Efficient Approaches to Solving Quadratic Diophantine Equations and their Time Complexity

Authors

  • Bal Bahadur Tamang Department of Mathematics, Mahendra Ratna Multiple Campus, Ilam, Tribhuvan University, Nepal
  • Ajaya Singh Central Department of Mathematics, Tribhuvan University, Nepal

DOI:

https://doi.org/10.3126/jnms.v6i2.63005

Keywords:

Diophantine equations, Continued fraction, Quadratic residue, Pythagorean triples, Time complexity

Abstract

In this paper, we present an efficient approach to solving quadratic Diophantine equations and analyze their time complexity. We propose a deterministic polynomial-time algorithm that provides an upper bound on the elementary operations required to solve such equations. We also present a non-deterministic polynomial-time algorithm for the construction of quadratic non-resiude modulo d, which is a more efficient alternative to the deterministic approach.

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Published

2024-02-26

How to Cite

Tamang, B. B., & Singh, A. (2024). Efficient Approaches to Solving Quadratic Diophantine Equations and their Time Complexity. Journal of Nepal Mathematical Society, 6(2), 1–6. https://doi.org/10.3126/jnms.v6i2.63005

Issue

Vol. 6 No. 2 (2024)

Section

Articles

License

© Nepal Mathematical Society