Found 275 Documents (Results 1–100)
Jeśmanowicz’ conjecture for non-primitive Pythagorean triples. (English) Zbl 1538.11091
Reviewer: Nikos Tzanakis (Iraklion)
Arithmetic progressions among powerful numbers. (English) Zbl 1515.11089
Reviewer: Giovanni Coppola (Napoli)
Variations of Lehmer’s conjecture for Ramanujan’s tau-function. (English) Zbl 1497.11080
Reviewer: Gökhan Soydan (Bursa)
On consecutive perfect powers with elementary methods. (English) Zbl 1518.11030
Nathanson, Melvyn B. (ed.), Combinatorial and additive number theory IV. Selected papers based on the presentations at the CANT 2019 and 2020 workshops, New York, NY, USA, May 21–24, 2019 and virtual, June 1–5, 2020. Cham: Springer. Springer Proc. Math. Stat. 347, 385-400 (2021).
Reviewer: Gökhan Soydan (Bursa)
On some equations related to Ma’s conjecture. (Chinese. English summary) Zbl 1488.11086
Dynamical uniform boundedness and the \(abc\)-conjecture. (English) Zbl 1468.14059
Reviewer: Władysław Narkiewicz (Wrocław)
Skolem’s conjecture confirmed for a family of exponential equations. III. (English) Zbl 1484.11100
Reviewer: Jan-Hendrik Evertse (Leiden)
Solving \(a x^p + b y^p = c z^p\) with \(abc\) containing an arbitrary number of prime factors. (English) Zbl 1478.11040
Reviewer: Andrzej Dąbrowski (Szczecin)
Elliptic curves. 2nd revised and updated edition. (English) Zbl 1446.14001
Hackensack, NJ: World Scientific (ISBN 978-981-12-2183-5/hbk; 978-981-12-2185-9/ebook). x, 308 p. (2020).
ABC implies there are infinitely many non-Fibonacci-Wieferich primes. (English) Zbl 1442.11056
Reviewer: Krassimir Atanassov (Sofia)
On Serre’s modularity conjecture and Fermat’s equation over quadratic imaginary fields of class number one. (English) Zbl 1472.11098
Reviewer: Balasubramanian Sury (Bangalore)
On the prime decomposition of integers of the form \(\frac{z^n-y^n}{z-y}\). (English) Zbl 1489.11007
The generalized Nagell-Ljunggren problem: powers with repetitive representations. (English) Zbl 1475.11050
Reviewer: Michael A. Bennett (Vancouver)
On Baker’s explicit \(abc\)-conjecture. (English) Zbl 1438.11091
Reviewer: Günter Lettl (Graz)
On Fermat’s equation over some quadratic imaginary number fields. (English) Zbl 1444.11050
Reviewer: Balasubramanian Sury (Bangalore)
An elementary approach to the Diophantine equation \(ax^m + by^n = z^r\) using center of mass. (English) Zbl 1394.11028
Reviewer: Dirk Werner (Berlin)
MSC:
11D41
On a modular Fermat equation. (English) Zbl 1410.11074
Discriminant equations in Diophantine number theory. (English) Zbl 1361.11002
New Mathematical Monographs 32. Cambridge: Cambridge University Press (ISBN 978-1-107-09761-2/hbk; 978-1-316-16076-3/ebook). xviii, 457 p. (2017).
Reviewer: Dimitros Poulakis (Thessaloniki)
Corrigendum to “On a conjecture of Schäffer concerning the equation \(1^k+x^k=y^n\)”. (English) Zbl 1377.11040
Reviewer: Gökhan Soydan (Bursa)
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)
The proof of the \(l^2\) decoupling conjecture. (English) Zbl 1322.42014
Reviewer: Elijah Liflyand (Ramat-Gan)
On a conjecture of Schäffer concerning the equation \(1^k + \ldots + x^k = y^n\). (English) Zbl 1377.11039
Reviewer: Gökhan Soydan (Bursa)
Random Thue and Fermat equations. (English) Zbl 1364.11081
Reviewer: Günter Lettl (Graz)
The abc conjecture. (Portuguese) Zbl 1384.11062
Around ABC. (English) Zbl 1384.11061
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)
The abc conjecture. (Spanish. English summary) Zbl 1381.11024
On the solvability of the Diophantine equation \(x^2+y^{2n}=z^3\). (Chinese. English summary) Zbl 1313.11066
MSC:
11D41
On the solutions of the exponential Diophantine equation \(a^x+b^y=(m^2+1)^z\). (English) Zbl 1274.11086
The shuffle variant of Terai’s conjecture on exponential Diophantine equations. (English) Zbl 1274.11087
Integral Brauer-Manin obstructions for sums of two squares and a power. (English) Zbl 1320.11027
Reviewer: B. Z. Moroz (Bonn)
A matrix related to the theorem of Fermat and the Goldbach conjecture. (English) Zbl 1275.11009
Farkas, Hershel M. (ed.) et al., From Fourier analysis and number theory to Radon transforms and geometry. In Memory of Leon Ehrenpreis. Berlin: Springer (ISBN 978-1-4614-4074-1/hbk; 978-1-4614-4075-8/ebook). Developments in Mathematics 28, 217-232 (2013).
Reviewer: Trueman MacHenry (Toronto)
Generalizations of classical results on Jeśmanowicz’ conjecture concerning Pythagorean triples. (English) Zbl 1309.11029
Siegel’s theorem and the Shafarevich conjecture. (English. French summary) Zbl 1271.11065
Baker’s explicit \(abc\)-conjecture and applications. (English) Zbl 1276.11048
Reviewer: Maurice Mignotte (Strasbourg)
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)
Some applications of the \(abc\)-conjecture to the Diophantine equation \(qy^{m}=f(x)\). (English) Zbl 1251.11018
Reviewer: Lajos Hajdu (Debrecen)
On the Diophantine equation \({n \choose k_1,\dots,k_s}=x^l\). (English) Zbl 1257.11031
Reviewer: András Bazsó (Debrecen)
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)
Exceptional cases of Terai’s conjecture on Diophantine equations. (English) Zbl 1290.11069
Amou, Masaaki, (ed.) et al., Diophantine analysis and related fields 2011, DARF–2011. Proceedings of the conference, Musashino, Tokyo, Japan, March 3–5, 2011. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0947-7/pbk). AIP Conference Proceedings 1385, 87-96 (2011).
Terai’s conjecture on exponential Diophantine equations. (English) Zbl 1221.11092
Reviewer: Mihai Cipu (Bucureşti)
Reconstruction problems for graphs, Krawtchouk polynomials, and Diophantine equations. (English) Zbl 1246.11083
Dehmer, Matthias (ed.), Structural analysis of complex networks. Basel: Birkhäuser (ISBN 978-0-8176-4788-9/hbk; 978-0-8176-4789-6/ebook). 293-317 (2011).
Reviewer: Andrej Dujella (Zagreb)
Beyond the method of infinite descent. (English) Zbl 1540.11021
MSC:
11D41
An ABC analog for arithmetical functions. (English) Zbl 1247.11009
Reviewer: Emre Alkan (Istanbul)
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)
Neighboring powers. (English) Zbl 1247.11042
J. Number Theory 130, No. 3, 660-679 (2010); addendum 130, No. 7, 1571 (2010).
Reviewer: Maurice Mignotte (Strasbourg)
Fermat, Wiles and \(\mathrm{GL}(2)\). (Fermat, Wiles et \(\mathrm{GL}(2)\).) (French) Zbl 1322.11071
Harinck, Pascale (ed.) et al., Les représentations linéaires et le grand théorème de Fermat. Palaiseau: Les Éditions de l’École Polytechnique (ISBN 978-2-7302-1566-4/pbk). 113-126 (2009).
Serre’s modularity conjecture and new proofs of Fermat’s last theorem. (Polish) Zbl 1282.11056
Reviewer: Władysław Narkiewicz (Wrocław)
A curious strong resemblance between the Goldbach conjecture and Fermat last assertion. (English) Zbl 1215.11097
Reviewer: Florin Nicolae (Berlin)
The Igusa local zeta functions of \(\text{GL}_2(\mathbb Q_p)\)-orbit of Fermat’s binary form. (English) Zbl 1234.11158
Ene, Viviana (ed.) et al., Combinatorial aspects of commutative algebra. Exploratory workshop on combinatorial commutative algebra and computer algebra, Mangalia, Romania, May 29–31, 2008. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4758-9/pbk). Contemporary Mathematics 502, 59-71 (2009).
Reviewer: Mehmet Cenkci (Antalya)
Solutions of some nonlinear Diophantine matrix equations. (English) Zbl 1217.11034
Reviewer: Lajos Hajdu (Debrecen)
On the conjecture of Jeśmanowicz concerning Pythagorean triples. (English) Zbl 1225.11038
Reviewer: Maurice Mignotte (Strasbourg)
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)
A note on the Nagell-Ljunggren Diophantine equation \(\frac{x^{n}-1}{x-1} = y^q\). (English) Zbl 1228.11041
MSC:
11D41
A note on the ABC-conjecture. (English) Zbl 1241.11034
Lecture notes on Diophantine analysis. With an appendix by Francesco Amoroso. (English) Zbl 1186.11001
Appunti. Scuola Normale Superiore di Pisa (Nuova Serie) 8. Pisa: Edizioni della Normale (ISBN 978-88-7642-341-3/pbk; 978-88-7642-517-2/ebook). xvi, 237 p. (2009).
Reviewer: Michel Waldschmidt (Paris)
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)
The ABC of arithmetics. (Spanish) Zbl 1281.11027
Reviewer: Franz Lemmermeyer (Jagstzell)
Artin’s conjecture for septic and unidecic forms. (English) Zbl 1241.11041
Reviewer: D. R. Heath-Brown (Oxford)
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).
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)
The \(abc\)-conjecture for algebraic numbers. (English) Zbl 1100.11034
Reviewer: Artūras Dubickas (Vilnius)
Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers. (English) Zbl 1113.11021
Reviewer: Wolfgang Schwarz (Frankfurt / Main)
Finite sets of binary forms. (English) Zbl 1102.11021
Reviewer: Alain Kraus (Paris)
MSC:
11D41
Congruent number problem. (English) Zbl 1169.11309
Reviewer: Florin Nicolae (Berlin)
On a problem of Brocard. (English) Zbl 1081.11020
Reviewer: Günter Lettl (Graz)
Lejeune Dirichlet. (Norwegian. English summary) Zbl 1072.01015
Reviewer: Reinhard Siegmund-Schultze (Cambridge)
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)
Equations over finite fields. An elementary approach. 2nd ed. (English) Zbl 1128.11032
Heber City, UT: Kendrick Press (ISBN 0-9740427-1-4/pbk). x, 333 p. (2004).
Reviewer: Olaf Ninnemann (Berlin)
Perfect powers in arithmetic progression. A note on the inhomogeneous case. (English) Zbl 1046.11018
Reviewer: Maurice Mignotte (Strasbourg)
MSC:
11D41
LLL \(\and\) ABC. (English) Zbl 1048.11021
Reviewer: Alf van der Poorten (Killara)
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 few Diophantine equations, in particular, Fermat’s Last Theorem. (English) Zbl 1080.11025
Reviewer: Nikos Tzanakis (Iraklion)
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)
Geometric theorems, Diophantine equations, and arithmetic functions. (English) Zbl 1004.11001
Rehoboth, NM: American Research Press. 298 p. (2002).
Reviewer: Štefan Porubský (Praha)
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