UGC Approved Journal no 63975(19)

ISSN: 2349-5162 | ESTD Year : 2014
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Published in:

Volume 9 Issue 2
February-2022
eISSN: 2349-5162

UGC and ISSN approved 7.95 impact factor UGC Approved Journal no 63975

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Published Paper ID:
JETIR2202033


Registration ID:
319761

Page Number

a266-a276

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Title

GENERAL CRITERION FOR SOLVABILITY OF THE GENERALIZED PELL’S EQUATION

Abstract

If d is a positive integer, not perfect square, Lagrange was the first to show that Pell's equation has an infinite number of solutions, and hence these solutions are non-trivial. It is a descriptive study in which the proposition is verified by the use of theorems as well as a number theoretic approach. The goal of this paper is to investigate and obtain solutions of the generalized Pell's equation. The study methods includes a review and debate of previously available documents to reach the solvability of generalized Pell's equation. There are many techniques for solving Pell's equations, but we observed the techniques are convergence of the continued fraction technique, PQa technique, LMM technique, and Brute-Force Search technique in the solutions of generalized Pell's equation.

Key Words

continue fraction, Diophantine equation, Pell’s equation, integer, rational

Cite This Article

"GENERAL CRITERION FOR SOLVABILITY OF THE GENERALIZED PELL’S EQUATION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.9, Issue 2, page no.a266-a276, February-2022, Available :http://www.jetir.org/papers/JETIR2202033.pdf

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2349-5162 | Impact Factor 7.95 Calculate by Google Scholar

An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 7.95 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator

Cite This Article

"GENERAL CRITERION FOR SOLVABILITY OF THE GENERALIZED PELL’S EQUATION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.9, Issue 2, page no. ppa266-a276, February-2022, Available at : http://www.jetir.org/papers/JETIR2202033.pdf

Publication Details

Published Paper ID: JETIR2202033
Registration ID: 319761
Published In: Volume 9 | Issue 2 | Year February-2022
DOI (Digital Object Identifier):
Page No: a266-a276
Country: Ilam, 01, Nepal .
Area: Mathematics
ISSN Number: 2349-5162
Publisher: IJ Publication


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