Found 517 Documents (Results 1–100)
Fermat’s last theorem, Schur’s theorem (in Ramsey theory), and the infinitude of the primes. (English) Zbl 1533.11010
On the exponential Diophantine equation \(p^x+q^y=z^3\): theorems and conjectures. (English) Zbl 1496.11057
Giri, Debasis (ed.) et al., Proceedings of the seventh international conference on mathematics and computing, ICMC 2021, Shibpur, India, March 2–5, 2021. Singapore: Springer. Adv. Intell. Syst. Comput. 1412, 711-723 (2022).
MSC:
11D61
Solutions to a class of integer matrix equation \(X^n + Y^n= \lambda^n I\) \((n \in \mathbb{N}, \lambda \in \mathbb{Z}, \lambda \neq 0)\). (Chinese. English summary) Zbl 1513.11101
MSC:
11D41
Fermat’s last theorem and modular curves over real quadratic fields. (English) Zbl 1503.11071
Reviewer: Andrzej Dąbrowski (Szczecin)
Sophie Germain, woman and mathematician. (Sophie Germain, femme et mathématicienne.) (French. English summary) Zbl 1519.01013
Reviewer: Franz Lemmermeyer (Jagstzell)
Improved lower bounds for possible solutions in the second case of the Fermat last theorem and in the Catalan equation. (English) Zbl 1469.11049
Retracted: An elementary proof of Fermat’s last theorem for all even exponents. (English) Zbl 1497.11075
J. Math. Cryptol. 14, 139-142 (2020); retraction note ibid. 14, 143 (2020).
MSC:
11D41
On asymptotic Fermat over \(\mathbb{Z}_p\)-extensions of \(\mathbb{Q}\). (English) Zbl 1492.11073
Reviewer: Lhoussain El Fadil (Fès)
A 2020 view of Fermat’s Last Theorem. (English) Zbl 1442.11004
Reviewer: Franz Lemmermeyer (Jagstzell)
On the prime decomposition of integers of the form \(\frac{z^n-y^n}{z-y}\). (English) Zbl 1489.11007
On Fermat’s equation over some quadratic imaginary number fields. (English) Zbl 1444.11050
Reviewer: Balasubramanian Sury (Bangalore)
Spaces and numbers. (Espaces et nombres.) (French) Zbl 1435.00007
Reviewer: Norbert Knarr (Stuttgart)
MSC:
00A09
Dirichlet. A mathematical biography. (English) Zbl 1412.01003
Cham: Birkhäuser (ISBN 978-3-030-01071-3/hbk; 978-3-030-01073-7/ebook). xix, 311 p. (2018).
Reviewer: Franz Lemmermeyer (Jagstzell)
A tale of two treatises (saga of the conquest of Mt Everest of number theory). (English) Zbl 1471.11004
Reviewer: Victor V. Pambuccian (Glendale)
Natural vector spaces (inward power and Minkowski norm of a natural vector, natural Boolean hypercubes) and a Fermat’s last theorem conjecture. (English) Zbl 1380.11094
MSC:
11Y40
Refinement of a generalized Fermat’s last theorem conjecture in natural vector spaces. (English) Zbl 1380.11095
MSC:
11Y40
The Abel Prize awarded for the proof of Fermat’s last theorem. (Czech) Zbl 1363.01011
Reviewer: Sergey Korotov (Bergen)
The generalized Fermat equation. (English) Zbl 1440.11037
Nash, John Forbes jun. (ed.) et al., Open problems in mathematics. Cham: Springer. 173-205 (2016).
Reviewer: Dimitros Poulakis (Thessaloniki)
Proof of Fermat’s last theorem for \(n=3\) using Tschirnhaus transformation. (English) Zbl 1342.11046
Chen, Ke (ed.) et al., Forging connections between computational mathematics and computational geometry. Papers from the 3rd international conference on computational mathematics and computational geometry, CMCGS 2014, Singapore, February 3–4, 2014. Cham: Springer (ISBN 978-3-319-16138-9/hbk; 978-3-319-16139-6/ebook). Springer Proceedings in Mathematics & Statistics 124, 133-136 (2016).
MSC:
11D41
Algebraic number theory and Fermat’s last theorem. 4th edition. (English) Zbl 1332.11001
Boca Raton, FL: CRC Press (ISBN 978-1-4987-3839-2/hbk; 978-1-4987-3841-5/ebook). xix, 322 p. (2016).
Reviewer: Werner Kleinert (Berlin)
Mathematics everywhere. From Pythagoras to big data. 4th extended edition. (Alles Mathematik. Von Pythagoras zu Big Data.) (German) Zbl 1333.00004
Heidelberg: Springer Spektrum (ISBN 978-3-658-09989-3/pbk; 978-3-658-09990-9/ebook). xi, 472 p. (2016).
Reviewer: Franz Lemmermeyer (Jagstzell)
Fermat equation and inert primes. (Équation de Fermat et nombres premiers inertes.) (French. English summary) Zbl 1390.11066
The Fermat theorem over \(\mathbb Q(\sqrt{5})\). (Sur le théorème de Fermat sur \(\mathbb Q(\sqrt{5})\).) (French. English summary) Zbl 1381.11025
Remarks on the first case of Fermat’s theorem over number fields. (Remarques sur le premier cas du théorème de Fermat sur les corps de nombres.) (French. English summary) Zbl 1364.11082
Reviewer: Dimitros Poulakis (Thessaloniki)
‘Codons’ instead of Pythagorean triples: an extension of Pythagorean theory. (English) Zbl 1371.11075
MSC:
11D09
Fermat’s last theorem. The proof. Translated from the Japanese by Masato Kuwata. (English) Zbl 1311.11005
Reviewer: Przemyslaw Chojecki (Oxford)
A mathematical odyssey. Journey from the real to the complex. (English) Zbl 1300.00008
New York, NY: Springer (ISBN 978-1-4614-8938-2/hbk; 978-1-4614-8939-9/ebook). xvi, 382 p. (2014).
Reviewer: Franka Miriam Brueckler (Zagreb)
A note on congruent numbers. (English) Zbl 1357.11037
History of classical Diophantine analysis. From Abū Kāmil to Fermat. (Histoire de l’analyse diophantienne classique. D’Abū Kāmil à Fermat.) (French) Zbl 1286.01005
Scientia Graeco-Arabica 12. Berlin: De Gruyter (ISBN 978-3-11-033685-6/hbk; 978-3-11-033788-4/ebook). x, 349 p. (2013).
Reviewer: Franz Lemmermeyer (Jagstzell)
An extension of the Pythagorean theorem and its application to Fermat’s last theorem. (English) Zbl 1290.11067
Fermat’s last theorem. Basic tools. Translated from the Japanese by Masato Kuwata. (English) Zbl 1311.11004
Reviewer: Stefan Kühnlein (Karlsruhe)
Learning modern algebra. From early attempts to prove Fermat’s last theorem. (English) Zbl 1277.97002
MAA Textbooks. Washington, DC: Mathematical Association of America (MAA) (ISBN 978-1-939512-01-7/hbk; 978-1-61444-612-5/ebook). xix, 459 p. (2013).
Reviewer: Robert W. van der Waall (Huizen)
Fermat’s Last Theorem on the equations \(X^N+Y^N=Z^N\). Theory, computations, history. (Der Große Satz von Fermat über die Gleichungen \(X^N+Y^N=Z^N\). Theorie, Berechnungen, Geschichte.) (German) Zbl 1266.01001
Berichte aus der Mathematik. Aachen: Shaker Verlag (ISBN 978-3-8440-1706-9/pbk). 85 p. (2013).
Reviewer: Franz Lemmermeyer (Jagstzell)
Pell’s equation and Fermat. (English) Zbl 1383.11037
Fermat and the difference of two squares. (English) Zbl 1383.11036
MSC:
11D41
The generalized Fermat equation. (English. French summary) Zbl 1365.11029
Belabas, Karim et al., Explicit methods in number theory. Rational points and Diophantine equations. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-359-1/pbk). Panoramas et Synthèses 36, 119-149 (2012).
Reviewer: Michael A. Bennett (Vancouver)
MSC:
11D41
Vandiver papers on cyclotomy revisited and Fermat’s last theorem. (English) Zbl 1309.11028
Algèbre et théorie des nombres 2012/2. Besançon: Presses Universitaires de Franche-Comté. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2012/2, 47-111 (2012).
Reviewer: Lawrence C. Washington (College Park)
An elementary proof of Euler-Fermat theorem. (English) Zbl 1251.97007
MSC:
97F60
Number theory 3. Iwasawa theory and modular forms. Transl. from the Japanese by Masato Kuwata. (English) Zbl 1259.11001
Translations of Mathematical Monographs 242; Iwanami Series in Modern Mathematics. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-2095-7/pbk). xiv, 226 p. (2012).
Reviewer: Franz Lemmermeyer (Jagstzell)
On Vandiver’s best result on FLT1. (English) Zbl 1300.11024
Pardalos, Panos M. (ed.) et al., Nonlinear analysis. Stability, approximation, and inequalities. In honor of Themistocles M. Rassias on the occasion of his 60th birthday. New York, NY: Springer (ISBN 978-1-4614-3497-9/hbk; 978-1-4614-3498-6/ebook). Springer Optimization and Its Applications 68, 417-430 (2012).
Reviewer: Maurice Mignotte (Strasbourg)
Sophie’s diary. 2nd ed. (English) Zbl 1239.01100
Washington, DC: Mathematical Association of America (MAA) (ISBN 978-0-88385-577-5/hbk; 978-1-61444-510-4/ebook). xi, 279 p. (2012).
Reviewer: Teodora-Liliana Rădulescu (Craiova)
Rational number theory in the 20th century. From PNT to FLT. (English) Zbl 1230.11001
Springer Monographs in Mathematics. Berlin: Springer (ISBN 978-0-85729-531-6/hbk; 978-0-85729-532-3/ebook). xiv, 654 p. (2012).
Reviewer: Franz Lemmermeyer (Jagstzell)
On the equation \(x^n+y^n=z^n\). (English) Zbl 1265.11058
MSC:
11D41
One, two, many: individuality and collectivity in mathematics. (English) Zbl 1219.00002
Reviewer: Teodora-Liliana Rădulescu (Craiova)
Beyond the method of infinite descent. (English) Zbl 1540.11021
MSC:
11D41
“Voici ce que j’ai trouvé:” Sophie Germain’s grand plan to prove Fermat’s last theorem. (English) Zbl 1205.01010
Reviewer: Franz Lemmermeyer (Jagstzell)
Analysis of the classical cyclotomic approach to Fermat’s last theorem. (English) Zbl 1272.11045
Actes de la conférence “Fonctions \(L\) et arithmétique”. Besançon: Laboratoire de Mathématique de Besançon. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2010, 85-119 (2010).
Reviewer: Lawrence C. Washington (College Park)
What does it take to prove Fermat’s last theorem? Grothendieck and the logic of number theory. (English) Zbl 1210.03029
Reviewer: Florin Nicolae (Berlin)
Mathematics everywhere. Transl. from the German by Philip G. Spain. (English) Zbl 1200.00015
Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4349-9/pbk). xiv, 330 p. (2010).
Reviewer: Svitlana P. Rogovchenko (Umeå)
On sums and products in \(\mathbb C[x]\). (English) Zbl 1253.11014
Reviewer: Weidong Gao (Tianjin)
On the history of Fermat’s last theorem: Fresh views on an old tale. (English) Zbl 1189.01014
Reviewer: Leon Harkleroad (Wilton)
Advanced number theory with applications. (English) Zbl 1200.11002
Discrete Mathematics and Its Applications. Boca Raton, FL: CRC Press (ISBN 978-1-4200-8328-6/hbk; 978-1-138-11325-1/pbk; 978-1-4200-8329-3/ebook). xiii, 466 p. (2010).
Reviewer: Werner Kleinert (Berlin)
Serre’s modularity conjecture and new proofs of Fermat’s last theorem. (Polish) Zbl 1282.11056
Reviewer: Władysław Narkiewicz (Wrocław)
Fermat’s last theorem: an enigma between arithmetics and ideas from 1630 till 1994. (Spanish) Zbl 1220.11002
Reviewer: Florin Nicolae (Berlin)
A curious strong resemblance between the Goldbach conjecture and Fermat last assertion. (English) Zbl 1215.11097
Reviewer: Florin Nicolae (Berlin)
A guide to elementary number theory. (English) Zbl 1205.11001
The Dolciani Mathematical Expositions 41; MAA Guides 5. Washington, DC: Mathematical Association of America (MAA) (ISBN 978-0-88385-347-4/hbk). x, 139 p. (2009).
Reviewer: Franz Lemmermeyer (Jagstzell)
Jacobi and Kummer’s ideal numbers. (English) Zbl 1178.01020
Reviewer: Roman Murawski (Poznań)
The way to the proof of Fermat’s last theorem. (English) Zbl 1201.11001
Reviewer: Stefan Kühnlein (Karlsruhe)
Mathematics everywhere. From Pythagoras to the CD player. 3rd revised ed. (Alles Mathematik. Von Pythagoras zum CD-Player.) (German) Zbl 1168.00001
Wiesbaden: Vieweg+Teubner (ISBN 978-3-8348-0416-7/pbk). x, 386 p. (2009).
Reviewer: Franz Lemmermeyer (Jagstzell)
Number crunching vs. number theory: computers and FLT, from Kummer to SWAC (1850–1960), and beyond. (English) Zbl 1147.11003
Reviewer: Jean-Paul Pier (Luxembourg)
Elliptic curves. Number theory and cryptography. 2nd ed. (English) Zbl 1200.11043
Boca Raton, FL: Chapman and Hall/CRC (ISBN 978-1-4200-7146-7/hbk). xviii, 513 p. (2008).
A combinatorial interpretation of the poly-Bernoulli numbers and two Fermat analogues. (English) Zbl 1165.11022
MSC:
11B68
Arithmetic for enthusiasts. Book 7. Kummer and Dedekind. Volume 1. From ideals to ideals. (Arithmétique pour amateurs. Livre 7. Kummer et Dedekind. Tome 1. Des idéaux aux idéaux.) (French) Zbl 1510.11011
Lyon: Aléas Éditeur (ISBN 978-2-84301-200-6/pbk). 421 p. (2007).
Reviewer: Franz Lemmermeyer (Jagstzell)
Fermat comes to America: Harry Schultz Vandiver and FLT (1914–1963). (English) Zbl 1244.01024
Reviewer: Olaf Ninnemann (Berlin)
On Euler’s hypothetical proof. (English. Russian original) Zbl 1209.11035
Math. Notes 82, No. 3, 352-356 (2007); translation from Mat. Zametki 82, No. 3, 395-400 (2007).
Reviewer: Franz Lemmermeyer (Jagstzell)
Number theory. Volume I: Tools and Diophantine equations. (English) Zbl 1119.11001
Graduate Texts in Mathematics 239. New York, NY: Springer (ISBN 978-0-387-49922-2/hbk). xxiii, 650 p. (2007).
Reviewer: Franz Lemmermeyer (Jagstzell)
Fermat’s theorem and its history. (Spanish) Zbl 1115.11001
Reviewer: Florin Nicolae (Berlin)
Elliptic curves. (English) Zbl 1112.14001
Kea Books. Charleston, SC: BookSurge, LLC (ISBN 1-4196-5257-5/pbk). viii, 238 p. (2006).
Reviewer: Werner Kleinert (Berlin)
From Fermat to Gauss: indefinite descent and methods of reduction in number theory. (English) Zbl 1191.11001
Algorismus 55. Augsburg: ERV Dr. Erwin Rauner Verlag (ISBN 3-936905-18-5/pbk). vii, 574 p. (2006).
Reviewer: Franz Lemmermeyer (Jagstzell)
The \(abc\)-conjecture for algebraic numbers. (English) Zbl 1100.11034
Reviewer: Artūras Dubickas (Vilnius)
A first course in modular forms. (English) Zbl 1062.11022
Graduate Texts in Mathematics 228. Berlin: Springer (ISBN 0-387-23229-X/hbk). xv, 436 p. (2005).
Reviewer: Werner Kleinert (Berlin)
The Fermat proof. (English) Zbl 1104.11001
Victoria: Trafford Publishing (ISBN 1-4120-2203-7/pbk). ix, 50 p. (2004).
Reviewer: Werner Kleinert (Berlin)
Elliptic curves. With appendices by Otto Forster, Ruth Lawrence, and Stefan Theisen. 2nd ed. (English) Zbl 1040.11043
Graduate Texts in Mathematics 111. New York, NY: Springer (ISBN 0-387-95490-2/hbk). xxi, 487 p. (2004).
Reviewer: Werner Kleinert (Berlin)
On a pair of Diophantine equations. (English) Zbl 1064.11026
Reviewer: Ming Luo (Chongqing)
MSC:
11D41
Mathematics for the coat pocket. From abacus to chance. 3. Aufl. (Mathematik für die Westentasche. Von Abakus bis Zufall.) (German) Zbl 1033.00005
München: Piper (ISBN 3-492-04353-4/hbk). 114 S. (2003).
Reviewer: Ralph-Hardo Schulz (Berlin)
Did Fermat prove his great theorem? The Pascal hypothesis. (Fermat a-t-il démontré son grand théorème? L’hypothèse “Pascal”.) (French) Zbl 1392.01005
Paris: L’Harmattan (ISBN 978-2-7475-2836-8; 978-2-296-29514-8/ebook). 187 p. (2002).
Reviewer: Franz Lemmermeyer (Jagstzell)
Mathematics everywhere. From Pythagoras to the CD player. 2., erweiterte Aufl. (Alles Mathematik. Von Pythagoras zum CD-Player.) (German) Zbl 1046.00001
Braunschweig: Vieweg (ISBN 3-528-13131-4/pbk). vii, 342 S. (2002).
Reviewer: Klaus Dieter Bierstedt (Paderborn)
Algebraic number theory and Fermat’s last theorem. Revised 3rd ed. (English) Zbl 0994.11001
Natick, MA: A K Peters. xix, 313 p. (2002).
Reviewer: Wladyslaw Narkiewicz (Wrocław)
Mathematical vistas. From a room with many windows. (English) Zbl 1011.00001
Undergraduate Texts in Mathematics. New York, NY: Springer. xiv, 335 p. (2002).
Reviewer: Helmut Koch (Berlin)
Invitation to the mathematics of Fermat-Wiles. Transl. from the French by Leila Schneps. (English) Zbl 1036.11001
San Diego, CA: Academic Press (ISBN 0-12-339251-9/hbk). xi, 381 p. (2002).
Reviewer: Werner Kleinert (Berlin)
The Fermat conjecture [Fermat’s Last Theorem]. (Spanish) Zbl 1093.11021
Reviewer: Nuria Vila (Barcelona)
Modular forms and Diophantine questions. (English) Zbl 1020.11002
Chen, Louis H. Y. (ed.) et al., Challenges for the 21st century. Papers from the international conference on fundamental sciences: mathematics and theoretical physics (ICFS 2000), Singapore, March 13-17, 2000. Singapore: World Scientific. 162-182 (2001).
Reviewer: A.J.van der Poorten (North Ryde)
Mathematical mountaintops. The five most famous problems of all time. (English) Zbl 0983.00001
Oxford: Oxford University Press. 186 p. (2001).
Reviewer: Günter M.Ziegler (Berlin)
Valuations of ideals, evolutions and the vanishing of cohomology groups. (English) Zbl 1091.13510
Herzog, Jürgen (ed.) et al., Geometric and combinatorial aspects of commutative algebra. Papers based on lectures delivered at the international conference on commutative algebra and algebraic geometry, Messina, Italy, June 16–20, 1999. New York, NY: Marcel Dekker (ISBN 0-8247-0567-X/pbk). Lect. Notes Pure Appl. Math. 217, 245-258 (2001).
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