Characterization of Diophantine Equations a+y2=z2, Pythagorean n-Tuples, and Algebraic Structures

Roberto Amato

International Journal of Mathematics and Mathematical Sciences, 2025, vol. 2025, 1-19

Abstract: Let N,Z, and Q be the sets of natural, integers, and rational numbers, respectively. Our objective, involving a predetermined positive integer a, is to study a characterization of Diophantine equations of the form a+y2=z2. Building on this result, we aim to obtain a characterization for Pythagorean n-tuples. Furthermore, we seek to prove the existence of a commutative infinite monoid in the set of Diophantine equations a+y2=z2 with elements in N. Additionally, we intend to establish a commutative infinite monoid with elements in N or Z on the set of Pythagorean quadruples. Moreover, in the set of Pythagorean quadruples, we aim to find a commutative infinite group with elements in Q or Z. To achieve these results, we prove the existence of some suitable binary operations.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ijmms/2025/5516311.pdf (application/pdf)
http://downloads.hindawi.com/journals/ijmms/2025/5516311.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:5516311

DOI: 10.1155/ijmm/5516311

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().