The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture. We prove various cases of the Image Conjecture and show that how it leads to another fascinating and elusive assertion that we here dub the Factorial Conjecture. Various cases of the Factorial Conjecture are proved.
van den Essen, Arno; Wright, David; and Zhao, Wenhua, "On the Image Conjecture" (2011). Mathematics Faculty Publications. 2.