SOLUTIONS OF PELL'S EQUATION INVOLVING SOPHIE GERMAIN PRIMES
By
Manju Somanath1, V. A. Bindu2 and Radhika Das3
Department of Mathematics,
1National College, (Affiliated to Bharathidasan University), Tiruchirappalli, India-620 002
2;3Rajagiri School of Engineering & Technology, Kakkanad, Cochin, Kerala, India-682 039,
(Research Scholars, National College, Affiliated to Bharathidasan University, Tamil Nadu, India-620 002)
Email: manjusomanath@nct.ac.in, binduva@rajagiritech.edu.in, radhikad@rajagiritech.edu.in
(Received: March 07, 2023; In format: March 27, 2023; Revised: September 06, 2023;
Accepted: September 27, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53204
Abstract
We bring forth one of the most sought after and intriguing space pertaining to the magical world of Number Theory; and our attempts to uncover the continuing research and developments to find solutions for different aspects of the Pells equation. As indicated in this research paper, we attempt to find the possible solutions for the Pells equation x2 = 41y2-5m for all choice of m ∈ N. In this paper, we focused primarily on Pell's equations involving the Sophie Germain primes and present to you another mysterious series and pattern typically associated with the Pells equation. As we proceed through the research, we will bring to the fore the recurrence relations among the identied solutions.
2020 Mathematical Sciences Classification: 11D09.
Keywords and Phrases: Pell's equation, Diophantine equations, Integer solutions, Recurrence relation, Sophie Germain Primes.