SOLUSI PERSAMAAN DIOPHANTINE NONLINEAR (8n)x +py = z2 UNTUK p SEBARANG BILANGAN PRIMA GANJIL DAN BILANGAN ASLI n ≥ 1

Abstract

This article discusses the nonnegative integer solution of nonlinear Diophantine equation (8n)x + py = z2 subject to some odd prime number p for n = 1 and n ≥ 2, which is solved by Catalan conjecture, exponential property, and congruency. This property aims to determine the value (nx, y, z). Analytically different solutions are obtained based on the values of n and p taken in the nonlinear Diophantine equation.