Edit Profile (opens in new tab) Bennett, Michael A. Co-Author Distance Author ID: bennett.michael-a Published as: Bennett, Michael A.; Bennett, M. A.; Bennett, Michael more...less Further Spellings: Bennett, Mike Homepage: https://www.math.ubc.ca/~bennett/ External Links: MGP Documents Indexed: 98 Publications since 1993, including 1 Additional arXiv Preprint 4 Contributions as Editor Reviewing Activity: 10 Reviews Co-Authors: 54 Co-Authors with 69 Joint Publications 1,311 Co-Co-Authors all top 5 Co-Authors 33 single-authored 11 Siksek, Samir 5 Bauer, Mark L. 5 Mignotte, Maurice 4 Berndt, Bruce Carl 4 Boston, Nigel 4 Bugeaud, Yann 4 Dahmen, Sander R. 4 Diamond, Harold George 4 Hildebrand, Adolf J. 4 Martin, Greg 4 O’Bryant, Kevin 4 Patel, Vandita 4 Philipp, Walter 4 Rechnitzer, Andrew Daniel 4 Walsh, Peter Gareth 4 Yazdani, Soroosh 3 Bajpai, Prajeet 3 Chen, Imin 3 Gherga, Adela 3 Győry, Kálmán 3 Pintér, Ákos 2 Filaseta, Michael A. 2 Ghadermarzi, Amir 2 Mulholland, Jamie 2 Trifonov, Ognian 1 Billerey, Nicolas 1 Bruni, Carmen 1 Chan, Tsz Ho 1 Cipu, Mihai 1 de Weger, Benjamin M. M. 1 Dummigan, N. P. 1 Ellenberg, Jordan Stuart 1 Freitas, Nuno 1 Garbuz, Ben 1 Hajdu, Lajos 1 Ingram, Patrick 1 Koutsianas, Angelos 1 Kreso, Dijana 1 Levin, Aaron 1 Luca, Florian 1 Marten, Adam 1 Michaud-Jacobs, Philippe 1 Mihăilescu, Preda 1 Ng, Nathan C. 1 Okazaki, Ryotaro 1 Pink, István 1 Rábai, Zsolt 1 Reznick, Bruce 1 Scheerer, Adrian-Maria 1 Skinner, Christopher M. 1 Togbé, Alain 1 van Luijk, Ronald M. 1 Vatsal, Vinayak 1 Wooley, Trevor D. all top 5 Serials 12 Acta Arithmetica 6 Transactions of the American Mathematical Society 5 Mathematics of Computation 5 Compositio Mathematica 5 Publicationes Mathematicae Debrecen 5 International Journal of Number Theory 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Journal für die Reine und Angewandte Mathematik 3 Indagationes Mathematicae. New Series 3 Journal de Théorie des Nombres de Bordeaux 3 Integers 3 Algebra & Number Theory 2 Rocky Mountain Journal of Mathematics 2 Canadian Journal of Mathematics 2 Journal of Number Theory 2 Mathematika 2 Proceedings of the American Mathematical Society 2 Proceedings of the London Mathematical Society. Third Series 2 Comptes Rendus Mathématiques de l’Académie des Sciences 2 Annals of Mathematics. Second Series 1 American Mathematical Monthly 1 Bulletin of the Australian Mathematical Society 1 Periodica Mathematica Hungarica 1 Annales des Sciences Mathématiques du Québec 1 Bulletin of the London Mathematical Society 1 Canadian Mathematical Bulletin 1 Illinois Journal of Mathematics 1 Journal of Combinatorial Theory. Series A 1 Mathematische Annalen 1 Monatshefte für Mathematik 1 L’Enseignement Mathématique. 2e Série 1 Glasnik Matematički. Serija III 1 Journal of the Australian Mathematical Society. Series A 1 Experimental Mathematics 1 The Ramanujan Journal 1 LMS Journal of Computation and Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Research in Number Theory all top 5 Fields 102 Number theory (11-XX) 5 Algebraic geometry (14-XX) 4 General and overarching topics; collections (00-XX) 2 Functions of a complex variable (30-XX) 2 Approximations and expansions (41-XX) 1 Combinatorics (05-XX) 1 Geometry (51-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 83 Publications have been cited 783 times in 479 Documents Cited by ▼ Year ▼ Ternary Diophantine equations via Galois representations and modular forms. Zbl 1053.11025 Bennett, Michael A.; Skinner, Chris M. 90 2004 On the number of solutions of simultaneous Pell equations. Zbl 1044.11011 Bennett, Michael A. 45 1998 Explicit bounds for primes in arithmetic progressions. Zbl 1440.11180 Bennett, Michael A.; Martin, Greg; O’Bryant, Kevin; Rechnitzer, Andrew 42 2018 Rational approximation to algebraic numbers of small height: The Diophantine equation \(|ax^n-by^n|=1\). Zbl 1002.11059 Bennett, Michael A. 32 2001 The Diophantine equation \(A^4 + 2^{\delta }B^2 = C^n\). Zbl 1218.11035 Bennett, Michael A.; Ellenberg, Jordan S.; Ng, Nathan C. 31 2010 On some exponential equations of S. S. Pillai. Zbl 0984.11014 Bennett, Michael A. 28 2001 Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. Zbl 1010.11020 Bauer, Mark; Bennett, Michael A. 25 2002 Powers from products of consecutive terms in arithmetic progression. Zbl 1178.11033 Bennett, M. A.; Bruin, N.; Győry, K.; Hajdu, L. 24 2006 Ternary Diophantine equations of signature \((p,p,3)\). Zbl 1096.11013 Bennett, Michael A.; Vatsal, Vinayak; Yazdani, Soroosh 23 2004 On the Diophantine equation \(1^k+ 2^k+\cdots+ x^k= y^n\). Zbl 1066.11013 Bennett, Michael A.; Győry, Kálmán; Pintér, Ákos 19 2004 Generalized Fermat equations: a miscellany. Zbl 1390.11065 Bennett, Michael A.; Chen, Imin; Dahmen, Sander R.; Yazdani, Soroosh 17 2015 On the number of solutions of simultaneous Pell equations. II. Zbl 1165.11034 Bennett, Michael A.; Cipu, Mihai; Mignotte, Maurice; Okazaki, Ryotaro 15 2006 The Diophantine equation \(b^2X^4-dY^2=1\). Zbl 0980.11021 Bennett, Michael A.; Walsh, Gary 15 1999 On the representation of unity by binary cubic forms. Zbl 0972.11014 Bennett, Michael A. 14 2001 Perfect powers with few binary digits and related Diophantine problems. II. Zbl 1291.11016 Bennett, Michael A.; Bugeaud, Yann; Mignotte, Maurice 14 2012 On a question of Erdős and Graham. Zbl 1155.11019 Bauer, Mark; Bennett, Michael A. 13 2007 Products of consecutive integers. Zbl 1152.11321 Bennett, Michael A. 13 2004 Superelliptic equations arising from sums of consecutive powers. Zbl 1401.11076 Bennett, Michael A.; Patel, Vandita; Siksek, Samir 13 2016 Effective measures of irrationality for certain algebraic numbers. Zbl 0880.11055 Bennett, Michael A. 12 1997 Perfect powers that are sums of consecutive cubes. Zbl 1437.11046 Bennett, Michael A.; Patel, Vandita; Siksek, Samir 12 2017 On the diophantine equation \(| ax^n-by^n|=1\). Zbl 0892.11041 Bennett, Michael A.; de Weger, Benjamin M. M. 11 1998 Multi-Frey \(\mathbb Q\)-curves and the Diophantine equation \(a^2+b^6=c^n\). Zbl 1264.11022 Bennett, Michael A.; Chen, Imin 11 2012 Binomial Thue equations and polynomial powers. Zbl 1126.11018 Bennett, M. A.; Győry, K.; Mignotte, M.; Pintér, Á. 10 2006 Explicit lower bounds for rational approximation to algebraic numbers. Zbl 0879.11038 Bennett, Michael A. 10 1997 Simultaneous rational approximation to binomial functions. Zbl 0873.11042 Bennett, Michael A. 10 1996 Mordell’s equation: a classical approach. Zbl 1371.11077 Bennett, Michael A.; Ghadermarzi, Amir 10 2015 Klein forms and the generalized superelliptic equation. Zbl 1321.11059 Bennett, Michael A.; Dahmen, Sander R. 10 2013 Lucas’ square pyramid problem revisited. Zbl 1090.11019 Bennett, Michael A. 9 2002 Perfect powers with few binary digits and related Diophantine problems. Zbl 1303.11084 Bennett, Michael A.; Bugeaud, Yann; Mignotte, Maurice 9 2013 Fractional parts of powers of rational numbers. Zbl 0791.11030 Bennett, Michael A. 8 1993 Odd values of the Ramanujan tau function. Zbl 1525.11034 Bennett, Michael A.; Gherga, Adela; Patel, Vandita; Siksek, Samir 8 2022 Squares from blocks of consecutive integers: a problem of Erdős and Graham. Zbl 1270.11026 Bennett, Michael A.; Van Luijk, Ronald 8 2012 The Nagell-Ljunggren equation via Runge’s method. Zbl 1395.11060 Bennett, Michael A.; Levin, Aaron 8 2015 The Diophantine equation \((x^{k} - 1)(y^{k} - 1) = (z^{k} - 1)^{t}\). Zbl 1169.11015 Bennett, Michael A. 7 2007 The generalized Fermat equation. Zbl 1440.11037 Bennett, Michael; Mihăilescu, Preda; Siksek, Samir 7 2016 Perfect powers with three digits. Zbl 1372.11009 Bennett, Michael A.; Bugeaud, Yann 7 2014 The representation of integers by binary additive forms. Zbl 0889.11033 Bennett, M. A.; Dummigan, N. P.; Wooley, T. D. 6 1998 On the factorization of consecutive integers. Zbl 1223.11040 Bennett, M. A.; Filaseta, M.; Trifonov, O. 6 2009 Simultaneous approximation to pairs of algebraic numbers. Zbl 0842.11029 Bennett, Michael A. 6 1995 Rational points on Erdős-Selfridge superelliptic curves. Zbl 1407.11081 Bennett, Michael A.; Siksek, Samir 6 2016 Shifted powers in binary recurrence sequences. Zbl 1371.11081 Bennett, Michael A.; Dahmen, Sander R.; Mignotte, Maurice; Siksek, Samir 6 2015 Intersections of recurrence sequences. Zbl 1318.11095 Bennett, Michael A.; Pintér, Ákos 6 2015 Solving families of simultaneous Pell equations. Zbl 0894.11007 Bennett, Michael A. 5 1997 A conjecture of Erdős, supersingular primes and short character sums. Zbl 1440.11039 Bennett, Michael; Siksek, Samir 5 2020 On the equation \(a^3 + b^{3n} = c^2\). Zbl 1306.11025 Bennett, Michael A.; Chen, Imin; Dahmen, Sander R.; Yazdani, Soroosh 5 2014 A generalization of a theorem of Bumby on quartic Diophantine equations. Zbl 1122.11019 Bennett, Michael A.; Togbé, Alain; Walsh, P. G. 4 2006 Yet another generalization of the Ramanujan-Nagell equation. Zbl 1177.11030 Bennett, M. A.; Filaseta, M.; Trifonov, O. 4 2008 Torsion subgroups of elliptic curves in short Weierstrass form. Zbl 1136.11311 Bennett, Michael A.; Ingram, Patrick 4 2005 Bounds on sizes of generalized caps in \(\mathrm{AG} (n,q)\) via the Croot-Lev-Pach polynomial method. Zbl 1421.05027 Bennett, Michael 4 2019 Computing elliptic curves over \(\mathbb{Q}\): bad reduction at one prime. Zbl 1410.11045 Bennett, Michael A.; Rechnitzer, Andrew 4 2017 Computing elliptic curves over \(\mathbb {Q}\). Zbl 1468.11123 Bennett, Michael A.; Gherga, Adela; Rechnitzer, Andrew 4 2019 Integral points on congruent number curves. Zbl 1318.11047 Bennett, Michael A. 4 2013 Prime factors of consecutive integers. Zbl 1211.11102 Bauer, Mark; Bennett, Michael A. 4 2008 Sums of two \(S\)-units via Frey-Hellegouarch curves. Zbl 1407.11049 Bennett, Michael A.; Billerey, Nicolas 4 2017 An ideal Waring problem with restricted summands. Zbl 0793.11026 Bennett, Michael A. 3 1994 Twisted extensions of the cubic case of Fermat’s last theorem. Zbl 1273.11059 Bennett, Michael A.; Luca, Florian; Mulholland, Jamie 3 2011 The equation \(x^{2n}+y^{2n}=z^5\). Zbl 1138.11009 Bennett, Michael A. 3 2006 Powers in recurrence sequences: Pell equations. Zbl 1125.11019 Bennett, Michael A. 3 2005 Pillai’s conjecture revisited. Zbl 1045.11021 Bennett, Michael A. 3 2003 Irrationality via the hypergeometric method. Zbl 1142.11051 Bennett, Michael A. 3 2008 Counting zeros of Dirichlet \(L\)-functions. Zbl 1475.11148 Bennett, Michael A.; Martin, Greg; O’Bryant, Kevin; Rechnitzer, Andrew 3 2021 Sums of two cubes as twisted perfect powers, revisited. Zbl 1440.11036 Bennett, Michael A.; Bruni, Carmen; Freitas, Nuno 3 2018 Perfect powers with few ternary digits. Zbl 1275.11018 Bennett, Michael A. 3 2012 Effective results for restricted rational approximation to quadratic irrationals. Zbl 1306.11053 Bennett, Michael A.; Bugeaud, Yann 3 2012 Shifted powers in Lucas-Lehmer sequences. Zbl 1435.11067 Bennett, Michael A.; Patel, Vandita; Siksek, Samir 3 2019 Number theory for the millennium III. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Zbl 1002.00007 2 2002 Differences between perfect powers. Zbl 1151.11320 Bennett, Michael A. 2 2008 The equation \((x-d)^5+x^5+(x+d)^5=y^n\). Zbl 1475.11049 Bennett, Michael A.; Koutsianas, Angelos 2 2021 Extremal families of cubic Thue equations. Zbl 1395.11049 Bennett, Michael A.; Ghadermarzi, Amir 2 2015 A superelliptic equation involving alternating sums of powers. Zbl 1249.11049 Bennett, Michael A. 2 2011 A local version of Szpiro’s conjecture. Zbl 1294.11086 Bennett, Michael A.; Yazdani, Soroosh 2 2012 Powers from five terms in arithmetic progression. Zbl 1198.11034 Bennett, Michael A. 2 2008 Powers from products of \(k\) terms in progression: finiteness for small \(k\). Zbl 1410.11027 Bennett, Michael A. 2 2018 Differences between perfect powers: the Lebesgue-Nagell equation. Zbl 07618833 Bennett, Michael A.; Siksek, Samir 2 2023 On the Diophantine equation \(x^n+y^n=2^{\alpha} pz^2\). Zbl 1213.11079 Bennett, Michael A.; Mulholland, Jamie 1 2006 On consecutive integers of the form \(ax^2, by^2\) and \(cz^2\). Zbl 0928.11017 Bennett, Michael A. 1 1999 Solving norm form equations via lattice basis reduction. Zbl 0877.11017 Bennett, Michael A. 1 1996 Number theory for the millennium I. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Zbl 1002.00005 1 2002 Simultaneous quadratic equations with few or no solutions. Zbl 0993.11015 Bennett, Michael A.; Walsh, Gary 1 2000 Goormaghtigh’s equation: small parameters. Zbl 1449.11059 Bennett, Michael A.; Garbuz, Ben; Marten, Adam 1 2020 Positive rational solutions to \(x^y=y^{mx}\): a number-theoretic excursion. Zbl 1046.11019 Bennett, Michael A.; Reznick, Bruce 1 2004 The polynomial-exponential equation \(1 + 2^a + 6^b = y^q\). Zbl 1399.11098 Bennett, Michael A. 1 2017 Squares with three nonzero digits. Zbl 1414.11046 Bennett, Michael A.; Scheerer, Adrian-Maria 1 2017 Differences between perfect powers: the Lebesgue-Nagell equation. Zbl 07618833 Bennett, Michael A.; Siksek, Samir 2 2023 Odd values of the Ramanujan tau function. Zbl 1525.11034 Bennett, Michael A.; Gherga, Adela; Patel, Vandita; Siksek, Samir 8 2022 Counting zeros of Dirichlet \(L\)-functions. Zbl 1475.11148 Bennett, Michael A.; Martin, Greg; O’Bryant, Kevin; Rechnitzer, Andrew 3 2021 The equation \((x-d)^5+x^5+(x+d)^5=y^n\). Zbl 1475.11049 Bennett, Michael A.; Koutsianas, Angelos 2 2021 A conjecture of Erdős, supersingular primes and short character sums. Zbl 1440.11039 Bennett, Michael; Siksek, Samir 5 2020 Goormaghtigh’s equation: small parameters. Zbl 1449.11059 Bennett, Michael A.; Garbuz, Ben; Marten, Adam 1 2020 Bounds on sizes of generalized caps in \(\mathrm{AG} (n,q)\) via the Croot-Lev-Pach polynomial method. Zbl 1421.05027 Bennett, Michael 4 2019 Computing elliptic curves over \(\mathbb {Q}\). Zbl 1468.11123 Bennett, Michael A.; Gherga, Adela; Rechnitzer, Andrew 4 2019 Shifted powers in Lucas-Lehmer sequences. Zbl 1435.11067 Bennett, Michael A.; Patel, Vandita; Siksek, Samir 3 2019 Explicit bounds for primes in arithmetic progressions. Zbl 1440.11180 Bennett, Michael A.; Martin, Greg; O’Bryant, Kevin; Rechnitzer, Andrew 42 2018 Sums of two cubes as twisted perfect powers, revisited. Zbl 1440.11036 Bennett, Michael A.; Bruni, Carmen; Freitas, Nuno 3 2018 Powers from products of \(k\) terms in progression: finiteness for small \(k\). Zbl 1410.11027 Bennett, Michael A. 2 2018 Perfect powers that are sums of consecutive cubes. Zbl 1437.11046 Bennett, Michael A.; Patel, Vandita; Siksek, Samir 12 2017 Computing elliptic curves over \(\mathbb{Q}\): bad reduction at one prime. Zbl 1410.11045 Bennett, Michael A.; Rechnitzer, Andrew 4 2017 Sums of two \(S\)-units via Frey-Hellegouarch curves. Zbl 1407.11049 Bennett, Michael A.; Billerey, Nicolas 4 2017 The polynomial-exponential equation \(1 + 2^a + 6^b = y^q\). Zbl 1399.11098 Bennett, Michael A. 1 2017 Squares with three nonzero digits. Zbl 1414.11046 Bennett, Michael A.; Scheerer, Adrian-Maria 1 2017 Superelliptic equations arising from sums of consecutive powers. Zbl 1401.11076 Bennett, Michael A.; Patel, Vandita; Siksek, Samir 13 2016 The generalized Fermat equation. Zbl 1440.11037 Bennett, Michael; Mihăilescu, Preda; Siksek, Samir 7 2016 Rational points on Erdős-Selfridge superelliptic curves. Zbl 1407.11081 Bennett, Michael A.; Siksek, Samir 6 2016 Generalized Fermat equations: a miscellany. Zbl 1390.11065 Bennett, Michael A.; Chen, Imin; Dahmen, Sander R.; Yazdani, Soroosh 17 2015 Mordell’s equation: a classical approach. Zbl 1371.11077 Bennett, Michael A.; Ghadermarzi, Amir 10 2015 The Nagell-Ljunggren equation via Runge’s method. Zbl 1395.11060 Bennett, Michael A.; Levin, Aaron 8 2015 Shifted powers in binary recurrence sequences. Zbl 1371.11081 Bennett, Michael A.; Dahmen, Sander R.; Mignotte, Maurice; Siksek, Samir 6 2015 Intersections of recurrence sequences. Zbl 1318.11095 Bennett, Michael A.; Pintér, Ákos 6 2015 Extremal families of cubic Thue equations. Zbl 1395.11049 Bennett, Michael A.; Ghadermarzi, Amir 2 2015 Perfect powers with three digits. Zbl 1372.11009 Bennett, Michael A.; Bugeaud, Yann 7 2014 On the equation \(a^3 + b^{3n} = c^2\). Zbl 1306.11025 Bennett, Michael A.; Chen, Imin; Dahmen, Sander R.; Yazdani, Soroosh 5 2014 Klein forms and the generalized superelliptic equation. Zbl 1321.11059 Bennett, Michael A.; Dahmen, Sander R. 10 2013 Perfect powers with few binary digits and related Diophantine problems. Zbl 1303.11084 Bennett, Michael A.; Bugeaud, Yann; Mignotte, Maurice 9 2013 Integral points on congruent number curves. Zbl 1318.11047 Bennett, Michael A. 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 Multi-Frey \(\mathbb Q\)-curves and the Diophantine equation \(a^2+b^6=c^n\). Zbl 1264.11022 Bennett, Michael A.; Chen, Imin 11 2012 Squares from blocks of consecutive integers: a problem of Erdős and Graham. Zbl 1270.11026 Bennett, Michael A.; Van Luijk, Ronald 8 2012 Perfect powers with few ternary digits. Zbl 1275.11018 Bennett, Michael A. 3 2012 Effective results for restricted rational approximation to quadratic irrationals. Zbl 1306.11053 Bennett, Michael A.; Bugeaud, Yann 3 2012 A local version of Szpiro’s conjecture. Zbl 1294.11086 Bennett, Michael A.; Yazdani, Soroosh 2 2012 Twisted extensions of the cubic case of Fermat’s last theorem. Zbl 1273.11059 Bennett, Michael A.; Luca, Florian; Mulholland, Jamie 3 2011 A superelliptic equation involving alternating sums of powers. Zbl 1249.11049 Bennett, Michael A. 2 2011 The Diophantine equation \(A^4 + 2^{\delta }B^2 = C^n\). Zbl 1218.11035 Bennett, Michael A.; Ellenberg, Jordan S.; Ng, Nathan C. 31 2010 On the factorization of consecutive integers. Zbl 1223.11040 Bennett, M. A.; Filaseta, M.; Trifonov, O. 6 2009 Yet another generalization of the Ramanujan-Nagell equation. Zbl 1177.11030 Bennett, M. A.; Filaseta, M.; Trifonov, O. 4 2008 Prime factors of consecutive integers. Zbl 1211.11102 Bauer, Mark; Bennett, Michael A. 4 2008 Irrationality via the hypergeometric method. Zbl 1142.11051 Bennett, Michael A. 3 2008 Differences between perfect powers. Zbl 1151.11320 Bennett, Michael A. 2 2008 Powers from five terms in arithmetic progression. Zbl 1198.11034 Bennett, Michael A. 2 2008 On a question of Erdős and Graham. Zbl 1155.11019 Bauer, Mark; Bennett, Michael A. 13 2007 The Diophantine equation \((x^{k} - 1)(y^{k} - 1) = (z^{k} - 1)^{t}\). Zbl 1169.11015 Bennett, Michael A. 7 2007 Powers from products of consecutive terms in arithmetic progression. Zbl 1178.11033 Bennett, M. A.; Bruin, N.; Győry, K.; Hajdu, L. 24 2006 On the number of solutions of simultaneous Pell equations. II. Zbl 1165.11034 Bennett, Michael A.; Cipu, Mihai; Mignotte, Maurice; Okazaki, Ryotaro 15 2006 Binomial Thue equations and polynomial powers. Zbl 1126.11018 Bennett, M. A.; Győry, K.; Mignotte, M.; Pintér, Á. 10 2006 A generalization of a theorem of Bumby on quartic Diophantine equations. Zbl 1122.11019 Bennett, Michael A.; Togbé, Alain; Walsh, P. G. 4 2006 The equation \(x^{2n}+y^{2n}=z^5\). Zbl 1138.11009 Bennett, Michael A. 3 2006 On the Diophantine equation \(x^n+y^n=2^{\alpha} pz^2\). Zbl 1213.11079 Bennett, Michael A.; Mulholland, Jamie 1 2006 Torsion subgroups of elliptic curves in short Weierstrass form. Zbl 1136.11311 Bennett, Michael A.; Ingram, Patrick 4 2005 Powers in recurrence sequences: Pell equations. Zbl 1125.11019 Bennett, Michael A. 3 2005 Ternary Diophantine equations via Galois representations and modular forms. Zbl 1053.11025 Bennett, Michael A.; Skinner, Chris M. 90 2004 Ternary Diophantine equations of signature \((p,p,3)\). Zbl 1096.11013 Bennett, Michael A.; Vatsal, Vinayak; Yazdani, Soroosh 23 2004 On the Diophantine equation \(1^k+ 2^k+\cdots+ x^k= y^n\). Zbl 1066.11013 Bennett, Michael A.; Győry, Kálmán; Pintér, Ákos 19 2004 Products of consecutive integers. Zbl 1152.11321 Bennett, Michael A. 13 2004 Positive rational solutions to \(x^y=y^{mx}\): a number-theoretic excursion. Zbl 1046.11019 Bennett, Michael A.; Reznick, Bruce 1 2004 Pillai’s conjecture revisited. Zbl 1045.11021 Bennett, Michael A. 3 2003 Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. Zbl 1010.11020 Bauer, Mark; Bennett, Michael A. 25 2002 Lucas’ square pyramid problem revisited. Zbl 1090.11019 Bennett, Michael A. 9 2002 Number theory for the millennium III. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Zbl 1002.00007 2 2002 Number theory for the millennium I. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Zbl 1002.00005 1 2002 Rational approximation to algebraic numbers of small height: The Diophantine equation \(|ax^n-by^n|=1\). Zbl 1002.11059 Bennett, Michael A. 32 2001 On some exponential equations of S. S. Pillai. Zbl 0984.11014 Bennett, Michael A. 28 2001 On the representation of unity by binary cubic forms. Zbl 0972.11014 Bennett, Michael A. 14 2001 Simultaneous quadratic equations with few or no solutions. Zbl 0993.11015 Bennett, Michael A.; Walsh, Gary 1 2000 The Diophantine equation \(b^2X^4-dY^2=1\). Zbl 0980.11021 Bennett, Michael A.; Walsh, Gary 15 1999 On consecutive integers of the form \(ax^2, by^2\) and \(cz^2\). Zbl 0928.11017 Bennett, Michael A. 1 1999 On the number of solutions of simultaneous Pell equations. Zbl 1044.11011 Bennett, Michael A. 45 1998 On the diophantine equation \(| ax^n-by^n|=1\). Zbl 0892.11041 Bennett, Michael A.; de Weger, Benjamin M. M. 11 1998 The representation of integers by binary additive forms. Zbl 0889.11033 Bennett, M. A.; Dummigan, N. P.; Wooley, T. D. 6 1998 Effective measures of irrationality for certain algebraic numbers. Zbl 0880.11055 Bennett, Michael A. 12 1997 Explicit lower bounds for rational approximation to algebraic numbers. Zbl 0879.11038 Bennett, Michael A. 10 1997 Solving families of simultaneous Pell equations. Zbl 0894.11007 Bennett, Michael A. 5 1997 Simultaneous rational approximation to binomial functions. Zbl 0873.11042 Bennett, Michael A. 10 1996 Solving norm form equations via lattice basis reduction. Zbl 0877.11017 Bennett, Michael A. 1 1996 Simultaneous approximation to pairs of algebraic numbers. Zbl 0842.11029 Bennett, Michael A. 6 1995 An ideal Waring problem with restricted summands. Zbl 0793.11026 Bennett, Michael A. 3 1994 Fractional parts of powers of rational numbers. Zbl 0791.11030 Bennett, Michael A. 8 1993 all cited Publications top 5 cited Publications all top 5 Cited by 424 Authors 44 Bennett, Michael A. 19 Siksek, Samir 19 Togbé, Alain 17 Le, Maohua 16 Fujita, Yasutsugu 14 Hajdu, Lajos 14 Luca, Florian 13 Bugeaud, Yann 12 Freitas, Nuno 11 Tengely, Szabolcs 10 He, Bo 10 Miyazaki, Takafumi 10 Saradha, N. 10 Terai, Nobuhiro 10 Ziegler, Volker 9 Mignotte, Maurice 9 Pintér, Ákos 9 Soydan, Gokhan 8 Laishram, Shanta 8 Patel, Vandita 7 Pink, István 6 Akhtari, Shabnam 6 Bordignon, Matteo 6 Chen, Imin 6 Fu, Ruiqin 6 Koutsianas, Angelos 6 Styer, Robert Alan 6 Walsh, Peter Gareth 6 Yang, Hai 6 Zhang, Zhongfeng 5 Cipu, Mihai 5 Dujella, Andrej 5 Filaseta, Michael A. 5 Filipin, Alan 5 Győry, Kálmán 5 Michaud-Jacobs, Philippe 5 Scott, Reese 5 Sharma, Divyum 5 Zhang, Yong 4 Billerey, Nicolas 4 Dąbrowski, Andrzej Bogdan 4 Dahmen, Sander R. 4 Das, Pranabesh 4 Dieulefait, Luis Victor 4 Gómez, Carlos Alexis 4 Jadrijević, Borka 4 Keskin, Refik 4 Shorey, Tarlok Nath 4 Ulas, Maciej 4 Wang, Tingting 3 Bazsó, András 3 Bérczes, Attila 3 Bravo, Jhon Jairo 3 Cai, Tianxin 3 Chen, Jianhua 3 Dey, Pallab Kanti 3 Draziotis, Konstantinos A. 3 Ghadermarzi, Amir 3 Gherga, Adela 3 Grundman, Helen G. 3 Heintze, Sebastian 3 Kaneko, Hajime 3 Levin, Aaron 3 Luo, Jiagui 3 Martin, Greg 3 Öğüt, Ümmügülsüm 3 Rechnitzer, Andrew Daniel 3 Skałba, Mariusz 3 Stewart, Cameron L. 3 Tijdeman, Robert 3 Tornero, José María 3 Trifonov, Ognian 3 Voutier, Paul M. 3 Vukusic, Ingrid 3 Wakabayashi, Isao 3 Xiao, Stanley Yao 3 Yuan, Pingzhi 3 Zhu, Huilin 2 Abu Muriefah, Fadwa S. 2 Amdeberhan, Tewodros 2 Argáez-García, Alejandro 2 Bajpai, Prajeet 2 Balakrishnan, Jennifer S. 2 Banerjee, Pradipto 2 Barrios, Alexander J. 2 Burness, Timothy C. 2 Chałupka, Karolina 2 Chan, Stephanie F. 2 Chim, Kwok Chi 2 Corvaja, Pietro 2 Deng, Moujie 2 Dubickas, Artūras 2 Ernvall-Hytönen, Anne-Maria 2 Francis, Forrest J. 2 Gallardo, Luis Henri 2 García-Selfa, Irene 2 Goedhart, Eva G. 2 González-Jiménez, Enrique 2 Gou, Su 2 Gun, Sanoli ...and 324 more Authors all top 5 Cited in 121 Serials 71 Journal of Number Theory 33 International Journal of Number Theory 21 Periodica Mathematica Hungarica 20 Mathematics of Computation 18 Bulletin of the Australian Mathematical Society 18 Journal de Théorie des Nombres de Bordeaux 17 Acta Arithmetica 13 Transactions of the American Mathematical Society 11 Rocky Mountain Journal of Mathematics 11 Indagationes Mathematicae. New Series 10 Acta Mathematica Hungarica 10 The Ramanujan Journal 8 Mathematika 8 Research in Number Theory 7 Functiones et Approximatio. Commentarii Mathematici 7 Integers 6 Mathematische Annalen 5 Proceedings of the American Mathematical Society 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Canadian Journal of Mathematics 4 Compositio Mathematica 4 Glasgow Mathematical Journal 4 Monatshefte für Mathematik 4 Proceedings of the Japan Academy. Series A 4 Revista Matemática Iberoamericana 3 Indian Journal of Pure & Applied Mathematics 3 Archiv der Mathematik 3 Colloquium Mathematicum 3 Czechoslovak Mathematical Journal 3 Journal of the London Mathematical Society. Second Series 3 Journal of Pure and Applied Algebra 3 Quaestiones Mathematicae 3 Experimental Mathematics 3 Journal of Integer Sequences 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Algebra & Number Theory 3 Moscow Journal of Combinatorics and Number Theory 2 Mathematical Notes 2 Advances in Mathematics 2 Bulletin of the London Mathematical Society 2 Canadian Mathematical Bulletin 2 Duke Mathematical Journal 2 Journal of Algebra 2 Journal für die Reine und Angewandte Mathematik 2 Mathematica Slovaca 2 Mathematische Zeitschrift 2 Memoirs of the American Mathematical Society 2 Glasnik Matematički. Serija III 2 Finite Fields and their Applications 2 The New York Journal of Mathematics 2 Documenta Mathematica 2 Journal of Inequalities and Applications 2 Journal of the Australian Mathematical Society 2 Oberwolfach Reports 2 Bulletin of the Hellenic Mathematical Society 2 AIMS Mathematics 1 American Mathematical Monthly 1 Communications in Algebra 1 Discrete Mathematics 1 Israel Journal of Mathematics 1 The Mathematical Gazette 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Algebra and Logic 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Computation 1 International Journal of Mathematics and Mathematical Sciences 1 Inventiones Mathematicae 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Michigan Mathematical Journal 1 Osaka Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the London Mathematical Society. Third Series 1 Theoretical Computer Science 1 Tokyo Journal of Mathematics 1 Tsukuba Journal of Mathematics 1 Chinese Annals of Mathematics. Series A 1 Bulletin of the Iranian Mathematical Society 1 Physica D 1 Boletim da Sociedade Portuguesa de Matemática 1 Journal of Symbolic Computation 1 Algorithmica 1 Publicacions Matemàtiques 1 Forum Mathematicum 1 Elemente der Mathematik 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Expositiones Mathematicae 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 SUT Journal of Mathematics 1 Journal of Mathematical Sciences (New York) 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Turkish Journal of Mathematics 1 The Journal of Artificial Intelligence Research (JAIR) 1 Journal of Difference Equations and Applications 1 Acta Mathematica et Informatica Universitatis Ostraviensis 1 Doklady Mathematics 1 Mathematical Communications 1 Theory of Computing Systems ...and 21 more Serials all top 5 Cited in 20 Fields 465 Number theory (11-XX) 19 Algebraic geometry (14-XX) 8 Group theory and generalizations (20-XX) 8 Special functions (33-XX) 5 Combinatorics (05-XX) 5 Computer science (68-XX) 4 Approximations and expansions (41-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 General and overarching topics; collections (00-XX) 2 Commutative algebra (13-XX) 2 Manifolds and cell complexes (57-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Probability theory and stochastic processes (60-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year