On a symmetricity property connected to the Euclidean algorithm

Cherukupally, S (2020) On a symmetricity property connected to the Euclidean algorithm. In: Integers, 20 . pp. 1-21.

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Abstract

We study an object: a sequence (collection) of arithmetic progressions with the property that the jth terms of the ith and (i+1)th progressions are the multiplicative inverses of each other, modulo the (j + 1)th term of the ith progression. In the study we address some combinatorial and algorithmic issues on a mirror symmetry (called the symmetricity property) satisfied by leading terms of progressions of such an object. The issues are in connection with the number of divisors k of integers of the form x2 y2, with k falling in specific intervals. Our study explores a new perspective on the quotient sequence of the standard Euclidean algorithm on relatively-prime input pairs. Some open issues are left concerning the symmetricity property. © 2020, Colgate University. All rights reserved.

Item Type:	Journal Article
Publication:	Integers
Publisher:	Colgate University
Additional Information:	The copyright for this article belongs to Colgate University.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	07 Feb 2023 09:14
Last Modified:	07 Feb 2023 09:14
URI:	https://eprints.iisc.ac.in/id/eprint/79993

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