Elementary Methods for Solving Diophantine Equations

Given the equation f(x1, x2, …, xn) = 0, we write it in the equivalent form $$f_1(x_1, x_2, \ldots , x_n)f_2(x_1, x_2, \ldots , x_n) \cdots f_k(x_1, x_2, \ldots, x_n) = a,$$