PERCEIVING SOLUTIONS FOR THE EXPONENTIAL DIOPHANTINE EQUATION ma + nb = c2 UNITING TWIN PRIMES
By
A. Gowri Shankari1 and G. Janaki2
1,2PG and Research Department of Mathematics, Cauvery College for Women (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India - 620018.
Email: gowrirajinikanth@gmail.com, janakikarun@rediffmail.com
(Received: April 27, 2024; In format: May 05, 2024; Revised : June 09, 2025; Accepted: June 28, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55131
Abstract
In this study, an exponential Diophantine equation ma + nb = c2 where m, n are twin primes and a, b, c are non-negative integers is measured for all the possibilities of a + b = 0, 1, 2, 3 and demonstrated that all potential integer solutions are (m, n, a, b, c) = (3, 5, 1, 0, 2),(17, 19, 1, 1, 6) and (71, 73, 1, 1, 12) by adhering to basic mathematical rules.
2020 Mathematical Sciences Classification: 11D61
Keywords and Phrases: Exponential Diophantine equation, integer solutions, divisibility.