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
doaj +2 more sources
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
doaj +3 more sources
Enhancing readiness degree for Industrial Internet of Things adoption in manufacturing enterprises: An integrated Pythagorean fuzzy approach [PDF]
HeliyonThis study proposes a hybrid multi-criteria decision-making (MCDM) methodology designed to enhance the readiness for adopting the Industrial Internet of Things (IIoT) in manufacturing enterprises.
Detcharat Sumrit
doaj +2 more sources
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
doaj +2 more sources
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
europepmc +6 more sources
Pythagorean Triples with Common Sides
Journal of Mathematics, 2019 There exist a finite number of Pythagorean triples that have a common leg. In this paper we derive the formulas that generate pairs of primitive Pythagorean triples with common legs and also show the process of how to determine all the primitive and ...
Raymond Calvin Ochieng +2 more
doaj +3 more sources
Fermat numbers and Fibonacci numbers on Heron triangles [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 We mainly give necessary and sufficient conditions for being a Heron triangle in the case of certain classes of an isosceles triangles with the three sides (𝑎, 𝑎, 𝑐), where 𝑐 is an arbitrary positive integer, and 𝑎 is a Fermat or Fibonacci prime.
Chinnawat Tangkanchanawong +1 more
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms
Axioms, 2022 We introduce the notion of a Pythagorean hypersurface immersed into an n+1-dimensional pseudo-Riemannian space form of constant sectional curvature c∈−1,0,1.
Muhittin Evren Aydın +2 more
doaj +1 more source