A Note on the Diophantine Equation 3x + 63y = z2

Abstract

Diophantine equations are gradually drawing attention in the study of hydrogen spectrum, eco- nomics, Biology, quantum Hall effect, chemistry, cryptography etc. Different types of schemes are employed to find solution of Diophantine equations. Some special types of Diophantine equations could be addressed with the help of Catalan’s conjecture and Congruence theory. The Diophantine equation is addressed in this paper to find the solution(s) in non-negative integers. It is found that the equation has only two solutions of as and in non-negative integers.