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2024 | OriginalPaper | Chapter

Generalized Diophantine m-Tuples: A Survey

Author : Shubham Gupta

Published in: Class Groups of Number Fields and Related Topics

Publisher: Springer Nature Singapore

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Abstract

This survey article deals with the Diophantine m-tuples in positive integers as well as in some commutative rings with unity. In the first section, we give a brief history of the Diophantine m-tuples with the property D(n). We focus on these two problems: how many ways we can extend a Diophantine pair or triple to Diophantine quadruple; and how large a Diophantine m-tuple can be. In the last section, we generalize the concept of Diophantine m-tuples from positive integers to any commutative ring of unity and discuss some results on the line of the above problems.

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Title: Generalized Diophantine m-Tuples: A Survey
Author: Shubham Gupta
Publisher: Springer Nature Singapore
Book: Class Groups of Number Fields and Related Topics
Print ISBN: 978-981-9769-10-0

Electronic ISBN: 978-981-9769-11-7

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-981-97-6911-7_15

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