Found 131 Documents (Results 1–100)
Required condition for a congruent number: \(pq\) with primes \(p \equiv 1 \pmod 8\) and \(q \equiv 3 \pmod 8\). (English) Zbl 07895027
The Monsky matrices and non-congruent numbers. (English) Zbl 07855908
Reviewer: Yong Zhang (Changsha)
On certain Diophantine equations concerning the areas and perimeters of rational triangles. (English) Zbl 07829408
Reviewer: István Gaál (Debrecen)
Diophantine equations, class groups and non-congruent numbers. (English) Zbl 07784982
Reviewer: Maciej Ulas (Kraków)
A \(K3\) surface related to Leonardo Pisano’s work on congruent numbers. (English) Zbl 1525.14047
Reviewer: Noriko Yui (Kingston)
Rational \(\theta\)-parallelogram envelopes via \(\theta\)-congruent elliptic curves. (English) Zbl 1532.11076
Reviewer: Rubén A. Hidalgo (Temuco)
A family of congruent number elliptic curves of rank three. (English) Zbl 07712934
Reviewer: Noburo Ishii (Kyōto)
A necessary condition for \(p\) and \(2p\) to be congruent for a prime \(p \equiv 1 \pmod 8\). (English) Zbl 1512.11005
On the extension of even families of non-congruent numbers. (English) Zbl 1525.11065
Reviewer: Maciej Ulas (Kraków)
MSC:
11G05
Distribution of the 2-Selmer rank under twisting. (English. French summary) Zbl 1506.11089
Algèbre et théorie des nombres 2022. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2022. Besançon: Presses Universitaires de Franche-Comté. 59-133 (2022).
On congruent domination number of disjoint and one point union of graphs. (English) Zbl 1504.05225
MSC:
05C69
A remark on prime (non)congruent numbers. (English) Zbl 1514.11034
Reviewer: Noriko Yui (Kingston)
On the 2-part of the class number of \(\mathbb{Q}(\sqrt{\pm D})\) for a congruent number \(D\). (English) Zbl 1518.11045
Reviewer: Claude Levesque (Québec)
Families of non-congruent numbers with odd prime factors of the form \(8k + 3\). (English) Zbl 1498.11146
Families of even noncongruent numbers with arbitrarily many pairs of prime factors. (English) Zbl 1535.11086
Reviewer: Yong Zhang (Changsha)
Hyperbolic congruent numbers. (English) Zbl 1481.11029
On \(\theta\)-congruent numbers over real number fields. (English) Zbl 1468.11124
Reviewer: Maciej Ulas (Kraków)
Congruent number problem and Goldfeld conjecture. (Chinese. English summary) Zbl 1499.11218
Families of non-congruent numbers with arbitrarily many pairs of prime factors. (English) Zbl 1459.11085
Reviewer: Dimitros Poulakis (Thessaloniki)
Two pearls from number theory: congruent numbers and the distribution of prime numbers. (Zwei Perlen der Zahlentheorie: kongruente Zahlen und Primzahlverteilung.) (German) Zbl 1475.11012
Reviewer: Franz Lemmermeyer (Jagstzell)
Joint distribution for the Selmer ranks of the congruent number curves. (English) Zbl 1524.11121
Reviewer: Sungkon Chang (Savannah)
Central \(L\)-values of elliptic curves and local polynomials. (English) Zbl 1484.11148
Reviewer: Sajad Salami (Rio de Janeiro)
A shifted sum for the congruent number problem. (English) Zbl 1475.11173
Reviewer: Lee Troupe (Macon)
The non-congruent numbers via Monsky’s formula. (English) Zbl 1462.11050
Reviewer: Andrej Dujella (Zagreb)
Congruent number elliptic curves related to integral solutions of \(m^2=n^2+nl+n^2\). (English) Zbl 1470.11152
New generalizations of congruent numbers. (English) Zbl 1460.11082
Reviewer: Nikos Tzanakis (Iraklion)
An extension theorem for generating new families of non-congruent numbers. (English) Zbl 1441.11149
MSC:
11G05
A parametrization of \(\theta\)-congruent numbers with many prime factors and with prescribed prime factors. (English) Zbl 1469.11170
Families of even non-congruent numbers with prime factors in each odd congruence class modulo eight. (English) Zbl 1429.11108
MSC:
11G05
Congruent elliptic curves with non-trivial Shafarevich-Tate groups: distribution part. (English) Zbl 1431.11076
Congruent number problem. (English) Zbl 1411.11066
Lin, Chang-Shou (ed.) et al., Proceedings of the sixth international congress of Chinese mathematicians, ICCM 2013, Taipei, Taiwan, July 14–19, 2013. Volume I. Somerville, MA: International Press; Beijing: Higher Education Press. Adv. Lect. Math. (ALM) 36, 135-151 (2017).
The book of numbers. Translated from the Chinese by the author and Jiu Ding. (English) Zbl 1358.11001
Hackensack, NJ: World Scientific (ISBN 978-981-4759-43-4/hbk; 978-981-4759-45-8/ebook). xxvii, 340 p. (2017).
Reviewer: Balasubramanian Sury (Bangalore)
Squarefree parts of polynomial values. (English. French summary) Zbl 1415.11148
On the congruent number problem over integers of cyclic number fields. (English) Zbl 1389.11084
Math. Slovaca 66, No. 3, 561-564 (2016); corrigendum ibid. 69, No. 5, 1233 (2019).
Decomposition of balls in \(\mathbb{R}^{d}\). (English) Zbl 1344.52007
Reviewer: Elizaveta Zamorzaeva (Chişinău)
New explicit constructions of differentially 4-uniform permutations via special partitions of \(\mathbb{F}_{2^{2 k}}\). (English) Zbl 1408.94957
Quantity of non-congruent struts in alternate division. (English) Zbl 1345.52006
Reviewer: Geir Agnarsson (Fairfax)
Congruent number problem and arithmetic of elliptic curves. (English) Zbl 1397.11071
Cheng, Shiu-Yuen (ed.) et al., Introduction to modern mathematics. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-305-0/pbk). Advanced Lectures in Mathematics (ALM) 33, 409-423 (2015).
On second 2-descent and non-congruent numbers. (English) Zbl 1339.11067
Acta Arith. 170, No. 4, 343-360 (2015); errata ibid. 202, No. 2, 203 (2022).
Reviewer: Nikos Tzanakis (Iraklion)
On high rank \(\pi/3\) and \(2\pi/3\)-congruent number elliptic curves. (English) Zbl 1321.11062
Reviewer: Noburo Ishii (Kyoto)
MSC:
11G05
A note on congruent numbers. (English) Zbl 1357.11037
Extending Djoković’s lattice reduction algorithm to include isotropic lattices. (English) Zbl 1312.11021
Reviewer: Andrew G. Earnest (Carbondale)
Contact graphs of unit sphere packings revisited. (English) Zbl 1273.52022
Reviewer: Christian Richter (Jena)
Fermat and the difference of two squares. (English) Zbl 1383.11036
MSC:
11D41
The asymptotic normality of the number of congruent cycles in a random permutation. (English. Russian original) Zbl 1266.60044
Discrete Math. Appl. 22, No. 1, 91-100 (2012); translation from Diskretn. Mat. 24, No. 1, 123-131 (2012).
On Tate-Shafarevich groups of families of elliptic curves. (English) Zbl 1272.11076
Reviewer: Franz Lemmermeyer (Jagstzell)
Congruent numbers. (English) Zbl 1298.11052
Reviewer: Fumio Hazama (Hatoyama)
Contact numbers for congruent sphere packings in Euclidean 3-space. (English) Zbl 1259.52013
Reviewer: A. E. Litvak (Edmonton)
MSC:
52C17
A generalization of the congruent number problem. (English) Zbl 1273.11092
MSC:
11G05
Arithmetic progressions on congruent number elliptic curves. (English) Zbl 1247.11086
Reviewer: Noburo Ishii (Kyoto)
MSC:
11G05
Packing a cake into a box. (English) Zbl 1218.52015
Reviewer: Agota H. Temesvári (Pécs)
Congruent number elliptic curves with rank at least three. (English) Zbl 1218.11057
Reviewer: Florin Nicolae (Berlin)
MSC:
11G05
A method of computations of congruent numbers and elliptic curves. (English) Zbl 1200.11040
Reviewer: Florin Nicolae (Berlin)
A search for high rank congruent number elliptic curves. (English) Zbl 1201.11058
Reviewer: Florin Nicolae (Berlin)
MSC:
11G05
Symmetry and transitive properties of monohedral \(f\)-triangulations of the Riemannian sphere. (English) Zbl 1211.52018
Reviewer: Josef Mikeš (Olomouc)
Right triangles with algebraic sides and elliptic curves over number fields. (English) Zbl 1209.11053
Reviewer: Jasbir Singh Chahal (Provo)
2-Selmer groups and the Birch-Swinnerton-Dyer conjecture for the congruent number curves. (English) Zbl 1245.11078
Selmer groups and Tate-Shafarevich groups for the congruent number problem. (English) Zbl 1180.11017
Reviewer: Patrick Ingram (Waterloo, Ontario)
On integral similitude matrices. (English) Zbl 1177.11026
Reviewer: Maciej Ulas (Kraków)
Acceleration of linear congruent generators. (English) Zbl 1249.65002
MSC:
65C10
Congruent number problems and their variants. (English) Zbl 1161.11014
Buhler, J. P. (ed.) et al., Algorithmic number theory. Lattices, number fields, curves and cryptography. Cambridge: Cambridge University Press (ISBN 978-0-521-80854-5/hbk). Mathematical Sciences Research Institute Publications 44, 613-639 (2008).
Reviewer: Fumio Hazama (Hatoyama)
A study on the algorithm of solving the problem of remainders. (Chinese. English summary) Zbl 1174.11302
Efficient verification of Tunnell’s criterion. (English) Zbl 1183.11015
Reviewer: Fumio Hazama (Hatoyama)
Constructing new non-congruent numbers by graph theory. (English) Zbl 1126.11030
Kanemitsu, S. (ed.) et al., Number theory. Sailing on the sea of number theory. Proceedings of the 4th China-Japan seminar on number theory, Weihai, China, August 30–September 3, 2006. Hackensack, NJ: World Scientific (ISBN 978-981-270-810-6/hbk). Series on Number Theory and its Applications 2, 24-38 (2007).
Reviewer: Patrick Ingram (Toronto)
MSC:
11G05
A graphical approach to computing Selmer groups of congruent number curves. (English) Zbl 1197.11065
MSC:
11G05
New series of odd non-congruent numbers. (English) Zbl 1118.11029
Reviewer: Jannis A. Antoniadis (Iraklion)
MSC:
11G05
A criterion for elliptic curves with second lowest 2-power in \(L(1)\). II. (English) Zbl 1122.11041
Reviewer: Amilcar Pacheco (Rio de Janeiro)
The shortest vectors of lattices connected with a linear congruent generator. (English. Russian original) Zbl 1111.11033
Discrete Math. Appl. 14, No. 5, 479-500 (2004); translation from Diskretn. Mat. 16, No. 4, 88-109 (2004).
Reviewer: Gabriele Nebe (Aachen)
On elliptic curves \(y^{2} = x^{3}-n^{2}x\) with rank zero. (English) Zbl 1076.11036
Reviewer: Xu Fei (Beijing)
MSC:
11G05
A note on the curve \(Y^2=(X+p)(X^2+p^2)\). (English) Zbl 1051.11028
Reviewer: Fumio Hazama (Hatoyama)
The program package MONC for distributed computations by a Monte Carlo method. (Russian. English summary) Zbl 1052.65002
A matrix linear congruent generator over a Galois ring of odd characteristic. (Russian) Zbl 1116.94009
Reviewer: Ivan Landjev (Sofia)
Some families of non-congruent numbers. (English) Zbl 1047.11055
Reviewer: Fumio Hazama (Hatoyama)
A congruence operator in the modeling of continuous distributions. (Russian, English) Zbl 1086.65500
Zh. Vychisl. Mat. Mat. Fiz. 42, No. 11, 1636-1645 (2002); translation in Comput. Math. Math. Phys. 42, No. 11, 1572-1580 (2002).
On certain rational cuboid problems. (English) Zbl 1022.11014
Reviewer: D.Poulakis (Thessaloniki)
MSC:
11D72
A note on the Selmer group of the elliptic curve \(y^ 2=x^ 3+Dx\). (English) Zbl 1040.11042
MSC:
11G05
A note on the congruent distribution of the number of prime factors of natural numbers. (English) Zbl 0986.11066
Reviewer: T.Kubota (Nagoya)
Generating uniform random vectors. (English) Zbl 1005.65007
Reviewer: Jaroslav Král’ (Praha)
Multiple congruent convolutions of probability densities and estimates in the \(L^\infty([0,1)^n)\) space. (English. Russian original) Zbl 0985.60010
Comput. Math. Math. Phys. 40, No. 2, 293-303 (2000); translation from Zh. Vychisl. Mat. Mat. Fiz. 40, No. 2, 307-317 (2000).
Reviewer: Alexey Tret’yakov (Siedlce)
\(\theta\)-congruent numbers and elliptic curves. (English) Zbl 0970.11020
Reviewer: A.Dąbrowski (Szczecin)
Matrix representatives for three-dimensional bilinear forms over finite fields. (English) Zbl 0951.11014
\(\theta\)-congruent numbers. (English) Zbl 0920.11035
Győry, Kálmán (ed.) et al., Number theory. Diophantine, computational and algebraic aspects. Proceedings of the international conference, Eger, Hungary, July 29–August 2, 1996. Berlin: de Gruyter. 235-241 (1998).
Reviewer: E.L.Cohen (Ottawa)
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