TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

Analysis of discrete algorithms using the Diophantine equations for efficient problem solving

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* Corresponding author · click or hover a name for details

pp. 505–513Vol. 29Issue 2-AFebruary 2026DOI: 10.47974/JDMSC-2490 Crossmark XML
Received:
09 Apr 2025
Published Online:
07 Feb 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2490
Pages:
505–513

Abstract

This paper looks at how Diophantine equations can be used to analyze and improve discrete algorithms so that they can solve problems more quickly. Finding integer answers to polynomial equations using Diophantine equations is a strong way to solve problems in combinatorics, number theory, and computational complexity. We use Diophantine methods to look into how these equations can help us find the best ways to optimise discrete structures like traversing graphs, routing networks, and allocating resources. The study focusses on how useful Diophantine equations are for answering real-world computer problems, especially those that need to be solved using integers and optimized. We look at different mathematical ways to use these equations and talk about how efficient they are and how they might help algorithms work better.

Keywords

Subject Classifications

30G25

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