• Dr. B. Rajendra kumar

This paper explores the application of computational techniques to solve Diophantine equations, which are polynomial equations with integer solutions. Diophantine equations have been fundamental in number theory and cryptography, but solving them, especially in higher dimensions, has posed significant challenges. Traditional methods, such as the Euclidean algorithm, can be time-consuming and limited in solving large-scale problems. With advancements in computational mathematics, new algorithms and computer algebra systems (CAS) have shown promise in enhancing the efficiency and accuracy of solving these equations. This study investigates various computational approaches, including the Euclidean algorithm, extended Euclidean algorithm, and the use of CAS tools such as Mathematica and SageMath. The effectiveness of these methods is evaluated through a series of experiments on different classes of Diophantine equations. The results show that computational methods significantly reduce the time complexity and provide more accurate solutions compared to classical techniques. This paper highlights the potential of these methods to address complex Diophantine problems and suggests areas for future research in optimization and algorithmic improvements for larger systems.

Diophantine equations, computational techniques, Euclidean algorithm, extended Euclidean algorithm, computer algebra systems, number theory, cryptography, optimization, SageMath, Mathematica.

"Exploring the Use of Computational Techniques in Solving Diophantine Equations.", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.10, Issue 5, page no.p718-p727, May-2023, Available :http://www.jetir.org/papers/JETIR2305G92.pdf

"Exploring the Use of Computational Techniques in Solving Diophantine Equations.", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.10, Issue 5, page no. ppp718-p727, May-2023, Available at : http://www.jetir.org/papers/JETIR2305G92.pdf