On the diophantine equation x² + 4.7ᵇ = y²ʳ - Yow, Kai Siong; Sapar, Siti Hasana; Atan, Kamel Ariffin (Universiti Putra Malaysia Press, 2013)
This paper investigates and determines the solutions for the Diophantine equation x²+ 4.7ᵇ= y²ͬ, where x, y, bare all positive intergers and r> 1. By substituting the values of rand b respectively, generators of x and yͬ 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.