On the Exponential Diophantine Equation 19p+ 73q = r2

Abstract

This paper discusses the problem of finding whole number solutions of Diophantine equation 19^P + 73^q = r² where P, q, r are whole numbers. For this, author has used congruence modulo method. Results indicate that the Diophantine equation 19^P + 73^q = r², where P, q, r are whole numbers, has no whole numbers solution.