Relevant bibliographies by topics / Primitive pythagorean triples

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Academic literature on the topic 'Primitive pythagorean triples'

Author: Grafiati
Published: 5 June 2025
Last updated: 2 August 2025

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Journal articles on the topic "Primitive pythagorean triples"

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Ochieng, Raymond Calvin, Chiteng’a John Chikunji, and Vitalis Onyango-Otieno. "Pythagorean Triples with Common Sides." Journal of Mathematics 2019 (April 1, 2019): 1–8. http://dx.doi.org/10.1155/2019/4286517.

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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 nonprimitive Pythagorean triples for a given leg of a Pythagorean triple.
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Koszegyova, Lucia, Evelin Csókási, and Juraj Hirjak. "Structure of Primitive Pythagorean Triples in Generating Trees." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 2127–41. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5323.

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A Pythagorean triple is a triple of positive integers $(a,b,c)$ such that $a^2+b^2=c^2$. If $a,b$ are coprime, then it is called a primitive Pythagorean triple. It is known that every primitive Pythagorean triple can be generated from the triple $(3,4,5)$ using multiplication by unique number and order of three specific $3\times3$ matrices, which yields a ternary tree of triplets. Two such trees were described by Berggren and Price, respectively. A different approach is to view the primitive Pythagorean triples as points in the three-dimensional Euclidean space. In this paper, we prove that th
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Eckert, Ernest J. "Primitive Pythagorean Triples." College Mathematics Journal 23, no. 5 (1992): 413. http://dx.doi.org/10.2307/2686417.

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Eckert, Ernest J. "Primitive Pythagorean Triples." College Mathematics Journal 23, no. 5 (1992): 413–17. http://dx.doi.org/10.1080/07468342.1992.11973493.

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Casinillo, Leomarich F., and Emily L. Casinillo. "SOME NOTES ON A GENERALIZED VERSION OF PYTHAGOREAN TRIPLES." Jurnal Riset dan Aplikasi Matematika (JRAM) 4, no. 2 (2020): 103. http://dx.doi.org/10.26740/jram.v4n2.p103-107.

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A Pythagorean triple is a set of three positive integers a, b and c that satisfy the Diophantine equation a^2+b^2=c^2. The triple is said to be primitive if gcd(a, b, c)=1 and each pair of integers and are relatively prime, otherwise known as non-primitive. In this paper, the generalized version of the formula that generates primitive and non-primitive Pythagorean triples that depends on two positive integers k and n, that is, P_T=(a(k, n), b(k, n), c(k, n)) were constructed. Further, we determined the values of k and n that generates primitive Pythagorean triples and give some important resul
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Lefton, Phyllis. "A Matrix Method for Generating Pythagorean Triples." Mathematics Teacher 80, no. 2 (1987): 103–8. http://dx.doi.org/10.5951/mt.80.2.0103.

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This article describes a program that uses an interesting matrix method to generate Pythagorean triples -that is, solutions of the equation a2 + b2 = c2 for which a, b, and c are integers. Only primitive triples are found, that is, those for which a > 0, b > 0, c > 0, and the greatest common divisor of a, b, and c is one. This result suffices because nonprimitive triples are just multiples of primitive ones. We shall use the abbreviation PPT for primitive Pythagorean triple.
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Gandhi, K. Raja Rama, and D. Narasimha Murty. "Generalization of Pythagorean Triplets, Quadruple." Bulletin of Society for Mathematical Services and Standards 1 (March 2012): 40–45. http://dx.doi.org/10.18052/www.scipress.com/bsmass.1.40.

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The method of computing Pythagorean triples is well known. All though the classical formulas produce all primitive triples, which do not generate all possible triples, specially non-primitive triples. This paper presents a novel approach to produce all likely triples both primitive and non-primitive, Quadruple for any extent.
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Amato, Roberto. "A characterization of primitive Pythagorean triples." Palestine Journal of Mathematics 12, no. 2 (2023): 524–29. https://doi.org/10.5281/zenodo.10460794.

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The main aim of this paper is to present an analytic result which characterizes the primitive Pythagorean triples via a cathetus. This way has the convenience to find easily all primitive Pythagorean triples x, y, z ∈ N where x is a predetermined integer.
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Tirman, Alvin. "Pythagorean Triples." Mathematics Teacher 79, no. 8 (1986): 652–55. http://dx.doi.org/10.5951/mt.79.8.0652.

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If a class of students completing a course in plane geometry is asked to cite a few examples of primitive Pythagorean triples (those whose greatest common divisor is 1), their answers can be assumed to be 3, 4, 5; 5, 12, 13; 8. 15, 17: and 7, 24, 25.
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Austin, Jathan. "A note on generating primitive Pythagorean triples using matrices." Notes on Number Theory and Discrete Mathematics 29, no. 2 (2023): 402–6. http://dx.doi.org/10.7546/nntdm.2023.29.2.402-406.

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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.
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Dissertations / Theses on the topic "Primitive pythagorean triples"

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Rainey, Jena Melissa. "Some partitions of the set of primitive Pythagorean triples." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 1995. http://digitalcommons.auctr.edu/dissertations/2503.

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A primitive Pythagorean triple is a set of positive integers, x, y and z, such that x and y are relatively prime and x2+y2=z2. In this thesis several partitions of the set Pp of primitive Pythagorean triples are studied. Also interesting properties of these partitions are derived. These properties are used to develop a two-dimensional array of Pp.
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Book chapters on the topic "Primitive pythagorean triples"

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Bradley, Christopher J. "Shapes and numbers." In Challenges in Geometry. Oxford University PressOxford, 2005. http://dx.doi.org/10.1093/oso/9780198566915.003.0005.

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Abstract The ‘numbers’ in the title of this chapter are actually integers, but the title is determined by the fact that well-known names for what we consider here are such things as triangular numbers, polygonal numbers, and polyhedral numbers. In this chapter we try to provide material that is either new or less well known, rather than provide what tends to be given in books on recreational mathematics. We start by considering the triangular numbers in some detail, highlighting their connection with the squares, and in particular dealing with the representation of positive integers as the sum
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