ON THE DIOPHANTINE EQUATIONS x² + 139ᵐ = yⁿ AND x² + 499ᵐ = yⁿ
By
Shivangi Asthana¹ and M. M. Singh²
¹Department of Mathematics, North-Eastern Hill University, Shillong, Meghalaya India-793022
²Department of Basic Sciences and Social Sciences, North-Eastern Hill University, Shillong, Meghalaya, India-793022
Email: shivangiasthana.1@gmail.com, mmsingh2004@gmail.com
(Received: April 17, 2022; In format July 23, 2022; Revised; April 02, 2023; Accepted : April 10, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53124
Abstract
In this paper, we consider the Diophantine equations x² + 139ᵐ = yⁿ and x² + 499ᵐ = yⁿ n ≥ 3, m > 0 and determine solutions of the equations.
2020 Mathematical Sciences Classification: 11D41, 11D61.
Keywords and Phrases: Exponential Diophantine equations, integer solutions.