl 0284.10011 Mignotte, Maurice 5 1974 An inequality on the greatest roots of a polynomial. Zbl 0745.12001 Mignotte, M. 5 1991 Suites récurrentes linéaires. Zbl 0318.10005 Mignotte, Maurice 5 1975 The problem of Catalan. Zbl 1315.11003 Bilu, Yuri F.; Bugeaud, Yann; Mignotte, Maurice 5 2014 Statistiques sur \(\mathbb F_ q[X]\). Zbl 0519.60006 Mignotte, M.; Nicolas, J. L. 5 1983 On the equation \(y^x\pm x^y=z^2\). Zbl 1014.11024 Luca, Florian; Mignotte, Maurice 5 2000 The equation \(\frac{x^n-1}{x-1}=y^q\) has no solution with \(x\) square. Zbl 0940.11020 Bugeaud, Y.; Mignotte, M.; Roy, Y. 5 1999 Approximation des valeurs de fonctions transcendantes. Zbl 0305.10027 Mignotte, Maurice; Waldschmidt, Michel 5 1975 Lower bounds for Catalan’s equation. (Minorations pour l’équation de Catalan.) Zbl 0887.11018 Mignotte, Maurice; Roy, Yves 4 1997 Détermination des répetitions d’une certaine suite récurrente linéaire. (Determination of repetitions of a certain linear recurrence sequence). Zbl 0626.10009 Mignotte, Maurice 4 1986 Sur les multiples des polynômes irréductibles. Zbl 0405.12021 Mignotte, Maurice 4 1975 Passage d’une mesure d’approximation à une mesure de transcendance. (Passage from an approximation measure to a transcendence measure). Zbl 0763.11032 Diaz, Guy; Mignotte, Maurice 4 1991 Estimates for polynomial roots. Zbl 0996.12001 Mignotte, Maurice; Ştefănescu, Doru 4 2001 A note on addition chains. Zbl 1231.11143 Mignotte, Maurice; Tall, Amadou 4 2011 On the representation of Fibonacci and Lucas numbers in an integer base. Zbl 1367.11064 Bugeaud, Yann; Cipu, Mihai; Mignotte, Maurice 4 2013 A variant of an inequality of Gel’fond and Mahler. Zbl 0790.31005 Avanissian, V.; Mignotte, M. 3 1994 On the smallest divisor of a polynomial. Zbl 0804.12001 Mignotte, Maurice; Glesser, Philippe 3 1994 A kit for linear forms in three logarithms. With an appendix by Michel Laurent. Zbl 07833098 Mignotte, Maurice; Voutier, Paul 1 2024 There is no Diophantine \(D(-1)\)-quadruple. Zbl 1531.11032 Bonciocat, Nicolae Ciprian; Cipu, Mihai; Mignotte, Maurice 11 2022 Two-parameter families of uniquely extendable Diophantine triples. Zbl 1419.11054 Cipu, Mihai; Fujita, Yasutsugu; Mignotte, Maurice 11 2018 Improvements of Lagrange’s bound for polynomial roots. Zbl 1358.65028 Batra, Prashant; Mignotte, Maurice; Ştefănescu, Doru 6 2017 Irreducibility criteria for compositions of polynomials with integer coefficients. Zbl 1360.11109 Bonciocat, Nicolae Ciprian; Bugeaud, Yann; Cipu, Mihai; Mignotte, Maurice 1 2017 Shifted powers in binary recurrence sequences. Zbl 1371.11081 Bennett, Michael A.; Dahmen, Sander R.; Mignotte, Maurice; Siksek, Samir 8 2015 Irreducibility criteria for sums of two relatively prime multivariate polynomials. Zbl 1363.11095 Bonciocat, Nicolae Ciprian; Bugeaud, Yann; Cipu, Mihai; Mignotte, Maurice 2 2015 The problem of Catalan. Zbl 1315.11003 Bilu, Yuri F.; Bugeaud, Yann; Mignotte, Maurice 5 2014 Perfect powers with few binary digits and related Diophantine problems. Zbl 1303.11084 Bennett, Michael A.; Bugeaud, Yann; Mignotte, Maurice 9 2013 Irreducibility criteria for sums of two relatively prime polynomials. Zbl 1303.11119 Bonciocat, Nicolae Ciprian; Bugeaud, Yann; Cipu, Mihai; Mignotte, Maurice 6 2013 On the representation of Fibonacci and Lucas numbers in an integer base. Zbl 1367.11064 Bugeaud, Yann; Cipu, Mihai; Mignotte, Maurice 4 2013 Perfect powers with few binary digits and related Diophantine problems. II. Zbl 1291.11016 Bennett, Michael A.; Bugeaud, Yann; Mignotte, Maurice 14 2012 On \(D(-1)\)-quadruples. Zbl 1354.11024 Bonciocat, Nicolae Ciprian; Cipu, Mihai; Mignotte, Maurice 10 2012 The non-extendibility of some parametric families of \(D(-1)\)-triples. Zbl 1255.11015 Filipin, Alan; Fujita, Yasutsugu; Mignotte, Maurice 6 2012 Some Pólya-type irreducibility criteria for multivariate polynomials. Zbl 1318.11136 Bonciocat, Nicolae Ciprian; Bugeaud, Yann; Cipu, Mihai; Mignotte, Maurice 2 2012 Elementary trigonometric sums related to quadratic residues. Zbl 1252.11058 Laradji, Abdallah; Mignotte, Maurice; Tzanakis, Nikos 1 2012 An arithmetical property of third-order linear recurrent sequences. (Une propriété arithmétique des suites récurrentes linéaires d’ordre trois.) Zbl 1257.11014 Fall, Oumar; Diankha, Oumar; Mignotte, Maurice; Sanghare, Mamadou 1 2012 A note on addition chains. Zbl 1231.11143 Mignotte, Maurice; Tall, Amadou 4 2011 On \(px^{2}+q^{2n}=y^{p}\) and related Diophantine equations. Zbl 1229.11055 Laradji, A.; Mignotte, M.; Tzanakis, N. 2 2011 Testing degenerate polynomials. Zbl 1281.12003 Cipu, Mihai; Diouf, Ismaïla; Mignotte, Maurice 1 2011 Polynomial root separation. Zbl 1205.11032 Bugeaud, Yann; Mignotte, Maurice 21 2010 Approximate polynomial GCD: small degree and small height perturbations. Zbl 1248.11106 von zur Gathen, Joachim; Mignotte, Maurice; Shparlinski, Igor E. 6 2010 On a conjecture on exponential Diophantine equations. Zbl 1235.11031 Cipu, Mihai; Mignotte, Maurice 8 2009 Arithmetic properties of the integer part of the powers of an algebraic number. Zbl 1234.11098 Luca, Florian; Mignotte, Maurice 2 2009 Fibonacci numbers at most one away from a perfect power. Zbl 1156.11008 Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 32 2008 Integral points on hyperelliptic curves. Zbl 1168.11026 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir; Stoll, Michael; Tengely, Szabolcs 24 2008 A multi-Frey approach to some multi-parameter families of Diophantine equations. Zbl 1156.11014 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir 16 2008 Linear forms in two and three logarithms and interpolation determinants. Zbl 1198.11071 Mignotte, M. 16 2008 Almost powers in the Lucas sequence. Zbl 1204.11030 Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 13 2008 Number theory. Volume II: Analytic and modern tools. Zbl 1119.11002 Cohen, Henri 216 2007 On the family of Diophantine triples \(\{k-1, k+1, 16k^3 - 4k\}\). Zbl 1168.11007 Bugeaud, Yann; Dujella, Andrej; Mignotte, Maurice 22 2007 On the number of solutions to systems of Pell equations. Zbl 1137.11018 Cipu, Mihai; Mignotte, Maurice 18 2007 Perfect powers from products of terms in Lucas sequences. Zbl 1137.11011 Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 9 2007 Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers. Zbl 1113.11021 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir 231 2006 Classical and modular approaches to exponential Diophantine equations. II: The Lebesgue-Nagell equation. Zbl 1128.11013 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir 52 2006 On the number of solutions of simultaneous Pell equations. II. Zbl 1165.11034 Bennett, Michael A.; Cipu, Mihai; Mignotte, Maurice; Okazaki, Ryotaro 16 2006 Binomial Thue equations and polynomial powers. Zbl 1126.11018 Bennett, M. A.; Győry, K.; Mignotte, M.; Pintér, Á. 13 2006 \(\varphi(F_{11})=88\). Zbl 1132.11003 Luca, Florian; Mignotte, Maurice 3 2006 On Fibonacci numbers with few prime divisors. Zbl 1087.11009 Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 6 2005 On perfect powers in Lucas sequences. Zbl 1114.11014 Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir 2 2005 On the distance between roots of integer polynomials. Zbl 1071.11016 Bugeaud, Yann; Mignotte, Maurice 20 2004 On Fibonacci numbers of the form \(q^ky^k\). (Sur les nombres de Fibonacci de la forme \(q^ky^p\).) Zbl 1113.11010 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir 10 2004 Linear recurrent sequences and polynomial roots. Zbl 1028.12002 Mignotte, Maurice; Ştefănescu, Doru 1 2003 The Nagell-Ljunggren equation \(\frac{x^n-1}{x-1}=y^q\). (L’équation de Nagell-Ljunggren \(\frac{x^n-1}{x-1}=y^q\).) Zbl 1040.11015 Bugeaud, Yann; Mignotte, Maurice 11 2002 On the Diophantine equation \((x^ n-1)/(x-1)=y^ q\). III. (Sur l’équation diophantienne \((x^ n-1)/(x-1)=y^ q\). III.) Zbl 1102.11305 Bugeaud, Yann; Hanrot, Guillaume; Mignotte, Maurice 8 2002 On the Diophantine equation \((x^n -1)/(x-1)=y^q\) with negative \(x\). Zbl 1031.11019 Bugeaud, Yann; Mignotte, Maurice 1 2002 Existence of primitive divisors of Lucas and Lehmer numbers (with an appendix by M. Mignotte). Zbl 0995.11010 Bilu, Yu.; Hanrot, G.; Voutier, P. M. 209 2001 On simple \(K_4\)-groups. Zbl 0989.20017 Bugeaud, Yann; Cao, Zhenfu; Mignotte, Maurice 31 2001 Catalan’s equation just before 2000. Zbl 1065.11019 Mignotte, Maurice 7 2001 Estimates for polynomial roots. Zbl 0996.12001 Mignotte, Maurice; Ştefănescu, Doru 4 2001 Upper bounds for the coefficients of irreducible integer polynomials in several variables. Zbl 0978.11007 Amoroso, Francesco; Mignotte, Maurice 2 2001 On the Diophantine equation \({x^ n-1\over x-1}=y^ q\). Zbl 1064.11030 Bugeaud, Yann; Mignotte, Maurice; Roy, Yves 10 2000 Pethő’s cubics. Zbl 0960.11020 Mignotte, Maurice 5 2000 On the equation \(y^x\pm x^y=z^2\). Zbl 1014.11024 Luca, Florian; Mignotte, Maurice 5 2000 Bounds for the roots of lacunary polynomials. Zbl 0965.12001 Mignotte, Maurice 1 2000 Polynomials: an algorithmic approach. Zbl 0927.12004 Mignotte, Maurice; Ştefănescu, Doru 46 1999 On integers with identical digits. Zbl 1033.11012 Bugeaud, Yann; Mignotte, Maurice 16 1999 On the diophantine equation \(x^p-x=y^q-y\). Zbl 0949.11022 Mignotte, M.; Pethő, A. 5 1999 The equation \(\frac{x^n-1}{x-1}=y^q\) has no solution with \(x\) square. Zbl 0940.11020 Bugeaud, Y.; Mignotte, M.; Roy, Y. 5 1999 On the diophantine equation \(\frac{x^n-1}{x-1}= y^q\). II. (Sur l’équation diophantienne \(\frac{x^n-1}{x-1}= y^q\). II.) Zbl 0946.11008 Bugeaud, Yann; Mignotte, Maurice 3 1999 On the roots of lacunary polynomials. Zbl 0924.26009 Mignotte, Maurice; Ştefănescu, Doru 1 1999 A remark on Catalan’s equation. (Une remarque sur l’équation de Catalan.) Zbl 0933.11012 Mignotte, Maurice 1 1999 A corollary to a theorem of Laurent-Mignotte-Nesterenko. Zbl 0919.11051 Mignotte, M. 16 1998 Complete resolution of some families of diophantine equations. Zbl 0916.11016 Mignotte, Maurice 2 1998 Embedding the \(3x+1\) conjecture in a \(3x+d\) context. Zbl 0918.11008 Belaga, Edward G.; Mignotte, Maurice 1 1998 On the Diophantine equation \(D_1x^2+D_2^m=4y^n\). Zbl 1028.11019 Mignotte, M. 5 1997 Lower bounds for Catalan’s equation. (Minorations pour l’équation de Catalan.) Zbl 0887.11018 Mignotte, Maurice; Roy, Yves 4 1997 Lower bounds for Catalan’s equation. Zbl 0905.11019 Mignotte, Maurice; Roy, Yves 1 1997 Complete solutions of a family of quartic Thue and index form equations. Zbl 0853.11022 Mignotte, Maurice; Pethö, Attila; Roth, Ralf 17 1996 On the diophantine equations \(x^ 2+ 74= y^ 5\) and \(x^ 2+ 86= y^ 5\). Zbl 0847.11011 Mignotte, Maurice; de Weger, Benjamin M. M. 16 1996 On the family of Thue equations \(x^ 3 - (n-1)x^ 2y - (n+2)xy^ 2 - y^ 3 = k\). Zbl 0862.11028 Mignotte, M.; Pethö, A.; Lemmermeyer, F. 15 1996 A note on the equation \(ax^ n-by^ n=c\). Zbl 0861.11025 Mignotte, Maurice 13 1996 On the distribution of the roots of polynomials. Zbl 0867.26009 Amoroso, Francesco; Mignotte, Maurice 7 1996 The equations \((x+1) \cdots (x+k) = (y+1) \cdots (y+m),\quad m=5,6\). Zbl 0867.11019 Mignotte, M.; Shorey, T. N. 1 1996 Linear forms in two logarithms and interpolation determinants. (Formes linéaires en deux logarithmes et déterminants d’interpolation.) Zbl 0843.11036 Laurent, Michel; Mignotte, Maurice; Nesterenko, Yuri 112 1995 On the distance between the roots of a polynomial. Zbl 0835.12002 Mignotte, Maurice 19 1995 Catalan’s equation has no new solution with either exponent less than 10651. Zbl 0857.11012 Mignotte, Maurice; Roy, Yves 6 1995 A criterion on Catalan’s equation. Zbl 0829.11016 Mignotte, Maurice 5 1995 On the system of diophantine equations \(x^ 2 - 6y^ 2 = -5\) and \(x = 2z^ 2 -1\). Zbl 0849.11031 Mignotte, Maurice; Pethö, Attila 2 1995 On algebraic numbers of small measure: linear forms in one logarithm. (Nombres algébriques de petite mesure et formes linéaires en un logarithme.) Zbl 0848.11047 Bugeaud, Yann; Mignotte, Maurice; Normandin, Frédéric 2 1995 The root separation of polynomials and some applications. Zbl 0833.65044 Petković, M.; Mignotte, M.; Trajković, M. 1 1995 On algebraic numbers of small height: Linear forms in one logarithm. Zbl 0801.11033 Mignotte, Maurice; Waldschmidt, Michel 11 1994 A variant of an inequality of Gel’fond and Mahler. Zbl 0790.31005 Avanissian, V.; Mignotte, M. 3 1994 On the smallest divisor of a polynomial. Zbl 0804.12001 Mignotte, Maurice; Glesser, Philippe 3 1994 On the Catalan equation. II. (Sur l’équation de Catalan. II.) Zbl 0797.11036 Mignotte, M. 2 1994 Landau’s inequality via Hadamard’s. Zbl 0827.30004 Mignotte, Maurice; Glesser, Philippe 2 1994 Verification of a conjecture of E. Thomas. Zbl 0780.11013 Mignotte, Maurice 30 1993 On squares in certain Lucas sequences. (Sur les carrés dans certaines suites de Lucas.) Zbl 0795.11007 Mignotte, Maurice; Pethö, Attila 9 1993 Mathematics for computer algebra. Transl. from the French by Catherine Mignotte. Zbl 0741.11002 Mignotte, Maurice 71 1992 Remarque sur une question relative à des fonctions conjuguées. (Remark on a question on conjugate functions). Zbl 0773.31002 Mignotte, Maurice 9 1992 On the product of the largest roots of a polynomial. Zbl 0756.65074 Mignotte, Maurice 3 1992 Sur l’équation de Catalan. (On Catalan’s equation). Zbl 0749.11025 Mignotte, Maurice 2 1992 Corrigendum and addendum: On a family of cubics. Zbl 0763.11011 Mignotte, M.; Tzanakis, N. 1 1992 On a family of cubics. Zbl 0734.11025 Mignotte, M.; Tzanakis, N. 14 1991 Arithmetical study of recurrence sequences. Zbl 0683.10010 Mignotte, M.; Tzanakis, N. 7 1991 An inequality on the greatest roots of a polynomial. Zbl 0745.12001 Mignotte, M. 5 1991 Passage d’une mesure d’approximation à une mesure de transcendance. (Passage from an approximation measure to a transcendence measure). Zbl 0763.11032 Diaz, Guy; Mignotte, Maurice 4 1991 An inequality about irreducible factors of integer polynomials. II. Zbl 0739.11010 Glesser, Philippe; Mignotte, Maurice 1 1991 On finding the largest root of a polynomial. Zbl 0715.65033 Davenport, J. H.; Mignotte, M. 6 1990 On some arithmetical properties of weighted sums of S-units. Zbl 0738.11034 Györy, K.; Mignotte, M.; Shorey, T. N. 3 1990 ...and 54 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,155 Authors 105 Luca, Florian 71 Togbé, Alain 48 Mignotte, Maurice 30 Dubickas, Artūras 28 Bugeaud, Yann 28 Keskin, Refik 22 Bennett, Michael A. 22 Gómez, Carlos Alexis 21 Le, Maohua 20 Bravo, Jhon Jairo 20 Fujita, Yasutsugu 20 Pethő, Attila 20 Rihane, Salah Eddine 19 Cipu, Mihai 19 Erduvan, Fatih 19 Ziegler, Volker 18 Siksek, Samir 16 Marques, Diego 15 Ddamulira, Mahadi 15 Filipin, Alan 15 Şiar, Zafer 15 Worrell, James Benjamin 14 Ouaknine, Joel O. 12 Adédji, Kouèssi Norbert 12 Hajdu, Lajos 12 He, Bo 12 Pintér, Ákos 11 Miyazaki, Takafumi 11 Shparlinski, Igor E. 9 Pink, István 9 Tengely, Szabolcs 9 Waldschmidt, Michel 8 Dujella, Andrej 8 Patel, Vandita 7 Bhoi, Kisan 7 Gonzalez-Vega, Laureano 7 Miao, Fuyou 7 Mihăilescu, Preda 7 Pan, Victor Yakovlevich 7 Panda, Gopal Krishna 7 Ray, Prasanta Kumar 7 Rayaguru, Sai Gopal 7 Trojovský, Pavel 7 Tsigaridas, Elias P. 6 Bérczes, Attila 6 Bonciocat, Nicolae Ciprian 6 Dehmer, Matthias 6 Emiris, Ioannis Z. 6 Faye, Bernadette 6 Hare, Kevin G. 6 Heuberger, Clemens 6 Hirata-Kohno, Noriko 6 Meng, Keju 6 Rojas, J. Maurice 6 Rout, Sudhansu Sekhar 6 Salvy, Bruno 6 Soldo, Ivan 6 Szalay, László 6 Tichy, Robert Franz 6 Tzanakis, Nikos 5 Adegbindin, Chèfiath Awero 5 Bilu, Yuri F. 5 Bravo, Eric Fernando 5 Chen, Imin 5 Emmert-Streib, Frank 5 Fuchs, Clemens 5 Gómez, Jhonny Carpediem 5 Götze, Friedrich 5 Hernández Hernández, Santos 5 Kafle, Bir 5 Mehlhorn, Kurt 5 Normenyo, Benedict Vasco 5 Odjoumani, Japhet 5 Patel, Bijan Kumar 5 Pritsker, Igor E. 5 Ruohonen, Keijo 5 Shi, Wujie 5 Soydan, Gokhan 5 Tall, Amadou Makhtar 5 Tchammou, Euloge B. 5 Ulas, Maciej 5 Voutier, Paul M. 5 Yap, Chee-Keng 4 Akhtari, Shabnam 4 Alahmadi, Adel N. 4 Almagor, Shaull 4 Balakrishnan, Jennifer S. 4 Bell, Paul C. 4 Bertók, Csanád 4 Billerey, Nicolas 4 Bliznac Trebješanin, Marija 4 Budarina, Natalia Viktorovna 4 Chakraborty, Kalyan 4 Chen, Zengqiang 4 Cheng, Jinsan 4 Collins, George E. 4 Díaz-Toca, Gema María 4 Dieulefait, Luis Victor 4 Diouf, Ismaïla 4 Edjeou, Bilizimbéyé ...and 1,055 more Authors all top 5 Cited in 246 Serials 107 Journal of Number Theory 71 Journal of Symbolic Computation 40 Mathematics of Computation 39 Journal de Théorie des Nombres de Bordeaux 38 International Journal of Number Theory 29 Periodica Mathematica Hungarica 25 Theoretical Computer Science 23 Monatshefte für Mathematik 21 Boletín de la Sociedad Matemática Mexicana. 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