Results 31 to 40 of about 2,846 (143)
On the algebraic structure of Pythagorean triples
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e NaturaliA Pythagorean triple is an ordered triple of integers (a,b,c) ≠ (0, 0, 0) such that a^2 + b^2 = c^2. It is well known that the set ℘ of all Pythagorean triples has an intrinsic structure of commutative monoid with respect to a suitable binary operation (℘
Giuseppina Anatriello, Giovanni Vincenzi
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Pythagorean triangles of equal areas
International Journal of Mathematics and Mathematical Sciences, 1988 The main intent in this paper is to find triples of Rational Pythagorean Triangles (abbr. RPT) having equal areas. A new method of solving a2+ab+b2=c2 is to set a=y−1, b=y+1, y∈N−{0,1} and get Pell's equation c2−3y2=1. To solve a2−ab−b2=c2, we set a=12(y+
Malvina Baica
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Some Fibonacci congruences with square moduli [PDF]
Notes on Number Theory and Discrete MathematicsFibonacci congruence with prime moduli have been extensively studied. Square moduli are obviously not prime numbers, so why study such congruences?
Anthony G. Shannon +2 more
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, 2017 The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics.
BN Delone +11 more
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International Journal of Intelligent Systems, Volume 2026, Issue 1, 2026.Sustainable supplier selection is a high‐impact decision problem in which organizations must jointly evaluate economic performance, environmental impact, and social responsibility under heterogeneous stakeholder preferences, asymmetric decision authority, and predominantly linguistic assessments. Conventional multiattribute group decision‐making (MAGDM)
Amirhossein Nafei +3 more
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An Analytical Study of Diophantine Equations of Pythagorean Form: Causal Inferences on Hypothesized Relations between Quadratic and Non-quadratic Triples [PDF]
Athens Journal of EducationIn XVII century, presumably between 1637 and 1638, with a note in the margin of Diophantus’ “Arithmetica”, Pierre de Fermat stated that Diophantine equations of the Pythagorean form, x^n+y^n=z^n, have no integer solutions for n>2, and (x,y,z)>0.
Carmelo R. Cartiere
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Diophantine Equation 41k2−nx+4kny=41k2+nz
Journal of Mathematics, Volume 2026, Issue 1, 2026.Let (a, b, c) be a primitive Pythagorean triple such that a2 + b2 = c2 with 2|b. In 1956, L. Jesmanowicz conjectured that, for any positive integer n, the equation (an)x + (bn)y = (cn)z has only the positive solution (x, y, z) = (2, 2, 2). In 1959, Lu Wenduan claimed that if n = 1 and (a, b, c) = (4k2 − 1, 4k, 4k2 + 1), then the conjecture is true ...
Nai-juan Deng +2 more
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Partition regularity of Pythagorean pairs
Forum of Mathematics, PiWe address a core partition regularity problem in Ramsey theory by proving that every finite coloring of the positive integers contains monochromatic Pythagorean pairs (i.e., $x,y\in {\mathbb N}$ such that $x^2\pm y^2=z^2$ for some $z ...
Nikos Frantzikinakis +2 more
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Analysing Student Work Involving Geometric Concepts [PDF]
, 2015 Hyunyi Jung reflects on why students struggle to understand ...
Jung, Hyunyi
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An Interval‐Valued Fermatean Neutrosophic Framework for Sustainable Transportation Under Uncertainty
Journal of Mathematics, Volume 2026, Issue 1, 2026.Transportation planning is facing heightened complexity because the dynamic parameters influenced by globalization and unpredictable technological disruptions. Traditional models are not capable to handle interval‐based uncertainties related to supply, demand, and costs, especially as the scale of suppliers and customers expands.
Muhammad Kamran +4 more
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