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certain\nfiniteness results for diophantine equations over algebraic number\nfields can be extended, by using deep algebraic geometrical arguments,\nto rather general cases when the ground domain of unknowns is a\nfinitely generated field or a finitely generated subring of it.\nThe purpose of this paper is to establish a surprisingly elementary\nmethod, through a concrete equation, to obtain these kind of general\nresults.\nLet f(X, Y) and g(X, Y) he binary forms (homogeneous polynomials in two\nvariables) with complex coefficients of degree m and n, respectively.\nThe binary form fg splits into linear factors (over C) and in the\nsequel, we suppose that the linear factors are pairwise\nnon-proportional. 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