1Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur-273402, Uttar Pradesh, India E-mail: sudhanshu30187@gmail.com
2Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun-248179, Uttarakhand, India E-mail: lmupadhyaya@rediffmail.com, hetchres@gmail.com
*Corresponding Author: Sudhanshu Aggarwal, Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur-273402, Uttar Pradesh, India E-mail: sudhanshu30187@gmail.com
Online published on 28 December, 2022.
In this paper, authors have examined the Diophantine equation 8α + 67β = γ2, where α,β, γ are non-negative integers, for non-negative integer solutions. Authors used Catalan's conjecture for this purpose. Results of the present paper show that the Diophantine equation 8α + 67β = γ2, where α,β,γ are non-negative integers, has a unique solution in non-negative integers and this solution is given by (α, β, γ) = (1,0,3).
Diophantine Equation, Catalan Conjecture, Solution, Integers
