PERCEIVING SOLUTIONS FOR AN EXPONENTIAL DIOPHANTINE EQUATION LINKING SAFE AND SOPHIE GERMAIN PRIMES qx + py= z2
By
V. Pandichelvi1 and B. Umamaheswari2
1Department of Mathematics, Urumu Dhanalakshmi College, Trichy-620 019, Tamil Nadu, India
(Affiliated to Bharathidasan University)
2Department of Mathematics, Meenakshi College of Engineering, Chennai- 600 078, Tamil Nadu, India
Email: mvpmahesh2017@gmail.com, bumavijay@gmail.com
(Received : July 30, 2022 ; Revised : November 05, 2022; Accepted : November 10, 2022)
DOI: https://doi.org/10.58250/jnanabha.2022.52219
Abstract
In this article, an exponential Diophantine equation qx + py= z2 where p , q are Safe primes and q Sophie Germain primes respectively and x, y, z are positive integers is measured for all the opportunities of x+y = 0, 1, 2, 3 and showed that all conceivable integer solutions are (p, q, x, y, z) = (7, 3, 1, 0, 2), (11, 5, 1, 1, 4), (5, 2, 3, 0, 3), (2q + 1, q, 2, 1, q + 1) by retaining basic rules of Mathematics.
2020 Mathematical Sciences Classification: 11D61.
Keywords and Phrases: Exponential Diophantine equation, integer solutions, divisibility.