  Let k be a field of characteristic zero. Let phi be a k-endomorphism of the
polynomial algebra k[x_1,...,x_n]. It is known that phi is an automorphism if
and only if it maps irreducible polynomials to irreducible polynomials. In this
paper we show that phi satisfies the jacobian condition if and only if it maps
irreducible polynomials to square-free polynomials. Therefore, the Jacobian
Conjecture is equivalent to the following statement: every k-endomorphism of
k[x_1,...,x_n], mapping irreducible polynomials to square-free polynomials,
maps irreducible polynomials to irreducible polynomials.
