Right-angled triangles with almost prime hypotenuse. (English) Zbl 07881678
Reviewer: Jonas Šiaulys (Vilnius)
Found 202 Documents (Results 1–100)
Groups and monoid in the set of Pythagorean triples. (English) Zbl 1541.11030
Reviewer: Ahmet Tekcan (Bursa)
MSC:
11D09
Solutions of \(x_1^2+x_2^2-x_3^2=n^2\) with small \(x_3\). (English) Zbl 07796579
Reviewer: Meinhard Peters (Münster)
Wild goose and triangular numbers. (Oies sauvages et nombres triangulaires.) (French) Zbl 07811767
Reviewer: Franz Lemmermeyer (Jagstzell)
MSC:
11D09
A note on positive integer triples \((a, b, c)\) generated by the equation \(a^{-1} + b^{-1} = c^{-1}\). (English) Zbl 1538.11089
On practical numbers of some special forms. (English) Zbl 1529.11046
Reviewer: Mehdi Hassani (Zanjan)
A rational algorithm for checking the congruence of unitoid matrices. (Russian. English summary) Zbl 07617330
Plimpton 322: a study of rectangles. (English) Zbl 1508.01004
Reviewer: Duncan J. Melville (Canton)
MSC:
01A17
On primitive solutions of the Diophantine equation \(x^2 + y^2 = M\). (English) Zbl 1501.11048
Reviewer: Balasubramanian Sury (Bangalore)
On certain Diophantine equations involving triangular numbers. (English) Zbl 1479.11053
Reviewer: Wai Yan Pong (Carson)
MSC:
11D09
Generation of family of Pythagorean \(n\)-tuples from a seed Pythagorean \(n\)-tuple. (English) Zbl 1536.11059
MSC:
11D09
A new approach to generate formulae for Pythagoreans triples, quadruples and their generalisation to \(n\)-tuples. (English) Zbl 1513.11094
MSC:
11D09
Generalized Fibonacci sequences in Pythagorean triple preserving matrices. (English) Zbl 1477.11029
Reviewer: Attila Bérczes (Debrecen)
A heuristic rational algorithm for checking the congruence of normal matrices. (English. Russian original) Zbl 1470.65086
Comput. Math. Math. Phys. 60, No. 10, 1601-1608 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 10, 1656-1663 (2020).
A note on Pythagorean triples. (English) Zbl 1478.11043
Exploring continued fractions. From the integers to solar eclipses. (English) Zbl 1496.11009
AMS/MAA Dolciani Mathematical Expositions 53. Providence, RI: MAA Press/American Mathematical Society (AMS) (ISBN 978-1-4704-6128-7/pbk; 978-1-4704-5156-1/ebook). xix, 480 p. (2019).
Reviewer: Franz Lemmermeyer (Jagstzell)
Pairs of Pythagorean triangles with given ratios between catheti. (English) Zbl 1471.11123
Reviewer: Nikos Tzanakis (Iraklion)
The origin of the Beauregard-Suryanarayan product on Pythagorean triples. (English) Zbl 1451.11023
Reviewer: István Gaál (Debrecen)
Distribution of rational points on the circle of unit radius. (English. Russian original) Zbl 1436.11012
Izv. Math. 83, No. 5, 1008-1049 (2019); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 83, No. 5, 107-148 (2019).
Reviewer: Thomas B. Ward (Leeds)
Congruent number elliptic curves related to integral solutions of \(m^2=n^2+nl+n^2\). (English) Zbl 1470.11152
On a function introduced by Erdös and Nicolas. (English) Zbl 1442.11013
Reviewer: Mehdi Hassani (Zanjan)
MSC:
11A25
Algebraic geometry on imaginary triangles. (English) Zbl 1411.14034
Reviewer: Hans-Peter Schröcker (Innsbruck)
Formally proving the Boolean Pythagorean triples conjecture. (English) Zbl 1403.68222
Eiter, Thomas (ed.) et al., LPAR-21. 21st international conference on logic for programming, artificial intelligence and reasoning, Maun, Botswana, May 8–12, 2017. Selected papers. Manchester: EasyChair. EPiC Series in Computing 46, 509-522 (2017).
MSC:
68T15
Generalized Riemann sums. (English) Zbl 1391.26029
Ji, Lizhen (ed.) et al., From Riemann to differential geometry and relativity. Cham: Springer (ISBN 978-3-319-60038-3/hbk; 978-3-319-60039-0/ebook). 457-479 (2017).
Reviewer: Robert W. van der Waall (Amsterdam)
Plimpton 322 is Babylonian exact sexagesimal trigonometry. (English) Zbl 1416.01002
Reviewer: Victor V. Pambuccian (Glendale)
MSC:
01A17
A characterization of Pythagorean triples. (English) Zbl 1420.11059
MSC:
11D09
A note on Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. (English) Zbl 1431.11046
On certain Diophantine equations of the form \(z^2=f(x)^2\pm g(y)^2\). (English) Zbl 1387.11025
MSC:
11D41
Families of primitive Pythagorean triples involving terms of generalized Fibonacci and Lucas sequences. (English) Zbl 1406.11015
MSC:
11B39
Antieigenvalue analysis for continuum mechanics, economics, and number theory. (English) Zbl 1344.47011
Reviewer: Khristo N. Boyadzhiev (Ada)
The call of the primes. Surprising patterns, peculiar puzzles, and other marvels of mathematics. (English) Zbl 1341.00012
Amherst, NY: Prometheus Books (ISBN 978-1-63388-148-8/pbk). 330 p. (2016).
Reviewer: Panayiotis Vlamos (Athena)
A note on Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. (English) Zbl 1499.11171
MSC:
11D61
Pythagorean triples in multiplicative groups of prime power order. (English) Zbl 1384.11056
MSC:
11D09
On the Diophantine equation \((n(7^{2r}- 4))^x + (n(4\cdot7^r))^y= (n(7^{2r}+ 4))^z\). (Chinese. English summary) Zbl 1349.11073
MSC:
11D61
Diophantine equations and Hilbert’s theorem 90. (English) Zbl 1311.11107
J. Math., Univ. Tokushima 48, 35-40 (2014); erratum ibid. 51, 71 (2017).
On Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. (English) Zbl 1309.11030
MSC:
11D61
Generalizations of classical results on Jeśmanowicz’ conjecture concerning Pythagorean triples. II. (English) Zbl 1310.11040
A note on the Diophantine equation \((na)^x + (nb)^y = (nc)^z\). (English) Zbl 1372.11046
MSC:
11D61
Babylonian number theory and trigonometric functions: trigonometric table and Pythagorean triples in the mathematical tablet Plimpton 322. (English) Zbl 1290.01008
Knobloch, Eberhard (ed.) et al., Seki, founder of modern mathematics in Japan. A commemoration on his tercentenary. Collected papers of the international conference on the history of mathematics in memory of Seki Takakazu, Tokyo, Japan, August 25–31, 2008. Tokyo: Springer (ISBN 978-4-431-54272-8/hbk; 978-4-431-54273-5/ebook). Springer Proceedings in Mathematics & Statistics 39, 31-47 (2013).
Reviewer: Hermann Hunger (Wien)
MSC:
01A17
Generalizations of classical results on Jeśmanowicz’ conjecture concerning Pythagorean triples. (English) Zbl 1309.11029
On a special set of symmetric Pythagorean triple preserving matrices. (English) Zbl 1331.11021
Reviewer: Mircea Crâşmăreanu (Iaşi)
Triangular squares: some new identities. (English) Zbl 1311.11021
Reviewer: Le Maohua (Zhanjiang)
MSC:
11D09
A family of formulae for pi. (English) Zbl 1345.11091
Reviewer: Cristinel Mortici (Târgovişte)
MSC:
11Y60
A notebook-trip to the land of maths: from Babylon via Pythagoras to Fermat, Euler, Gauss, Jacobi, Dedekind into the digital age. (Notebook-Reise ins Mathe-Land: von Babylon über Pythagoras zu Fermat, Euler, Gauß, Jacobi, Dedekind bis ins digitale Zeitalter.) (German) Zbl 1284.01012
Baierl, Rudolf (ed.), A. Friedrich Hirzebruch. B. Historische Arbeiten zu Fluiden: Hans Gebelein, Ernst Mohr. C. Bedeutsame Aspekte zur Geschichte der Mathematik, Babylon. Berlin: Berliner Mathematische Gesellschaft (BMG) (ISBN 978-3-940170-21-7/pbk). Forum der Berliner Mathematischen Gesellschaft 21, 109-126 (2012).
Reviewer: Silke Göbel (Berlin)
Pellian sequences and squares. (English) Zbl 1309.11025
Odd-powered triples and Pellian sequences. (English) Zbl 1292.11005
MSC:
11A05
Analysis of the two-fraction method for generating primitive Pythagoras triples. (English) Zbl 1257.97002
A very useful Pythagorean tree. (English) Zbl 1252.00007
Silva, Jorge Nuno (ed.), Proceedings of the recreational mathematics colloquium II, University of Évora, Portugal, April 27–30, 2011. Lisboa: Associação Ludus (ISBN 978-989-97346-2-3/pbk). 3-15 (2012).
Almost prime Pythagorean triples in thin orbits. (English) Zbl 1273.11055
Reviewer: Ranjeet Sehmi (Chandigarh)
Some interesting infinite families of primitive Pythagorean triples. (English) Zbl 1277.11027
Reviewer: Andrej Dujella (Zagreb)
On a Diophantine equation that generates all integral Apollonian gaskets. (English) Zbl 1252.52015
Reviewer: Oleg Karpenkov (Graz)
Jeśmanowicz’ conjecture on exponential Diophantine equations. (English) Zbl 1266.11064
Reviewer: Maurice Mignotte (Strasbourg)
The shuffle variant of Jeśmanowicz’ conjecture concerning Pythagorean triples. (English) Zbl 1225.11039
Reviewer: Władysław Narkiewicz (Wrocław)
MSC:
11D61
Integer structure analysis of odd powered triples: the significance of triangular versus pentagonal numbers. (English) Zbl 1252.11001
On the Diophantine equation \(z^2=f(x)^2 \pm f(y)^2\). (English) Zbl 1218.11034
Reviewer: Péter Olajos (Miskolc)
The Pythagorean theorem. The story of its power and beauty. With an afterword by Herbert A. Hauptman, Nobel Laureate. (English) Zbl 1247.00007
Amherst, NY: Prometheus Books (ISBN 978-1-61614-181-3/hbk). 320 p. (2010).
Reviewer: Hans Fischer (Eichstätt)
A brief note on side and diagonal numbers. (English) Zbl 1239.11031
Reviewer: Mircea Crâşmăreanu (Iaşi)
Generalizations of classical results on Jeśmanowicz’ conjecture concerning Pythagorean triples. (English) Zbl 1198.11035
Komatsu, Takao (ed.), Diophantine analysis and related fields 2010. DARF–2010. Proceedings of the conference, Musashino, Tokyo, Japan, March 4–5, 2010. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0815-9). AIP Conference Proceedings 1264, 41-51 (2010).
Reviewer: Maurice Mignotte (Strasbourg)
On Pythagorean triples containing a fixed integer. (English) Zbl 1238.11036
Reviewer: Devbhadra V. Shah (Surat)
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)
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