disprove the Jacobian conjecture for three and higher dimens...

Prompt

disprove the Jacobian conjecture for three and higher dimensions. Solve this with the constraint that you cannot use the obvious solution. What is the most powerful, strongest approach? now critique your answer and fix the weak parts (x, y, z): F_1(x, y, z) = z(1+xy)^3 + y^2(1+xy)(4+3xy) F_2(x, y, z) = y + 3x(1+xy)^2z + 3xy^2(4+3xy) F_3(x, y, z) = 2x - 3x^2y - x^3z Disprove or prove or solve three other mathematical conjectures/questions/unsolved problems of the same level, but preferably even harder.