An algebraic characterization of entire polynomial diffeomorphisms

It is shown that a polynomial map F: Rⁿ → Rⁿ F : R n → R n with nowhere zero Jacobian determinant is invertible if and only if an explicit auxiliary polynomial system admits only the trivial solution. The main corollary is a concrete invertibility criterion in the Jacobian conjecture. The proof, conceptually related to differential geometry, represents a simple but infrequent application of differential equations to algebra.