On the diophantine equation 8a + 67ß = ?2

Abstract

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).