Solutions of the Diophantine Equation 1325𝒙 + 143𝒚 = z2

Abstract

In this paper, authors have examined the Diophantine equation1325^𝑥+ 143^𝑦 = 𝑧², where 𝑥,𝑦,𝑧 are non-negative integers, for solving it into the set of non-negative integers. Authors have used famous Catalan’s Conjecture for this. Results of this paper indicate that this equation has a unique solution in the set of non-negative integers and this solution is given by (𝑥,𝑦,𝑧) = (0,1,12).