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Relevant bibliographies by topics / Pythagorean quadruples

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Academic literature on the topic 'Pythagorean quadruples'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Pythagorean quadruples"

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Wadhawan, Narinder. "SELF GENERATING n-TUPLES." Graduate Journal of Interdisciplinary Research, Reports and Reviews 1, no. 1 (2023): 18–27. https://doi.org/10.34256/gjir3.v1i1.5.

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Background: The Pythagorean triple based on Pythagorean Theorem, were known in to ancient Babylon and Egypt. The interrelation of the three was known as far back as thousands of years, but it was Pythagoras who explicitly explained their equation.Purpose: Different methods have been put forth by the mathematicians for generation of Pythagorean’s triple and n-tuples but this paper provides a unique method how these get self-generated by use of simple algebraic expansions.Methods: An algebraic quantity (a+b) squared equals to (a-b) squared plus 4ab and if a or b is assigned such a value that mak

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Overmars, Anthony, and Sitalakshmi Venkatraman. "New Semi-Prime Factorization and Application in Large RSA Key Attacks." Journal of Cybersecurity and Privacy 1, no. 4 (2021): 660–74. http://dx.doi.org/10.3390/jcp1040033.

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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 secure digital communications. Hence, alternate approaches to solve the semi-prime factorization problem are proposed. Recently, Pythagorean tuples to factor semi-primes have been explored to consider Fermat’s Christmas theorem, with the two squares having opposite parity. This paper is motivated by the property that the integer separating these

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3

Nelsen, Roger. "Proof Without Words: Pythagorean Quadruples." College Mathematics Journal 45, no. 3 (2014): 179. http://dx.doi.org/10.4169/college.math.j.45.3.179.

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Maran, A. K. "A Simple Solution for Diophantine Equations of Second, Third and Fourth Power." Mapana - Journal of Sciences 4, no. 1 (2005): 96–100. http://dx.doi.org/10.12723/mjs.6.17.

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We know already that the set Of positive integers, which are satisfying the Pythagoras equation Of three variables and four variables cre called Pythagorean triples and quadruples respectively. These cre Diophantine equation OF second power. The all unknowns in this Pythagorean equation have already Seen by mathematicians Euclid and Diophantine. Hcvwever the solution defined by Euclid are Diophantine is also again having unknowns. The only to solve the Diophantine equations wos and error method. Moreover, the trial and error method to obtain these values are not so practical and easy especiall

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Ojera, Dariel. "Unveiling the Properties and Relationship of Yellowstone Permutation Sequence." Psychology and Education: A Multidisciplinary Journal 27, no. 2 (2024): 173–84. https://doi.org/10.5281/zenodo.13993059.

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This paper explores a mathematical sequence known as the Yellowstone permutation, introduced by Zumkeller (2004). This sequence, characterized by alternating even and odd integers with prime and composite number patterns, is studied for its unique properties and connections to mathematical structures like Pythagorean triples and quadruples. The research employs descriptive and expository methods to explore the sequence’s nature, establishing it as infinite, containing infinitely many primes, and ensuring that all integers appear at least once. The paper also delves into how the Yellowsto

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6

Booze, David A. "Delving Deeper: Visualizing Pythagorean Triples and Beyond." Mathematics Teacher 104, no. 5 (2010): 393–98. http://dx.doi.org/10.5951/mt.104.5.0393.

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Exploring the algebraic properties that form the framework for analytical generation of Pythagorean triples and quadruples is a challenging topic for high school algebra students. I have had considerable success in motivating my students to explore these properties by using a visual method. Students can use this visual method to find Pythagorean triples and quadruples easily and can capably and colorfully supply as many integer solutions as they desire to these well-known equations. Here I will present a visual method for producing integer solutions to the equations a2 + b2 = c2 and a2 + b2 +

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7

Booze, David A. "Delving Deeper: Visualizing Pythagorean Triples and Beyond." Mathematics Teacher 104, no. 5 (2010): 393–98. http://dx.doi.org/10.5951/mt.104.5.0393.

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Abstract:

Exploring the algebraic properties that form the framework for analytical generation of Pythagorean triples and quadruples is a challenging topic for high school algebra students. I have had considerable success in motivating my students to explore these properties by using a visual method. Students can use this visual method to find Pythagorean triples and quadruples easily and can capably and colorfully supply as many integer solutions as they desire to these well-known equations. Here I will present a visual method for producing integer solutions to the equations a2 + b2 = c2 and a2 + b2 +

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8

M., Stupel, Sigler Avi(Berman), and Jahangiri J. "A generalization of Pythagorean triples for desirable quadrilaterals." Journal of Progressive Research in Mathematics 13, no. 2 (2018): 2282–90. https://doi.org/10.5281/zenodo.3974664.

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We explore the generalization of famous Pythagorean triples (a, b, c) for triangles to Pythagorean quadruples (a, b, c, d) for desirable quadrilaterals. Using number theory and geometrical techniques including Diophantine equations and Ptolemy’s Theorem, we show that there are infinite number of such quadrilaterals with specific relations between their sides and diagonals. We conclude our paper with an open question for further investigation.

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Frisch, Sophie, and Leonid Vaserstein. "Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples." Journal of Pure and Applied Algebra 216, no. 1 (2012): 184–91. http://dx.doi.org/10.1016/j.jpaa.2011.06.002.

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10

Oliverio, Paul. "Self-Generating Pythagorean Quadruples and N -Tuples." Fibonacci Quarterly 34, no. 2 (1996): 98–101. http://dx.doi.org/10.1080/00150517.1996.12429074.

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Book chapters on the topic "Pythagorean quadruples"

1

Hirayama, Hiroshi. "Numerical Calculation by Quadruple Precision Higher Order Taylor Series Method of the Pythagorean Problem of Three Bodies." In Integral Methods in Science and Engineering. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16077-7_14.

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