On the Diophantine Equation x² + 4.7^b = y^2r

This paper investigates and determines the solutions for the Diophantine equation x² + 4.7^b = y^2r, where x, y, b are all positive intergers and r 1. By substituting the values of r and b respectively, generators of x and yr can be determined and classified into different categories. Then, by using geometric progression method, a general formula for each category can be obtained. The necessary conditions to obtain the integral solutions of x and y are also investigated.