Results 1 to 10 of about 2,846 (143)
The group of primitive Pythagorean triples over Gaussian integers [PDF]
Heliyon, 2023 A group structure of the set of primitive Pythagorean triples over Gaussian integers is investigated. In addition, we show that it is a free abelian group.
Attawut Wongpradit, Ekkasit Sangwisut
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Groups and monoids of Pythagorean triples connected to conics [PDF]
Open Mathematics, 2017 We define operations that give the set of all Pythagorean triples a structure of commutative monoid. In particular, we define these operations by using injections between integer triples and 3 × 3 matrices.
Murru Nadir +3 more
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Datasets on the statistical and algebraic properties of primitive Pythagorean triples [PDF]
Data in Brief, 2017 The data in this article was obtained from the algebraic and statistical analysis of the first 331 primitive Pythagorean triples. The ordered sample is a subset of the larger Pythagorean triples.
Hilary I. Okagbue +5 more
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Localization-delocalization wavepacket transition in Pythagorean aperiodic potentials. [PDF]
Sci Rep, 2016 We introduce a composite optical lattice created by two mutually rotated square patterns and allowing observation of continuous transformation between incommensurate and completely periodic structures upon variation of the rotation angle θ.
Huang C +5 more
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On Pell, Pell-Lucas, and balancing numbers [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers ...
Gül Karadeniz Gözeri
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A note on generating primitive Pythagorean triples using matrices [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We present matrices that generate families of primitive Pythagorean triples that arise from generalized Fibonacci sequences. We then present similar results for generalized Lucas sequences and primitive Pythagorean triples.
Jathan Austin
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Some Results on a Generalized Version of Congruent Numbers
InPrime, 2021 This paper aims to construct a new formula that generates a generalized version of congruent numbers based on a generalized version of Pythagorean triples.
Leomarich F. Casinillo +1 more
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New Semi-Prime Factorization and Application in Large RSA Key Attacks
Journal of Cybersecurity and Privacy, 2021 Semi-prime factorization is an increasingly important number theoretic problem, since it is computationally intractable. Further, this property has been applied in public-key cryptography, such as the Rivest–Shamir–Adleman (RSA) encryption systems for ...
Anthony Overmars +1 more
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On Pythagorean Triples and the Primitive Roots Modulo a Prime
Journal of Mathematics, 2021 In this paper, we use the elementary methods and the estimates for character sums to study a problem related to primitive roots and the Pythagorean triples and prove the following result: let p be an odd prime large enough.
Jingzhe Wang
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Metallic means and Pythagorean triples [PDF]
Notes on Number Theory and Discrete MathematicsIn this article, we study the connection between Pythagorean triples and metallic means. We derive several interconnecting identities between different metallic means.
Chetansing Rajput, Hariprasad Manjunath
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